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
[ 52, 71, 74, 48 ]
73
[ "74-48=26", "52/26=2", "71+2=73" ]
Current State: 73:[52, 71, 74, 48], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [52, 71, 26] Generated Node #2: [52, 71, 26] from Operation: 74-48=26 Current State: 73:[52, 71, 26], Operations: ['74-48=26'] Exploring Operation: 52/26=2, Resulting Numbers: [71, 2] Generated Node #3: [71, 2] from Operation: 52/26=2 Current State: 73:[71, 2], Operations: ['74-48=26', '52/26=2'] Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[52, 71, 74, 48], Operations: [] Exploring Operation: 74-48=26, Resulting Numbers: [52, 71, 26] Generated Node #0,0: 73:[52, 71, 26] Operation: 74-48=26 Exploring Operation: 71+48=119, Resulting Numbers: [52, 74, 119] Generated Node #0,1: 73:[52, 74, 119] Operation: 71+48=119 Exploring Operation: 52-48=4, Resulting Numbers: [71, 74, 4] Generated Node #0,2: 73:[71, 74, 4] Operation: 52-48=4 Exploring Operation: 52+48=100, Resulting Numbers: [71, 74, 100] Generated Node #0,3: 73:[71, 74, 100] Operation: 52+48=100 Moving to Node #0,3 Current State: 73:[71, 74, 100], Operations: ['52+48=100'] Exploring Operation: 74-71=3, Resulting Numbers: [100, 3] Generated Node #0,3,0: 73:[100, 3] Operation: 74-71=3 Exploring Operation: 100-74=26, Resulting Numbers: [71, 26] Generated Node #0,3,1: 73:[71, 26] Operation: 100-74=26 Exploring Operation: 71+74=145, Resulting Numbers: [100, 145] Generated Node #0,3,2: 73:[100, 145] Operation: 71+74=145 Exploring Operation: 100-71=29, Resulting Numbers: [74, 29] Generated Node #0,3,3: 73:[74, 29] Operation: 100-71=29 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 73:[74, 29], Operations: ['52+48=100', '100-71=29'] Exploring Operation: 74*29=2146, Resulting Numbers: [2146] 2146,73 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,73 unequal: No Solution Exploring Operation: 74+29=103, Resulting Numbers: [103] 103,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 73:[71, 26], Operations: ['52+48=100', '100-74=26'] Exploring Operation: 71+26=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 71*26=1846, Resulting Numbers: [1846] 1846,73 unequal: No Solution Exploring Operation: 71-26=45, Resulting Numbers: [45] 45,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 73:[100, 3], Operations: ['52+48=100', '74-71=3'] Exploring Operation: 100+3=103, Resulting Numbers: [103] 103,73 unequal: No Solution Exploring Operation: 100-3=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 100*3=300, Resulting Numbers: [300] 300,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 73:[100, 145], Operations: ['52+48=100', '71+74=145'] Exploring Operation: 100*145=14500, Resulting Numbers: [14500] 14500,73 unequal: No Solution Exploring Operation: 100+145=245, Resulting Numbers: [245] 245,73 unequal: No Solution Exploring Operation: 145-100=45, Resulting Numbers: [45] 45,73 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: 73:[52, 74, 119], Operations: ['71+48=119'] Exploring Operation: 119-74=45, Resulting Numbers: [52, 45] Generated Node #0,1,0: 73:[52, 45] Operation: 119-74=45 Exploring Operation: 52+74=126, Resulting Numbers: [119, 126] Generated Node #0,1,1: 73:[119, 126] Operation: 52+74=126 Exploring Operation: 74-52=22, Resulting Numbers: [119, 22] Generated Node #0,1,2: 73:[119, 22] Operation: 74-52=22 Exploring Operation: 119-52=67, Resulting Numbers: [74, 67] Generated Node #0,1,3: 73:[74, 67] Operation: 119-52=67 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 73:[74, 67], Operations: ['71+48=119', '119-52=67'] Exploring Operation: 74*67=4958, Resulting Numbers: [4958] 4958,73 unequal: No Solution Exploring Operation: 74+67=141, Resulting Numbers: [141] 141,73 unequal: No Solution Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 73:[52, 45], Operations: ['71+48=119', '119-74=45'] Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,73 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 73:[119, 22], Operations: ['71+48=119', '74-52=22'] Exploring Operation: 119*22=2618, Resulting Numbers: [2618] 2618,73 unequal: No Solution Exploring Operation: 119-22=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 119+22=141, Resulting Numbers: [141] 141,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 73:[119, 126], Operations: ['71+48=119', '52+74=126'] Exploring Operation: 119+126=245, Resulting Numbers: [245] 245,73 unequal: No Solution Exploring Operation: 126-119=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 119*126=14994, Resulting Numbers: [14994] 14994,73 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: 73:[52, 71, 26], Operations: ['74-48=26'] Exploring Operation: 52-26=26, Resulting Numbers: [71, 26] Generated Node #0,0,0: 73:[71, 26] Operation: 52-26=26 Exploring Operation: 71+26=97, Resulting Numbers: [52, 97] Generated Node #0,0,1: 73:[52, 97] Operation: 71+26=97 Exploring Operation: 71-26=45, Resulting Numbers: [52, 45] Generated Node #0,0,2: 73:[52, 45] Operation: 71-26=45 Exploring Operation: 52+26=78, Resulting Numbers: [71, 78] Generated Node #0,0,3: 73:[71, 78] Operation: 52+26=78 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 73:[71, 78], Operations: ['74-48=26', '52+26=78'] Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 71*78=5538, Resulting Numbers: [5538] 5538,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 73:[52, 97], Operations: ['74-48=26', '71+26=97'] Exploring Operation: 52*97=5044, Resulting Numbers: [5044] 5044,73 unequal: No Solution Exploring Operation: 52+97=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 97-52=45, Resulting Numbers: [45] 45,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 73:[71, 26], Operations: ['74-48=26', '52-26=26'] Exploring Operation: 71+26=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 71*26=1846, Resulting Numbers: [1846] 1846,73 unequal: No Solution Exploring Operation: 71-26=45, Resulting Numbers: [45] 45,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 73:[52, 45], Operations: ['74-48=26', '71-26=45'] Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,73 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,73 unequal: No Solution Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,73 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: 73:[71, 74, 4], Operations: ['52-48=4'] Exploring Operation: 74-4=70, Resulting Numbers: [71, 70] Generated Node #0,2,0: 73:[71, 70] Operation: 74-4=70 Exploring Operation: 71-4=67, Resulting Numbers: [74, 67] Generated Node #0,2,1: 73:[74, 67] Operation: 71-4=67 Exploring Operation: 71+4=75, Resulting Numbers: [74, 75] Generated Node #0,2,2: 73:[74, 75] Operation: 71+4=75 Exploring Operation: 74+4=78, Resulting Numbers: [71, 78] Generated Node #0,2,3: 73:[71, 78] Operation: 74+4=78 Moving to Node #0,2,2 Current State: 73:[74, 75], Operations: ['52-48=4', '71+4=75'] Exploring Operation: 74+75=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 75-74=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 74*75=5550, Resulting Numbers: [5550] 5550,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[71, 70], Operations: ['52-48=4', '74-4=70'] Exploring Operation: 71*70=4970, Resulting Numbers: [4970] 4970,73 unequal: No Solution Exploring Operation: 71-70=1, Resulting Numbers: [1] 1,73 unequal: No Solution Exploring Operation: 71+70=141, Resulting Numbers: [141] 141,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[71, 78], Operations: ['52-48=4', '74+4=78'] Exploring Operation: 71+78=149, Resulting Numbers: [149] 149,73 unequal: No Solution Exploring Operation: 71*78=5538, Resulting Numbers: [5538] 5538,73 unequal: No Solution Exploring Operation: 78-71=7, Resulting Numbers: [7] 7,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[74, 67], Operations: ['52-48=4', '71-4=67'] Exploring Operation: 74+67=141, Resulting Numbers: [141] 141,73 unequal: No Solution Exploring Operation: 74*67=4958, Resulting Numbers: [4958] 4958,73 unequal: No Solution Exploring Operation: 74-67=7, Resulting Numbers: [7] 7,73 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 27, 9, 26, 77 ]
69
[ "27-9=18", "77-26=51", "18+51=69" ]
Current State: 69:[27, 9, 26, 77], Operations: [] Exploring Operation: 27-9=18, Resulting Numbers: [26, 77, 18] Generated Node #2: [26, 77, 18] from Operation: 27-9=18 Current State: 69:[26, 77, 18], Operations: ['27-9=18'] Exploring Operation: 77-26=51, Resulting Numbers: [18, 51] Generated Node #3: [18, 51] from Operation: 77-26=51 Current State: 69:[18, 51], Operations: ['27-9=18', '77-26=51'] Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[27, 9, 26, 77], Operations: [] Exploring Operation: 27-26=1, Resulting Numbers: [9, 77, 1] Generated Node #0,0: 69:[9, 77, 1] Operation: 27-26=1 Exploring Operation: 77-9=68, Resulting Numbers: [27, 26, 68] Generated Node #0,1: 69:[27, 26, 68] Operation: 77-9=68 Exploring Operation: 27-9=18, Resulting Numbers: [26, 77, 18] Generated Node #0,2: 69:[26, 77, 18] Operation: 27-9=18 Exploring Operation: 26-9=17, Resulting Numbers: [27, 77, 17] Generated Node #0,3: 69:[27, 77, 17] Operation: 26-9=17 Exploring Operation: 27/9=3, Resulting Numbers: [26, 77, 3] Generated Node #0,4: 69:[26, 77, 3] Operation: 27/9=3 Moving to Node #0,1 Current State: 69:[27, 26, 68], Operations: ['77-9=68'] Exploring Operation: 68-27=41, Resulting Numbers: [26, 41] Generated Node #0,1,0: 69:[26, 41] Operation: 68-27=41 Exploring Operation: 27+68=95, Resulting Numbers: [26, 95] Generated Node #0,1,1: 69:[26, 95] Operation: 27+68=95 Exploring Operation: 68-26=42, Resulting Numbers: [27, 42] Generated Node #0,1,2: 69:[27, 42] Operation: 68-26=42 Exploring Operation: 27-26=1, Resulting Numbers: [68, 1] Generated Node #0,1,3: 69:[68, 1] Operation: 27-26=1 Exploring Operation: 27+26=53, Resulting Numbers: [68, 53] Generated Node #0,1,4: 69:[68, 53] Operation: 27+26=53 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[68, 1], Operations: ['77-9=68', '27-26=1'] Exploring Operation: 68-1=67, Resulting Numbers: [67] 67,69 unequal: No Solution Exploring Operation: 68/1=68, Resulting Numbers: [68] 68,69 unequal: No Solution Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[27, 9, 26, 77], Operations: [] Exploring Operation: 77-9=68, Resulting Numbers: [27, 26, 68] Generated Node #0,1: 69:[27, 26, 68] Operation: 77-9=68 Moving to Node #0,1 Current State: 69:[27, 26, 68], Operations: ['77-9=68'] Exploring Operation: 27-26=1, Resulting Numbers: [68, 1] Generated Node #0,1,3: 69:[68, 1] Operation: 27-26=1 Moving to Node #0,1,3 Current State: 69:[68, 1], Operations: ['77-9=68', '27-26=1'] Exploring Operation: 68+1=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 10, 33, 12, 5 ]
29
[ "10*5=50", "33-12=21", "50-21=29" ]
Current State: 29:[10, 33, 12, 5], Operations: [] Exploring Operation: 10*5=50, Resulting Numbers: [33, 12, 50] Generated Node #2: [33, 12, 50] from Operation: 10*5=50 Current State: 29:[33, 12, 50], Operations: ['10*5=50'] Exploring Operation: 33-12=21, Resulting Numbers: [50, 21] Generated Node #3: [50, 21] from Operation: 33-12=21 Current State: 29:[50, 21], Operations: ['10*5=50', '33-12=21'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[10, 33, 12, 5], Operations: [] Exploring Operation: 33-5=28, Resulting Numbers: [10, 12, 28] Generated Node #0,0: 29:[10, 12, 28] Operation: 33-5=28 Exploring Operation: 10*5=50, Resulting Numbers: [33, 12, 50] Generated Node #0,1: 29:[33, 12, 50] Operation: 10*5=50 Exploring Operation: 10+5=15, Resulting Numbers: [33, 12, 15] Generated Node #0,2: 29:[33, 12, 15] Operation: 10+5=15 Exploring Operation: 10+12=22, Resulting Numbers: [33, 5, 22] Generated Node #0,3: 29:[33, 5, 22] Operation: 10+12=22 Exploring Operation: 12+5=17, Resulting Numbers: [10, 33, 17] Generated Node #0,4: 29:[10, 33, 17] Operation: 12+5=17 Moving to Node #0,2 Current State: 29:[33, 12, 15], Operations: ['10+5=15'] Exploring Operation: 33+12=45, Resulting Numbers: [15, 45] Generated Node #0,2,0: 29:[15, 45] Operation: 33+12=45 Exploring Operation: 33-15=18, Resulting Numbers: [12, 18] Generated Node #0,2,1: 29:[12, 18] Operation: 33-15=18 Exploring Operation: 12+15=27, Resulting Numbers: [33, 27] Generated Node #0,2,2: 29:[33, 27] Operation: 12+15=27 Exploring Operation: 15-12=3, Resulting Numbers: [33, 3] Generated Node #0,2,3: 29:[33, 3] Operation: 15-12=3 Exploring Operation: 33-12=21, Resulting Numbers: [15, 21] Generated Node #0,2,4: 29:[15, 21] Operation: 33-12=21 Moving to Node #0,4 Current State: 29:[10, 33, 17], Operations: ['12+5=17'] Exploring Operation: 33-17=16, Resulting Numbers: [10, 16] Generated Node #0,4,0: 29:[10, 16] Operation: 33-17=16 Exploring Operation: 17-10=7, Resulting Numbers: [33, 7] Generated Node #0,4,1: 29:[33, 7] Operation: 17-10=7 Exploring Operation: 10+17=27, Resulting Numbers: [33, 27] Generated Node #0,4,2: 29:[33, 27] Operation: 10+17=27 Exploring Operation: 33-10=23, Resulting Numbers: [17, 23] Generated Node #0,4,3: 29:[17, 23] Operation: 33-10=23 Exploring Operation: 10+33=43, Resulting Numbers: [17, 43] Generated Node #0,4,4: 29:[17, 43] Operation: 10+33=43 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 29:[33, 27], Operations: ['12+5=17', '10+17=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 29:[17, 23], Operations: ['12+5=17', '33-10=23'] Exploring Operation: 17+23=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 17*23=391, Resulting Numbers: [391] 391,29 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 29:[33, 7], Operations: ['12+5=17', '17-10=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 33-7=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 33*7=231, Resulting Numbers: [231] 231,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 29:[17, 43], Operations: ['12+5=17', '10+33=43'] Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 17*43=731, Resulting Numbers: [731] 731,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 29:[10, 16], Operations: ['12+5=17', '33-17=16'] Exploring Operation: 10*16=160, Resulting Numbers: [160] 160,29 unequal: No Solution Exploring Operation: 16-10=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 10+16=26, Resulting Numbers: [26] 26,29 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: 29:[33, 5, 22], Operations: ['10+12=22'] Exploring Operation: 33-22=11, Resulting Numbers: [5, 11] Generated Node #0,3,0: 29:[5, 11] Operation: 33-22=11 Exploring Operation: 5+22=27, Resulting Numbers: [33, 27] Generated Node #0,3,1: 29:[33, 27] Operation: 5+22=27 Exploring Operation: 22-5=17, Resulting Numbers: [33, 17] Generated Node #0,3,2: 29:[33, 17] Operation: 22-5=17 Exploring Operation: 33+5=38, Resulting Numbers: [22, 38] Generated Node #0,3,3: 29:[22, 38] Operation: 33+5=38 Exploring Operation: 33-5=28, Resulting Numbers: [22, 28] Generated Node #0,3,4: 29:[22, 28] Operation: 33-5=28 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 29:[33, 27], Operations: ['10+12=22', '5+22=27'] Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 29:[22, 28], Operations: ['10+12=22', '33-5=28'] Exploring Operation: 22+28=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 22*28=616, Resulting Numbers: [616] 616,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 29:[33, 17], Operations: ['10+12=22', '22-5=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 33*17=561, Resulting Numbers: [561] 561,29 unequal: No Solution Exploring Operation: 33+17=50, Resulting Numbers: [50] 50,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 29:[22, 38], Operations: ['10+12=22', '33+5=38'] Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,29 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 29:[5, 11], Operations: ['10+12=22', '33-22=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,29 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,29 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,29 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: 29:[10, 12, 28], Operations: ['33-5=28'] Exploring Operation: 10+28=38, Resulting Numbers: [12, 38] Generated Node #0,0,0: 29:[12, 38] Operation: 10+28=38 Exploring Operation: 10+12=22, Resulting Numbers: [28, 22] Generated Node #0,0,1: 29:[28, 22] Operation: 10+12=22 Exploring Operation: 12-10=2, Resulting Numbers: [28, 2] Generated Node #0,0,2: 29:[28, 2] Operation: 12-10=2 Exploring Operation: 12+28=40, Resulting Numbers: [10, 40] Generated Node #0,0,3: 29:[10, 40] Operation: 12+28=40 Exploring Operation: 28-10=18, Resulting Numbers: [12, 18] Generated Node #0,0,4: 29:[12, 18] Operation: 28-10=18 Moving to Node #0,1 Current State: 29:[33, 12, 50], Operations: ['10*5=50'] Exploring Operation: 12+50=62, Resulting Numbers: [33, 62] Generated Node #0,1,0: 29:[33, 62] Operation: 12+50=62 Exploring Operation: 50-12=38, Resulting Numbers: [33, 38] Generated Node #0,1,1: 29:[33, 38] Operation: 50-12=38 Exploring Operation: 33-12=21, Resulting Numbers: [50, 21] Generated Node #0,1,2: 29:[50, 21] Operation: 33-12=21 Exploring Operation: 33+12=45, Resulting Numbers: [50, 45] Generated Node #0,1,3: 29:[50, 45] Operation: 33+12=45 Exploring Operation: 50-33=17, Resulting Numbers: [12, 17] Generated Node #0,1,4: 29:[12, 17] Operation: 50-33=17 Moving to Node #0,2,2 Current State: 29:[33, 27], Operations: ['10+5=15', '12+15=27'] Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,29 unequal: No Solution Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[28, 22], Operations: ['33-5=28', '10+12=22'] Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,29 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[33, 38], Operations: ['10*5=50', '50-12=38'] Exploring Operation: 38-33=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 33+38=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 33*38=1254, Resulting Numbers: [1254] 1254,29 unequal: No Solution Moving to Node #0,2,4 Current State: 29:[15, 21], Operations: ['10+5=15', '33-12=21'] Exploring Operation: 15+21=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 15*21=315, Resulting Numbers: [315] 315,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[12, 38], Operations: ['33-5=28', '10+28=38'] Exploring Operation: 12*38=456, Resulting Numbers: [456] 456,29 unequal: No Solution Exploring Operation: 12+38=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[12, 18], Operations: ['10+5=15', '33-15=18'] Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,29 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[28, 2], Operations: ['33-5=28', '12-10=2'] Exploring Operation: 28-2=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,29 unequal: No Solution Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[12, 18], Operations: ['33-5=28', '28-10=18'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 12+18=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 12*18=216, Resulting Numbers: [216] 216,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[50, 21], Operations: ['10*5=50', '33-12=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,29 unequal: No Solution Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[10, 33, 12, 5], Operations: [] Exploring Operation: 10*5=50, Resulting Numbers: [33, 12, 50] Generated Node #0,1: 29:[33, 12, 50] Operation: 10*5=50 Moving to Node #0,1 Current State: 29:[33, 12, 50], Operations: ['10*5=50'] Exploring Operation: 33-12=21, Resulting Numbers: [50, 21] Generated Node #0,1,2: 29:[50, 21] Operation: 33-12=21 Moving to Node #0,1,2 Current State: 29:[50, 21], Operations: ['10*5=50', '33-12=21'] Exploring Operation: 50-21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
0.921007
hs_5
sum_heuristic
[ 49, 47, 1, 72 ]
74
[ "49-47=2", "1*72=72", "2+72=74" ]
Current State: 74:[49, 47, 1, 72], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [1, 72, 2] Generated Node #2: [1, 72, 2] from Operation: 49-47=2 Current State: 74:[1, 72, 2], Operations: ['49-47=2'] Exploring Operation: 1*72=72, Resulting Numbers: [2, 72] Generated Node #3: [2, 72] from Operation: 1*72=72 Current State: 74:[2, 72], Operations: ['49-47=2', '1*72=72'] Exploring Operation: 2+72=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[49, 47, 1, 72], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [1, 72, 2] Generated Node #0,0: 74:[1, 72, 2] Operation: 49-47=2 Exploring Operation: 49*1=49, Resulting Numbers: [47, 72, 49] Generated Node #0,1: 74:[47, 72, 49] Operation: 49*1=49 Exploring Operation: 47-1=46, Resulting Numbers: [49, 72, 46] Generated Node #0,2: 74:[49, 72, 46] Operation: 47-1=46 Exploring Operation: 1+72=73, Resulting Numbers: [49, 47, 73] Generated Node #0,3: 74:[49, 47, 73] Operation: 1+72=73 Exploring Operation: 49-1=48, Resulting Numbers: [47, 72, 48] Generated Node #0,4: 74:[47, 72, 48] Operation: 49-1=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[1, 72, 2], Operations: ['49-47=2'] Exploring Operation: 1*72=72, Resulting Numbers: [2, 72] Generated Node #0,0,0: 74:[2, 72] Operation: 1*72=72 Exploring Operation: 72/1=72, Resulting Numbers: [2, 72] Generated Node #0,0,1: 74:[2, 72] Operation: 72/1=72 Exploring Operation: 1+72=73, Resulting Numbers: [2, 73] Generated Node #0,0,2: 74:[2, 73] Operation: 1+72=73 Exploring Operation: 72+2=74, Resulting Numbers: [1, 74] Generated Node #0,0,3: 74:[1, 74] Operation: 72+2=74 Exploring Operation: 1*2=2, Resulting Numbers: [72, 2] Generated Node #0,0,4: 74:[72, 2] Operation: 1*2=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 74:[2, 73], Operations: ['49-47=2', '1+72=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,74 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,74 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 74:[1, 74], Operations: ['49-47=2', '72+2=74'] Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[49, 47, 1, 72], Operations: [] Exploring Operation: 49-47=2, Resulting Numbers: [1, 72, 2] Generated Node #0,0: 74:[1, 72, 2] Operation: 49-47=2 Moving to Node #0,0 Current State: 74:[1, 72, 2], Operations: ['49-47=2'] Exploring Operation: 72+2=74, Resulting Numbers: [1, 74] Generated Node #0,0,3: 74:[1, 74] Operation: 72+2=74 Moving to Node #0,0,3 Current State: 74:[1, 74], Operations: ['49-47=2', '72+2=74'] Exploring Operation: 74/1=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 37, 99, 32, 93 ]
43
[ "99+93=192", "192/32=6", "37+6=43" ]
Current State: 43:[37, 99, 32, 93], Operations: [] Exploring Operation: 99+93=192, Resulting Numbers: [37, 32, 192] Generated Node #2: [37, 32, 192] from Operation: 99+93=192 Current State: 43:[37, 32, 192], Operations: ['99+93=192'] Exploring Operation: 192/32=6, Resulting Numbers: [37, 6] Generated Node #3: [37, 6] from Operation: 192/32=6 Current State: 43:[37, 6], Operations: ['99+93=192', '192/32=6'] Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[37, 99, 32, 93], Operations: [] Exploring Operation: 99-37=62, Resulting Numbers: [32, 93, 62] Generated Node #0,0: 43:[32, 93, 62] Operation: 99-37=62 Exploring Operation: 99-93=6, Resulting Numbers: [37, 32, 6] Generated Node #0,1: 43:[37, 32, 6] Operation: 99-93=6 Exploring Operation: 93-37=56, Resulting Numbers: [99, 32, 56] Generated Node #0,2: 43:[99, 32, 56] Operation: 93-37=56 Moving to Node #0,1 Current State: 43:[37, 32, 6], Operations: ['99-93=6'] Exploring Operation: 37-6=31, Resulting Numbers: [32, 31] Generated Node #0,1,0: 43:[32, 31] Operation: 37-6=31 Exploring Operation: 37+6=43, Resulting Numbers: [32, 43] Generated Node #0,1,1: 43:[32, 43] Operation: 37+6=43 Exploring Operation: 32+6=38, Resulting Numbers: [37, 38] Generated Node #0,1,2: 43:[37, 38] Operation: 32+6=38 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[32, 43], Operations: ['99-93=6', '37+6=43'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,43 unequal: No Solution No 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: 43:[37, 38], Operations: ['99-93=6', '32+6=38'] Exploring Operation: 37*38=1406, Resulting Numbers: [1406] 1406,43 unequal: No Solution Exploring Operation: 37+38=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 38-37=1, Resulting Numbers: [1] 1,43 unequal: No Solution No 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: 43:[32, 31], Operations: ['99-93=6', '37-6=31'] Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,43 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,43 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: 43:[32, 93, 62], Operations: ['99-37=62'] Exploring Operation: 62-32=30, Resulting Numbers: [93, 30] Generated Node #0,0,0: 43:[93, 30] Operation: 62-32=30 Exploring Operation: 93-62=31, Resulting Numbers: [32, 31] Generated Node #0,0,1: 43:[32, 31] Operation: 93-62=31 Exploring Operation: 93-32=61, Resulting Numbers: [62, 61] Generated Node #0,0,2: 43:[62, 61] Operation: 93-32=61 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[32, 31], Operations: ['99-37=62', '93-62=31'] Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,43 unequal: No Solution No 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: 43:[62, 61], Operations: ['99-37=62', '93-32=61'] Exploring Operation: 62-61=1, Resulting Numbers: [1] 1,43 unequal: No Solution Exploring Operation: 62+61=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 62*61=3782, Resulting Numbers: [3782] 3782,43 unequal: No Solution No 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: 43:[93, 30], Operations: ['99-37=62', '62-32=30'] Exploring Operation: 93-30=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 93*30=2790, Resulting Numbers: [2790] 2790,43 unequal: No Solution Exploring Operation: 93+30=123, Resulting Numbers: [123] 123,43 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: 43:[99, 32, 56], Operations: ['93-37=56'] Exploring Operation: 56-32=24, Resulting Numbers: [99, 24] Generated Node #0,2,0: 43:[99, 24] Operation: 56-32=24 Exploring Operation: 99-56=43, Resulting Numbers: [32, 43] Generated Node #0,2,1: 43:[32, 43] Operation: 99-56=43 Exploring Operation: 99-32=67, Resulting Numbers: [56, 67] Generated Node #0,2,2: 43:[56, 67] Operation: 99-32=67 Moving to Node #0,2,1 Current State: 43:[32, 43], Operations: ['93-37=56', '99-56=43'] Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,43 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[56, 67], Operations: ['93-37=56', '99-32=67'] Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,43 unequal: No Solution Exploring Operation: 56+67=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 56*67=3752, Resulting Numbers: [3752] 3752,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[99, 24], Operations: ['93-37=56', '56-32=24'] Exploring Operation: 99-24=75, Resulting Numbers: [75] 75,43 unequal: No Solution Exploring Operation: 99+24=123, Resulting Numbers: [123] 123,43 unequal: No Solution Exploring Operation: 99*24=2376, Resulting Numbers: [2376] 2376,43 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 40, 69, 11, 67 ]
65
[ "69+11=80", "80/40=2", "67-2=65" ]
Current State: 65:[40, 69, 11, 67], Operations: [] Exploring Operation: 69+11=80, Resulting Numbers: [40, 67, 80] Generated Node #2: [40, 67, 80] from Operation: 69+11=80 Current State: 65:[40, 67, 80], Operations: ['69+11=80'] Exploring Operation: 80/40=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 80/40=2 Current State: 65:[67, 2], Operations: ['69+11=80', '80/40=2'] Exploring Operation: 67-2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[40, 69, 11, 67], Operations: [] Exploring Operation: 69-40=29, Resulting Numbers: [11, 67, 29] Generated Node #0,0: 65:[11, 67, 29] Operation: 69-40=29 Moving to Node #0,0 Current State: 65:[11, 67, 29], Operations: ['69-40=29'] Exploring Operation: 29-11=18, Resulting Numbers: [67, 18] Generated Node #0,0,0: 65:[67, 18] Operation: 29-11=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[67, 18], Operations: ['69-40=29', '29-11=18'] Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,65 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
[ 25, 47, 32, 90 ]
31
[ "47-32=15", "90/15=6", "25+6=31" ]
Current State: 31:[25, 47, 32, 90], Operations: [] Exploring Operation: 47-32=15, Resulting Numbers: [25, 90, 15] Generated Node #2: [25, 90, 15] from Operation: 47-32=15 Current State: 31:[25, 90, 15], Operations: ['47-32=15'] Exploring Operation: 90/15=6, Resulting Numbers: [25, 6] Generated Node #3: [25, 6] from Operation: 90/15=6 Current State: 31:[25, 6], Operations: ['47-32=15', '90/15=6'] Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[25, 47, 32, 90], Operations: [] Exploring Operation: 90-47=43, Resulting Numbers: [25, 32, 43] Generated Node #0,0: 31:[25, 32, 43] Operation: 90-47=43 Exploring Operation: 90-32=58, Resulting Numbers: [25, 47, 58] Generated Node #0,1: 31:[25, 47, 58] Operation: 90-32=58 Moving to Node #0,0 Current State: 31:[25, 32, 43], Operations: ['90-47=43'] Exploring Operation: 43-25=18, Resulting Numbers: [32, 18] Generated Node #0,0,0: 31:[32, 18] Operation: 43-25=18 Exploring Operation: 43-32=11, Resulting Numbers: [25, 11] Generated Node #0,0,1: 31:[25, 11] Operation: 43-32=11 Moving to Node #0,1 Current State: 31:[25, 47, 58], Operations: ['90-32=58'] Exploring Operation: 58-25=33, Resulting Numbers: [47, 33] Generated Node #0,1,0: 31:[47, 33] Operation: 58-25=33 Exploring Operation: 58-47=11, Resulting Numbers: [25, 11] Generated Node #0,1,1: 31:[25, 11] Operation: 58-47=11 Moving to Node #0,0,0 Current State: 31:[32, 18], Operations: ['90-47=43', '43-25=18'] Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,31 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,31 unequal: No Solution Moving to Node #0,1,0 Current State: 31:[47, 33], Operations: ['90-32=58', '58-25=33'] Exploring Operation: 47+33=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[25, 11], Operations: ['90-47=43', '43-32=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,31 unequal: No Solution Moving to Node #0,1,1 Current State: 31:[25, 11], Operations: ['90-32=58', '58-47=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,31 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,31 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 87, 9, 10, 53 ]
56
[ "87-53=34", "9*10=90", "90-34=56" ]
Current State: 56:[87, 9, 10, 53], Operations: [] Exploring Operation: 87-53=34, Resulting Numbers: [9, 10, 34] Generated Node #2: [9, 10, 34] from Operation: 87-53=34 Current State: 56:[9, 10, 34], Operations: ['87-53=34'] Exploring Operation: 9*10=90, Resulting Numbers: [34, 90] Generated Node #3: [34, 90] from Operation: 9*10=90 Current State: 56:[34, 90], Operations: ['87-53=34', '9*10=90'] Exploring Operation: 90-34=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[87, 9, 10, 53], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [10, 53, 78] Generated Node #0,0: 56:[10, 53, 78] Operation: 87-9=78 Exploring Operation: 87-10=77, Resulting Numbers: [9, 53, 77] Generated Node #0,1: 56:[9, 53, 77] Operation: 87-10=77 Exploring Operation: 87-53=34, Resulting Numbers: [9, 10, 34] Generated Node #0,2: 56:[9, 10, 34] Operation: 87-53=34 Start Sub Search at level 1: Moving to Node #0,2 Current State: 56:[9, 10, 34], Operations: ['87-53=34'] Exploring Operation: 34-9=25, Resulting Numbers: [10, 25] Generated Node #0,2,0: 56:[10, 25] Operation: 34-9=25 Exploring Operation: 10-9=1, Resulting Numbers: [34, 1] Generated Node #0,2,1: 56:[34, 1] Operation: 10-9=1 Exploring Operation: 34-10=24, Resulting Numbers: [9, 24] Generated Node #0,2,2: 56:[9, 24] Operation: 34-10=24 Moving to Node #0,2,0 Current State: 56:[10, 25], Operations: ['87-53=34', '34-9=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,56 unequal: No Solution Moving to Node #0,2,2 Current State: 56:[9, 24], Operations: ['87-53=34', '34-10=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,56 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,56 unequal: No Solution Moving to Node #0,2,1 Current State: 56:[34, 1], Operations: ['87-53=34', '10-9=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,56 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,56 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,56 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[9, 53, 77], Operations: ['87-10=77'] Exploring Operation: 77-9=68, Resulting Numbers: [53, 68] Generated Node #0,1,0: 56:[53, 68] Operation: 77-9=68 Exploring Operation: 9+53=62, Resulting Numbers: [77, 62] Generated Node #0,1,1: 56:[77, 62] Operation: 9+53=62 Exploring Operation: 77-53=24, Resulting Numbers: [9, 24] Generated Node #0,1,2: 56:[9, 24] Operation: 77-53=24 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 56:[9, 24], Operations: ['87-10=77', '77-53=24'] Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,56 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,56 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:[53, 68], Operations: ['87-10=77', '77-9=68'] Exploring Operation: 53*68=3604, Resulting Numbers: [3604] 3604,56 unequal: No Solution Exploring Operation: 68-53=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 53+68=121, Resulting Numbers: [121] 121,56 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 #0,1,1 Current State: 56:[77, 62], Operations: ['87-10=77', '9+53=62'] Exploring Operation: 77+62=139, Resulting Numbers: [139] 139,56 unequal: No Solution Exploring Operation: 77-62=15, Resulting Numbers: [15] 15,56 unequal: No Solution Exploring Operation: 77*62=4774, Resulting Numbers: [4774] 4774,56 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 #0,0 Current State: 56:[10, 53, 78], Operations: ['87-9=78'] Exploring Operation: 78-53=25, Resulting Numbers: [10, 25] Generated Node #0,0,0: 56:[10, 25] Operation: 78-53=25 Exploring Operation: 78-10=68, Resulting Numbers: [53, 68] Generated Node #0,0,1: 56:[53, 68] Operation: 78-10=68 Exploring Operation: 10+53=63, Resulting Numbers: [78, 63] Generated Node #0,0,2: 56:[78, 63] Operation: 10+53=63 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 56:[10, 25], Operations: ['87-9=78', '78-53=25'] Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,56 unequal: No Solution Exploring Operation: 10*25=250, Resulting Numbers: [250] 250,56 unequal: No Solution Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,56 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:[53, 68], Operations: ['87-9=78', '78-10=68'] Exploring Operation: 53*68=3604, Resulting Numbers: [3604] 3604,56 unequal: No Solution Exploring Operation: 53+68=121, Resulting Numbers: [121] 121,56 unequal: No Solution Exploring Operation: 68-53=15, Resulting Numbers: [15] 15,56 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 #0,0,2 Current State: 56:[78, 63], Operations: ['87-9=78', '10+53=63'] Exploring Operation: 78*63=4914, Resulting Numbers: [4914] 4914,56 unequal: No Solution Exploring Operation: 78+63=141, Resulting Numbers: [141] 141,56 unequal: No Solution Exploring Operation: 78-63=15, Resulting Numbers: [15] 15,56 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_3
mult_heuristic
[ 62, 12, 93, 14 ]
39
[ "12+14=26", "93*26=2418", "2418/62=39" ]
Current State: 39:[62, 12, 93, 14], Operations: [] Exploring Operation: 12+14=26, Resulting Numbers: [62, 93, 26] Generated Node #2: [62, 93, 26] from Operation: 12+14=26 Current State: 39:[62, 93, 26], Operations: ['12+14=26'] Exploring Operation: 93*26=2418, Resulting Numbers: [62, 2418] Generated Node #3: [62, 2418] from Operation: 93*26=2418 Current State: 39:[62, 2418], Operations: ['12+14=26', '93*26=2418'] Exploring Operation: 2418/62=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[62, 12, 93, 14], Operations: [] Exploring Operation: 93-62=31, Resulting Numbers: [12, 14, 31] Generated Node #0,0: 39:[12, 14, 31] Operation: 93-62=31 Moving to Node #0,0 Current State: 39:[12, 14, 31], Operations: ['93-62=31'] Exploring Operation: 12+31=43, Resulting Numbers: [14, 43] Generated Node #0,0,0: 39:[14, 43] Operation: 12+31=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[14, 43], Operations: ['93-62=31', '12+31=43'] Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 2, 55, 84, 75 ]
62
[ "55-2=53", "84-75=9", "53+9=62" ]
Current State: 62:[2, 55, 84, 75], Operations: [] Exploring Operation: 55-2=53, Resulting Numbers: [84, 75, 53] Generated Node #2: [84, 75, 53] from Operation: 55-2=53 Current State: 62:[84, 75, 53], Operations: ['55-2=53'] Exploring Operation: 84-75=9, Resulting Numbers: [53, 9] Generated Node #3: [53, 9] from Operation: 84-75=9 Current State: 62:[53, 9], Operations: ['55-2=53', '84-75=9'] Exploring Operation: 53+9=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[2, 55, 84, 75], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [2, 55, 9] Generated Node #0,0: 62:[2, 55, 9] Operation: 84-75=9 Exploring Operation: 84/2=42, Resulting Numbers: [55, 75, 42] Generated Node #0,1: 62:[55, 75, 42] Operation: 84/2=42 Exploring Operation: 75-55=20, Resulting Numbers: [2, 84, 20] Generated Node #0,2: 62:[2, 84, 20] Operation: 75-55=20 Exploring Operation: 2+55=57, Resulting Numbers: [84, 75, 57] Generated Node #0,3: 62:[84, 75, 57] Operation: 2+55=57 Exploring Operation: 84-55=29, Resulting Numbers: [2, 75, 29] Generated Node #0,4: 62:[2, 75, 29] Operation: 84-55=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[2, 55, 9], Operations: ['84-75=9'] Exploring Operation: 55+9=64, Resulting Numbers: [2, 64] Generated Node #0,0,0: 62:[2, 64] Operation: 55+9=64 Exploring Operation: 55-9=46, Resulting Numbers: [2, 46] Generated Node #0,0,1: 62:[2, 46] Operation: 55-9=46 Exploring Operation: 9-2=7, Resulting Numbers: [55, 7] Generated Node #0,0,2: 62:[55, 7] Operation: 9-2=7 Exploring Operation: 2+55=57, Resulting Numbers: [9, 57] Generated Node #0,0,3: 62:[9, 57] Operation: 2+55=57 Exploring Operation: 55-2=53, Resulting Numbers: [9, 53] Generated Node #0,0,4: 62:[9, 53] Operation: 55-2=53 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[2, 64], Operations: ['84-75=9', '55+9=64'] Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,62 unequal: No Solution Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[2, 55, 84, 75], Operations: [] Exploring Operation: 84-75=9, Resulting Numbers: [2, 55, 9] Generated Node #0,0: 62:[2, 55, 9] Operation: 84-75=9 Moving to Node #0,0 Current State: 62:[2, 55, 9], Operations: ['84-75=9'] Exploring Operation: 55+9=64, Resulting Numbers: [2, 64] Generated Node #0,0,0: 62:[2, 64] Operation: 55+9=64 Moving to Node #0,0,0 Current State: 62:[2, 64], Operations: ['84-75=9', '55+9=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 2, 69, 34, 69 ]
37
[ "2+34=36", "69/69=1", "36+1=37" ]
Current State: 37:[2, 69, 34, 69], Operations: [] Exploring Operation: 2+34=36, Resulting Numbers: [69, 69, 36] Generated Node #2: [69, 69, 36] from Operation: 2+34=36 Current State: 37:[69, 69, 36], Operations: ['2+34=36'] Exploring Operation: 69/69=1, Resulting Numbers: [36, 1] Generated Node #3: [36, 1] from Operation: 69/69=1 Current State: 37:[36, 1], Operations: ['2+34=36', '69/69=1'] Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[2, 69, 34, 69], Operations: [] Exploring Operation: 69-2=67, Resulting Numbers: [69, 34, 67] Generated Node #0,0: 37:[69, 34, 67] Operation: 69-2=67 Exploring Operation: 69-2=67, Resulting Numbers: [34, 69, 67] Generated Node #0,1: 37:[34, 69, 67] Operation: 69-2=67 Exploring Operation: 2+34=36, Resulting Numbers: [69, 69, 36] Generated Node #0,2: 37:[69, 69, 36] Operation: 2+34=36 Moving to Node #0,0 Current State: 37:[69, 34, 67], Operations: ['69-2=67'] Exploring Operation: 67-34=33, Resulting Numbers: [69, 33] Generated Node #0,0,0: 37:[69, 33] Operation: 67-34=33 Exploring Operation: 69-67=2, Resulting Numbers: [34, 2] Generated Node #0,0,1: 37:[34, 2] Operation: 69-67=2 Exploring Operation: 69-34=35, Resulting Numbers: [67, 35] Generated Node #0,0,2: 37:[67, 35] Operation: 69-34=35 Moving to Node #0,1 Current State: 37:[34, 69, 67], Operations: ['69-2=67'] Exploring Operation: 69-67=2, Resulting Numbers: [34, 2] Generated Node #0,1,0: 37:[34, 2] Operation: 69-67=2 Exploring Operation: 67-34=33, Resulting Numbers: [69, 33] Generated Node #0,1,1: 37:[69, 33] Operation: 67-34=33 Exploring Operation: 69-34=35, Resulting Numbers: [67, 35] Generated Node #0,1,2: 37:[67, 35] Operation: 69-34=35 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[67, 35], Operations: ['69-2=67', '69-34=35'] Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,37 unequal: No Solution Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[69, 33], Operations: ['69-2=67', '67-34=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,37 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[34, 2], Operations: ['69-2=67', '69-67=2'] Exploring Operation: 34+2=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,37 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: 37:[69, 69, 36], Operations: ['2+34=36'] Exploring Operation: 69/69=1, Resulting Numbers: [36, 1] Generated Node #0,2,0: 37:[36, 1] Operation: 69/69=1 Exploring Operation: 69-36=33, Resulting Numbers: [69, 33] Generated Node #0,2,1: 37:[69, 33] Operation: 69-36=33 Exploring Operation: 69-36=33, Resulting Numbers: [69, 33] Generated Node #0,2,2: 37:[69, 33] Operation: 69-36=33 Moving to Node #0,0,2 Current State: 37:[67, 35], Operations: ['69-2=67', '69-34=35'] Exploring Operation: 67-35=32, Resulting Numbers: [32] 32,37 unequal: No Solution Exploring Operation: 67*35=2345, Resulting Numbers: [2345] 2345,37 unequal: No Solution Exploring Operation: 67+35=102, Resulting Numbers: [102] 102,37 unequal: No Solution Moving to Node #0,0,0 Current State: 37:[69, 33], Operations: ['69-2=67', '67-34=33'] Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,37 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[69, 33], Operations: ['2+34=36', '69-36=33'] Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,37 unequal: No Solution Moving to Node #0,2,1 Current State: 37:[69, 33], Operations: ['2+34=36', '69-36=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,37 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[36, 1], Operations: ['2+34=36', '69/69=1'] Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[2, 69, 34, 69], Operations: [] Exploring Operation: 2+34=36, Resulting Numbers: [69, 69, 36] Generated Node #0,2: 37:[69, 69, 36] Operation: 2+34=36 Moving to Node #0,2 Current State: 37:[69, 69, 36], Operations: ['2+34=36'] Exploring Operation: 69/69=1, Resulting Numbers: [36, 1] Generated Node #0,2,0: 37:[36, 1] Operation: 69/69=1 Moving to Node #0,2,0 Current State: 37:[36, 1], Operations: ['2+34=36', '69/69=1'] Exploring Operation: 36+1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.967014
hs_3
sum_heuristic
[ 48, 28, 16, 4 ]
88
[ "48+28=76", "16-4=12", "76+12=88" ]
Current State: 88:[48, 28, 16, 4], Operations: [] Exploring Operation: 48+28=76, Resulting Numbers: [16, 4, 76] Generated Node #2: [16, 4, 76] from Operation: 48+28=76 Current State: 88:[16, 4, 76], Operations: ['48+28=76'] Exploring Operation: 16-4=12, Resulting Numbers: [76, 12] Generated Node #3: [76, 12] from Operation: 16-4=12 Current State: 88:[76, 12], Operations: ['48+28=76', '16-4=12'] Exploring Operation: 76+12=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[48, 28, 16, 4], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [16, 4, 20] Generated Node #0,0: 88:[16, 4, 20] Operation: 48-28=20 Exploring Operation: 48/16=3, Resulting Numbers: [28, 4, 3] Generated Node #0,1: 88:[28, 4, 3] Operation: 48/16=3 Exploring Operation: 28+16=44, Resulting Numbers: [48, 4, 44] Generated Node #0,2: 88:[48, 4, 44] Operation: 28+16=44 Exploring Operation: 28-16=12, Resulting Numbers: [48, 4, 12] Generated Node #0,3: 88:[48, 4, 12] Operation: 28-16=12 Exploring Operation: 28/4=7, Resulting Numbers: [48, 16, 7] Generated Node #0,4: 88:[48, 16, 7] Operation: 28/4=7 Moving to Node #0,2 Current State: 88:[48, 4, 44], Operations: ['28+16=44'] Exploring Operation: 48-44=4, Resulting Numbers: [4, 4] Generated Node #0,2,0: 88:[4, 4] Operation: 48-44=4 Exploring Operation: 48-4=44, Resulting Numbers: [44, 44] Generated Node #0,2,1: 88:[44, 44] Operation: 48-4=44 Exploring Operation: 44/4=11, Resulting Numbers: [48, 11] Generated Node #0,2,2: 88:[48, 11] Operation: 44/4=11 Exploring Operation: 48+44=92, Resulting Numbers: [4, 92] Generated Node #0,2,3: 88:[4, 92] Operation: 48+44=92 Exploring Operation: 48/4=12, Resulting Numbers: [44, 12] Generated Node #0,2,4: 88:[44, 12] Operation: 48/4=12 Moving to Node #0,3 Current State: 88:[48, 4, 12], Operations: ['28-16=12'] Exploring Operation: 12-4=8, Resulting Numbers: [48, 8] Generated Node #0,3,0: 88:[48, 8] Operation: 12-4=8 Exploring Operation: 48-4=44, Resulting Numbers: [12, 44] Generated Node #0,3,1: 88:[12, 44] Operation: 48-4=44 Exploring Operation: 48/4=12, Resulting Numbers: [12, 12] Generated Node #0,3,2: 88:[12, 12] Operation: 48/4=12 Exploring Operation: 12/4=3, Resulting Numbers: [48, 3] Generated Node #0,3,3: 88:[48, 3] Operation: 12/4=3 Exploring Operation: 48/12=4, Resulting Numbers: [4, 4] Generated Node #0,3,4: 88:[4, 4] Operation: 48/12=4 Moving to Node #0,0 Current State: 88:[16, 4, 20], Operations: ['48-28=20'] Exploring Operation: 16/4=4, Resulting Numbers: [20, 4] Generated Node #0,0,0: 88:[20, 4] Operation: 16/4=4 Exploring Operation: 20-16=4, Resulting Numbers: [4, 4] Generated Node #0,0,1: 88:[4, 4] Operation: 20-16=4 Exploring Operation: 16-4=12, Resulting Numbers: [20, 12] Generated Node #0,0,2: 88:[20, 12] Operation: 16-4=12 Exploring Operation: 16+4=20, Resulting Numbers: [20, 20] Generated Node #0,0,3: 88:[20, 20] Operation: 16+4=20 Exploring Operation: 20/4=5, Resulting Numbers: [16, 5] Generated Node #0,0,4: 88:[16, 5] Operation: 20/4=5 Moving to Node #0,1 Current State: 88:[28, 4, 3], Operations: ['48/16=3'] Exploring Operation: 28-3=25, Resulting Numbers: [4, 25] Generated Node #0,1,0: 88:[4, 25] Operation: 28-3=25 Exploring Operation: 4+3=7, Resulting Numbers: [28, 7] Generated Node #0,1,1: 88:[28, 7] Operation: 4+3=7 Exploring Operation: 28*3=84, Resulting Numbers: [4, 84] Generated Node #0,1,2: 88:[4, 84] Operation: 28*3=84 Exploring Operation: 28/4=7, Resulting Numbers: [3, 7] Generated Node #0,1,3: 88:[3, 7] Operation: 28/4=7 Exploring Operation: 28-4=24, Resulting Numbers: [3, 24] Generated Node #0,1,4: 88:[3, 24] Operation: 28-4=24 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[3, 7], Operations: ['48/16=3', '28/4=7'] Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,88 unequal: No Solution Exploring Operation: 3+7=10, Resulting Numbers: [10] 10,88 unequal: No Solution Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,88 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 #0,1,0 Current State: 88:[4, 25], Operations: ['48/16=3', '28-3=25'] Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 4+25=29, Resulting Numbers: [29] 29,88 unequal: No Solution Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,88 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 #0,1,4 Current State: 88:[3, 24], Operations: ['48/16=3', '28-4=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,88 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,88 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 #0,1,2 Current State: 88:[4, 84], Operations: ['48/16=3', '28*3=84'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,88 unequal: No Solution Exploring Operation: 4*84=336, Resulting Numbers: [336] 336,88 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[48, 28, 16, 4], Operations: [] Exploring Operation: 48/16=3, Resulting Numbers: [28, 4, 3] Generated Node #0,1: 88:[28, 4, 3] Operation: 48/16=3 Moving to Node #0,1 Current State: 88:[28, 4, 3], Operations: ['48/16=3'] Exploring Operation: 28*3=84, Resulting Numbers: [4, 84] Generated Node #0,1,2: 88:[4, 84] Operation: 28*3=84 Moving to Node #0,1,2 Current State: 88:[4, 84], Operations: ['48/16=3', '28*3=84'] Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic
[ 24, 38, 50, 28 ]
76
[ "50-24=26", "28-26=2", "38*2=76" ]
Current State: 76:[24, 38, 50, 28], Operations: [] Exploring Operation: 50-24=26, Resulting Numbers: [38, 28, 26] Generated Node #2: [38, 28, 26] from Operation: 50-24=26 Current State: 76:[38, 28, 26], Operations: ['50-24=26'] Exploring Operation: 28-26=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 28-26=2 Current State: 76:[38, 2], Operations: ['50-24=26', '28-26=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[24, 38, 50, 28], Operations: [] Exploring Operation: 24+50=74, Resulting Numbers: [38, 28, 74] Generated Node #0,0: 76:[38, 28, 74] Operation: 24+50=74 Exploring Operation: 28-24=4, Resulting Numbers: [38, 50, 4] Generated Node #0,1: 76:[38, 50, 4] Operation: 28-24=4 Exploring Operation: 50+28=78, Resulting Numbers: [24, 38, 78] Generated Node #0,2: 76:[24, 38, 78] Operation: 50+28=78 Exploring Operation: 50-28=22, Resulting Numbers: [24, 38, 22] Generated Node #0,3: 76:[24, 38, 22] Operation: 50-28=22 Exploring Operation: 50-24=26, Resulting Numbers: [38, 28, 26] Generated Node #0,4: 76:[38, 28, 26] Operation: 50-24=26 Moving to Node #0,2 Current State: 76:[24, 38, 78], Operations: ['50+28=78'] Exploring Operation: 78-24=54, Resulting Numbers: [38, 54] Generated Node #0,2,0: 76:[38, 54] Operation: 78-24=54 Exploring Operation: 38-24=14, Resulting Numbers: [78, 14] Generated Node #0,2,1: 76:[78, 14] Operation: 38-24=14 Exploring Operation: 78-38=40, Resulting Numbers: [24, 40] Generated Node #0,2,2: 76:[24, 40] Operation: 78-38=40 Exploring Operation: 24+78=102, Resulting Numbers: [38, 102] Generated Node #0,2,3: 76:[38, 102] Operation: 24+78=102 Exploring Operation: 24+38=62, Resulting Numbers: [78, 62] Generated Node #0,2,4: 76:[78, 62] Operation: 24+38=62 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 76:[78, 14], Operations: ['50+28=78', '38-24=14'] Exploring Operation: 78*14=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 78+14=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 78-14=64, Resulting Numbers: [64] 64,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 76:[24, 40], Operations: ['50+28=78', '78-38=40'] Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,76 unequal: No Solution Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[38, 54], Operations: ['50+28=78', '78-24=54'] Exploring Operation: 38+54=92, Resulting Numbers: [92] 92,76 unequal: No Solution Exploring Operation: 38*54=2052, Resulting Numbers: [2052] 2052,76 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 76:[78, 62], Operations: ['50+28=78', '24+38=62'] Exploring Operation: 78*62=4836, Resulting Numbers: [4836] 4836,76 unequal: No Solution Exploring Operation: 78-62=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 78+62=140, Resulting Numbers: [140] 140,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 76:[38, 102], Operations: ['50+28=78', '24+78=102'] Exploring Operation: 38+102=140, Resulting Numbers: [140] 140,76 unequal: No Solution Exploring Operation: 102-38=64, Resulting Numbers: [64] 64,76 unequal: No Solution Exploring Operation: 38*102=3876, Resulting Numbers: [3876] 3876,76 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: 76:[24, 38, 22], Operations: ['50-28=22'] Exploring Operation: 38-22=16, Resulting Numbers: [24, 16] Generated Node #0,3,0: 76:[24, 16] Operation: 38-22=16 Exploring Operation: 24-22=2, Resulting Numbers: [38, 2] Generated Node #0,3,1: 76:[38, 2] Operation: 24-22=2 Exploring Operation: 24+22=46, Resulting Numbers: [38, 46] Generated Node #0,3,2: 76:[38, 46] Operation: 24+22=46 Exploring Operation: 24+38=62, Resulting Numbers: [22, 62] Generated Node #0,3,3: 76:[22, 62] Operation: 24+38=62 Exploring Operation: 38-24=14, Resulting Numbers: [22, 14] Generated Node #0,3,4: 76:[22, 14] Operation: 38-24=14 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 76:[38, 2], Operations: ['50-28=22', '24-22=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,76 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[24, 38, 50, 28], Operations: [] Exploring Operation: 50-28=22, Resulting Numbers: [24, 38, 22] Generated Node #0,3: 76:[24, 38, 22] Operation: 50-28=22 Moving to Node #0,3 Current State: 76:[24, 38, 22], Operations: ['50-28=22'] Exploring Operation: 24-22=2, Resulting Numbers: [38, 2] Generated Node #0,3,1: 76:[38, 2] Operation: 24-22=2 Moving to Node #0,3,1 Current State: 76:[38, 2], Operations: ['50-28=22', '24-22=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_5
mult_heuristic
[ 20, 10, 70, 39 ]
44
[ "70-20=50", "50/10=5", "39+5=44" ]
Current State: 44:[20, 10, 70, 39], Operations: [] Exploring Operation: 70-20=50, Resulting Numbers: [10, 39, 50] Generated Node #2: [10, 39, 50] from Operation: 70-20=50 Current State: 44:[10, 39, 50], Operations: ['70-20=50'] Exploring Operation: 50/10=5, Resulting Numbers: [39, 5] Generated Node #3: [39, 5] from Operation: 50/10=5 Current State: 44:[39, 5], Operations: ['70-20=50', '50/10=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[20, 10, 70, 39], Operations: [] Exploring Operation: 70-20=50, Resulting Numbers: [10, 39, 50] Generated Node #0,0: 44:[10, 39, 50] Operation: 70-20=50 Exploring Operation: 70-39=31, Resulting Numbers: [20, 10, 31] Generated Node #0,1: 44:[20, 10, 31] Operation: 70-39=31 Exploring Operation: 70/10=7, Resulting Numbers: [20, 39, 7] Generated Node #0,2: 44:[20, 39, 7] Operation: 70/10=7 Moving to Node #0,2 Current State: 44:[20, 39, 7], Operations: ['70/10=7'] Exploring Operation: 39+7=46, Resulting Numbers: [20, 46] Generated Node #0,2,0: 44:[20, 46] Operation: 39+7=46 Exploring Operation: 20-7=13, Resulting Numbers: [39, 13] Generated Node #0,2,1: 44:[39, 13] Operation: 20-7=13 Exploring Operation: 39-20=19, Resulting Numbers: [7, 19] Generated Node #0,2,2: 44:[7, 19] Operation: 39-20=19 Moving to Node #0,0 Current State: 44:[10, 39, 50], Operations: ['70-20=50'] Exploring Operation: 50/10=5, Resulting Numbers: [39, 5] Generated Node #0,0,0: 44:[39, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [39, 40] Generated Node #0,0,1: 44:[39, 40] Operation: 50-10=40 Exploring Operation: 50-39=11, Resulting Numbers: [10, 11] Generated Node #0,0,2: 44:[10, 11] Operation: 50-39=11 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 44:[10, 11], Operations: ['70-20=50', '50-39=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,44 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,44 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 44:[39, 5], Operations: ['70-20=50', '50/10=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[20, 10, 70, 39], Operations: [] Exploring Operation: 70-20=50, Resulting Numbers: [10, 39, 50] Generated Node #0,0: 44:[10, 39, 50] Operation: 70-20=50 Moving to Node #0,0 Current State: 44:[10, 39, 50], Operations: ['70-20=50'] Exploring Operation: 50/10=5, Resulting Numbers: [39, 5] Generated Node #0,0,0: 44:[39, 5] Operation: 50/10=5 Moving to Node #0,0,0 Current State: 44:[39, 5], Operations: ['70-20=50', '50/10=5'] Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 92, 91, 42, 93 ]
21
[ "92*42=3864", "91+93=184", "3864/184=21" ]
Current State: 21:[92, 91, 42, 93], Operations: [] Exploring Operation: 92*42=3864, Resulting Numbers: [91, 93, 3864] Generated Node #2: [91, 93, 3864] from Operation: 92*42=3864 Current State: 21:[91, 93, 3864], Operations: ['92*42=3864'] Exploring Operation: 91+93=184, Resulting Numbers: [3864, 184] Generated Node #3: [3864, 184] from Operation: 91+93=184 Current State: 21:[3864, 184], Operations: ['92*42=3864', '91+93=184'] Exploring Operation: 3864/184=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[92, 91, 42, 93], Operations: [] Exploring Operation: 92-42=50, Resulting Numbers: [91, 93, 50] Generated Node #0,0: 21:[91, 93, 50] Operation: 92-42=50 Exploring Operation: 93-91=2, Resulting Numbers: [92, 42, 2] Generated Node #0,1: 21:[92, 42, 2] Operation: 93-91=2 Exploring Operation: 93-92=1, Resulting Numbers: [91, 42, 1] Generated Node #0,2: 21:[91, 42, 1] Operation: 93-92=1 Exploring Operation: 92-91=1, Resulting Numbers: [42, 93, 1] Generated Node #0,3: 21:[42, 93, 1] Operation: 92-91=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[92, 42, 2], Operations: ['93-91=2'] Exploring Operation: 42/2=21, Resulting Numbers: [92, 21] Generated Node #0,1,0: 21:[92, 21] Operation: 42/2=21 Exploring Operation: 92-42=50, Resulting Numbers: [2, 50] Generated Node #0,1,1: 21:[2, 50] Operation: 92-42=50 Exploring Operation: 92/2=46, Resulting Numbers: [42, 46] Generated Node #0,1,2: 21:[42, 46] Operation: 92/2=46 Exploring Operation: 92-2=90, Resulting Numbers: [42, 90] Generated Node #0,1,3: 21:[42, 90] Operation: 92-2=90 Moving to Node #0,1,1 Current State: 21:[2, 50], Operations: ['93-91=2', '92-42=50'] Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,21 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[42, 46], Operations: ['93-91=2', '92/2=46'] Exploring Operation: 42*46=1932, Resulting Numbers: [1932] 1932,21 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,21 unequal: No Solution Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[92, 21], Operations: ['93-91=2', '42/2=21'] Exploring Operation: 92*21=1932, Resulting Numbers: [1932] 1932,21 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,21 unequal: No Solution Exploring Operation: 92+21=113, Resulting Numbers: [113] 113,21 unequal: No Solution Moving to Node #0,1,3 Current State: 21:[42, 90], Operations: ['93-91=2', '92-2=90'] Exploring Operation: 42+90=132, Resulting Numbers: [132] 132,21 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 42*90=3780, Resulting Numbers: [3780] 3780,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[91, 42, 1], Operations: ['93-92=1'] Exploring Operation: 91-1=90, Resulting Numbers: [42, 90] Generated Node #0,2,0: 21:[42, 90] Operation: 91-1=90 Exploring Operation: 42-1=41, Resulting Numbers: [91, 41] Generated Node #0,2,1: 21:[91, 41] Operation: 42-1=41 Exploring Operation: 91-42=49, Resulting Numbers: [1, 49] Generated Node #0,2,2: 21:[1, 49] Operation: 91-42=49 Exploring Operation: 91*1=91, Resulting Numbers: [42, 91] Generated Node #0,2,3: 21:[42, 91] Operation: 91*1=91 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[1, 49], Operations: ['93-92=1', '91-42=49'] Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,21 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,21 unequal: No Solution Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,21 unequal: No Solution No 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: 21:[42, 90], Operations: ['93-92=1', '91-1=90'] Exploring Operation: 42*90=3780, Resulting Numbers: [3780] 3780,21 unequal: No Solution Exploring Operation: 42+90=132, Resulting Numbers: [132] 132,21 unequal: No Solution Exploring Operation: 90-42=48, Resulting Numbers: [48] 48,21 unequal: No Solution No 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: 21:[91, 41], Operations: ['93-92=1', '42-1=41'] Exploring Operation: 91*41=3731, Resulting Numbers: [3731] 3731,21 unequal: No Solution Exploring Operation: 91-41=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 91+41=132, Resulting Numbers: [132] 132,21 unequal: No Solution No 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: 21:[42, 91], Operations: ['93-92=1', '91*1=91'] Exploring Operation: 42+91=133, Resulting Numbers: [133] 133,21 unequal: No Solution Exploring Operation: 42*91=3822, Resulting Numbers: [3822] 3822,21 unequal: No Solution Exploring Operation: 91-42=49, Resulting Numbers: [49] 49,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 21:[42, 93, 1], Operations: ['92-91=1'] Exploring Operation: 93-1=92, Resulting Numbers: [42, 92] Generated Node #0,3,0: 21:[42, 92] Operation: 93-1=92 Exploring Operation: 93-42=51, Resulting Numbers: [1, 51] Generated Node #0,3,1: 21:[1, 51] Operation: 93-42=51 Exploring Operation: 42*1=42, Resulting Numbers: [93, 42] Generated Node #0,3,2: 21:[93, 42] Operation: 42*1=42 Exploring Operation: 42-1=41, Resulting Numbers: [93, 41] Generated Node #0,3,3: 21:[93, 41] Operation: 42-1=41 Moving to Node #0,3,1 Current State: 21:[1, 51], Operations: ['92-91=1', '93-42=51'] Exploring Operation: 1+51=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 51-1=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 1*51=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,3,3 Current State: 21:[93, 41], Operations: ['92-91=1', '42-1=41'] Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 93*41=3813, Resulting Numbers: [3813] 3813,21 unequal: No Solution Exploring Operation: 93+41=134, Resulting Numbers: [134] 134,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[42, 92], Operations: ['92-91=1', '93-1=92'] Exploring Operation: 42+92=134, Resulting Numbers: [134] 134,21 unequal: No Solution Exploring Operation: 42*92=3864, Resulting Numbers: [3864] 3864,21 unequal: No Solution Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,21 unequal: No Solution Moving to Node #0,3,2 Current State: 21:[93, 42], Operations: ['92-91=1', '42*1=42'] Exploring Operation: 93*42=3906, Resulting Numbers: [3906] 3906,21 unequal: No Solution Exploring Operation: 93+42=135, Resulting Numbers: [135] 135,21 unequal: No Solution Exploring Operation: 93-42=51, Resulting Numbers: [51] 51,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[91, 93, 50], Operations: ['92-42=50'] Exploring Operation: 91+93=184, Resulting Numbers: [50, 184] Generated Node #0,0,0: 21:[50, 184] Operation: 91+93=184 Exploring Operation: 93-91=2, Resulting Numbers: [50, 2] Generated Node #0,0,1: 21:[50, 2] Operation: 93-91=2 Exploring Operation: 91-50=41, Resulting Numbers: [93, 41] Generated Node #0,0,2: 21:[93, 41] Operation: 91-50=41 Exploring Operation: 93-50=43, Resulting Numbers: [91, 43] Generated Node #0,0,3: 21:[91, 43] Operation: 93-50=43 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[50, 2], Operations: ['92-42=50', '93-91=2'] Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,21 unequal: No Solution Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,21 unequal: No Solution No 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: 21:[93, 41], Operations: ['92-42=50', '91-50=41'] Exploring Operation: 93*41=3813, Resulting Numbers: [3813] 3813,21 unequal: No Solution Exploring Operation: 93-41=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 93+41=134, Resulting Numbers: [134] 134,21 unequal: No Solution No 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: 21:[91, 43], Operations: ['92-42=50', '93-50=43'] Exploring Operation: 91*43=3913, Resulting Numbers: [3913] 3913,21 unequal: No Solution Exploring Operation: 91+43=134, Resulting Numbers: [134] 134,21 unequal: No Solution Exploring Operation: 91-43=48, Resulting Numbers: [48] 48,21 unequal: No Solution No 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: 21:[50, 184], Operations: ['92-42=50', '91+93=184'] Exploring Operation: 50*184=9200, Resulting Numbers: [9200] 9200,21 unequal: No Solution Exploring Operation: 50+184=234, Resulting Numbers: [234] 234,21 unequal: No Solution Exploring Operation: 184-50=134, Resulting Numbers: [134] 134,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 44, 49, 89, 38 ]
56
[ "49-44=5", "89-38=51", "5+51=56" ]
Current State: 56:[44, 49, 89, 38], Operations: [] Exploring Operation: 49-44=5, Resulting Numbers: [89, 38, 5] Generated Node #2: [89, 38, 5] from Operation: 49-44=5 Current State: 56:[89, 38, 5], Operations: ['49-44=5'] Exploring Operation: 89-38=51, Resulting Numbers: [5, 51] Generated Node #3: [5, 51] from Operation: 89-38=51 Current State: 56:[5, 51], Operations: ['49-44=5', '89-38=51'] Exploring Operation: 5+51=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[44, 49, 89, 38], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [44, 49, 51] Generated Node #0,0: 56:[44, 49, 51] Operation: 89-38=51 Moving to Node #0,0 Current State: 56:[44, 49, 51], Operations: ['89-38=51'] Exploring Operation: 49-44=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 56:[51, 5] Operation: 49-44=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[51, 5], Operations: ['89-38=51', '49-44=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[44, 49, 89, 38], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [44, 49, 51] Generated Node #0,0: 56:[44, 49, 51] Operation: 89-38=51 Moving to Node #0,0 Current State: 56:[44, 49, 51], Operations: ['89-38=51'] Exploring Operation: 49-44=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 56:[51, 5] Operation: 49-44=5 Moving to Node #0,0,0 Current State: 56:[51, 5], Operations: ['89-38=51', '49-44=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 68, 54, 84, 45 ]
51
[ "68-54=14", "84/14=6", "45+6=51" ]
Current State: 51:[68, 54, 84, 45], Operations: [] Exploring Operation: 68-54=14, Resulting Numbers: [84, 45, 14] Generated Node #2: [84, 45, 14] from Operation: 68-54=14 Current State: 51:[84, 45, 14], Operations: ['68-54=14'] Exploring Operation: 84/14=6, Resulting Numbers: [45, 6] Generated Node #3: [45, 6] from Operation: 84/14=6 Current State: 51:[45, 6], Operations: ['68-54=14', '84/14=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[68, 54, 84, 45], Operations: [] Exploring Operation: 84-68=16, Resulting Numbers: [54, 45, 16] Generated Node #0,0: 51:[54, 45, 16] Operation: 84-68=16 Moving to Node #0,0 Current State: 51:[54, 45, 16], Operations: ['84-68=16'] Exploring Operation: 54-45=9, Resulting Numbers: [16, 9] Generated Node #0,0,0: 51:[16, 9] Operation: 54-45=9 Moving to Node #0,0,0 Current State: 51:[16, 9], Operations: ['84-68=16', '54-45=9'] Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,51 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 67, 61, 12, 8 ]
90
[ "67-61=6", "12*8=96", "96-6=90" ]
Current State: 90:[67, 61, 12, 8], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [12, 8, 6] Generated Node #2: [12, 8, 6] from Operation: 67-61=6 Current State: 90:[12, 8, 6], Operations: ['67-61=6'] Exploring Operation: 12*8=96, Resulting Numbers: [6, 96] Generated Node #3: [6, 96] from Operation: 12*8=96 Current State: 90:[6, 96], Operations: ['67-61=6', '12*8=96'] Exploring Operation: 96-6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[67, 61, 12, 8], Operations: [] Exploring Operation: 67-61=6, Resulting Numbers: [12, 8, 6] Generated Node #0,0: 90:[12, 8, 6] Operation: 67-61=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[12, 8, 6], Operations: ['67-61=6'] Exploring Operation: 12-8=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 90:[6, 4] Operation: 12-8=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[6, 4], Operations: ['67-61=6', '12-8=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 37, 39, 84, 91 ]
83
[ "37+39=76", "91-84=7", "76+7=83" ]
Current State: 83:[37, 39, 84, 91], Operations: [] Exploring Operation: 37+39=76, Resulting Numbers: [84, 91, 76] Generated Node #2: [84, 91, 76] from Operation: 37+39=76 Current State: 83:[84, 91, 76], Operations: ['37+39=76'] Exploring Operation: 91-84=7, Resulting Numbers: [76, 7] Generated Node #3: [76, 7] from Operation: 91-84=7 Current State: 83:[76, 7], Operations: ['37+39=76', '91-84=7'] Exploring Operation: 76+7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[37, 39, 84, 91], Operations: [] Exploring Operation: 91-39=52, Resulting Numbers: [37, 84, 52] Generated Node #0,0: 83:[37, 84, 52] Operation: 91-39=52 Exploring Operation: 84-37=47, Resulting Numbers: [39, 91, 47] Generated Node #0,1: 83:[39, 91, 47] Operation: 84-37=47 Exploring Operation: 37+39=76, Resulting Numbers: [84, 91, 76] Generated Node #0,2: 83:[84, 91, 76] Operation: 37+39=76 Exploring Operation: 91-37=54, Resulting Numbers: [39, 84, 54] Generated Node #0,3: 83:[39, 84, 54] Operation: 91-37=54 Moving to Node #0,2 Current State: 83:[84, 91, 76], Operations: ['37+39=76'] Exploring Operation: 91-84=7, Resulting Numbers: [76, 7] Generated Node #0,2,0: 83:[76, 7] Operation: 91-84=7 Exploring Operation: 84+76=160, Resulting Numbers: [91, 160] Generated Node #0,2,1: 83:[91, 160] Operation: 84+76=160 Exploring Operation: 91-76=15, Resulting Numbers: [84, 15] Generated Node #0,2,2: 83:[84, 15] Operation: 91-76=15 Exploring Operation: 84-76=8, Resulting Numbers: [91, 8] Generated Node #0,2,3: 83:[91, 8] Operation: 84-76=8 Moving to Node #0,3 Current State: 83:[39, 84, 54], Operations: ['91-37=54'] Exploring Operation: 84-39=45, Resulting Numbers: [54, 45] Generated Node #0,3,0: 83:[54, 45] Operation: 84-39=45 Exploring Operation: 39+54=93, Resulting Numbers: [84, 93] Generated Node #0,3,1: 83:[84, 93] Operation: 39+54=93 Exploring Operation: 54-39=15, Resulting Numbers: [84, 15] Generated Node #0,3,2: 83:[84, 15] Operation: 54-39=15 Exploring Operation: 39+84=123, Resulting Numbers: [54, 123] Generated Node #0,3,3: 83:[54, 123] Operation: 39+84=123 Moving to Node #0,0 Current State: 83:[37, 84, 52], Operations: ['91-39=52'] Exploring Operation: 37+52=89, Resulting Numbers: [84, 89] Generated Node #0,0,0: 83:[84, 89] Operation: 37+52=89 Exploring Operation: 84-37=47, Resulting Numbers: [52, 47] Generated Node #0,0,1: 83:[52, 47] Operation: 84-37=47 Exploring Operation: 37+84=121, Resulting Numbers: [52, 121] Generated Node #0,0,2: 83:[52, 121] Operation: 37+84=121 Exploring Operation: 52-37=15, Resulting Numbers: [84, 15] Generated Node #0,0,3: 83:[84, 15] Operation: 52-37=15 Moving to Node #0,1 Current State: 83:[39, 91, 47], Operations: ['84-37=47'] Exploring Operation: 91-39=52, Resulting Numbers: [47, 52] Generated Node #0,1,0: 83:[47, 52] Operation: 91-39=52 Exploring Operation: 39+91=130, Resulting Numbers: [47, 130] Generated Node #0,1,1: 83:[47, 130] Operation: 39+91=130 Exploring Operation: 39+47=86, Resulting Numbers: [91, 86] Generated Node #0,1,2: 83:[91, 86] Operation: 39+47=86 Exploring Operation: 47-39=8, Resulting Numbers: [91, 8] Generated Node #0,1,3: 83:[91, 8] Operation: 47-39=8 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 83:[91, 86], Operations: ['84-37=47', '39+47=86'] Exploring Operation: 91*86=7826, Resulting Numbers: [7826] 7826,83 unequal: No Solution Exploring Operation: 91-86=5, Resulting Numbers: [5] 5,83 unequal: No Solution Exploring Operation: 91+86=177, Resulting Numbers: [177] 177,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 83:[47, 52], Operations: ['84-37=47', '91-39=52'] Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,83 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,83 unequal: No Solution Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 83:[47, 130], Operations: ['84-37=47', '39+91=130'] Exploring Operation: 130-47=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[37, 39, 84, 91], Operations: [] Exploring Operation: 84-37=47, Resulting Numbers: [39, 91, 47] Generated Node #0,1: 83:[39, 91, 47] Operation: 84-37=47 Moving to Node #0,1 Current State: 83:[39, 91, 47], Operations: ['84-37=47'] Exploring Operation: 39+91=130, Resulting Numbers: [47, 130] Generated Node #0,1,1: 83:[47, 130] Operation: 39+91=130 Moving to Node #0,1,1 Current State: 83:[47, 130], Operations: ['84-37=47', '39+91=130'] Exploring Operation: 130-47=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
mult_heuristic
[ 80, 11, 19, 37 ]
28
[ "80+19=99", "99/11=9", "37-9=28" ]
Current State: 28:[80, 11, 19, 37], Operations: [] Exploring Operation: 80+19=99, Resulting Numbers: [11, 37, 99] Generated Node #2: [11, 37, 99] from Operation: 80+19=99 Current State: 28:[11, 37, 99], Operations: ['80+19=99'] Exploring Operation: 99/11=9, Resulting Numbers: [37, 9] Generated Node #3: [37, 9] from Operation: 99/11=9 Current State: 28:[37, 9], Operations: ['80+19=99', '99/11=9'] Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[80, 11, 19, 37], Operations: [] Exploring Operation: 80-37=43, Resulting Numbers: [11, 19, 43] Generated Node #0,0: 28:[11, 19, 43] Operation: 80-37=43 Exploring Operation: 80-11=69, Resulting Numbers: [19, 37, 69] Generated Node #0,1: 28:[19, 37, 69] Operation: 80-11=69 Exploring Operation: 80-19=61, Resulting Numbers: [11, 37, 61] Generated Node #0,2: 28:[11, 37, 61] Operation: 80-19=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[11, 19, 43], Operations: ['80-37=43'] Exploring Operation: 43-11=32, Resulting Numbers: [19, 32] Generated Node #0,0,0: 28:[19, 32] Operation: 43-11=32 Exploring Operation: 19-11=8, Resulting Numbers: [43, 8] Generated Node #0,0,1: 28:[43, 8] Operation: 19-11=8 Exploring Operation: 43-19=24, Resulting Numbers: [11, 24] Generated Node #0,0,2: 28:[11, 24] Operation: 43-19=24 Moving to Node #0,0,2 Current State: 28:[11, 24], Operations: ['80-37=43', '43-19=24'] Exploring Operation: 11+24=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 11*24=264, Resulting Numbers: [264] 264,28 unequal: No Solution Moving to Node #0,0,0 Current State: 28:[19, 32], Operations: ['80-37=43', '43-11=32'] Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,28 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,28 unequal: No Solution Moving to Node #0,0,1 Current State: 28:[43, 8], Operations: ['80-37=43', '19-11=8'] Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 43*8=344, Resulting Numbers: [344] 344,28 unequal: No Solution Exploring Operation: 43+8=51, Resulting Numbers: [51] 51,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[11, 37, 61], Operations: ['80-19=61'] Exploring Operation: 37-11=26, Resulting Numbers: [61, 26] Generated Node #0,2,0: 28:[61, 26] Operation: 37-11=26 Exploring Operation: 61-11=50, Resulting Numbers: [37, 50] Generated Node #0,2,1: 28:[37, 50] Operation: 61-11=50 Exploring Operation: 61-37=24, Resulting Numbers: [11, 24] Generated Node #0,2,2: 28:[11, 24] Operation: 61-37=24 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[11, 24], Operations: ['80-19=61', '61-37=24'] Exploring Operation: 11*24=264, Resulting Numbers: [264] 264,28 unequal: No Solution Exploring Operation: 11+24=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 24-11=13, Resulting Numbers: [13] 13,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[37, 50], Operations: ['80-19=61', '61-11=50'] Exploring Operation: 37*50=1850, Resulting Numbers: [1850] 1850,28 unequal: No Solution Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 37+50=87, Resulting Numbers: [87] 87,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 28:[61, 26], Operations: ['80-19=61', '37-11=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,28 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,28 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[19, 37, 69], Operations: ['80-11=69'] Exploring Operation: 69-37=32, Resulting Numbers: [19, 32] Generated Node #0,1,0: 28:[19, 32] Operation: 69-37=32 Exploring Operation: 69-19=50, Resulting Numbers: [37, 50] Generated Node #0,1,1: 28:[37, 50] Operation: 69-19=50 Exploring Operation: 37-19=18, Resulting Numbers: [69, 18] Generated Node #0,1,2: 28:[69, 18] Operation: 37-19=18 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[19, 32], Operations: ['80-11=69', '69-37=32'] Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,28 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 28:[37, 50], Operations: ['80-11=69', '69-19=50'] Exploring Operation: 50-37=13, Resulting Numbers: [13] 13,28 unequal: No Solution Exploring Operation: 37+50=87, Resulting Numbers: [87] 87,28 unequal: No Solution Exploring Operation: 37*50=1850, Resulting Numbers: [1850] 1850,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 28:[69, 18], Operations: ['80-11=69', '37-19=18'] Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,28 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,28 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 90, 35, 87, 76 ]
44
[ "90-35=55", "87-76=11", "55-11=44" ]
Current State: 44:[90, 35, 87, 76], Operations: [] Exploring Operation: 90-35=55, Resulting Numbers: [87, 76, 55] Generated Node #2: [87, 76, 55] from Operation: 90-35=55 Current State: 44:[87, 76, 55], Operations: ['90-35=55'] Exploring Operation: 87-76=11, Resulting Numbers: [55, 11] Generated Node #3: [55, 11] from Operation: 87-76=11 Current State: 44:[55, 11], Operations: ['90-35=55', '87-76=11'] Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[90, 35, 87, 76], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [35, 76, 3] Generated Node #0,0: 44:[35, 76, 3] Operation: 90-87=3 Exploring Operation: 90-35=55, Resulting Numbers: [87, 76, 55] Generated Node #0,1: 44:[87, 76, 55] Operation: 90-35=55 Exploring Operation: 90-76=14, Resulting Numbers: [35, 87, 14] Generated Node #0,2: 44:[35, 87, 14] Operation: 90-76=14 Exploring Operation: 87-76=11, Resulting Numbers: [90, 35, 11] Generated Node #0,3: 44:[90, 35, 11] Operation: 87-76=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[35, 76, 3], Operations: ['90-87=3'] Exploring Operation: 76-35=41, Resulting Numbers: [3, 41] Generated Node #0,0,0: 44:[3, 41] Operation: 76-35=41 Exploring Operation: 35+3=38, Resulting Numbers: [76, 38] Generated Node #0,0,1: 44:[76, 38] Operation: 35+3=38 Exploring Operation: 76-3=73, Resulting Numbers: [35, 73] Generated Node #0,0,2: 44:[35, 73] Operation: 76-3=73 Exploring Operation: 35-3=32, Resulting Numbers: [76, 32] Generated Node #0,0,3: 44:[76, 32] Operation: 35-3=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 44:[3, 41], Operations: ['90-87=3', '76-35=41'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[90, 35, 87, 76], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [35, 76, 3] Generated Node #0,0: 44:[35, 76, 3] Operation: 90-87=3 Moving to Node #0,0 Current State: 44:[35, 76, 3], Operations: ['90-87=3'] Exploring Operation: 76-35=41, Resulting Numbers: [3, 41] Generated Node #0,0,0: 44:[3, 41] Operation: 76-35=41 Moving to Node #0,0,0 Current State: 44:[3, 41], Operations: ['90-87=3', '76-35=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 41, 28, 2, 60 ]
87
[ "41+60=101", "28/2=14", "101-14=87" ]
Current State: 87:[41, 28, 2, 60], Operations: [] Exploring Operation: 41+60=101, Resulting Numbers: [28, 2, 101] Generated Node #2: [28, 2, 101] from Operation: 41+60=101 Current State: 87:[28, 2, 101], Operations: ['41+60=101'] Exploring Operation: 28/2=14, Resulting Numbers: [101, 14] Generated Node #3: [101, 14] from Operation: 28/2=14 Current State: 87:[101, 14], Operations: ['41+60=101', '28/2=14'] Exploring Operation: 101-14=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[41, 28, 2, 60], Operations: [] Exploring Operation: 60-28=32, Resulting Numbers: [41, 2, 32] Generated Node #0,0: 87:[41, 2, 32] Operation: 60-28=32 Exploring Operation: 60-41=19, Resulting Numbers: [28, 2, 19] Generated Node #0,1: 87:[28, 2, 19] Operation: 60-41=19 Exploring Operation: 41+60=101, Resulting Numbers: [28, 2, 101] Generated Node #0,2: 87:[28, 2, 101] Operation: 41+60=101 Exploring Operation: 28+60=88, Resulting Numbers: [41, 2, 88] Generated Node #0,3: 87:[41, 2, 88] Operation: 28+60=88 Exploring Operation: 60/2=30, Resulting Numbers: [41, 28, 30] Generated Node #0,4: 87:[41, 28, 30] Operation: 60/2=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[28, 2, 19], Operations: ['60-41=19'] Exploring Operation: 28+2=30, Resulting Numbers: [19, 30] Generated Node #0,1,0: 87:[19, 30] Operation: 28+2=30 Exploring Operation: 2*19=38, Resulting Numbers: [28, 38] Generated Node #0,1,1: 87:[28, 38] Operation: 2*19=38 Exploring Operation: 2+19=21, Resulting Numbers: [28, 21] Generated Node #0,1,2: 87:[28, 21] Operation: 2+19=21 Exploring Operation: 28-2=26, Resulting Numbers: [19, 26] Generated Node #0,1,3: 87:[19, 26] Operation: 28-2=26 Exploring Operation: 28-19=9, Resulting Numbers: [2, 9] Generated Node #0,1,4: 87:[2, 9] Operation: 28-19=9 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 87:[2, 9], Operations: ['60-41=19', '28-19=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[28, 21], Operations: ['60-41=19', '2+19=21'] Exploring Operation: 28*21=588, Resulting Numbers: [588] 588,87 unequal: No Solution Exploring Operation: 28-21=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 28+21=49, Resulting Numbers: [49] 49,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[28, 38], Operations: ['60-41=19', '2*19=38'] Exploring Operation: 28*38=1064, Resulting Numbers: [1064] 1064,87 unequal: No Solution Exploring Operation: 28+38=66, Resulting Numbers: [66] 66,87 unequal: No Solution Exploring Operation: 38-28=10, Resulting Numbers: [10] 10,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[19, 30], Operations: ['60-41=19', '28+2=30'] Exploring Operation: 30-19=11, Resulting Numbers: [11] 11,87 unequal: No Solution Exploring Operation: 19+30=49, Resulting Numbers: [49] 49,87 unequal: No Solution Exploring Operation: 19*30=570, Resulting Numbers: [570] 570,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 87:[19, 26], Operations: ['60-41=19', '28-2=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,87 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[41, 2, 88], Operations: ['28+60=88'] Exploring Operation: 2+88=90, Resulting Numbers: [41, 90] Generated Node #0,3,0: 87:[41, 90] Operation: 2+88=90 Exploring Operation: 41*2=82, Resulting Numbers: [88, 82] Generated Node #0,3,1: 87:[88, 82] Operation: 41*2=82 Exploring Operation: 88-2=86, Resulting Numbers: [41, 86] Generated Node #0,3,2: 87:[41, 86] Operation: 88-2=86 Exploring Operation: 41-2=39, Resulting Numbers: [88, 39] Generated Node #0,3,3: 87:[88, 39] Operation: 41-2=39 Exploring Operation: 41+2=43, Resulting Numbers: [88, 43] Generated Node #0,3,4: 87:[88, 43] Operation: 41+2=43 Moving to Node #0,3,1 Current State: 87:[88, 82], Operations: ['28+60=88', '41*2=82'] Exploring Operation: 88+82=170, Resulting Numbers: [170] 170,87 unequal: No Solution Exploring Operation: 88*82=7216, Resulting Numbers: [7216] 7216,87 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,87 unequal: No Solution Moving to Node #0,3,3 Current State: 87:[88, 39], Operations: ['28+60=88', '41-2=39'] Exploring Operation: 88+39=127, Resulting Numbers: [127] 127,87 unequal: No Solution Exploring Operation: 88*39=3432, Resulting Numbers: [3432] 3432,87 unequal: No Solution Exploring Operation: 88-39=49, Resulting Numbers: [49] 49,87 unequal: No Solution Moving to Node #0,3,2 Current State: 87:[41, 86], Operations: ['28+60=88', '88-2=86'] Exploring Operation: 41*86=3526, Resulting Numbers: [3526] 3526,87 unequal: No Solution Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 41+86=127, Resulting Numbers: [127] 127,87 unequal: No Solution Moving to Node #0,3,0 Current State: 87:[41, 90], Operations: ['28+60=88', '2+88=90'] Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,87 unequal: No Solution Exploring Operation: 41+90=131, Resulting Numbers: [131] 131,87 unequal: No Solution Exploring Operation: 41*90=3690, Resulting Numbers: [3690] 3690,87 unequal: No Solution Moving to Node #0,3,4 Current State: 87:[88, 43], Operations: ['28+60=88', '41+2=43'] Exploring Operation: 88*43=3784, Resulting Numbers: [3784] 3784,87 unequal: No Solution Exploring Operation: 88-43=45, Resulting Numbers: [45] 45,87 unequal: No Solution Exploring Operation: 88+43=131, Resulting Numbers: [131] 131,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 87:[41, 28, 30], Operations: ['60/2=30'] Exploring Operation: 41+28=69, Resulting Numbers: [30, 69] Generated Node #0,4,0: 87:[30, 69] Operation: 41+28=69 Exploring Operation: 41-30=11, Resulting Numbers: [28, 11] Generated Node #0,4,1: 87:[28, 11] Operation: 41-30=11 Exploring Operation: 30-28=2, Resulting Numbers: [41, 2] Generated Node #0,4,2: 87:[41, 2] Operation: 30-28=2 Exploring Operation: 41+30=71, Resulting Numbers: [28, 71] Generated Node #0,4,3: 87:[28, 71] Operation: 41+30=71 Exploring Operation: 41-28=13, Resulting Numbers: [30, 13] Generated Node #0,4,4: 87:[30, 13] Operation: 41-28=13 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 87:[28, 11], Operations: ['60/2=30', '41-30=11'] Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,87 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 87:[30, 13], Operations: ['60/2=30', '41-28=13'] Exploring Operation: 30*13=390, Resulting Numbers: [390] 390,87 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,87 unequal: No Solution Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 87:[41, 2], Operations: ['60/2=30', '30-28=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,87 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 87:[28, 71], Operations: ['60/2=30', '41+30=71'] Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,87 unequal: No Solution Exploring Operation: 28*71=1988, Resulting Numbers: [1988] 1988,87 unequal: No Solution Exploring Operation: 28+71=99, Resulting Numbers: [99] 99,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 87:[30, 69], Operations: ['60/2=30', '41+28=69'] Exploring Operation: 30+69=99, Resulting Numbers: [99] 99,87 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,87 unequal: No Solution Exploring Operation: 30*69=2070, Resulting Numbers: [2070] 2070,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[41, 2, 32], Operations: ['60-28=32'] Exploring Operation: 41-2=39, Resulting Numbers: [32, 39] Generated Node #0,0,0: 87:[32, 39] Operation: 41-2=39 Exploring Operation: 41+32=73, Resulting Numbers: [2, 73] Generated Node #0,0,1: 87:[2, 73] Operation: 41+32=73 Exploring Operation: 41-32=9, Resulting Numbers: [2, 9] Generated Node #0,0,2: 87:[2, 9] Operation: 41-32=9 Exploring Operation: 41*2=82, Resulting Numbers: [32, 82] Generated Node #0,0,3: 87:[32, 82] Operation: 41*2=82 Exploring Operation: 32-2=30, Resulting Numbers: [41, 30] Generated Node #0,0,4: 87:[41, 30] Operation: 32-2=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[2, 9], Operations: ['60-28=32', '41-32=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[32, 82], Operations: ['60-28=32', '41*2=82'] Exploring Operation: 32*82=2624, Resulting Numbers: [2624] 2624,87 unequal: No Solution Exploring Operation: 82-32=50, Resulting Numbers: [50] 50,87 unequal: No Solution Exploring Operation: 32+82=114, Resulting Numbers: [114] 114,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[32, 39], Operations: ['60-28=32', '41-2=39'] Exploring Operation: 32*39=1248, Resulting Numbers: [1248] 1248,87 unequal: No Solution Exploring Operation: 39-32=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 32+39=71, Resulting Numbers: [71] 71,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 87:[41, 30], Operations: ['60-28=32', '32-2=30'] Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,87 unequal: No Solution Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,87 unequal: No Solution Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[2, 73], Operations: ['60-28=32', '41+32=73'] Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,87 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[28, 2, 101], Operations: ['41+60=101'] Exploring Operation: 28-2=26, Resulting Numbers: [101, 26] Generated Node #0,2,0: 87:[101, 26] Operation: 28-2=26 Exploring Operation: 28+2=30, Resulting Numbers: [101, 30] Generated Node #0,2,1: 87:[101, 30] Operation: 28+2=30 Exploring Operation: 2+101=103, Resulting Numbers: [28, 103] Generated Node #0,2,2: 87:[28, 103] Operation: 2+101=103 Exploring Operation: 101-28=73, Resulting Numbers: [2, 73] Generated Node #0,2,3: 87:[2, 73] Operation: 101-28=73 Exploring Operation: 101-2=99, Resulting Numbers: [28, 99] Generated Node #0,2,4: 87:[28, 99] Operation: 101-2=99 Moving to Node #0,2,4 Current State: 87:[28, 99], Operations: ['41+60=101', '101-2=99'] Exploring Operation: 28*99=2772, Resulting Numbers: [2772] 2772,87 unequal: No Solution Exploring Operation: 28+99=127, Resulting Numbers: [127] 127,87 unequal: No Solution Exploring Operation: 99-28=71, Resulting Numbers: [71] 71,87 unequal: No Solution Moving to Node #0,2,3 Current State: 87:[2, 73], Operations: ['41+60=101', '101-28=73'] Exploring Operation: 2+73=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 73-2=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 2*73=146, Resulting Numbers: [146] 146,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[101, 30], Operations: ['41+60=101', '28+2=30'] Exploring Operation: 101*30=3030, Resulting Numbers: [3030] 3030,87 unequal: No Solution Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 101+30=131, Resulting Numbers: [131] 131,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[101, 26], Operations: ['41+60=101', '28-2=26'] Exploring Operation: 101+26=127, Resulting Numbers: [127] 127,87 unequal: No Solution Exploring Operation: 101-26=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 101*26=2626, Resulting Numbers: [2626] 2626,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[28, 103], Operations: ['41+60=101', '2+101=103'] Exploring Operation: 28+103=131, Resulting Numbers: [131] 131,87 unequal: No Solution Exploring Operation: 28*103=2884, Resulting Numbers: [2884] 2884,87 unequal: No Solution Exploring Operation: 103-28=75, Resulting Numbers: [75] 75,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 42, 67, 24, 49 ]
84
[ "42+67=109", "49-24=25", "109-25=84" ]
Current State: 84:[42, 67, 24, 49], Operations: [] Exploring Operation: 42+67=109, Resulting Numbers: [24, 49, 109] Generated Node #2: [24, 49, 109] from Operation: 42+67=109 Current State: 84:[24, 49, 109], Operations: ['42+67=109'] Exploring Operation: 49-24=25, Resulting Numbers: [109, 25] Generated Node #3: [109, 25] from Operation: 49-24=25 Current State: 84:[109, 25], Operations: ['42+67=109', '49-24=25'] Exploring Operation: 109-25=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[42, 67, 24, 49], Operations: [] Exploring Operation: 67-24=43, Resulting Numbers: [42, 49, 43] Generated Node #0,0: 84:[42, 49, 43] Operation: 67-24=43 Exploring Operation: 67-49=18, Resulting Numbers: [42, 24, 18] Generated Node #0,1: 84:[42, 24, 18] Operation: 67-49=18 Moving to Node #0,1 Current State: 84:[42, 24, 18], Operations: ['67-49=18'] Exploring Operation: 24+18=42, Resulting Numbers: [42, 42] Generated Node #0,1,0: 84:[42, 42] Operation: 24+18=42 Exploring Operation: 24-18=6, Resulting Numbers: [42, 6] Generated Node #0,1,1: 84:[42, 6] Operation: 24-18=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[42, 42], Operations: ['67-49=18', '24+18=42'] Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[42, 67, 24, 49], Operations: [] Exploring Operation: 67-49=18, Resulting Numbers: [42, 24, 18] Generated Node #0,1: 84:[42, 24, 18] Operation: 67-49=18 Moving to Node #0,1 Current State: 84:[42, 24, 18], Operations: ['67-49=18'] Exploring Operation: 24+18=42, Resulting Numbers: [42, 42] Generated Node #0,1,0: 84:[42, 42] Operation: 24+18=42 Moving to Node #0,1,0 Current State: 84:[42, 42], Operations: ['67-49=18', '24+18=42'] Exploring Operation: 42+42=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 9, 49, 70, 49 ]
62
[ "70-9=61", "49/49=1", "61+1=62" ]
Current State: 62:[9, 49, 70, 49], Operations: [] Exploring Operation: 70-9=61, Resulting Numbers: [49, 49, 61] Generated Node #2: [49, 49, 61] from Operation: 70-9=61 Current State: 62:[49, 49, 61], Operations: ['70-9=61'] Exploring Operation: 49/49=1, Resulting Numbers: [61, 1] Generated Node #3: [61, 1] from Operation: 49/49=1 Current State: 62:[61, 1], Operations: ['70-9=61', '49/49=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[9, 49, 70, 49], Operations: [] Exploring Operation: 9+49=58, Resulting Numbers: [70, 49, 58] Generated Node #0,0: 62:[70, 49, 58] Operation: 9+49=58 Exploring Operation: 49/49=1, Resulting Numbers: [9, 70, 1] Generated Node #0,1: 62:[9, 70, 1] Operation: 49/49=1 Exploring Operation: 9+49=58, Resulting Numbers: [49, 70, 58] Generated Node #0,2: 62:[49, 70, 58] Operation: 9+49=58 Exploring Operation: 49-49=0, Resulting Numbers: [9, 70, 0] Generated Node #0,3: 62:[9, 70, 0] Operation: 49-49=0 Exploring Operation: 70-9=61, Resulting Numbers: [49, 49, 61] Generated Node #0,4: 62:[49, 49, 61] Operation: 70-9=61 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[9, 70, 1], Operations: ['49/49=1'] Exploring Operation: 70-9=61, Resulting Numbers: [1, 61] Generated Node #0,1,0: 62:[1, 61] Operation: 70-9=61 Exploring Operation: 9/1=9, Resulting Numbers: [70, 9] Generated Node #0,1,1: 62:[70, 9] Operation: 9/1=9 Exploring Operation: 9-1=8, Resulting Numbers: [70, 8] Generated Node #0,1,2: 62:[70, 8] Operation: 9-1=8 Exploring Operation: 9*1=9, Resulting Numbers: [70, 9] Generated Node #0,1,3: 62:[70, 9] Operation: 9*1=9 Exploring Operation: 70-1=69, Resulting Numbers: [9, 69] Generated Node #0,1,4: 62:[9, 69] Operation: 70-1=69 Moving to Node #0,1,0 Current State: 62:[1, 61], Operations: ['49/49=1', '70-9=61'] Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[9, 49, 70, 49], Operations: [] Exploring Operation: 49/49=1, Resulting Numbers: [9, 70, 1] Generated Node #0,1: 62:[9, 70, 1] Operation: 49/49=1 Moving to Node #0,1 Current State: 62:[9, 70, 1], Operations: ['49/49=1'] Exploring Operation: 70-9=61, Resulting Numbers: [1, 61] Generated Node #0,1,0: 62:[1, 61] Operation: 70-9=61 Moving to Node #0,1,0 Current State: 62:[1, 61], Operations: ['49/49=1', '70-9=61'] Exploring Operation: 1+61=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 72, 2, 65, 81 ]
25
[ "72+65=137", "2*81=162", "162-137=25" ]
Current State: 25:[72, 2, 65, 81], Operations: [] Exploring Operation: 72+65=137, Resulting Numbers: [2, 81, 137] Generated Node #2: [2, 81, 137] from Operation: 72+65=137 Current State: 25:[2, 81, 137], Operations: ['72+65=137'] Exploring Operation: 2*81=162, Resulting Numbers: [137, 162] Generated Node #3: [137, 162] from Operation: 2*81=162 Current State: 25:[137, 162], Operations: ['72+65=137', '2*81=162'] Exploring Operation: 162-137=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[72, 2, 65, 81], Operations: [] Exploring Operation: 81-65=16, Resulting Numbers: [72, 2, 16] Generated Node #0,0: 25:[72, 2, 16] Operation: 81-65=16 Exploring Operation: 72-65=7, Resulting Numbers: [2, 81, 7] Generated Node #0,1: 25:[2, 81, 7] Operation: 72-65=7 Exploring Operation: 81-72=9, Resulting Numbers: [2, 65, 9] Generated Node #0,2: 25:[2, 65, 9] Operation: 81-72=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[2, 65, 9], Operations: ['81-72=9'] Exploring Operation: 9-2=7, Resulting Numbers: [65, 7] Generated Node #0,2,0: 25:[65, 7] Operation: 9-2=7 Exploring Operation: 65-9=56, Resulting Numbers: [2, 56] Generated Node #0,2,1: 25:[2, 56] Operation: 65-9=56 Exploring Operation: 65-2=63, Resulting Numbers: [9, 63] Generated Node #0,2,2: 25:[9, 63] Operation: 65-2=63 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[2, 56], Operations: ['81-72=9', '65-9=56'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,25 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[65, 7], Operations: ['81-72=9', '9-2=7'] Exploring Operation: 65+7=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 65-7=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 65*7=455, Resulting Numbers: [455] 455,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[9, 63], Operations: ['81-72=9', '65-2=63'] Exploring Operation: 63-9=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 63/9=7, Resulting Numbers: [7] 7,25 unequal: No Solution Exploring Operation: 9+63=72, Resulting Numbers: [72] 72,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[72, 2, 16], Operations: ['81-65=16'] Exploring Operation: 16/2=8, Resulting Numbers: [72, 8] Generated Node #0,0,0: 25:[72, 8] Operation: 16/2=8 Exploring Operation: 72-16=56, Resulting Numbers: [2, 56] Generated Node #0,0,1: 25:[2, 56] Operation: 72-16=56 Exploring Operation: 72/2=36, Resulting Numbers: [16, 36] Generated Node #0,0,2: 25:[16, 36] Operation: 72/2=36 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 25:[16, 36], Operations: ['81-65=16', '72/2=36'] Exploring Operation: 36-16=20, Resulting Numbers: [20] 20,25 unequal: No Solution Exploring Operation: 16*36=576, Resulting Numbers: [576] 576,25 unequal: No Solution Exploring Operation: 16+36=52, Resulting Numbers: [52] 52,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[2, 56], Operations: ['81-65=16', '72-16=56'] Exploring Operation: 2+56=58, Resulting Numbers: [58] 58,25 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 25:[72, 8], Operations: ['81-65=16', '16/2=8'] Exploring Operation: 72-8=64, Resulting Numbers: [64] 64,25 unequal: No Solution Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,25 unequal: No Solution Exploring Operation: 72/8=9, Resulting Numbers: [9] 9,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[2, 81, 7], Operations: ['72-65=7'] Exploring Operation: 81-2=79, Resulting Numbers: [7, 79] Generated Node #0,1,0: 25:[7, 79] Operation: 81-2=79 Exploring Operation: 7-2=5, Resulting Numbers: [81, 5] Generated Node #0,1,1: 25:[81, 5] Operation: 7-2=5 Exploring Operation: 81-7=74, Resulting Numbers: [2, 74] Generated Node #0,1,2: 25:[2, 74] Operation: 81-7=74 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 25:[2, 74], Operations: ['72-65=7', '81-7=74'] Exploring Operation: 74/2=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 74-2=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 2+74=76, Resulting Numbers: [76] 76,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 25:[7, 79], Operations: ['72-65=7', '81-2=79'] Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,25 unequal: No Solution Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,25 unequal: No Solution Exploring Operation: 7*79=553, Resulting Numbers: [553] 553,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 25:[81, 5], Operations: ['72-65=7', '7-2=5'] Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,25 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,25 unequal: No Solution Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 37, 52, 53, 47 ]
85
[ "52-37=15", "53+47=100", "100-15=85" ]
Current State: 85:[37, 52, 53, 47], Operations: [] Exploring Operation: 52-37=15, Resulting Numbers: [53, 47, 15] Generated Node #2: [53, 47, 15] from Operation: 52-37=15 Current State: 85:[53, 47, 15], Operations: ['52-37=15'] Exploring Operation: 53+47=100, Resulting Numbers: [15, 100] Generated Node #3: [15, 100] from Operation: 53+47=100 Current State: 85:[15, 100], Operations: ['52-37=15', '53+47=100'] Exploring Operation: 100-15=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[37, 52, 53, 47], Operations: [] Exploring Operation: 53-52=1, Resulting Numbers: [37, 47, 1] Generated Node #0,0: 85:[37, 47, 1] Operation: 53-52=1 Exploring Operation: 53-47=6, Resulting Numbers: [37, 52, 6] Generated Node #0,1: 85:[37, 52, 6] Operation: 53-47=6 Exploring Operation: 52-47=5, Resulting Numbers: [37, 53, 5] Generated Node #0,2: 85:[37, 53, 5] Operation: 52-47=5 Moving to Node #0,2 Current State: 85:[37, 53, 5], Operations: ['52-47=5'] Exploring Operation: 37+53=90, Resulting Numbers: [5, 90] Generated Node #0,2,0: 85:[5, 90] Operation: 37+53=90 Exploring Operation: 53-37=16, Resulting Numbers: [5, 16] Generated Node #0,2,1: 85:[5, 16] Operation: 53-37=16 Exploring Operation: 37-5=32, Resulting Numbers: [53, 32] Generated Node #0,2,2: 85:[53, 32] Operation: 37-5=32 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[5, 16], Operations: ['52-47=5', '53-37=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,85 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,85 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 #0,2,0 Current State: 85:[5, 90], Operations: ['52-47=5', '37+53=90'] Exploring Operation: 90/5=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[37, 52, 53, 47], Operations: [] Exploring Operation: 52-47=5, Resulting Numbers: [37, 53, 5] Generated Node #0,2: 85:[37, 53, 5] Operation: 52-47=5 Moving to Node #0,2 Current State: 85:[37, 53, 5], Operations: ['52-47=5'] Exploring Operation: 37+53=90, Resulting Numbers: [5, 90] Generated Node #0,2,0: 85:[5, 90] Operation: 37+53=90 Moving to Node #0,2,0 Current State: 85:[5, 90], Operations: ['52-47=5', '37+53=90'] Exploring Operation: 90-5=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 4, 88, 18, 91 ]
58
[ "91-88=3", "18*3=54", "4+54=58" ]
Current State: 58:[4, 88, 18, 91], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [4, 18, 3] Generated Node #2: [4, 18, 3] from Operation: 91-88=3 Current State: 58:[4, 18, 3], Operations: ['91-88=3'] Exploring Operation: 18*3=54, Resulting Numbers: [4, 54] Generated Node #3: [4, 54] from Operation: 18*3=54 Current State: 58:[4, 54], Operations: ['91-88=3', '18*3=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[4, 88, 18, 91], Operations: [] Exploring Operation: 88-18=70, Resulting Numbers: [4, 91, 70] Generated Node #0,0: 58:[4, 91, 70] Operation: 88-18=70 Exploring Operation: 91-18=73, Resulting Numbers: [4, 88, 73] Generated Node #0,1: 58:[4, 88, 73] Operation: 91-18=73 Exploring Operation: 91-88=3, Resulting Numbers: [4, 18, 3] Generated Node #0,2: 58:[4, 18, 3] Operation: 91-88=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[4, 18, 3], Operations: ['91-88=3'] Exploring Operation: 18*3=54, Resulting Numbers: [4, 54] Generated Node #0,2,0: 58:[4, 54] Operation: 18*3=54 Exploring Operation: 4+18=22, Resulting Numbers: [3, 22] Generated Node #0,2,1: 58:[3, 22] Operation: 4+18=22 Exploring Operation: 18/3=6, Resulting Numbers: [4, 6] Generated Node #0,2,2: 58:[4, 6] Operation: 18/3=6 Moving to Node #0,2,0 Current State: 58:[4, 54], Operations: ['91-88=3', '18*3=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[4, 88, 18, 91], Operations: [] Exploring Operation: 91-88=3, Resulting Numbers: [4, 18, 3] Generated Node #0,2: 58:[4, 18, 3] Operation: 91-88=3 Moving to Node #0,2 Current State: 58:[4, 18, 3], Operations: ['91-88=3'] Exploring Operation: 18*3=54, Resulting Numbers: [4, 54] Generated Node #0,2,0: 58:[4, 54] Operation: 18*3=54 Moving to Node #0,2,0 Current State: 58:[4, 54], Operations: ['91-88=3', '18*3=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 20, 6, 84, 40 ]
21
[ "40/20=2", "6-2=4", "84/4=21" ]
Current State: 21:[20, 6, 84, 40], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [6, 84, 2] Generated Node #2: [6, 84, 2] from Operation: 40/20=2 Current State: 21:[6, 84, 2], Operations: ['40/20=2'] Exploring Operation: 6-2=4, Resulting Numbers: [84, 4] Generated Node #3: [84, 4] from Operation: 6-2=4 Current State: 21:[84, 4], Operations: ['40/20=2', '6-2=4'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 6, 84, 40], Operations: [] Exploring Operation: 84-20=64, Resulting Numbers: [6, 40, 64] Generated Node #0,0: 21:[6, 40, 64] Operation: 84-20=64 Exploring Operation: 84/6=14, Resulting Numbers: [20, 40, 14] Generated Node #0,1: 21:[20, 40, 14] Operation: 84/6=14 Exploring Operation: 84-40=44, Resulting Numbers: [20, 6, 44] Generated Node #0,2: 21:[20, 6, 44] Operation: 84-40=44 Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[20, 6, 44], Operations: ['84-40=44'] Exploring Operation: 44-20=24, Resulting Numbers: [6, 24] Generated Node #0,2,0: 21:[6, 24] Operation: 44-20=24 Exploring Operation: 44-6=38, Resulting Numbers: [20, 38] Generated Node #0,2,1: 21:[20, 38] Operation: 44-6=38 Exploring Operation: 20+6=26, Resulting Numbers: [44, 26] Generated Node #0,2,2: 21:[44, 26] Operation: 20+6=26 Moving to Node #0,2,0 Current State: 21:[6, 24], Operations: ['84-40=44', '44-20=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[20, 38], Operations: ['84-40=44', '44-6=38'] Exploring Operation: 20*38=760, Resulting Numbers: [760] 760,21 unequal: No Solution Exploring Operation: 38-20=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 20+38=58, Resulting Numbers: [58] 58,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[44, 26], Operations: ['84-40=44', '20+6=26'] Exploring Operation: 44*26=1144, Resulting Numbers: [1144] 1144,21 unequal: No Solution Exploring Operation: 44+26=70, Resulting Numbers: [70] 70,21 unequal: No Solution Exploring Operation: 44-26=18, Resulting Numbers: [18] 18,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[20, 40, 14], Operations: ['84/6=14'] Exploring Operation: 40-20=20, Resulting Numbers: [14, 20] Generated Node #0,1,0: 21:[14, 20] Operation: 40-20=20 Exploring Operation: 40-14=26, Resulting Numbers: [20, 26] Generated Node #0,1,1: 21:[20, 26] Operation: 40-14=26 Exploring Operation: 40/20=2, Resulting Numbers: [14, 2] Generated Node #0,1,2: 21:[14, 2] Operation: 40/20=2 Moving to Node #0,1,1 Current State: 21:[20, 26], Operations: ['84/6=14', '40-14=26'] Exploring Operation: 20+26=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 20*26=520, Resulting Numbers: [520] 520,21 unequal: No Solution Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[14, 20], Operations: ['84/6=14', '40-20=20'] Exploring Operation: 14*20=280, Resulting Numbers: [280] 280,21 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,21 unequal: No Solution Moving to Node #0,1,2 Current State: 21:[14, 2], Operations: ['84/6=14', '40/20=2'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,21 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[6, 40, 64], Operations: ['84-20=64'] Exploring Operation: 64-6=58, Resulting Numbers: [40, 58] Generated Node #0,0,0: 21:[40, 58] Operation: 64-6=58 Exploring Operation: 40-6=34, Resulting Numbers: [64, 34] Generated Node #0,0,1: 21:[64, 34] Operation: 40-6=34 Exploring Operation: 64-40=24, Resulting Numbers: [6, 24] Generated Node #0,0,2: 21:[6, 24] Operation: 64-40=24 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 21:[6, 24], Operations: ['84-20=64', '64-40=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,21 unequal: No Solution No 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: 21:[40, 58], Operations: ['84-20=64', '64-6=58'] Exploring Operation: 40+58=98, Resulting Numbers: [98] 98,21 unequal: No Solution Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,21 unequal: No Solution Exploring Operation: 40*58=2320, Resulting Numbers: [2320] 2320,21 unequal: No Solution No 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: 21:[64, 34], Operations: ['84-20=64', '40-6=34'] Exploring Operation: 64+34=98, Resulting Numbers: [98] 98,21 unequal: No Solution Exploring Operation: 64-34=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 64*34=2176, Resulting Numbers: [2176] 2176,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 54, 44, 14, 43 ]
69
[ "54+44=98", "43-14=29", "98-29=69" ]
Current State: 69:[54, 44, 14, 43], Operations: [] Exploring Operation: 54+44=98, Resulting Numbers: [14, 43, 98] Generated Node #2: [14, 43, 98] from Operation: 54+44=98 Current State: 69:[14, 43, 98], Operations: ['54+44=98'] Exploring Operation: 43-14=29, Resulting Numbers: [98, 29] Generated Node #3: [98, 29] from Operation: 43-14=29 Current State: 69:[98, 29], Operations: ['54+44=98', '43-14=29'] Exploring Operation: 98-29=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[54, 44, 14, 43], Operations: [] Exploring Operation: 54-44=10, Resulting Numbers: [14, 43, 10] Generated Node #0,0: 69:[14, 43, 10] Operation: 54-44=10 Exploring Operation: 54-43=11, Resulting Numbers: [44, 14, 11] Generated Node #0,1: 69:[44, 14, 11] Operation: 54-43=11 Exploring Operation: 44-43=1, Resulting Numbers: [54, 14, 1] Generated Node #0,2: 69:[54, 14, 1] Operation: 44-43=1 Moving to Node #0,2 Current State: 69:[54, 14, 1], Operations: ['44-43=1'] Exploring Operation: 54+14=68, Resulting Numbers: [1, 68] Generated Node #0,2,0: 69:[1, 68] Operation: 54+14=68 Exploring Operation: 54+1=55, Resulting Numbers: [14, 55] Generated Node #0,2,1: 69:[14, 55] Operation: 54+1=55 Exploring Operation: 54-14=40, Resulting Numbers: [1, 40] Generated Node #0,2,2: 69:[1, 40] Operation: 54-14=40 Moving to Node #0,0 Current State: 69:[14, 43, 10], Operations: ['54-44=10'] Exploring Operation: 14+43=57, Resulting Numbers: [10, 57] Generated Node #0,0,0: 69:[10, 57] Operation: 14+43=57 Exploring Operation: 43-10=33, Resulting Numbers: [14, 33] Generated Node #0,0,1: 69:[14, 33] Operation: 43-10=33 Exploring Operation: 43-14=29, Resulting Numbers: [10, 29] Generated Node #0,0,2: 69:[10, 29] Operation: 43-14=29 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[10, 29], Operations: ['54-44=10', '43-14=29'] Exploring Operation: 10*29=290, Resulting Numbers: [290] 290,69 unequal: No Solution Exploring Operation: 29-10=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 10+29=39, Resulting Numbers: [39] 39,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[10, 57], Operations: ['54-44=10', '14+43=57'] Exploring Operation: 10*57=570, Resulting Numbers: [570] 570,69 unequal: No Solution Exploring Operation: 10+57=67, Resulting Numbers: [67] 67,69 unequal: No Solution Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[14, 33], Operations: ['54-44=10', '43-10=33'] Exploring Operation: 14*33=462, Resulting Numbers: [462] 462,69 unequal: No Solution Exploring Operation: 14+33=47, Resulting Numbers: [47] 47,69 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,69 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: 69:[44, 14, 11], Operations: ['54-43=11'] Exploring Operation: 44+14=58, Resulting Numbers: [11, 58] Generated Node #0,1,0: 69:[11, 58] Operation: 44+14=58 Exploring Operation: 44-14=30, Resulting Numbers: [11, 30] Generated Node #0,1,1: 69:[11, 30] Operation: 44-14=30 Exploring Operation: 44/11=4, Resulting Numbers: [14, 4] Generated Node #0,1,2: 69:[14, 4] Operation: 44/11=4 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[14, 4], Operations: ['54-43=11', '44/11=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[11, 30], Operations: ['54-43=11', '44-14=30'] Exploring Operation: 11+30=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 11*30=330, Resulting Numbers: [330] 330,69 unequal: No Solution Exploring Operation: 30-11=19, Resulting Numbers: [19] 19,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[11, 58], Operations: ['54-43=11', '44+14=58'] Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,69 unequal: No Solution Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[54, 44, 14, 43], Operations: [] Exploring Operation: 54-43=11, Resulting Numbers: [44, 14, 11] Generated Node #0,1: 69:[44, 14, 11] Operation: 54-43=11 Moving to Node #0,1 Current State: 69:[44, 14, 11], Operations: ['54-43=11'] Exploring Operation: 44+14=58, Resulting Numbers: [11, 58] Generated Node #0,1,0: 69:[11, 58] Operation: 44+14=58 Moving to Node #0,1,0 Current State: 69:[11, 58], Operations: ['54-43=11', '44+14=58'] Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.971354
hs_3
sum_heuristic
[ 53, 16, 25, 74 ]
62
[ "53-16=37", "25+74=99", "99-37=62" ]
Current State: 62:[53, 16, 25, 74], Operations: [] Exploring Operation: 53-16=37, Resulting Numbers: [25, 74, 37] Generated Node #2: [25, 74, 37] from Operation: 53-16=37 Current State: 62:[25, 74, 37], Operations: ['53-16=37'] Exploring Operation: 25+74=99, Resulting Numbers: [37, 99] Generated Node #3: [37, 99] from Operation: 25+74=99 Current State: 62:[37, 99], Operations: ['53-16=37', '25+74=99'] Exploring Operation: 99-37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[53, 16, 25, 74], Operations: [] Exploring Operation: 53-25=28, Resulting Numbers: [16, 74, 28] Generated Node #0,0: 62:[16, 74, 28] Operation: 53-25=28 Exploring Operation: 53-16=37, Resulting Numbers: [25, 74, 37] Generated Node #0,1: 62:[25, 74, 37] Operation: 53-16=37 Exploring Operation: 74-16=58, Resulting Numbers: [53, 25, 58] Generated Node #0,2: 62:[53, 25, 58] Operation: 74-16=58 Exploring Operation: 25-16=9, Resulting Numbers: [53, 74, 9] Generated Node #0,3: 62:[53, 74, 9] Operation: 25-16=9 Exploring Operation: 53+16=69, Resulting Numbers: [25, 74, 69] Generated Node #0,4: 62:[25, 74, 69] Operation: 53+16=69 Moving to Node #0,2 Current State: 62:[53, 25, 58], Operations: ['74-16=58'] Exploring Operation: 58-25=33, Resulting Numbers: [53, 33] Generated Node #0,2,0: 62:[53, 33] Operation: 58-25=33 Exploring Operation: 25+58=83, Resulting Numbers: [53, 83] Generated Node #0,2,1: 62:[53, 83] Operation: 25+58=83 Exploring Operation: 53-25=28, Resulting Numbers: [58, 28] Generated Node #0,2,2: 62:[58, 28] Operation: 53-25=28 Exploring Operation: 58-53=5, Resulting Numbers: [25, 5] Generated Node #0,2,3: 62:[25, 5] Operation: 58-53=5 Exploring Operation: 53+25=78, Resulting Numbers: [58, 78] Generated Node #0,2,4: 62:[58, 78] Operation: 53+25=78 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 62:[58, 28], Operations: ['74-16=58', '53-25=28'] Exploring Operation: 58+28=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 58*28=1624, Resulting Numbers: [1624] 1624,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 62:[25, 5], Operations: ['74-16=58', '58-53=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,62 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 62:[53, 33], Operations: ['74-16=58', '58-25=33'] Exploring Operation: 53*33=1749, Resulting Numbers: [1749] 1749,62 unequal: No Solution Exploring Operation: 53-33=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 53+33=86, Resulting Numbers: [86] 86,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 62:[58, 78], Operations: ['74-16=58', '53+25=78'] Exploring Operation: 58+78=136, Resulting Numbers: [136] 136,62 unequal: No Solution Exploring Operation: 58*78=4524, Resulting Numbers: [4524] 4524,62 unequal: No Solution Exploring Operation: 78-58=20, Resulting Numbers: [20] 20,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 62:[53, 83], Operations: ['74-16=58', '25+58=83'] Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 53*83=4399, Resulting Numbers: [4399] 4399,62 unequal: No Solution Exploring Operation: 53+83=136, Resulting Numbers: [136] 136,62 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: 62:[25, 74, 37], Operations: ['53-16=37'] Exploring Operation: 74-25=49, Resulting Numbers: [37, 49] Generated Node #0,1,0: 62:[37, 49] Operation: 74-25=49 Exploring Operation: 74/37=2, Resulting Numbers: [25, 2] Generated Node #0,1,1: 62:[25, 2] Operation: 74/37=2 Exploring Operation: 25+37=62, Resulting Numbers: [74, 62] Generated Node #0,1,2: 62:[74, 62] Operation: 25+37=62 Exploring Operation: 37-25=12, Resulting Numbers: [74, 12] Generated Node #0,1,3: 62:[74, 12] Operation: 37-25=12 Exploring Operation: 74-37=37, Resulting Numbers: [25, 37] Generated Node #0,1,4: 62:[25, 37] Operation: 74-37=37 Moving to Node #0,4 Current State: 62:[25, 74, 69], Operations: ['53+16=69'] Exploring Operation: 25+69=94, Resulting Numbers: [74, 94] Generated Node #0,4,0: 62:[74, 94] Operation: 25+69=94 Exploring Operation: 69-25=44, Resulting Numbers: [74, 44] Generated Node #0,4,1: 62:[74, 44] Operation: 69-25=44 Exploring Operation: 74-25=49, Resulting Numbers: [69, 49] Generated Node #0,4,2: 62:[69, 49] Operation: 74-25=49 Exploring Operation: 25+74=99, Resulting Numbers: [69, 99] Generated Node #0,4,3: 62:[69, 99] Operation: 25+74=99 Exploring Operation: 74-69=5, Resulting Numbers: [25, 5] Generated Node #0,4,4: 62:[25, 5] Operation: 74-69=5 Moving to Node #0,3 Current State: 62:[53, 74, 9], Operations: ['25-16=9'] Exploring Operation: 53+9=62, Resulting Numbers: [74, 62] Generated Node #0,3,0: 62:[74, 62] Operation: 53+9=62 Exploring Operation: 74-53=21, Resulting Numbers: [9, 21] Generated Node #0,3,1: 62:[9, 21] Operation: 74-53=21 Exploring Operation: 74-9=65, Resulting Numbers: [53, 65] Generated Node #0,3,2: 62:[53, 65] Operation: 74-9=65 Exploring Operation: 74+9=83, Resulting Numbers: [53, 83] Generated Node #0,3,3: 62:[53, 83] Operation: 74+9=83 Exploring Operation: 53-9=44, Resulting Numbers: [74, 44] Generated Node #0,3,4: 62:[74, 44] Operation: 53-9=44 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[74, 62], Operations: ['25-16=9', '53+9=62'] Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,62 unequal: No Solution Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,62 unequal: No Solution Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 62:[53, 65], Operations: ['25-16=9', '74-9=65'] Exploring Operation: 65-53=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 53*65=3445, Resulting Numbers: [3445] 3445,62 unequal: No Solution Exploring Operation: 53+65=118, Resulting Numbers: [118] 118,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 62:[9, 21], Operations: ['25-16=9', '74-53=21'] Exploring Operation: 9+21=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 9*21=189, Resulting Numbers: [189] 189,62 unequal: No Solution Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 62:[74, 44], Operations: ['25-16=9', '53-9=44'] Exploring Operation: 74*44=3256, Resulting Numbers: [3256] 3256,62 unequal: No Solution Exploring Operation: 74-44=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 74+44=118, Resulting Numbers: [118] 118,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 62:[53, 83], Operations: ['25-16=9', '74+9=83'] Exploring Operation: 83-53=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 53+83=136, Resulting Numbers: [136] 136,62 unequal: No Solution Exploring Operation: 53*83=4399, Resulting Numbers: [4399] 4399,62 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: 62:[16, 74, 28], Operations: ['53-25=28'] Exploring Operation: 16+74=90, Resulting Numbers: [28, 90] Generated Node #0,0,0: 62:[28, 90] Operation: 16+74=90 Exploring Operation: 28-16=12, Resulting Numbers: [74, 12] Generated Node #0,0,1: 62:[74, 12] Operation: 28-16=12 Exploring Operation: 74-16=58, Resulting Numbers: [28, 58] Generated Node #0,0,2: 62:[28, 58] Operation: 74-16=58 Exploring Operation: 74-28=46, Resulting Numbers: [16, 46] Generated Node #0,0,3: 62:[16, 46] Operation: 74-28=46 Exploring Operation: 16+28=44, Resulting Numbers: [74, 44] Generated Node #0,0,4: 62:[74, 44] Operation: 16+28=44 Moving to Node #0,1,1 Current State: 62:[25, 2], Operations: ['53-16=37', '74/37=2'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,62 unequal: No Solution Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,62 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[28, 58], Operations: ['53-25=28', '74-16=58'] Exploring Operation: 58-28=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 28+58=86, Resulting Numbers: [86] 86,62 unequal: No Solution Exploring Operation: 28*58=1624, Resulting Numbers: [1624] 1624,62 unequal: No Solution Moving to Node #0,4,4 Current State: 62:[25, 5], Operations: ['53+16=69', '74-69=5'] Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,62 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,62 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,62 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,62 unequal: No Solution Moving to Node #0,1,4 Current State: 62:[25, 37], Operations: ['53-16=37', '74-37=37'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[53, 16, 25, 74], Operations: [] Exploring Operation: 53-16=37, Resulting Numbers: [25, 74, 37] Generated Node #0,1: 62:[25, 74, 37] Operation: 53-16=37 Moving to Node #0,1 Current State: 62:[25, 74, 37], Operations: ['53-16=37'] Exploring Operation: 74-37=37, Resulting Numbers: [25, 37] Generated Node #0,1,4: 62:[25, 37] Operation: 74-37=37 Moving to Node #0,1,4 Current State: 62:[25, 37], Operations: ['53-16=37', '74-37=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.93316
hs_5
mult_heuristic
[ 92, 28, 22, 18 ]
11
[ "28+18=46", "92/46=2", "22/2=11" ]
Current State: 11:[92, 28, 22, 18], Operations: [] Exploring Operation: 28+18=46, Resulting Numbers: [92, 22, 46] Generated Node #2: [92, 22, 46] from Operation: 28+18=46 Current State: 11:[92, 22, 46], Operations: ['28+18=46'] Exploring Operation: 92/46=2, Resulting Numbers: [22, 2] Generated Node #3: [22, 2] from Operation: 92/46=2 Current State: 11:[22, 2], Operations: ['28+18=46', '92/46=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[92, 28, 22, 18], Operations: [] Exploring Operation: 92-28=64, Resulting Numbers: [22, 18, 64] Generated Node #0,0: 11:[22, 18, 64] Operation: 92-28=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[22, 18, 64], Operations: ['92-28=64'] Exploring Operation: 64-22=42, Resulting Numbers: [18, 42] Generated Node #0,0,0: 11:[18, 42] Operation: 64-22=42 Moving to Node #0,0,0 Current State: 11:[18, 42], Operations: ['92-28=64', '64-22=42'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,11 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 8, 74, 71 ]
97
[ "6*8=48", "74+71=145", "145-48=97" ]
Current State: 97:[6, 8, 74, 71], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [74, 71, 48] Generated Node #2: [74, 71, 48] from Operation: 6*8=48 Current State: 97:[74, 71, 48], Operations: ['6*8=48'] Exploring Operation: 74+71=145, Resulting Numbers: [48, 145] Generated Node #3: [48, 145] from Operation: 74+71=145 Current State: 97:[48, 145], Operations: ['6*8=48', '74+71=145'] Exploring Operation: 145-48=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[6, 8, 74, 71], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [74, 71, 48] Generated Node #0,0: 97:[74, 71, 48] Operation: 6*8=48 Exploring Operation: 6+74=80, Resulting Numbers: [8, 71, 80] Generated Node #0,1: 97:[8, 71, 80] Operation: 6+74=80 Exploring Operation: 6+8=14, Resulting Numbers: [74, 71, 14] Generated Node #0,2: 97:[74, 71, 14] Operation: 6+8=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[74, 71, 48], Operations: ['6*8=48'] Exploring Operation: 74+48=122, Resulting Numbers: [71, 122] Generated Node #0,0,0: 97:[71, 122] Operation: 74+48=122 Exploring Operation: 74+71=145, Resulting Numbers: [48, 145] Generated Node #0,0,1: 97:[48, 145] Operation: 74+71=145 Exploring Operation: 71+48=119, Resulting Numbers: [74, 119] Generated Node #0,0,2: 97:[74, 119] Operation: 71+48=119 Moving to Node #0,0,2 Current State: 97:[74, 119], Operations: ['6*8=48', '71+48=119'] Exploring Operation: 74*119=8806, Resulting Numbers: [8806] 8806,97 unequal: No Solution Exploring Operation: 119-74=45, Resulting Numbers: [45] 45,97 unequal: No Solution Exploring Operation: 74+119=193, Resulting Numbers: [193] 193,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[71, 122], Operations: ['6*8=48', '74+48=122'] Exploring Operation: 71*122=8662, Resulting Numbers: [8662] 8662,97 unequal: No Solution Exploring Operation: 71+122=193, Resulting Numbers: [193] 193,97 unequal: No Solution Exploring Operation: 122-71=51, Resulting Numbers: [51] 51,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[48, 145], Operations: ['6*8=48', '74+71=145'] Exploring Operation: 48*145=6960, Resulting Numbers: [6960] 6960,97 unequal: No Solution Exploring Operation: 145-48=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[6, 8, 74, 71], Operations: [] Exploring Operation: 6*8=48, Resulting Numbers: [74, 71, 48] Generated Node #0,0: 97:[74, 71, 48] Operation: 6*8=48 Moving to Node #0,0 Current State: 97:[74, 71, 48], Operations: ['6*8=48'] Exploring Operation: 74+71=145, Resulting Numbers: [48, 145] Generated Node #0,0,1: 97:[48, 145] Operation: 74+71=145 Moving to Node #0,0,1 Current State: 97:[48, 145], Operations: ['6*8=48', '74+71=145'] Exploring Operation: 145-48=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 9, 29, 81, 14 ]
64
[ "14-9=5", "29*5=145", "145-81=64" ]
Current State: 64:[9, 29, 81, 14], Operations: [] Exploring Operation: 14-9=5, Resulting Numbers: [29, 81, 5] Generated Node #2: [29, 81, 5] from Operation: 14-9=5 Current State: 64:[29, 81, 5], Operations: ['14-9=5'] Exploring Operation: 29*5=145, Resulting Numbers: [81, 145] Generated Node #3: [81, 145] from Operation: 29*5=145 Current State: 64:[81, 145], Operations: ['14-9=5', '29*5=145'] Exploring Operation: 145-81=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[9, 29, 81, 14], Operations: [] Exploring Operation: 81-14=67, Resulting Numbers: [9, 29, 67] Generated Node #0,0: 64:[9, 29, 67] Operation: 81-14=67 Exploring Operation: 81/9=9, Resulting Numbers: [29, 14, 9] Generated Node #0,1: 64:[29, 14, 9] Operation: 81/9=9 Exploring Operation: 81-9=72, Resulting Numbers: [29, 14, 72] Generated Node #0,2: 64:[29, 14, 72] Operation: 81-9=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 64:[29, 14, 9], Operations: ['81/9=9'] Exploring Operation: 29-9=20, Resulting Numbers: [14, 20] Generated Node #0,1,0: 64:[14, 20] Operation: 29-9=20 Exploring Operation: 29-14=15, Resulting Numbers: [9, 15] Generated Node #0,1,1: 64:[9, 15] Operation: 29-14=15 Exploring Operation: 14-9=5, Resulting Numbers: [29, 5] Generated Node #0,1,2: 64:[29, 5] Operation: 14-9=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 64:[9, 15], Operations: ['81/9=9', '29-14=15'] Exploring Operation: 9*15=135, Resulting Numbers: [135] 135,64 unequal: No Solution Exploring Operation: 9+15=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 15-9=6, Resulting Numbers: [6] 6,64 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 #0,1,2 Current State: 64:[29, 5], Operations: ['81/9=9', '14-9=5'] Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,64 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,64 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,64 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 #0,1,0 Current State: 64:[14, 20], Operations: ['81/9=9', '29-9=20'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,64 unequal: No Solution Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,64 unequal: No Solution Exploring Operation: 14*20=280, Resulting Numbers: [280] 280,64 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:[9, 29, 67], Operations: ['81-14=67'] Exploring Operation: 67-29=38, Resulting Numbers: [9, 38] Generated Node #0,0,0: 64:[9, 38] Operation: 67-29=38 Exploring Operation: 29-9=20, Resulting Numbers: [67, 20] Generated Node #0,0,1: 64:[67, 20] Operation: 29-9=20 Exploring Operation: 9+29=38, Resulting Numbers: [67, 38] Generated Node #0,0,2: 64:[67, 38] Operation: 9+29=38 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[9, 38], Operations: ['81-14=67', '67-29=38'] Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,64 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,64 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 #0,0,1 Current State: 64:[67, 20], Operations: ['81-14=67', '29-9=20'] Exploring Operation: 67*20=1340, Resulting Numbers: [1340] 1340,64 unequal: No Solution Exploring Operation: 67-20=47, Resulting Numbers: [47] 47,64 unequal: No Solution Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,64 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 #0,0,2 Current State: 64:[67, 38], Operations: ['81-14=67', '9+29=38'] Exploring Operation: 67*38=2546, Resulting Numbers: [2546] 2546,64 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,64 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 #0,2 Current State: 64:[29, 14, 72], Operations: ['81-9=72'] Exploring Operation: 29-14=15, Resulting Numbers: [72, 15] Generated Node #0,2,0: 64:[72, 15] Operation: 29-14=15 Exploring Operation: 72-29=43, Resulting Numbers: [14, 43] Generated Node #0,2,1: 64:[14, 43] Operation: 72-29=43 Exploring Operation: 72-14=58, Resulting Numbers: [29, 58] Generated Node #0,2,2: 64:[29, 58] Operation: 72-14=58 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[72, 15], Operations: ['81-9=72', '29-14=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,64 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,64 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 #0,2,2 Current State: 64:[29, 58], Operations: ['81-9=72', '72-14=58'] Exploring Operation: 29+58=87, Resulting Numbers: [87] 87,64 unequal: No Solution Exploring Operation: 58-29=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 58/29=2, Resulting Numbers: [2] 2,64 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 #0,2,1 Current State: 64:[14, 43], Operations: ['81-9=72', '72-29=43'] Exploring Operation: 14+43=57, Resulting Numbers: [57] 57,64 unequal: No Solution Exploring Operation: 43-14=29, Resulting Numbers: [29] 29,64 unequal: No Solution Exploring Operation: 14*43=602, Resulting Numbers: [602] 602,64 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 No solution found.
0
hs_3
sum_heuristic
[ 47, 86, 76, 90 ]
53
[ "86-47=39", "90-76=14", "39+14=53" ]
Current State: 53:[47, 86, 76, 90], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [76, 90, 39] Generated Node #2: [76, 90, 39] from Operation: 86-47=39 Current State: 53:[76, 90, 39], Operations: ['86-47=39'] Exploring Operation: 90-76=14, Resulting Numbers: [39, 14] Generated Node #3: [39, 14] from Operation: 90-76=14 Current State: 53:[39, 14], Operations: ['86-47=39', '90-76=14'] Exploring Operation: 39+14=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[47, 86, 76, 90], Operations: [] Exploring Operation: 90-47=43, Resulting Numbers: [86, 76, 43] Generated Node #0,0: 53:[86, 76, 43] Operation: 90-47=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[86, 76, 43], Operations: ['90-47=43'] Exploring Operation: 86-43=43, Resulting Numbers: [76, 43] Generated Node #0,0,0: 53:[76, 43] Operation: 86-43=43 Moving to Node #0,0,0 Current State: 53:[76, 43], Operations: ['90-47=43', '86-43=43'] Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,53 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
[ 44, 5, 26, 30 ]
53
[ "44+5=49", "30-26=4", "49+4=53" ]
Current State: 53:[44, 5, 26, 30], Operations: [] Exploring Operation: 44+5=49, Resulting Numbers: [26, 30, 49] Generated Node #2: [26, 30, 49] from Operation: 44+5=49 Current State: 53:[26, 30, 49], Operations: ['44+5=49'] Exploring Operation: 30-26=4, Resulting Numbers: [49, 4] Generated Node #3: [49, 4] from Operation: 30-26=4 Current State: 53:[49, 4], Operations: ['44+5=49', '30-26=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[44, 5, 26, 30], Operations: [] Exploring Operation: 44+5=49, Resulting Numbers: [26, 30, 49] Generated Node #0,0: 53:[26, 30, 49] Operation: 44+5=49 Exploring Operation: 5+26=31, Resulting Numbers: [44, 30, 31] Generated Node #0,1: 53:[44, 30, 31] Operation: 5+26=31 Exploring Operation: 5+30=35, Resulting Numbers: [44, 26, 35] Generated Node #0,2: 53:[44, 26, 35] Operation: 5+30=35 Moving to Node #0,0 Current State: 53:[26, 30, 49], Operations: ['44+5=49'] Exploring Operation: 26+30=56, Resulting Numbers: [49, 56] Generated Node #0,0,0: 53:[49, 56] Operation: 26+30=56 Exploring Operation: 26+49=75, Resulting Numbers: [30, 75] Generated Node #0,0,1: 53:[30, 75] Operation: 26+49=75 Exploring Operation: 30-26=4, Resulting Numbers: [49, 4] Generated Node #0,0,2: 53:[49, 4] Operation: 30-26=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[49, 56], Operations: ['44+5=49', '26+30=56'] Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,53 unequal: No Solution Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[30, 75], Operations: ['44+5=49', '26+49=75'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 30+75=105, Resulting Numbers: [105] 105,53 unequal: No Solution Exploring Operation: 30*75=2250, Resulting Numbers: [2250] 2250,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 53:[49, 4], Operations: ['44+5=49', '30-26=4'] Exploring Operation: 49*4=196, Resulting Numbers: [196] 196,53 unequal: No Solution Exploring Operation: 49-4=45, Resulting Numbers: [45] 45,53 unequal: No Solution Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[44, 5, 26, 30], Operations: [] Exploring Operation: 44+5=49, Resulting Numbers: [26, 30, 49] Generated Node #0,0: 53:[26, 30, 49] Operation: 44+5=49 Moving to Node #0,0 Current State: 53:[26, 30, 49], Operations: ['44+5=49'] Exploring Operation: 30-26=4, Resulting Numbers: [49, 4] Generated Node #0,0,2: 53:[49, 4] Operation: 30-26=4 Moving to Node #0,0,2 Current State: 53:[49, 4], Operations: ['44+5=49', '30-26=4'] Exploring Operation: 49+4=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic
[ 23, 49, 6, 2 ]
15
[ "23-6=17", "2*17=34", "49-34=15" ]
Current State: 15:[23, 49, 6, 2], Operations: [] Exploring Operation: 23-6=17, Resulting Numbers: [49, 2, 17] Generated Node #2: [49, 2, 17] from Operation: 23-6=17 Current State: 15:[49, 2, 17], Operations: ['23-6=17'] Exploring Operation: 2*17=34, Resulting Numbers: [49, 34] Generated Node #3: [49, 34] from Operation: 2*17=34 Current State: 15:[49, 34], Operations: ['23-6=17', '2*17=34'] Exploring Operation: 49-34=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[23, 49, 6, 2], Operations: [] Exploring Operation: 23-6=17, Resulting Numbers: [49, 2, 17] Generated Node #0,0: 15:[49, 2, 17] Operation: 23-6=17 Exploring Operation: 49-23=26, Resulting Numbers: [6, 2, 26] Generated Node #0,1: 15:[6, 2, 26] Operation: 49-23=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[6, 2, 26], Operations: ['49-23=26'] Exploring Operation: 26-6=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 15:[2, 20] Operation: 26-6=20 Exploring Operation: 26/2=13, Resulting Numbers: [6, 13] Generated Node #0,1,1: 15:[6, 13] Operation: 26/2=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 15:[6, 13], Operations: ['49-23=26', '26/2=13'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,15 unequal: No Solution Exploring Operation: 6+13=19, Resulting Numbers: [19] 19,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 15:[2, 20], Operations: ['49-23=26', '26-6=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,15 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[49, 2, 17], Operations: ['23-6=17'] Exploring Operation: 49-2=47, Resulting Numbers: [17, 47] Generated Node #0,0,0: 15:[17, 47] Operation: 49-2=47 Exploring Operation: 49-17=32, Resulting Numbers: [2, 32] Generated Node #0,0,1: 15:[2, 32] Operation: 49-17=32 Moving to Node #0,0,1 Current State: 15:[2, 32], Operations: ['23-6=17', '49-17=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,15 unequal: No Solution Moving to Node #0,0,0 Current State: 15:[17, 47], Operations: ['23-6=17', '49-2=47'] Exploring Operation: 47-17=30, Resulting Numbers: [30] 30,15 unequal: No Solution Exploring Operation: 17+47=64, Resulting Numbers: [64] 64,15 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
[ 32, 85, 81, 77 ]
30
[ "85+77=162", "162/81=2", "32-2=30" ]
Current State: 30:[32, 85, 81, 77], Operations: [] Exploring Operation: 85+77=162, Resulting Numbers: [32, 81, 162] Generated Node #2: [32, 81, 162] from Operation: 85+77=162 Current State: 30:[32, 81, 162], Operations: ['85+77=162'] Exploring Operation: 162/81=2, Resulting Numbers: [32, 2] Generated Node #3: [32, 2] from Operation: 162/81=2 Current State: 30:[32, 2], Operations: ['85+77=162', '162/81=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[32, 85, 81, 77], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [32, 77, 4] Generated Node #0,0: 30:[32, 77, 4] Operation: 85-81=4 Exploring Operation: 85-77=8, Resulting Numbers: [32, 81, 8] Generated Node #0,1: 30:[32, 81, 8] Operation: 85-77=8 Moving to Node #0,0 Current State: 30:[32, 77, 4], Operations: ['85-81=4'] Exploring Operation: 77-4=73, Resulting Numbers: [32, 73] Generated Node #0,0,0: 30:[32, 73] Operation: 77-4=73 Exploring Operation: 77-32=45, Resulting Numbers: [4, 45] Generated Node #0,0,1: 30:[4, 45] Operation: 77-32=45 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[4, 45], Operations: ['85-81=4', '77-32=45'] Exploring Operation: 4+45=49, Resulting Numbers: [49] 49,30 unequal: No Solution Exploring Operation: 45-4=41, Resulting Numbers: [41] 41,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[32, 73], Operations: ['85-81=4', '77-4=73'] Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,30 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: 30:[32, 81, 8], Operations: ['85-77=8'] Exploring Operation: 81-32=49, Resulting Numbers: [8, 49] Generated Node #0,1,0: 30:[8, 49] Operation: 81-32=49 Exploring Operation: 81-8=73, Resulting Numbers: [32, 73] Generated Node #0,1,1: 30:[32, 73] Operation: 81-8=73 Moving to Node #0,1,0 Current State: 30:[8, 49], Operations: ['85-77=8', '81-32=49'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 8+49=57, Resulting Numbers: [57] 57,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[32, 73], Operations: ['85-77=8', '81-8=73'] Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,30 unequal: No Solution Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,30 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 87, 21, 7, 70 ]
14
[ "87-70=17", "21/7=3", "17-3=14" ]
Current State: 14:[87, 21, 7, 70], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [21, 7, 17] Generated Node #2: [21, 7, 17] from Operation: 87-70=17 Current State: 14:[21, 7, 17], Operations: ['87-70=17'] Exploring Operation: 21/7=3, Resulting Numbers: [17, 3] Generated Node #3: [17, 3] from Operation: 21/7=3 Current State: 14:[17, 3], Operations: ['87-70=17', '21/7=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[87, 21, 7, 70], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [21, 7, 17] Generated Node #0,0: 14:[21, 7, 17] Operation: 87-70=17 Exploring Operation: 70/7=10, Resulting Numbers: [87, 21, 10] Generated Node #0,1: 14:[87, 21, 10] Operation: 70/7=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[21, 7, 17], Operations: ['87-70=17'] Exploring Operation: 21-17=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 14:[7, 4] Operation: 21-17=4 Exploring Operation: 21-7=14, Resulting Numbers: [17, 14] Generated Node #0,0,1: 14:[17, 14] Operation: 21-7=14 Moving to Node #0,0,0 Current State: 14:[7, 4], Operations: ['87-70=17', '21-17=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 Moving to Node #0,0,1 Current State: 14:[17, 14], Operations: ['87-70=17', '21-7=14'] Exploring Operation: 17-14=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 17+14=31, Resulting Numbers: [31] 31,14 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 Current State: 14:[87, 21, 10], Operations: ['70/7=10'] Exploring Operation: 87-10=77, Resulting Numbers: [21, 77] Generated Node #0,1,0: 14:[21, 77] Operation: 87-10=77 Exploring Operation: 87-21=66, Resulting Numbers: [10, 66] Generated Node #0,1,1: 14:[10, 66] Operation: 87-21=66 Moving to Node #0,1,1 Current State: 14:[10, 66], Operations: ['70/7=10', '87-21=66'] Exploring Operation: 10+66=76, Resulting Numbers: [76] 76,14 unequal: No Solution Exploring Operation: 66-10=56, Resulting Numbers: [56] 56,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[21, 77], Operations: ['70/7=10', '87-10=77'] Exploring Operation: 21+77=98, Resulting Numbers: [98] 98,14 unequal: No Solution Exploring Operation: 77-21=56, Resulting Numbers: [56] 56,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 52, 78, 26, 42 ]
94
[ "78-52=26", "26+42=68", "26+68=94" ]
Current State: 94:[52, 78, 26, 42], Operations: [] Exploring Operation: 78-52=26, Resulting Numbers: [26, 42, 26] Generated Node #2: [26, 42, 26] from Operation: 78-52=26 Current State: 94:[26, 42, 26], Operations: ['78-52=26'] Exploring Operation: 26+42=68, Resulting Numbers: [68] 68,94 equal: Goal Reached Exploring Operation: 26+68=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[52, 78, 26, 42], Operations: [] Exploring Operation: 78/26=3, Resulting Numbers: [52, 42, 3] Generated Node #0,0: 94:[52, 42, 3] Operation: 78/26=3 Exploring Operation: 78+26=104, Resulting Numbers: [52, 42, 104] Generated Node #0,1: 94:[52, 42, 104] Operation: 78+26=104 Exploring Operation: 78-26=52, Resulting Numbers: [52, 42, 52] Generated Node #0,2: 94:[52, 42, 52] Operation: 78-26=52 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[52, 42, 3], Operations: ['78/26=3'] Exploring Operation: 52-3=49, Resulting Numbers: [42, 49] Generated Node #0,0,0: 94:[42, 49] Operation: 52-3=49 Exploring Operation: 42+3=45, Resulting Numbers: [52, 45] Generated Node #0,0,1: 94:[52, 45] Operation: 42+3=45 Exploring Operation: 52+42=94, Resulting Numbers: [3, 94] Generated Node #0,0,2: 94:[3, 94] Operation: 52+42=94 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[3, 94], Operations: ['78/26=3', '52+42=94'] Exploring Operation: 3+94=97, Resulting Numbers: [97] 97,94 unequal: No Solution Exploring Operation: 3*94=282, Resulting Numbers: [282] 282,94 unequal: No Solution Exploring Operation: 94-3=91, Resulting Numbers: [91] 91,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[42, 49], Operations: ['78/26=3', '52-3=49'] Exploring Operation: 42+49=91, Resulting Numbers: [91] 91,94 unequal: No Solution Exploring Operation: 42*49=2058, Resulting Numbers: [2058] 2058,94 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[52, 45], Operations: ['78/26=3', '42+3=45'] Exploring Operation: 52*45=2340, Resulting Numbers: [2340] 2340,94 unequal: No Solution Exploring Operation: 52-45=7, Resulting Numbers: [7] 7,94 unequal: No Solution Exploring Operation: 52+45=97, Resulting Numbers: [97] 97,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[52, 42, 52], Operations: ['78-26=52'] Exploring Operation: 42+52=94, Resulting Numbers: [52, 94] Generated Node #0,2,0: 94:[52, 94] Operation: 42+52=94 Exploring Operation: 52+42=94, Resulting Numbers: [52, 94] Generated Node #0,2,1: 94:[52, 94] Operation: 52+42=94 Exploring Operation: 52/52=1, Resulting Numbers: [42, 1] Generated Node #0,2,2: 94:[42, 1] Operation: 52/52=1 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[52, 94], Operations: ['78-26=52', '42+52=94'] Exploring Operation: 52+94=146, Resulting Numbers: [146] 146,94 unequal: No Solution Exploring Operation: 52*94=4888, Resulting Numbers: [4888] 4888,94 unequal: No Solution Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[52, 94], Operations: ['78-26=52', '52+42=94'] Exploring Operation: 52*94=4888, Resulting Numbers: [4888] 4888,94 unequal: No Solution Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 52+94=146, Resulting Numbers: [146] 146,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[42, 1], Operations: ['78-26=52', '52/52=1'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 42+1=43, Resulting Numbers: [43] 43,94 unequal: No Solution Exploring Operation: 42*1=42, Resulting Numbers: [42] 42,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[52, 42, 104], Operations: ['78+26=104'] Exploring Operation: 104/52=2, Resulting Numbers: [42, 2] Generated Node #0,1,0: 94:[42, 2] Operation: 104/52=2 Exploring Operation: 104-52=52, Resulting Numbers: [42, 52] Generated Node #0,1,1: 94:[42, 52] Operation: 104-52=52 Exploring Operation: 52+42=94, Resulting Numbers: [104, 94] Generated Node #0,1,2: 94:[104, 94] Operation: 52+42=94 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[42, 2], Operations: ['78+26=104', '104/52=2'] Exploring Operation: 42-2=40, Resulting Numbers: [40] 40,94 unequal: No Solution Exploring Operation: 42+2=44, Resulting Numbers: [44] 44,94 unequal: No Solution Exploring Operation: 42*2=84, Resulting Numbers: [84] 84,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[42, 52], Operations: ['78+26=104', '104-52=52'] Exploring Operation: 52-42=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 42+52=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[52, 78, 26, 42], Operations: [] Exploring Operation: 78+26=104, Resulting Numbers: [52, 42, 104] Generated Node #0,1: 94:[52, 42, 104] Operation: 78+26=104 Moving to Node #0,1 Current State: 94:[52, 42, 104], Operations: ['78+26=104'] Exploring Operation: 104-52=52, Resulting Numbers: [42, 52] Generated Node #0,1,1: 94:[42, 52] Operation: 104-52=52 Moving to Node #0,1,1 Current State: 94:[42, 52], Operations: ['78+26=104', '104-52=52'] Exploring Operation: 42+52=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.966146
hs_3
mult_heuristic
[ 29, 6, 12, 25 ]
54
[ "29-25=4", "12*4=48", "6+48=54" ]
Current State: 54:[29, 6, 12, 25], Operations: [] Exploring Operation: 29-25=4, Resulting Numbers: [6, 12, 4] Generated Node #2: [6, 12, 4] from Operation: 29-25=4 Current State: 54:[6, 12, 4], Operations: ['29-25=4'] Exploring Operation: 12*4=48, Resulting Numbers: [6, 48] Generated Node #3: [6, 48] from Operation: 12*4=48 Current State: 54:[6, 48], Operations: ['29-25=4', '12*4=48'] Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[29, 6, 12, 25], Operations: [] Exploring Operation: 6+12=18, Resulting Numbers: [29, 25, 18] Generated Node #0,0: 54:[29, 25, 18] Operation: 6+12=18 Exploring Operation: 29+25=54, Resulting Numbers: [6, 12, 54] Generated Node #0,1: 54:[6, 12, 54] Operation: 29+25=54 Exploring Operation: 29-25=4, Resulting Numbers: [6, 12, 4] Generated Node #0,2: 54:[6, 12, 4] Operation: 29-25=4 Exploring Operation: 29-12=17, Resulting Numbers: [6, 25, 17] Generated Node #0,3: 54:[6, 25, 17] Operation: 29-12=17 Moving to Node #0,1 Current State: 54:[6, 12, 54], Operations: ['29+25=54'] Exploring Operation: 54/6=9, Resulting Numbers: [12, 9] Generated Node #0,1,0: 54:[12, 9] Operation: 54/6=9 Exploring Operation: 12-6=6, Resulting Numbers: [54, 6] Generated Node #0,1,1: 54:[54, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [54, 2] Generated Node #0,1,2: 54:[54, 2] Operation: 12/6=2 Exploring Operation: 6+12=18, Resulting Numbers: [54, 18] Generated Node #0,1,3: 54:[54, 18] Operation: 6+12=18 Moving to Node #0,3 Current State: 54:[6, 25, 17], Operations: ['29-12=17'] Exploring Operation: 6+25=31, Resulting Numbers: [17, 31] Generated Node #0,3,0: 54:[17, 31] Operation: 6+25=31 Exploring Operation: 25-6=19, Resulting Numbers: [17, 19] Generated Node #0,3,1: 54:[17, 19] Operation: 25-6=19 Exploring Operation: 17-6=11, Resulting Numbers: [25, 11] Generated Node #0,3,2: 54:[25, 11] Operation: 17-6=11 Exploring Operation: 25-17=8, Resulting Numbers: [6, 8] Generated Node #0,3,3: 54:[6, 8] Operation: 25-17=8 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 54:[6, 8], Operations: ['29-12=17', '25-17=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,54 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 #0,3,1 Current State: 54:[17, 19], Operations: ['29-12=17', '25-6=19'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 17+19=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 17*19=323, Resulting Numbers: [323] 323,54 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 #0,3,2 Current State: 54:[25, 11], Operations: ['29-12=17', '17-6=11'] Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,54 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,54 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 #0,3,0 Current State: 54:[17, 31], Operations: ['29-12=17', '6+25=31'] Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 17+31=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 17*31=527, Resulting Numbers: [527] 527,54 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: 54:[6, 12, 4], Operations: ['29-25=4'] Exploring Operation: 12/4=3, Resulting Numbers: [6, 3] Generated Node #0,2,0: 54:[6, 3] Operation: 12/4=3 Exploring Operation: 12-6=6, Resulting Numbers: [4, 6] Generated Node #0,2,1: 54:[4, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [4, 2] Generated Node #0,2,2: 54:[4, 2] Operation: 12/6=2 Exploring Operation: 6+12=18, Resulting Numbers: [4, 18] Generated Node #0,2,3: 54:[4, 18] Operation: 6+12=18 Moving to Node #0,0 Current State: 54:[29, 25, 18], Operations: ['6+12=18'] Exploring Operation: 29-25=4, Resulting Numbers: [18, 4] Generated Node #0,0,0: 54:[18, 4] Operation: 29-25=4 Exploring Operation: 29+25=54, Resulting Numbers: [18, 54] Generated Node #0,0,1: 54:[18, 54] Operation: 29+25=54 Exploring Operation: 29-18=11, Resulting Numbers: [25, 11] Generated Node #0,0,2: 54:[25, 11] Operation: 29-18=11 Exploring Operation: 25-18=7, Resulting Numbers: [29, 7] Generated Node #0,0,3: 54:[29, 7] Operation: 25-18=7 Moving to Node #0,1,1 Current State: 54:[54, 6], Operations: ['29+25=54', '12-6=6'] Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,54 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[54, 18], Operations: ['29+25=54', '6+12=18'] Exploring Operation: 54*18=972, Resulting Numbers: [972] 972,54 unequal: No Solution Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[54, 2], Operations: ['29+25=54', '12/6=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,54 unequal: No Solution Exploring Operation: 54*2=108, Resulting Numbers: [108] 108,54 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,54 unequal: No Solution Exploring Operation: 54/2=27, Resulting Numbers: [27] 27,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[6, 3], Operations: ['29-25=4', '12/4=3'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[18, 54], Operations: ['6+12=18', '29+25=54'] Exploring Operation: 18*54=972, Resulting Numbers: [972] 972,54 unequal: No Solution Exploring Operation: 18+54=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,54 unequal: No Solution Moving to Node #0,2,2 Current State: 54:[4, 2], Operations: ['29-25=4', '12/6=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,54 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[4, 6], Operations: ['29-25=4', '12-6=6'] Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[18, 4], Operations: ['6+12=18', '29-25=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[4, 18], Operations: ['29-25=4', '6+12=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[12, 9], Operations: ['29+25=54', '54/6=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,54 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[29, 7], Operations: ['6+12=18', '25-18=7'] Exploring Operation: 29+7=36, Resulting Numbers: [36] 36,54 unequal: No Solution Exploring Operation: 29-7=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 29*7=203, Resulting Numbers: [203] 203,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[25, 11], Operations: ['6+12=18', '29-18=11'] Exploring Operation: 25*11=275, Resulting Numbers: [275] 275,54 unequal: No Solution Exploring Operation: 25-11=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 25+11=36, Resulting Numbers: [36] 36,54 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 12, 24, 7, 86 ]
12
[ "24/12=2", "86-2=84", "84/7=12" ]
Current State: 12:[12, 24, 7, 86], Operations: [] Exploring Operation: 24/12=2, Resulting Numbers: [7, 86, 2] Generated Node #2: [7, 86, 2] from Operation: 24/12=2 Current State: 12:[7, 86, 2], Operations: ['24/12=2'] Exploring Operation: 86-2=84, Resulting Numbers: [7, 84] Generated Node #3: [7, 84] from Operation: 86-2=84 Current State: 12:[7, 84], Operations: ['24/12=2', '86-2=84'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[12, 24, 7, 86], Operations: [] Exploring Operation: 24-7=17, Resulting Numbers: [12, 86, 17] Generated Node #0,0: 12:[12, 86, 17] Operation: 24-7=17 Exploring Operation: 86-12=74, Resulting Numbers: [24, 7, 74] Generated Node #0,1: 12:[24, 7, 74] Operation: 86-12=74 Exploring Operation: 86-24=62, Resulting Numbers: [12, 7, 62] Generated Node #0,2: 12:[12, 7, 62] Operation: 86-24=62 Exploring Operation: 24/12=2, Resulting Numbers: [7, 86, 2] Generated Node #0,3: 12:[7, 86, 2] Operation: 24/12=2 Exploring Operation: 24-12=12, Resulting Numbers: [7, 86, 12] Generated Node #0,4: 12:[7, 86, 12] Operation: 24-12=12 Moving to Node #0,2 Current State: 12:[12, 7, 62], Operations: ['86-24=62'] Exploring Operation: 12-7=5, Resulting Numbers: [62, 5] Generated Node #0,2,0: 12:[62, 5] Operation: 12-7=5 Exploring Operation: 62-12=50, Resulting Numbers: [7, 50] Generated Node #0,2,1: 12:[7, 50] Operation: 62-12=50 Exploring Operation: 7+62=69, Resulting Numbers: [12, 69] Generated Node #0,2,2: 12:[12, 69] Operation: 7+62=69 Exploring Operation: 62-7=55, Resulting Numbers: [12, 55] Generated Node #0,2,3: 12:[12, 55] Operation: 62-7=55 Exploring Operation: 12+7=19, Resulting Numbers: [62, 19] Generated Node #0,2,4: 12:[62, 19] Operation: 12+7=19 Moving to Node #0,3 Current State: 12:[7, 86, 2], Operations: ['24/12=2'] Exploring Operation: 86/2=43, Resulting Numbers: [7, 43] Generated Node #0,3,0: 12:[7, 43] Operation: 86/2=43 Exploring Operation: 7*2=14, Resulting Numbers: [86, 14] Generated Node #0,3,1: 12:[86, 14] Operation: 7*2=14 Exploring Operation: 86-2=84, Resulting Numbers: [7, 84] Generated Node #0,3,2: 12:[7, 84] Operation: 86-2=84 Exploring Operation: 7-2=5, Resulting Numbers: [86, 5] Generated Node #0,3,3: 12:[86, 5] Operation: 7-2=5 Exploring Operation: 86-7=79, Resulting Numbers: [2, 79] Generated Node #0,3,4: 12:[2, 79] Operation: 86-7=79 Moving to Node #0,1 Current State: 12:[24, 7, 74], Operations: ['86-12=74'] Exploring Operation: 74-24=50, Resulting Numbers: [7, 50] Generated Node #0,1,0: 12:[7, 50] Operation: 74-24=50 Exploring Operation: 24-7=17, Resulting Numbers: [74, 17] Generated Node #0,1,1: 12:[74, 17] Operation: 24-7=17 Exploring Operation: 74-7=67, Resulting Numbers: [24, 67] Generated Node #0,1,2: 12:[24, 67] Operation: 74-7=67 Exploring Operation: 7+74=81, Resulting Numbers: [24, 81] Generated Node #0,1,3: 12:[24, 81] Operation: 7+74=81 Exploring Operation: 24+7=31, Resulting Numbers: [74, 31] Generated Node #0,1,4: 12:[74, 31] Operation: 24+7=31 Moving to Node #0,4 Current State: 12:[7, 86, 12], Operations: ['24-12=12'] Exploring Operation: 12-7=5, Resulting Numbers: [86, 5] Generated Node #0,4,0: 12:[86, 5] Operation: 12-7=5 Exploring Operation: 7+86=93, Resulting Numbers: [12, 93] Generated Node #0,4,1: 12:[12, 93] Operation: 7+86=93 Exploring Operation: 7+12=19, Resulting Numbers: [86, 19] Generated Node #0,4,2: 12:[86, 19] Operation: 7+12=19 Exploring Operation: 86-7=79, Resulting Numbers: [12, 79] Generated Node #0,4,3: 12:[12, 79] Operation: 86-7=79 Exploring Operation: 86-12=74, Resulting Numbers: [7, 74] Generated Node #0,4,4: 12:[7, 74] Operation: 86-12=74 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 12:[7, 74], Operations: ['24-12=12', '86-12=74'] Exploring Operation: 7+74=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 7*74=518, Resulting Numbers: [518] 518,12 unequal: No Solution Exploring Operation: 74-7=67, Resulting Numbers: [67] 67,12 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 #0,4,3 Current State: 12:[12, 79], Operations: ['24-12=12', '86-7=79'] Exploring Operation: 12+79=91, Resulting Numbers: [91] 91,12 unequal: No Solution Exploring Operation: 12*79=948, Resulting Numbers: [948] 948,12 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,12 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 #0,4,0 Current State: 12:[86, 5], Operations: ['24-12=12', '12-7=5'] Exploring Operation: 86*5=430, Resulting Numbers: [430] 430,12 unequal: No Solution Exploring Operation: 86+5=91, Resulting Numbers: [91] 91,12 unequal: No Solution Exploring Operation: 86-5=81, Resulting Numbers: [81] 81,12 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 #0,4,1 Current State: 12:[12, 93], Operations: ['24-12=12', '7+86=93'] Exploring Operation: 12+93=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 12*93=1116, Resulting Numbers: [1116] 1116,12 unequal: No Solution Exploring Operation: 93-12=81, Resulting Numbers: [81] 81,12 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 #0,4,2 Current State: 12:[86, 19], Operations: ['24-12=12', '7+12=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,12 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,12 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,12 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: 12:[12, 86, 17], Operations: ['24-7=17'] Exploring Operation: 12+86=98, Resulting Numbers: [17, 98] Generated Node #0,0,0: 12:[17, 98] Operation: 12+86=98 Exploring Operation: 12+17=29, Resulting Numbers: [86, 29] Generated Node #0,0,1: 12:[86, 29] Operation: 12+17=29 Exploring Operation: 86-17=69, Resulting Numbers: [12, 69] Generated Node #0,0,2: 12:[12, 69] Operation: 86-17=69 Exploring Operation: 86-12=74, Resulting Numbers: [17, 74] Generated Node #0,0,3: 12:[17, 74] Operation: 86-12=74 Exploring Operation: 17-12=5, Resulting Numbers: [86, 5] Generated Node #0,0,4: 12:[86, 5] Operation: 17-12=5 Moving to Node #0,3,0 Current State: 12:[7, 43], Operations: ['24/12=2', '86/2=43'] Exploring Operation: 7+43=50, Resulting Numbers: [50] 50,12 unequal: No Solution Exploring Operation: 43-7=36, Resulting Numbers: [36] 36,12 unequal: No Solution Exploring Operation: 7*43=301, Resulting Numbers: [301] 301,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[7, 50], Operations: ['86-24=62', '62-12=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,12 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[7, 50], Operations: ['86-12=74', '74-24=50'] Exploring Operation: 7+50=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 50-7=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 7*50=350, Resulting Numbers: [350] 350,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[12, 55], Operations: ['86-24=62', '62-7=55'] Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 12+55=67, Resulting Numbers: [67] 67,12 unequal: No Solution Exploring Operation: 12*55=660, Resulting Numbers: [660] 660,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[62, 5], Operations: ['86-24=62', '12-7=5'] Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,12 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,12 unequal: No Solution Moving to Node #0,2,4 Current State: 12:[62, 19], Operations: ['86-24=62', '12+7=19'] Exploring Operation: 62+19=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 62*19=1178, Resulting Numbers: [1178] 1178,12 unequal: No Solution Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[12, 69], Operations: ['86-24=62', '7+62=69'] Exploring Operation: 12+69=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 12*69=828, Resulting Numbers: [828] 828,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[12, 69], Operations: ['24-7=17', '86-17=69'] Exploring Operation: 12+69=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 12*69=828, Resulting Numbers: [828] 828,12 unequal: No Solution Exploring Operation: 69-12=57, Resulting Numbers: [57] 57,12 unequal: No Solution Moving to Node #0,3,4 Current State: 12:[2, 79], Operations: ['24/12=2', '86-7=79'] Exploring Operation: 2+79=81, Resulting Numbers: [81] 81,12 unequal: No Solution Exploring Operation: 79-2=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 2*79=158, Resulting Numbers: [158] 158,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[17, 74], Operations: ['24-7=17', '86-12=74'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,12 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[24, 67], Operations: ['86-12=74', '74-7=67'] Exploring Operation: 24*67=1608, Resulting Numbers: [1608] 1608,12 unequal: No Solution Exploring Operation: 67-24=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 24+67=91, Resulting Numbers: [91] 91,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[74, 17], Operations: ['86-12=74', '24-7=17'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,12 unequal: No Solution Exploring Operation: 74*17=1258, Resulting Numbers: [1258] 1258,12 unequal: No Solution Exploring Operation: 74+17=91, Resulting Numbers: [91] 91,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[7, 84], Operations: ['24/12=2', '86-2=84'] Exploring Operation: 84-7=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 7+84=91, Resulting Numbers: [91] 91,12 unequal: No Solution Exploring Operation: 7*84=588, Resulting Numbers: [588] 588,12 unequal: No Solution Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[12, 24, 7, 86], Operations: [] Exploring Operation: 24/12=2, Resulting Numbers: [7, 86, 2] Generated Node #0,3: 12:[7, 86, 2] Operation: 24/12=2 Moving to Node #0,3 Current State: 12:[7, 86, 2], Operations: ['24/12=2'] Exploring Operation: 86-2=84, Resulting Numbers: [7, 84] Generated Node #0,3,2: 12:[7, 84] Operation: 86-2=84 Moving to Node #0,3,2 Current State: 12:[7, 84], Operations: ['24/12=2', '86-2=84'] Exploring Operation: 84/7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.922743
hs_5
mult_heuristic
[ 74, 68, 4, 81 ]
79
[ "74-68=6", "4+81=85", "85-6=79" ]
Current State: 79:[74, 68, 4, 81], Operations: [] Exploring Operation: 74-68=6, Resulting Numbers: [4, 81, 6] Generated Node #2: [4, 81, 6] from Operation: 74-68=6 Current State: 79:[4, 81, 6], Operations: ['74-68=6'] Exploring Operation: 4+81=85, Resulting Numbers: [6, 85] Generated Node #3: [6, 85] from Operation: 4+81=85 Current State: 79:[6, 85], Operations: ['74-68=6', '4+81=85'] Exploring Operation: 85-6=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[74, 68, 4, 81], Operations: [] Exploring Operation: 68+4=72, Resulting Numbers: [74, 81, 72] Generated Node #0,0: 79:[74, 81, 72] Operation: 68+4=72 Exploring Operation: 74+4=78, Resulting Numbers: [68, 81, 78] Generated Node #0,1: 79:[68, 81, 78] Operation: 74+4=78 Exploring Operation: 81-4=77, Resulting Numbers: [74, 68, 77] Generated Node #0,2: 79:[74, 68, 77] Operation: 81-4=77 Moving to Node #0,0 Current State: 79:[74, 81, 72], Operations: ['68+4=72'] Exploring Operation: 81-74=7, Resulting Numbers: [72, 7] Generated Node #0,0,0: 79:[72, 7] Operation: 81-74=7 Exploring Operation: 74+72=146, Resulting Numbers: [81, 146] Generated Node #0,0,1: 79:[81, 146] Operation: 74+72=146 Exploring Operation: 81-72=9, Resulting Numbers: [74, 9] Generated Node #0,0,2: 79:[74, 9] Operation: 81-72=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[81, 146], Operations: ['68+4=72', '74+72=146'] Exploring Operation: 81+146=227, Resulting Numbers: [227] 227,79 unequal: No Solution Exploring Operation: 146-81=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 81*146=11826, Resulting Numbers: [11826] 11826,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[74, 9], Operations: ['68+4=72', '81-72=9'] Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,79 unequal: No Solution Exploring Operation: 74*9=666, Resulting Numbers: [666] 666,79 unequal: No Solution Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[72, 7], Operations: ['68+4=72', '81-74=7'] Exploring Operation: 72*7=504, Resulting Numbers: [504] 504,79 unequal: No Solution Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[74, 68, 4, 81], Operations: [] Exploring Operation: 68+4=72, Resulting Numbers: [74, 81, 72] Generated Node #0,0: 79:[74, 81, 72] Operation: 68+4=72 Moving to Node #0,0 Current State: 79:[74, 81, 72], Operations: ['68+4=72'] Exploring Operation: 81-74=7, Resulting Numbers: [72, 7] Generated Node #0,0,0: 79:[72, 7] Operation: 81-74=7 Moving to Node #0,0,0 Current State: 79:[72, 7], Operations: ['68+4=72', '81-74=7'] Exploring Operation: 72+7=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 54, 70, 47, 12 ]
22
[ "54-47=7", "70/7=10", "12+10=22" ]
Current State: 22:[54, 70, 47, 12], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [70, 12, 7] Generated Node #2: [70, 12, 7] from Operation: 54-47=7 Current State: 22:[70, 12, 7], Operations: ['54-47=7'] Exploring Operation: 70/7=10, Resulting Numbers: [12, 10] Generated Node #3: [12, 10] from Operation: 70/7=10 Current State: 22:[12, 10], Operations: ['54-47=7', '70/7=10'] Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[54, 70, 47, 12], Operations: [] Exploring Operation: 70-54=16, Resulting Numbers: [47, 12, 16] Generated Node #0,0: 22:[47, 12, 16] Operation: 70-54=16 Exploring Operation: 54-47=7, Resulting Numbers: [70, 12, 7] Generated Node #0,1: 22:[70, 12, 7] Operation: 54-47=7 Exploring Operation: 70-47=23, Resulting Numbers: [54, 12, 23] Generated Node #0,2: 22:[54, 12, 23] Operation: 70-47=23 Moving to Node #0,0 Current State: 22:[47, 12, 16], Operations: ['70-54=16'] Exploring Operation: 16-12=4, Resulting Numbers: [47, 4] Generated Node #0,0,0: 22:[47, 4] Operation: 16-12=4 Exploring Operation: 47-12=35, Resulting Numbers: [16, 35] Generated Node #0,0,1: 22:[16, 35] Operation: 47-12=35 Exploring Operation: 47-16=31, Resulting Numbers: [12, 31] Generated Node #0,0,2: 22:[12, 31] Operation: 47-16=31 Moving to Node #0,2 Current State: 22:[54, 12, 23], Operations: ['70-47=23'] Exploring Operation: 23-12=11, Resulting Numbers: [54, 11] Generated Node #0,2,0: 22:[54, 11] Operation: 23-12=11 Exploring Operation: 54-23=31, Resulting Numbers: [12, 31] Generated Node #0,2,1: 22:[12, 31] Operation: 54-23=31 Exploring Operation: 54-12=42, Resulting Numbers: [23, 42] Generated Node #0,2,2: 22:[23, 42] Operation: 54-12=42 Moving to Node #0,1 Current State: 22:[70, 12, 7], Operations: ['54-47=7'] Exploring Operation: 70/7=10, Resulting Numbers: [12, 10] Generated Node #0,1,0: 22:[12, 10] Operation: 70/7=10 Exploring Operation: 70-12=58, Resulting Numbers: [7, 58] Generated Node #0,1,1: 22:[7, 58] Operation: 70-12=58 Exploring Operation: 70-7=63, Resulting Numbers: [12, 63] Generated Node #0,1,2: 22:[12, 63] Operation: 70-7=63 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[12, 10], Operations: ['54-47=7', '70/7=10'] Exploring Operation: 12*10=120, Resulting Numbers: [120] 120,22 unequal: No Solution Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[54, 70, 47, 12], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [70, 12, 7] Generated Node #0,1: 22:[70, 12, 7] Operation: 54-47=7 Moving to Node #0,1 Current State: 22:[70, 12, 7], Operations: ['54-47=7'] Exploring Operation: 70/7=10, Resulting Numbers: [12, 10] Generated Node #0,1,0: 22:[12, 10] Operation: 70/7=10 Moving to Node #0,1,0 Current State: 22:[12, 10], Operations: ['54-47=7', '70/7=10'] Exploring Operation: 12+10=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
mult_heuristic
[ 6, 25, 85, 26 ]
28
[ "6+25=31", "85-26=59", "59-31=28" ]
Current State: 28:[6, 25, 85, 26], Operations: [] Exploring Operation: 6+25=31, Resulting Numbers: [85, 26, 31] Generated Node #2: [85, 26, 31] from Operation: 6+25=31 Current State: 28:[85, 26, 31], Operations: ['6+25=31'] Exploring Operation: 85-26=59, Resulting Numbers: [31, 59] Generated Node #3: [31, 59] from Operation: 85-26=59 Current State: 28:[31, 59], Operations: ['6+25=31', '85-26=59'] Exploring Operation: 59-31=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[6, 25, 85, 26], Operations: [] Exploring Operation: 85-26=59, Resulting Numbers: [6, 25, 59] Generated Node #0,0: 28:[6, 25, 59] Operation: 85-26=59 Exploring Operation: 85-25=60, Resulting Numbers: [6, 26, 60] Generated Node #0,1: 28:[6, 26, 60] Operation: 85-25=60 Exploring Operation: 85-6=79, Resulting Numbers: [25, 26, 79] Generated Node #0,2: 28:[25, 26, 79] Operation: 85-6=79 Moving to Node #0,0 Current State: 28:[6, 25, 59], Operations: ['85-26=59'] Exploring Operation: 6+25=31, Resulting Numbers: [59, 31] Generated Node #0,0,0: 28:[59, 31] Operation: 6+25=31 Exploring Operation: 59-6=53, Resulting Numbers: [25, 53] Generated Node #0,0,1: 28:[25, 53] Operation: 59-6=53 Exploring Operation: 59-25=34, Resulting Numbers: [6, 34] Generated Node #0,0,2: 28:[6, 34] Operation: 59-25=34 Moving to Node #0,1 Current State: 28:[6, 26, 60], Operations: ['85-25=60'] Exploring Operation: 60-6=54, Resulting Numbers: [26, 54] Generated Node #0,1,0: 28:[26, 54] Operation: 60-6=54 Exploring Operation: 60-26=34, Resulting Numbers: [6, 34] Generated Node #0,1,1: 28:[6, 34] Operation: 60-26=34 Exploring Operation: 60/6=10, Resulting Numbers: [26, 10] Generated Node #0,1,2: 28:[26, 10] Operation: 60/6=10 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 28:[26, 10], Operations: ['85-25=60', '60/6=10'] Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,28 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,28 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 28:[6, 34], Operations: ['85-25=60', '60-26=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,28 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Moving to Node #0 Current State: 28:[6, 25, 85, 26], Operations: [] Exploring Operation: 85-25=60, Resulting Numbers: [6, 26, 60] Generated Node #0,1: 28:[6, 26, 60] Operation: 85-25=60 Moving to Node #0,1 Current State: 28:[6, 26, 60], Operations: ['85-25=60'] Exploring Operation: 60-26=34, Resulting Numbers: [6, 34] Generated Node #0,1,1: 28:[6, 34] Operation: 60-26=34 Moving to Node #0,1,1 Current State: 28:[6, 34], Operations: ['85-25=60', '60-26=34'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,28 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 27, 99, 4, 51 ]
39
[ "99-51=48", "48/4=12", "27+12=39" ]
Current State: 39:[27, 99, 4, 51], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [27, 4, 48] Generated Node #2: [27, 4, 48] from Operation: 99-51=48 Current State: 39:[27, 4, 48], Operations: ['99-51=48'] Exploring Operation: 48/4=12, Resulting Numbers: [27, 12] Generated Node #3: [27, 12] from Operation: 48/4=12 Current State: 39:[27, 12], Operations: ['99-51=48', '48/4=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[27, 99, 4, 51], Operations: [] Exploring Operation: 99-27=72, Resulting Numbers: [4, 51, 72] Generated Node #0,0: 39:[4, 51, 72] Operation: 99-27=72 Exploring Operation: 99-51=48, Resulting Numbers: [27, 4, 48] Generated Node #0,1: 39:[27, 4, 48] Operation: 99-51=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[27, 4, 48], Operations: ['99-51=48'] Exploring Operation: 48-27=21, Resulting Numbers: [4, 21] Generated Node #0,1,0: 39:[4, 21] Operation: 48-27=21 Exploring Operation: 48/4=12, Resulting Numbers: [27, 12] Generated Node #0,1,1: 39:[27, 12] Operation: 48/4=12 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[4, 21], Operations: ['99-51=48', '48-27=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,39 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,39 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 39:[27, 12], Operations: ['99-51=48', '48/4=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[27, 99, 4, 51], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [27, 4, 48] Generated Node #0,1: 39:[27, 4, 48] Operation: 99-51=48 Moving to Node #0,1 Current State: 39:[27, 4, 48], Operations: ['99-51=48'] Exploring Operation: 48/4=12, Resulting Numbers: [27, 12] Generated Node #0,1,1: 39:[27, 12] Operation: 48/4=12 Moving to Node #0,1,1 Current State: 39:[27, 12], Operations: ['99-51=48', '48/4=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 47, 9, 27, 46 ]
35
[ "47-9=38", "27+46=73", "73-38=35" ]
Current State: 35:[47, 9, 27, 46], Operations: [] Exploring Operation: 47-9=38, Resulting Numbers: [27, 46, 38] Generated Node #2: [27, 46, 38] from Operation: 47-9=38 Current State: 35:[27, 46, 38], Operations: ['47-9=38'] Exploring Operation: 27+46=73, Resulting Numbers: [38, 73] Generated Node #3: [38, 73] from Operation: 27+46=73 Current State: 35:[38, 73], Operations: ['47-9=38', '27+46=73'] Exploring Operation: 73-38=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[47, 9, 27, 46], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [47, 46, 3] Generated Node #0,0: 35:[47, 46, 3] Operation: 27/9=3 Exploring Operation: 46-9=37, Resulting Numbers: [47, 27, 37] Generated Node #0,1: 35:[47, 27, 37] Operation: 46-9=37 Exploring Operation: 47-9=38, Resulting Numbers: [27, 46, 38] Generated Node #0,2: 35:[27, 46, 38] Operation: 47-9=38 Exploring Operation: 9+27=36, Resulting Numbers: [47, 46, 36] Generated Node #0,3: 35:[47, 46, 36] Operation: 9+27=36 Exploring Operation: 47-46=1, Resulting Numbers: [9, 27, 1] Generated Node #0,4: 35:[9, 27, 1] Operation: 47-46=1 Start Sub Search at level 1: Moving to Node #0,4 Current State: 35:[9, 27, 1], Operations: ['47-46=1'] Exploring Operation: 27/9=3, Resulting Numbers: [1, 3] Generated Node #0,4,0: 35:[1, 3] Operation: 27/9=3 Exploring Operation: 9*1=9, Resulting Numbers: [27, 9] Generated Node #0,4,1: 35:[27, 9] Operation: 9*1=9 Exploring Operation: 27+1=28, Resulting Numbers: [9, 28] Generated Node #0,4,2: 35:[9, 28] Operation: 27+1=28 Exploring Operation: 9+27=36, Resulting Numbers: [1, 36] Generated Node #0,4,3: 35:[1, 36] Operation: 9+27=36 Exploring Operation: 9-1=8, Resulting Numbers: [27, 8] Generated Node #0,4,4: 35:[27, 8] Operation: 9-1=8 Moving to Node #0,4,3 Current State: 35:[1, 36], Operations: ['47-46=1', '9+27=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[47, 9, 27, 46], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [9, 27, 1] Generated Node #0,4: 35:[9, 27, 1] Operation: 47-46=1 Moving to Node #0,4 Current State: 35:[9, 27, 1], Operations: ['47-46=1'] Exploring Operation: 9+27=36, Resulting Numbers: [1, 36] Generated Node #0,4,3: 35:[1, 36] Operation: 9+27=36 Moving to Node #0,4,3 Current State: 35:[1, 36], Operations: ['47-46=1', '9+27=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 21, 54, 30, 40 ]
23
[ "54-21=33", "40-30=10", "33-10=23" ]
Current State: 23:[21, 54, 30, 40], Operations: [] Exploring Operation: 54-21=33, Resulting Numbers: [30, 40, 33] Generated Node #2: [30, 40, 33] from Operation: 54-21=33 Current State: 23:[30, 40, 33], Operations: ['54-21=33'] Exploring Operation: 40-30=10, Resulting Numbers: [33, 10] Generated Node #3: [33, 10] from Operation: 40-30=10 Current State: 23:[33, 10], Operations: ['54-21=33', '40-30=10'] Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[21, 54, 30, 40], Operations: [] Exploring Operation: 40-30=10, Resulting Numbers: [21, 54, 10] Generated Node #0,0: 23:[21, 54, 10] Operation: 40-30=10 Exploring Operation: 54-21=33, Resulting Numbers: [30, 40, 33] Generated Node #0,1: 23:[30, 40, 33] Operation: 54-21=33 Exploring Operation: 54-30=24, Resulting Numbers: [21, 40, 24] Generated Node #0,2: 23:[21, 40, 24] Operation: 54-30=24 Exploring Operation: 54-40=14, Resulting Numbers: [21, 30, 14] Generated Node #0,3: 23:[21, 30, 14] Operation: 54-40=14 Exploring Operation: 40-21=19, Resulting Numbers: [54, 30, 19] Generated Node #0,4: 23:[54, 30, 19] Operation: 40-21=19 Moving to Node #0,3 Current State: 23:[21, 30, 14], Operations: ['54-40=14'] Exploring Operation: 30+14=44, Resulting Numbers: [21, 44] Generated Node #0,3,0: 23:[21, 44] Operation: 30+14=44 Exploring Operation: 21+14=35, Resulting Numbers: [30, 35] Generated Node #0,3,1: 23:[30, 35] Operation: 21+14=35 Exploring Operation: 30-14=16, Resulting Numbers: [21, 16] Generated Node #0,3,2: 23:[21, 16] Operation: 30-14=16 Exploring Operation: 30-21=9, Resulting Numbers: [14, 9] Generated Node #0,3,3: 23:[14, 9] Operation: 30-21=9 Exploring Operation: 21-14=7, Resulting Numbers: [30, 7] Generated Node #0,3,4: 23:[30, 7] Operation: 21-14=7 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[21, 16], Operations: ['54-40=14', '30-14=16'] Exploring Operation: 21*16=336, Resulting Numbers: [336] 336,23 unequal: No Solution Exploring Operation: 21+16=37, Resulting Numbers: [37] 37,23 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[30, 35], Operations: ['54-40=14', '21+14=35'] Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,23 unequal: No Solution Exploring Operation: 30+35=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 30*35=1050, Resulting Numbers: [1050] 1050,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 23:[21, 44], Operations: ['54-40=14', '30+14=44'] Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,23 unequal: No Solution Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,23 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[21, 54, 30, 40], Operations: [] Exploring Operation: 54-40=14, Resulting Numbers: [21, 30, 14] Generated Node #0,3: 23:[21, 30, 14] Operation: 54-40=14 Moving to Node #0,3 Current State: 23:[21, 30, 14], Operations: ['54-40=14'] Exploring Operation: 30+14=44, Resulting Numbers: [21, 44] Generated Node #0,3,0: 23:[21, 44] Operation: 30+14=44 Moving to Node #0,3,0 Current State: 23:[21, 44], Operations: ['54-40=14', '30+14=44'] Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
mult_heuristic
[ 40, 4, 8, 8 ]
60
[ "40+4=44", "8+8=16", "44+16=60" ]
Current State: 60:[40, 4, 8, 8], Operations: [] Exploring Operation: 40+4=44, Resulting Numbers: [8, 8, 44] Generated Node #2: [8, 8, 44] from Operation: 40+4=44 Current State: 60:[8, 8, 44], Operations: ['40+4=44'] Exploring Operation: 8+8=16, Resulting Numbers: [44, 16] Generated Node #3: [44, 16] from Operation: 8+8=16 Current State: 60:[44, 16], Operations: ['40+4=44', '8+8=16'] Exploring Operation: 44+16=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[40, 4, 8, 8], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [4, 8, 5] Generated Node #0,0: 60:[4, 8, 5] Operation: 40/8=5 Exploring Operation: 40/8=5, Resulting Numbers: [4, 8, 5] Generated Node #0,1: 60:[4, 8, 5] Operation: 40/8=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[4, 8, 5], Operations: ['40/8=5'] Exploring Operation: 4+8=12, Resulting Numbers: [5, 12] Generated Node #0,0,0: 60:[5, 12] Operation: 4+8=12 Exploring Operation: 8-4=4, Resulting Numbers: [5, 4] Generated Node #0,0,1: 60:[5, 4] Operation: 8-4=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[5, 12], Operations: ['40/8=5', '4+8=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[40, 4, 8, 8], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [4, 8, 5] Generated Node #0,0: 60:[4, 8, 5] Operation: 40/8=5 Moving to Node #0,0 Current State: 60:[4, 8, 5], Operations: ['40/8=5'] Exploring Operation: 4+8=12, Resulting Numbers: [5, 12] Generated Node #0,0,0: 60:[5, 12] Operation: 4+8=12 Moving to Node #0,0,0 Current State: 60:[5, 12], Operations: ['40/8=5', '4+8=12'] Exploring Operation: 5*12=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 30, 56, 14, 87 ]
14
[ "30+56=86", "87-86=1", "14*1=14" ]
Current State: 14:[30, 56, 14, 87], Operations: [] Exploring Operation: 30+56=86, Resulting Numbers: [14, 87, 86] Generated Node #2: [14, 87, 86] from Operation: 30+56=86 Current State: 14:[14, 87, 86], Operations: ['30+56=86'] Exploring Operation: 87-86=1, Resulting Numbers: [14, 1] Generated Node #3: [14, 1] from Operation: 87-86=1 Current State: 14:[14, 1], Operations: ['30+56=86', '87-86=1'] Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[30, 56, 14, 87], Operations: [] Exploring Operation: 56-30=26, Resulting Numbers: [14, 87, 26] Generated Node #0,0: 14:[14, 87, 26] Operation: 56-30=26 Exploring Operation: 87-30=57, Resulting Numbers: [56, 14, 57] Generated Node #0,1: 14:[56, 14, 57] Operation: 87-30=57 Exploring Operation: 87-56=31, Resulting Numbers: [30, 14, 31] Generated Node #0,2: 14:[30, 14, 31] Operation: 87-56=31 Exploring Operation: 56/14=4, Resulting Numbers: [30, 87, 4] Generated Node #0,3: 14:[30, 87, 4] Operation: 56/14=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[30, 14, 31], Operations: ['87-56=31'] Exploring Operation: 30-14=16, Resulting Numbers: [31, 16] Generated Node #0,2,0: 14:[31, 16] Operation: 30-14=16 Exploring Operation: 31-30=1, Resulting Numbers: [14, 1] Generated Node #0,2,1: 14:[14, 1] Operation: 31-30=1 Exploring Operation: 30+14=44, Resulting Numbers: [31, 44] Generated Node #0,2,2: 14:[31, 44] Operation: 30+14=44 Exploring Operation: 31-14=17, Resulting Numbers: [30, 17] Generated Node #0,2,3: 14:[30, 17] Operation: 31-14=17 Moving to Node #0,2,1 Current State: 14:[14, 1], Operations: ['87-56=31', '31-30=1'] Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,14 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[30, 56, 14, 87], Operations: [] Exploring Operation: 87-56=31, Resulting Numbers: [30, 14, 31] Generated Node #0,2: 14:[30, 14, 31] Operation: 87-56=31 Moving to Node #0,2 Current State: 14:[30, 14, 31], Operations: ['87-56=31'] Exploring Operation: 31-30=1, Resulting Numbers: [14, 1] Generated Node #0,2,1: 14:[14, 1] Operation: 31-30=1 Moving to Node #0,2,1 Current State: 14:[14, 1], Operations: ['87-56=31', '31-30=1'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 44, 42, 88, 85 ]
45
[ "88/44=2", "85-42=43", "2+43=45" ]
Current State: 45:[44, 42, 88, 85], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [42, 85, 2] Generated Node #2: [42, 85, 2] from Operation: 88/44=2 Current State: 45:[42, 85, 2], Operations: ['88/44=2'] Exploring Operation: 85-42=43, Resulting Numbers: [2, 43] Generated Node #3: [2, 43] from Operation: 85-42=43 Current State: 45:[2, 43], Operations: ['88/44=2', '85-42=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[44, 42, 88, 85], Operations: [] Exploring Operation: 88-85=3, Resulting Numbers: [44, 42, 3] Generated Node #0,0: 45:[44, 42, 3] Operation: 88-85=3 Exploring Operation: 88-42=46, Resulting Numbers: [44, 85, 46] Generated Node #0,1: 45:[44, 85, 46] Operation: 88-42=46 Exploring Operation: 88/44=2, Resulting Numbers: [42, 85, 2] Generated Node #0,2: 45:[42, 85, 2] Operation: 88/44=2 Exploring Operation: 88-44=44, Resulting Numbers: [42, 85, 44] Generated Node #0,3: 45:[42, 85, 44] Operation: 88-44=44 Moving to Node #0,0 Current State: 45:[44, 42, 3], Operations: ['88-85=3'] Exploring Operation: 42/3=14, Resulting Numbers: [44, 14] Generated Node #0,0,0: 45:[44, 14] Operation: 42/3=14 Exploring Operation: 44+3=47, Resulting Numbers: [42, 47] Generated Node #0,0,1: 45:[42, 47] Operation: 44+3=47 Exploring Operation: 44-42=2, Resulting Numbers: [3, 2] Generated Node #0,0,2: 45:[3, 2] Operation: 44-42=2 Exploring Operation: 42+3=45, Resulting Numbers: [44, 45] Generated Node #0,0,3: 45:[44, 45] Operation: 42+3=45 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 45:[3, 2], Operations: ['88-85=3', '44-42=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,45 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 45:[44, 45], Operations: ['88-85=3', '42+3=45'] Exploring Operation: 44+45=89, Resulting Numbers: [89] 89,45 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,45 unequal: No Solution Exploring Operation: 44*45=1980, Resulting Numbers: [1980] 1980,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[44, 14], Operations: ['88-85=3', '42/3=14'] Exploring Operation: 44-14=30, Resulting Numbers: [30] 30,45 unequal: No Solution Exploring Operation: 44+14=58, Resulting Numbers: [58] 58,45 unequal: No Solution Exploring Operation: 44*14=616, Resulting Numbers: [616] 616,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[42, 47], Operations: ['88-85=3', '44+3=47'] Exploring Operation: 42*47=1974, Resulting Numbers: [1974] 1974,45 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 42+47=89, Resulting Numbers: [89] 89,45 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: 45:[44, 85, 46], Operations: ['88-42=46'] Exploring Operation: 85-44=41, Resulting Numbers: [46, 41] Generated Node #0,1,0: 45:[46, 41] Operation: 85-44=41 Exploring Operation: 85-46=39, Resulting Numbers: [44, 39] Generated Node #0,1,1: 45:[44, 39] Operation: 85-46=39 Exploring Operation: 44+85=129, Resulting Numbers: [46, 129] Generated Node #0,1,2: 45:[46, 129] Operation: 44+85=129 Exploring Operation: 46-44=2, Resulting Numbers: [85, 2] Generated Node #0,1,3: 45:[85, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[46, 41], Operations: ['88-42=46', '85-44=41'] Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 46*41=1886, Resulting Numbers: [1886] 1886,45 unequal: No Solution Exploring Operation: 46+41=87, Resulting Numbers: [87] 87,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[44, 39], Operations: ['88-42=46', '85-46=39'] Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,45 unequal: No Solution Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 45:[85, 2], Operations: ['88-42=46', '46-44=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,45 unequal: No Solution Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,45 unequal: No Solution Exploring Operation: 85*2=170, Resulting Numbers: [170] 170,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[46, 129], Operations: ['88-42=46', '44+85=129'] Exploring Operation: 46*129=5934, Resulting Numbers: [5934] 5934,45 unequal: No Solution Exploring Operation: 46+129=175, Resulting Numbers: [175] 175,45 unequal: No Solution Exploring Operation: 129-46=83, Resulting Numbers: [83] 83,45 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: 45:[42, 85, 44], Operations: ['88-44=44'] Exploring Operation: 42+44=86, Resulting Numbers: [85, 86] Generated Node #0,3,0: 45:[85, 86] Operation: 42+44=86 Exploring Operation: 85-42=43, Resulting Numbers: [44, 43] Generated Node #0,3,1: 45:[44, 43] Operation: 85-42=43 Exploring Operation: 85-44=41, Resulting Numbers: [42, 41] Generated Node #0,3,2: 45:[42, 41] Operation: 85-44=41 Exploring Operation: 44-42=2, Resulting Numbers: [85, 2] Generated Node #0,3,3: 45:[85, 2] Operation: 44-42=2 Moving to Node #0,2 Current State: 45:[42, 85, 2], Operations: ['88/44=2'] Exploring Operation: 42+2=44, Resulting Numbers: [85, 44] Generated Node #0,2,0: 45:[85, 44] Operation: 42+2=44 Exploring Operation: 42-2=40, Resulting Numbers: [85, 40] Generated Node #0,2,1: 45:[85, 40] Operation: 42-2=40 Exploring Operation: 85-42=43, Resulting Numbers: [2, 43] Generated Node #0,2,2: 45:[2, 43] Operation: 85-42=43 Exploring Operation: 85-2=83, Resulting Numbers: [42, 83] Generated Node #0,2,3: 45:[42, 83] Operation: 85-2=83 Moving to Node #0,3,1 Current State: 45:[44, 43], Operations: ['88-44=44', '85-42=43'] Exploring Operation: 44*43=1892, Resulting Numbers: [1892] 1892,45 unequal: No Solution Exploring Operation: 44+43=87, Resulting Numbers: [87] 87,45 unequal: No Solution Exploring Operation: 44-43=1, Resulting Numbers: [1] 1,45 unequal: No Solution Moving to Node #0,2,2 Current State: 45:[2, 43], Operations: ['88/44=2', '85-42=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[44, 42, 88, 85], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [42, 85, 2] Generated Node #0,2: 45:[42, 85, 2] Operation: 88/44=2 Moving to Node #0,2 Current State: 45:[42, 85, 2], Operations: ['88/44=2'] Exploring Operation: 85-42=43, Resulting Numbers: [2, 43] Generated Node #0,2,2: 45:[2, 43] Operation: 85-42=43 Moving to Node #0,2,2 Current State: 45:[2, 43], Operations: ['88/44=2', '85-42=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
0.954861
hs_4
sum_heuristic
[ 1, 4, 20, 29 ]
71
[ "1+4=5", "20*5=100", "100-29=71" ]
Current State: 71:[1, 4, 20, 29], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [20, 29, 5] Generated Node #2: [20, 29, 5] from Operation: 1+4=5 Current State: 71:[20, 29, 5], Operations: ['1+4=5'] Exploring Operation: 20*5=100, Resulting Numbers: [29, 100] Generated Node #3: [29, 100] from Operation: 20*5=100 Current State: 71:[29, 100], Operations: ['1+4=5', '20*5=100'] Exploring Operation: 100-29=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[1, 4, 20, 29], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [20, 29, 5] Generated Node #0,0: 71:[20, 29, 5] Operation: 1+4=5 Exploring Operation: 4*20=80, Resulting Numbers: [1, 29, 80] Generated Node #0,1: 71:[1, 29, 80] Operation: 4*20=80 Exploring Operation: 1+20=21, Resulting Numbers: [4, 29, 21] Generated Node #0,2: 71:[4, 29, 21] Operation: 1+20=21 Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[1, 29, 80], Operations: ['4*20=80'] Exploring Operation: 1*29=29, Resulting Numbers: [80, 29] Generated Node #0,1,0: 71:[80, 29] Operation: 1*29=29 Exploring Operation: 80-1=79, Resulting Numbers: [29, 79] Generated Node #0,1,1: 71:[29, 79] Operation: 80-1=79 Exploring Operation: 1+29=30, Resulting Numbers: [80, 30] Generated Node #0,1,2: 71:[80, 30] Operation: 1+29=30 Moving to Node #0,1,1 Current State: 71:[29, 79], Operations: ['4*20=80', '80-1=79'] Exploring Operation: 29*79=2291, Resulting Numbers: [2291] 2291,71 unequal: No Solution Exploring Operation: 29+79=108, Resulting Numbers: [108] 108,71 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,71 unequal: No Solution Moving to Node #0,1,2 Current State: 71:[80, 30], Operations: ['4*20=80', '1+29=30'] Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,71 unequal: No Solution Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,71 unequal: No Solution Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[80, 29], Operations: ['4*20=80', '1*29=29'] Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,71 unequal: No Solution Exploring Operation: 80*29=2320, Resulting Numbers: [2320] 2320,71 unequal: No Solution Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,71 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 Current State: 71:[20, 29, 5], Operations: ['1+4=5'] Exploring Operation: 20+5=25, Resulting Numbers: [29, 25] Generated Node #0,0,0: 71:[29, 25] Operation: 20+5=25 Exploring Operation: 20*5=100, Resulting Numbers: [29, 100] Generated Node #0,0,1: 71:[29, 100] Operation: 20*5=100 Exploring Operation: 20+29=49, Resulting Numbers: [5, 49] Generated Node #0,0,2: 71:[5, 49] Operation: 20+29=49 Moving to Node #0,0,1 Current State: 71:[29, 100], Operations: ['1+4=5', '20*5=100'] Exploring Operation: 29+100=129, Resulting Numbers: [129] 129,71 unequal: No Solution Exploring Operation: 100-29=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[1, 4, 20, 29], Operations: [] Exploring Operation: 1+4=5, Resulting Numbers: [20, 29, 5] Generated Node #0,0: 71:[20, 29, 5] Operation: 1+4=5 Moving to Node #0,0 Current State: 71:[20, 29, 5], Operations: ['1+4=5'] Exploring Operation: 20*5=100, Resulting Numbers: [29, 100] Generated Node #0,0,1: 71:[29, 100] Operation: 20*5=100 Moving to Node #0,0,1 Current State: 71:[29, 100], Operations: ['1+4=5', '20*5=100'] Exploring Operation: 100-29=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 72, 87, 99, 81 ]
83
[ "99-81=18", "72/18=4", "87-4=83" ]
Current State: 83:[72, 87, 99, 81], Operations: [] Exploring Operation: 99-81=18, Resulting Numbers: [72, 87, 18] Generated Node #2: [72, 87, 18] from Operation: 99-81=18 Current State: 83:[72, 87, 18], Operations: ['99-81=18'] Exploring Operation: 72/18=4, Resulting Numbers: [87, 4] Generated Node #3: [87, 4] from Operation: 72/18=4 Current State: 83:[87, 4], Operations: ['99-81=18', '72/18=4'] Exploring Operation: 87-4=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[72, 87, 99, 81], Operations: [] Exploring Operation: 99-72=27, Resulting Numbers: [87, 81, 27] Generated Node #0,0: 83:[87, 81, 27] Operation: 99-72=27 Moving to Node #0,0 Current State: 83:[87, 81, 27], Operations: ['99-72=27'] Exploring Operation: 87-27=60, Resulting Numbers: [81, 60] Generated Node #0,0,0: 83:[81, 60] Operation: 87-27=60 Moving to Node #0,0,0 Current State: 83:[81, 60], Operations: ['99-72=27', '87-27=60'] Exploring Operation: 81+60=141, Resulting Numbers: [141] 141,83 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 98, 73, 91, 5 ]
86
[ "98-73=25", "25/5=5", "91-5=86" ]
Current State: 86:[98, 73, 91, 5], Operations: [] Exploring Operation: 98-73=25, Resulting Numbers: [91, 5, 25] Generated Node #2: [91, 5, 25] from Operation: 98-73=25 Current State: 86:[91, 5, 25], Operations: ['98-73=25'] Exploring Operation: 25/5=5, Resulting Numbers: [91, 5] Generated Node #3: [91, 5] from Operation: 25/5=5 Current State: 86:[91, 5], Operations: ['98-73=25', '25/5=5'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[98, 73, 91, 5], Operations: [] Exploring Operation: 98-91=7, Resulting Numbers: [73, 5, 7] Generated Node #0,0: 86:[73, 5, 7] Operation: 98-91=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[73, 5, 7], Operations: ['98-91=7'] Exploring Operation: 73+7=80, Resulting Numbers: [5, 80] Generated Node #0,0,0: 86:[5, 80] Operation: 73+7=80 Moving to Node #0,0,0 Current State: 86:[5, 80], Operations: ['98-91=7', '73+7=80'] Exploring Operation: 5+80=85, Resulting Numbers: [85] 85,86 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
[ 33, 8, 31, 11 ]
21
[ "33+8=41", "31-11=20", "41-20=21" ]
Current State: 21:[33, 8, 31, 11], Operations: [] Exploring Operation: 33+8=41, Resulting Numbers: [31, 11, 41] Generated Node #2: [31, 11, 41] from Operation: 33+8=41 Current State: 21:[31, 11, 41], Operations: ['33+8=41'] Exploring Operation: 31-11=20, Resulting Numbers: [41, 20] Generated Node #3: [41, 20] from Operation: 31-11=20 Current State: 21:[41, 20], Operations: ['33+8=41', '31-11=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[33, 8, 31, 11], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [8, 31, 3] Generated Node #0,0: 21:[8, 31, 3] Operation: 33/11=3 Exploring Operation: 33-31=2, Resulting Numbers: [8, 11, 2] Generated Node #0,1: 21:[8, 11, 2] Operation: 33-31=2 Exploring Operation: 31-11=20, Resulting Numbers: [33, 8, 20] Generated Node #0,2: 21:[33, 8, 20] Operation: 31-11=20 Exploring Operation: 33-11=22, Resulting Numbers: [8, 31, 22] Generated Node #0,3: 21:[8, 31, 22] Operation: 33-11=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[8, 11, 2], Operations: ['33-31=2'] Exploring Operation: 11-8=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 21:[2, 3] Operation: 11-8=3 Exploring Operation: 11*2=22, Resulting Numbers: [8, 22] Generated Node #0,1,1: 21:[8, 22] Operation: 11*2=22 Exploring Operation: 11-2=9, Resulting Numbers: [8, 9] Generated Node #0,1,2: 21:[8, 9] Operation: 11-2=9 Exploring Operation: 8+11=19, Resulting Numbers: [2, 19] Generated Node #0,1,3: 21:[2, 19] Operation: 8+11=19 Moving to Node #0,1,0 Current State: 21:[2, 3], Operations: ['33-31=2', '11-8=3'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,21 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,21 unequal: No Solution Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[8, 22], Operations: ['33-31=2', '11*2=22'] Exploring Operation: 22-8=14, Resulting Numbers: [14] 14,21 unequal: No Solution Exploring Operation: 8+22=30, Resulting Numbers: [30] 30,21 unequal: No Solution Exploring Operation: 8*22=176, Resulting Numbers: [176] 176,21 unequal: No Solution Moving to Node #0,1,3 Current State: 21:[2, 19], Operations: ['33-31=2', '8+11=19'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,21 unequal: No Solution Exploring Operation: 2*19=38, Resulting Numbers: [38] 38,21 unequal: No Solution Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[33, 8, 31, 11], Operations: [] Exploring Operation: 33-31=2, Resulting Numbers: [8, 11, 2] Generated Node #0,1: 21:[8, 11, 2] Operation: 33-31=2 Moving to Node #0,1 Current State: 21:[8, 11, 2], Operations: ['33-31=2'] Exploring Operation: 8+11=19, Resulting Numbers: [2, 19] Generated Node #0,1,3: 21:[2, 19] Operation: 8+11=19 Moving to Node #0,1,3 Current State: 21:[2, 19], Operations: ['33-31=2', '8+11=19'] Exploring Operation: 2+19=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 38, 57, 7, 50 ]
38
[ "38+57=95", "7+50=57", "95-57=38" ]
Current State: 38:[38, 57, 7, 50], Operations: [] Exploring Operation: 38+57=95, Resulting Numbers: [7, 50, 95] Generated Node #2: [7, 50, 95] from Operation: 38+57=95 Current State: 38:[7, 50, 95], Operations: ['38+57=95'] Exploring Operation: 7+50=57, Resulting Numbers: [95, 57] Generated Node #3: [95, 57] from Operation: 7+50=57 Current State: 38:[95, 57], Operations: ['38+57=95', '7+50=57'] Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[38, 57, 7, 50], Operations: [] Exploring Operation: 57-50=7, Resulting Numbers: [38, 7, 7] Generated Node #0,0: 38:[38, 7, 7] Operation: 57-50=7 Exploring Operation: 57-38=19, Resulting Numbers: [7, 50, 19] Generated Node #0,1: 38:[7, 50, 19] Operation: 57-38=19 Exploring Operation: 57-7=50, Resulting Numbers: [38, 50, 50] Generated Node #0,2: 38:[38, 50, 50] Operation: 57-7=50 Exploring Operation: 50-7=43, Resulting Numbers: [38, 57, 43] Generated Node #0,3: 38:[38, 57, 43] Operation: 50-7=43 Moving to Node #0,0 Current State: 38:[38, 7, 7], Operations: ['57-50=7'] Exploring Operation: 7*7=49, Resulting Numbers: [38, 49] Generated Node #0,0,0: 38:[38, 49] Operation: 7*7=49 Exploring Operation: 7/7=1, Resulting Numbers: [38, 1] Generated Node #0,0,1: 38:[38, 1] Operation: 7/7=1 Exploring Operation: 7+7=14, Resulting Numbers: [38, 14] Generated Node #0,0,2: 38:[38, 14] Operation: 7+7=14 Exploring Operation: 7-7=0, Resulting Numbers: [38, 0] Generated Node #0,0,3: 38:[38, 0] Operation: 7-7=0 Moving to Node #0,1 Current State: 38:[7, 50, 19], Operations: ['57-38=19'] Exploring Operation: 7+19=26, Resulting Numbers: [50, 26] Generated Node #0,1,0: 38:[50, 26] Operation: 7+19=26 Exploring Operation: 50-7=43, Resulting Numbers: [19, 43] Generated Node #0,1,1: 38:[19, 43] Operation: 50-7=43 Exploring Operation: 7+50=57, Resulting Numbers: [19, 57] Generated Node #0,1,2: 38:[19, 57] Operation: 7+50=57 Exploring Operation: 50-19=31, Resulting Numbers: [7, 31] Generated Node #0,1,3: 38:[7, 31] Operation: 50-19=31 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 38:[19, 43], Operations: ['57-38=19', '50-7=43'] Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,38 unequal: No Solution Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,38 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 38:[7, 31], Operations: ['57-38=19', '50-19=31'] Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,38 unequal: No Solution Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[38, 57, 7, 50], Operations: [] Exploring Operation: 57-38=19, Resulting Numbers: [7, 50, 19] Generated Node #0,1: 38:[7, 50, 19] Operation: 57-38=19 Moving to Node #0,1 Current State: 38:[7, 50, 19], Operations: ['57-38=19'] Exploring Operation: 50-19=31, Resulting Numbers: [7, 31] Generated Node #0,1,3: 38:[7, 31] Operation: 50-19=31 Moving to Node #0,1,3 Current State: 38:[7, 31], Operations: ['57-38=19', '50-19=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_4
sum_heuristic
[ 65, 40, 53, 62 ]
10
[ "65+40=105", "53+62=115", "115-105=10" ]
Current State: 10:[65, 40, 53, 62], Operations: [] Exploring Operation: 65+40=105, Resulting Numbers: [53, 62, 105] Generated Node #2: [53, 62, 105] from Operation: 65+40=105 Current State: 10:[53, 62, 105], Operations: ['65+40=105'] Exploring Operation: 53+62=115, Resulting Numbers: [105, 115] Generated Node #3: [105, 115] from Operation: 53+62=115 Current State: 10:[105, 115], Operations: ['65+40=105', '53+62=115'] Exploring Operation: 115-105=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[65, 40, 53, 62], Operations: [] Exploring Operation: 65-53=12, Resulting Numbers: [40, 62, 12] Generated Node #0,0: 10:[40, 62, 12] Operation: 65-53=12 Exploring Operation: 65-62=3, Resulting Numbers: [40, 53, 3] Generated Node #0,1: 10:[40, 53, 3] Operation: 65-62=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[40, 53, 3], Operations: ['65-62=3'] Exploring Operation: 53-40=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 10:[3, 13] Operation: 53-40=13 Exploring Operation: 40-3=37, Resulting Numbers: [53, 37] Generated Node #0,1,1: 10:[53, 37] Operation: 40-3=37 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[3, 13], Operations: ['65-62=3', '53-40=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[65, 40, 53, 62], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [40, 53, 3] Generated Node #0,1: 10:[40, 53, 3] Operation: 65-62=3 Moving to Node #0,1 Current State: 10:[40, 53, 3], Operations: ['65-62=3'] Exploring Operation: 53-40=13, Resulting Numbers: [3, 13] Generated Node #0,1,0: 10:[3, 13] Operation: 53-40=13 Moving to Node #0,1,0 Current State: 10:[3, 13], Operations: ['65-62=3', '53-40=13'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 81, 37, 34, 23 ]
61
[ "81+37=118", "34+23=57", "118-57=61" ]
Current State: 61:[81, 37, 34, 23], Operations: [] Exploring Operation: 81+37=118, Resulting Numbers: [34, 23, 118] Generated Node #2: [34, 23, 118] from Operation: 81+37=118 Current State: 61:[34, 23, 118], Operations: ['81+37=118'] Exploring Operation: 34+23=57, Resulting Numbers: [118, 57] Generated Node #3: [118, 57] from Operation: 34+23=57 Current State: 61:[118, 57], Operations: ['81+37=118', '34+23=57'] Exploring Operation: 118-57=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[81, 37, 34, 23], Operations: [] Exploring Operation: 37+23=60, Resulting Numbers: [81, 34, 60] Generated Node #0,0: 61:[81, 34, 60] Operation: 37+23=60 Exploring Operation: 81-23=58, Resulting Numbers: [37, 34, 58] Generated Node #0,1: 61:[37, 34, 58] Operation: 81-23=58 Exploring Operation: 37+34=71, Resulting Numbers: [81, 23, 71] Generated Node #0,2: 61:[81, 23, 71] Operation: 37+34=71 Exploring Operation: 34+23=57, Resulting Numbers: [81, 37, 57] Generated Node #0,3: 61:[81, 37, 57] Operation: 34+23=57 Moving to Node #0,0 Current State: 61:[81, 34, 60], Operations: ['37+23=60'] Exploring Operation: 81+34=115, Resulting Numbers: [60, 115] Generated Node #0,0,0: 61:[60, 115] Operation: 81+34=115 Exploring Operation: 60-34=26, Resulting Numbers: [81, 26] Generated Node #0,0,1: 61:[81, 26] Operation: 60-34=26 Exploring Operation: 81-34=47, Resulting Numbers: [60, 47] Generated Node #0,0,2: 61:[60, 47] Operation: 81-34=47 Exploring Operation: 34+60=94, Resulting Numbers: [81, 94] Generated Node #0,0,3: 61:[81, 94] Operation: 34+60=94 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 61:[60, 47], Operations: ['37+23=60', '81-34=47'] Exploring Operation: 60+47=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 60*47=2820, Resulting Numbers: [2820] 2820,61 unequal: No Solution Exploring Operation: 60-47=13, Resulting Numbers: [13] 13,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 61:[81, 94], Operations: ['37+23=60', '34+60=94'] Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 81+94=175, Resulting Numbers: [175] 175,61 unequal: No Solution Exploring Operation: 81*94=7614, Resulting Numbers: [7614] 7614,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 61:[60, 115], Operations: ['37+23=60', '81+34=115'] Exploring Operation: 60*115=6900, Resulting Numbers: [6900] 6900,61 unequal: No Solution Exploring Operation: 60+115=175, Resulting Numbers: [175] 175,61 unequal: No Solution Exploring Operation: 115-60=55, Resulting Numbers: [55] 55,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[81, 26], Operations: ['37+23=60', '60-34=26'] Exploring Operation: 81+26=107, Resulting Numbers: [107] 107,61 unequal: No Solution Exploring Operation: 81-26=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 81*26=2106, Resulting Numbers: [2106] 2106,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 61:[81, 37, 57], Operations: ['34+23=57'] Exploring Operation: 37+57=94, Resulting Numbers: [81, 94] Generated Node #0,3,0: 61:[81, 94] Operation: 37+57=94 Exploring Operation: 81-57=24, Resulting Numbers: [37, 24] Generated Node #0,3,1: 61:[37, 24] Operation: 81-57=24 Exploring Operation: 81-37=44, Resulting Numbers: [57, 44] Generated Node #0,3,2: 61:[57, 44] Operation: 81-37=44 Exploring Operation: 81+37=118, Resulting Numbers: [57, 118] Generated Node #0,3,3: 61:[57, 118] Operation: 81+37=118 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 61:[57, 44], Operations: ['34+23=57', '81-37=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 No 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: 61:[81, 94], Operations: ['34+23=57', '37+57=94'] Exploring Operation: 81*94=7614, Resulting Numbers: [7614] 7614,61 unequal: No Solution Exploring Operation: 81+94=175, Resulting Numbers: [175] 175,61 unequal: No Solution Exploring Operation: 94-81=13, Resulting Numbers: [13] 13,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 61:[37, 24], Operations: ['34+23=57', '81-57=24'] Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,61 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,61 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[81, 37, 34, 23], Operations: [] Exploring Operation: 34+23=57, Resulting Numbers: [81, 37, 57] Generated Node #0,3: 61:[81, 37, 57] Operation: 34+23=57 Moving to Node #0,3 Current State: 61:[81, 37, 57], Operations: ['34+23=57'] Exploring Operation: 81-57=24, Resulting Numbers: [37, 24] Generated Node #0,3,1: 61:[37, 24] Operation: 81-57=24 Moving to Node #0,3,1 Current State: 61:[37, 24], Operations: ['34+23=57', '81-57=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 44, 87, 26, 24 ]
93
[ "87-44=43", "26+24=50", "43+50=93" ]
Current State: 93:[44, 87, 26, 24], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [26, 24, 43] Generated Node #2: [26, 24, 43] from Operation: 87-44=43 Current State: 93:[26, 24, 43], Operations: ['87-44=43'] Exploring Operation: 26+24=50, Resulting Numbers: [43, 50] Generated Node #3: [43, 50] from Operation: 26+24=50 Current State: 93:[43, 50], Operations: ['87-44=43', '26+24=50'] Exploring Operation: 43+50=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[44, 87, 26, 24], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [87, 26, 20] Generated Node #0,0: 93:[87, 26, 20] Operation: 44-24=20 Exploring Operation: 87-44=43, Resulting Numbers: [26, 24, 43] Generated Node #0,1: 93:[26, 24, 43] Operation: 87-44=43 Exploring Operation: 44-26=18, Resulting Numbers: [87, 24, 18] Generated Node #0,2: 93:[87, 24, 18] Operation: 44-26=18 Exploring Operation: 26-24=2, Resulting Numbers: [44, 87, 2] Generated Node #0,3: 93:[44, 87, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 93:[44, 87, 2], Operations: ['26-24=2'] Exploring Operation: 44/2=22, Resulting Numbers: [87, 22] Generated Node #0,3,0: 93:[87, 22] Operation: 44/2=22 Exploring Operation: 87-44=43, Resulting Numbers: [2, 43] Generated Node #0,3,1: 93:[2, 43] Operation: 87-44=43 Exploring Operation: 44*2=88, Resulting Numbers: [87, 88] Generated Node #0,3,2: 93:[87, 88] Operation: 44*2=88 Exploring Operation: 44-2=42, Resulting Numbers: [87, 42] Generated Node #0,3,3: 93:[87, 42] Operation: 44-2=42 Moving to Node #0,3,2 Current State: 93:[87, 88], Operations: ['26-24=2', '44*2=88'] Exploring Operation: 87+88=175, Resulting Numbers: [175] 175,93 unequal: No Solution Exploring Operation: 88-87=1, Resulting Numbers: [1] 1,93 unequal: No Solution Exploring Operation: 87*88=7656, Resulting Numbers: [7656] 7656,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[2, 43], Operations: ['26-24=2', '87-44=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,93 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,93 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,93 unequal: No Solution Moving to Node #0,3,0 Current State: 93:[87, 22], Operations: ['26-24=2', '44/2=22'] Exploring Operation: 87+22=109, Resulting Numbers: [109] 109,93 unequal: No Solution Exploring Operation: 87-22=65, Resulting Numbers: [65] 65,93 unequal: No Solution Exploring Operation: 87*22=1914, Resulting Numbers: [1914] 1914,93 unequal: No Solution Moving to Node #0,3,3 Current State: 93:[87, 42], Operations: ['26-24=2', '44-2=42'] Exploring Operation: 87+42=129, Resulting Numbers: [129] 129,93 unequal: No Solution Exploring Operation: 87-42=45, Resulting Numbers: [45] 45,93 unequal: No Solution Exploring Operation: 87*42=3654, Resulting Numbers: [3654] 3654,93 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:[87, 26, 20], Operations: ['44-24=20'] Exploring Operation: 26-20=6, Resulting Numbers: [87, 6] Generated Node #0,0,0: 93:[87, 6] Operation: 26-20=6 Exploring Operation: 26+20=46, Resulting Numbers: [87, 46] Generated Node #0,0,1: 93:[87, 46] Operation: 26+20=46 Exploring Operation: 87+20=107, Resulting Numbers: [26, 107] Generated Node #0,0,2: 93:[26, 107] Operation: 87+20=107 Exploring Operation: 87+26=113, Resulting Numbers: [20, 113] Generated Node #0,0,3: 93:[20, 113] Operation: 87+26=113 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[87, 6], Operations: ['44-24=20', '26-20=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,93 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[44, 87, 26, 24], Operations: [] Exploring Operation: 44-24=20, Resulting Numbers: [87, 26, 20] Generated Node #0,0: 93:[87, 26, 20] Operation: 44-24=20 Moving to Node #0,0 Current State: 93:[87, 26, 20], Operations: ['44-24=20'] Exploring Operation: 26-20=6, Resulting Numbers: [87, 6] Generated Node #0,0,0: 93:[87, 6] Operation: 26-20=6 Moving to Node #0,0,0 Current State: 93:[87, 6], Operations: ['44-24=20', '26-20=6'] Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 73, 32, 77, 76 ]
68
[ "77-73=4", "32/4=8", "76-8=68" ]
Current State: 68:[73, 32, 77, 76], Operations: [] Exploring Operation: 77-73=4, Resulting Numbers: [32, 76, 4] Generated Node #2: [32, 76, 4] from Operation: 77-73=4 Current State: 68:[32, 76, 4], Operations: ['77-73=4'] Exploring Operation: 32/4=8, Resulting Numbers: [76, 8] Generated Node #3: [76, 8] from Operation: 32/4=8 Current State: 68:[76, 8], Operations: ['77-73=4', '32/4=8'] Exploring Operation: 76-8=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[73, 32, 77, 76], Operations: [] Exploring Operation: 77-73=4, Resulting Numbers: [32, 76, 4] Generated Node #0,0: 68:[32, 76, 4] Operation: 77-73=4 Exploring Operation: 77-76=1, Resulting Numbers: [73, 32, 1] Generated Node #0,1: 68:[73, 32, 1] Operation: 77-76=1 Exploring Operation: 76-73=3, Resulting Numbers: [32, 77, 3] Generated Node #0,2: 68:[32, 77, 3] Operation: 76-73=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[73, 32, 1], Operations: ['77-76=1'] Exploring Operation: 73-1=72, Resulting Numbers: [32, 72] Generated Node #0,1,0: 68:[32, 72] Operation: 73-1=72 Exploring Operation: 32+1=33, Resulting Numbers: [73, 33] Generated Node #0,1,1: 68:[73, 33] Operation: 32+1=33 Exploring Operation: 73*1=73, Resulting Numbers: [32, 73] Generated Node #0,1,2: 68:[32, 73] Operation: 73*1=73 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 68:[32, 72], Operations: ['77-76=1', '73-1=72'] Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,68 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 68:[73, 33], Operations: ['77-76=1', '32+1=33'] Exploring Operation: 73+33=106, Resulting Numbers: [106] 106,68 unequal: No Solution Exploring Operation: 73*33=2409, Resulting Numbers: [2409] 2409,68 unequal: No Solution Exploring Operation: 73-33=40, Resulting Numbers: [40] 40,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 68:[32, 73], Operations: ['77-76=1', '73*1=73'] Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,68 unequal: No Solution Exploring Operation: 32*73=2336, Resulting Numbers: [2336] 2336,68 unequal: No Solution Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[32, 76, 4], Operations: ['77-73=4'] Exploring Operation: 76-32=44, Resulting Numbers: [4, 44] Generated Node #0,0,0: 68:[4, 44] Operation: 76-32=44 Exploring Operation: 76/4=19, Resulting Numbers: [32, 19] Generated Node #0,0,1: 68:[32, 19] Operation: 76/4=19 Exploring Operation: 76-4=72, Resulting Numbers: [32, 72] Generated Node #0,0,2: 68:[32, 72] Operation: 76-4=72 Moving to Node #0,0,1 Current State: 68:[32, 19], Operations: ['77-73=4', '76/4=19'] Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,68 unequal: No Solution Exploring Operation: 32+19=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 32*19=608, Resulting Numbers: [608] 608,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[32, 72], Operations: ['77-73=4', '76-4=72'] Exploring Operation: 72-32=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 32*72=2304, Resulting Numbers: [2304] 2304,68 unequal: No Solution Exploring Operation: 32+72=104, Resulting Numbers: [104] 104,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[4, 44], Operations: ['77-73=4', '76-32=44'] Exploring Operation: 4+44=48, Resulting Numbers: [48] 48,68 unequal: No Solution Exploring Operation: 44/4=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 44-4=40, Resulting Numbers: [40] 40,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[32, 77, 3], Operations: ['76-73=3'] Exploring Operation: 77-3=74, Resulting Numbers: [32, 74] Generated Node #0,2,0: 68:[32, 74] Operation: 77-3=74 Exploring Operation: 32+3=35, Resulting Numbers: [77, 35] Generated Node #0,2,1: 68:[77, 35] Operation: 32+3=35 Exploring Operation: 77-32=45, Resulting Numbers: [3, 45] Generated Node #0,2,2: 68:[3, 45] Operation: 77-32=45 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[32, 74], Operations: ['76-73=3', '77-3=74'] Exploring Operation: 74-32=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 32+74=106, Resulting Numbers: [106] 106,68 unequal: No Solution Exploring Operation: 32*74=2368, Resulting Numbers: [2368] 2368,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 68:[77, 35], Operations: ['76-73=3', '32+3=35'] Exploring Operation: 77+35=112, Resulting Numbers: [112] 112,68 unequal: No Solution Exploring Operation: 77*35=2695, Resulting Numbers: [2695] 2695,68 unequal: No Solution Exploring Operation: 77-35=42, Resulting Numbers: [42] 42,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 68:[3, 45], Operations: ['76-73=3', '77-32=45'] Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,68 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 84, 6, 29, 62 ]
77
[ "84/6=14", "29+62=91", "91-14=77" ]
Current State: 77:[84, 6, 29, 62], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [29, 62, 14] Generated Node #2: [29, 62, 14] from Operation: 84/6=14 Current State: 77:[29, 62, 14], Operations: ['84/6=14'] Exploring Operation: 29+62=91, Resulting Numbers: [14, 91] Generated Node #3: [14, 91] from Operation: 29+62=91 Current State: 77:[14, 91], Operations: ['84/6=14', '29+62=91'] Exploring Operation: 91-14=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[84, 6, 29, 62], Operations: [] Exploring Operation: 29+62=91, Resulting Numbers: [84, 6, 91] Generated Node #0,0: 77:[84, 6, 91] Operation: 29+62=91 Exploring Operation: 62-29=33, Resulting Numbers: [84, 6, 33] Generated Node #0,1: 77:[84, 6, 33] Operation: 62-29=33 Exploring Operation: 84-62=22, Resulting Numbers: [6, 29, 22] Generated Node #0,2: 77:[6, 29, 22] Operation: 84-62=22 Moving to Node #0,0 Current State: 77:[84, 6, 91], Operations: ['29+62=91'] Exploring Operation: 91-84=7, Resulting Numbers: [6, 7] Generated Node #0,0,0: 77:[6, 7] Operation: 91-84=7 Exploring Operation: 84-6=78, Resulting Numbers: [91, 78] Generated Node #0,0,1: 77:[91, 78] Operation: 84-6=78 Exploring Operation: 91-6=85, Resulting Numbers: [84, 85] Generated Node #0,0,2: 77:[84, 85] Operation: 91-6=85 Moving to Node #0,1 Current State: 77:[84, 6, 33], Operations: ['62-29=33'] Exploring Operation: 84/6=14, Resulting Numbers: [33, 14] Generated Node #0,1,0: 77:[33, 14] Operation: 84/6=14 Exploring Operation: 33-6=27, Resulting Numbers: [84, 27] Generated Node #0,1,1: 77:[84, 27] Operation: 33-6=27 Exploring Operation: 84-6=78, Resulting Numbers: [33, 78] Generated Node #0,1,2: 77:[33, 78] Operation: 84-6=78 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[84, 27], Operations: ['62-29=33', '33-6=27'] Exploring Operation: 84-27=57, Resulting Numbers: [57] 57,77 unequal: No Solution Exploring Operation: 84*27=2268, Resulting Numbers: [2268] 2268,77 unequal: No Solution Exploring Operation: 84+27=111, Resulting Numbers: [111] 111,77 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 #0,1,2 Current State: 77:[33, 78], Operations: ['62-29=33', '84-6=78'] Exploring Operation: 33+78=111, Resulting Numbers: [111] 111,77 unequal: No Solution Exploring Operation: 78-33=45, Resulting Numbers: [45] 45,77 unequal: No Solution Exploring Operation: 33*78=2574, Resulting Numbers: [2574] 2574,77 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 #0,1,0 Current State: 77:[33, 14], Operations: ['62-29=33', '84/6=14'] Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,77 unequal: No Solution Exploring Operation: 33+14=47, Resulting Numbers: [47] 47,77 unequal: No Solution Exploring Operation: 33*14=462, Resulting Numbers: [462] 462,77 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: 77:[6, 29, 22], Operations: ['84-62=22'] Exploring Operation: 22-6=16, Resulting Numbers: [29, 16] Generated Node #0,2,0: 77:[29, 16] Operation: 22-6=16 Exploring Operation: 29-6=23, Resulting Numbers: [22, 23] Generated Node #0,2,1: 77:[22, 23] Operation: 29-6=23 Exploring Operation: 29-22=7, Resulting Numbers: [6, 7] Generated Node #0,2,2: 77:[6, 7] Operation: 29-22=7 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 77:[6, 7], Operations: ['84-62=22', '29-22=7'] Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,77 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 #0,2,0 Current State: 77:[29, 16], Operations: ['84-62=22', '22-6=16'] Exploring Operation: 29-16=13, Resulting Numbers: [13] 13,77 unequal: No Solution Exploring Operation: 29+16=45, Resulting Numbers: [45] 45,77 unequal: No Solution Exploring Operation: 29*16=464, Resulting Numbers: [464] 464,77 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 #0,2,1 Current State: 77:[22, 23], Operations: ['84-62=22', '29-6=23'] Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,77 unequal: No Solution Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,77 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,77 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: 77:[6, 7], Operations: ['29+62=91', '91-84=7'] Exploring Operation: 6*7=42, Resulting Numbers: [42] 42,77 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 6+7=13, Resulting Numbers: [13] 13,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[91, 78], Operations: ['29+62=91', '84-6=78'] Exploring Operation: 91+78=169, Resulting Numbers: [169] 169,77 unequal: No Solution Exploring Operation: 91*78=7098, Resulting Numbers: [7098] 7098,77 unequal: No Solution Exploring Operation: 91-78=13, Resulting Numbers: [13] 13,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[84, 85], Operations: ['29+62=91', '91-6=85'] Exploring Operation: 84*85=7140, Resulting Numbers: [7140] 7140,77 unequal: No Solution Exploring Operation: 85-84=1, Resulting Numbers: [1] 1,77 unequal: No Solution Exploring Operation: 84+85=169, Resulting Numbers: [169] 169,77 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 67, 13, 35, 78 ]
33
[ "67+13=80", "35+78=113", "113-80=33" ]
Current State: 33:[67, 13, 35, 78], Operations: [] Exploring Operation: 67+13=80, Resulting Numbers: [35, 78, 80] Generated Node #2: [35, 78, 80] from Operation: 67+13=80 Current State: 33:[35, 78, 80], Operations: ['67+13=80'] Exploring Operation: 35+78=113, Resulting Numbers: [80, 113] Generated Node #3: [80, 113] from Operation: 35+78=113 Current State: 33:[80, 113], Operations: ['67+13=80', '35+78=113'] Exploring Operation: 113-80=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[67, 13, 35, 78], Operations: [] Exploring Operation: 78/13=6, Resulting Numbers: [67, 35, 6] Generated Node #0,0: 33:[67, 35, 6] Operation: 78/13=6 Exploring Operation: 78-67=11, Resulting Numbers: [13, 35, 11] Generated Node #0,1: 33:[13, 35, 11] Operation: 78-67=11 Moving to Node #0,1 Current State: 33:[13, 35, 11], Operations: ['78-67=11'] Exploring Operation: 35-13=22, Resulting Numbers: [11, 22] Generated Node #0,1,0: 33:[11, 22] Operation: 35-13=22 Exploring Operation: 13-11=2, Resulting Numbers: [35, 2] Generated Node #0,1,1: 33:[35, 2] Operation: 13-11=2 Moving to Node #0,0 Current State: 33:[67, 35, 6], Operations: ['78/13=6'] Exploring Operation: 67-35=32, Resulting Numbers: [6, 32] Generated Node #0,0,0: 33:[6, 32] Operation: 67-35=32 Exploring Operation: 67-6=61, Resulting Numbers: [35, 61] Generated Node #0,0,1: 33:[35, 61] Operation: 67-6=61 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[6, 32], Operations: ['78/13=6', '67-35=32'] Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,33 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 33:[35, 61], Operations: ['78/13=6', '67-6=61'] Exploring Operation: 61-35=26, Resulting Numbers: [26] 26,33 unequal: No Solution Exploring Operation: 35+61=96, Resulting Numbers: [96] 96,33 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: 33:[35, 2], Operations: ['78-67=11', '13-11=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached Moving to Node #0 Current State: 33:[67, 13, 35, 78], Operations: [] Exploring Operation: 78-67=11, Resulting Numbers: [13, 35, 11] Generated Node #0,1: 33:[13, 35, 11] Operation: 78-67=11 Moving to Node #0,1 Current State: 33:[13, 35, 11], Operations: ['78-67=11'] Exploring Operation: 13-11=2, Resulting Numbers: [35, 2] Generated Node #0,1,1: 33:[35, 2] Operation: 13-11=2 Moving to Node #0,1,1 Current State: 33:[35, 2], Operations: ['78-67=11', '13-11=2'] Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
0.986979
hs_2
mult_heuristic
[ 43, 63, 41, 31 ]
95
[ "43-41=2", "63*2=126", "126-31=95" ]
Current State: 95:[43, 63, 41, 31], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [63, 31, 2] Generated Node #2: [63, 31, 2] from Operation: 43-41=2 Current State: 95:[63, 31, 2], Operations: ['43-41=2'] Exploring Operation: 63*2=126, Resulting Numbers: [31, 126] Generated Node #3: [31, 126] from Operation: 63*2=126 Current State: 95:[31, 126], Operations: ['43-41=2', '63*2=126'] Exploring Operation: 126-31=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[43, 63, 41, 31], Operations: [] Exploring Operation: 43+63=106, Resulting Numbers: [41, 31, 106] Generated Node #0,0: 95:[41, 31, 106] Operation: 43+63=106 Exploring Operation: 63-41=22, Resulting Numbers: [43, 31, 22] Generated Node #0,1: 95:[43, 31, 22] Operation: 63-41=22 Exploring Operation: 43-41=2, Resulting Numbers: [63, 31, 2] Generated Node #0,2: 95:[63, 31, 2] Operation: 43-41=2 Exploring Operation: 63+41=104, Resulting Numbers: [43, 31, 104] Generated Node #0,3: 95:[43, 31, 104] Operation: 63+41=104 Exploring Operation: 63-43=20, Resulting Numbers: [41, 31, 20] Generated Node #0,4: 95:[41, 31, 20] Operation: 63-43=20 Moving to Node #0,4 Current State: 95:[41, 31, 20], Operations: ['63-43=20'] Exploring Operation: 41-31=10, Resulting Numbers: [20, 10] Generated Node #0,4,0: 95:[20, 10] Operation: 41-31=10 Exploring Operation: 31-20=11, Resulting Numbers: [41, 11] Generated Node #0,4,1: 95:[41, 11] Operation: 31-20=11 Exploring Operation: 41-20=21, Resulting Numbers: [31, 21] Generated Node #0,4,2: 95:[31, 21] Operation: 41-20=21 Exploring Operation: 41+31=72, Resulting Numbers: [20, 72] Generated Node #0,4,3: 95:[20, 72] Operation: 41+31=72 Exploring Operation: 41+20=61, Resulting Numbers: [31, 61] Generated Node #0,4,4: 95:[31, 61] Operation: 41+20=61 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 95:[20, 10], Operations: ['63-43=20', '41-31=10'] Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,95 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 95:[31, 21], Operations: ['63-43=20', '41-20=21'] Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,95 unequal: No Solution Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 95:[20, 72], Operations: ['63-43=20', '41+31=72'] Exploring Operation: 72-20=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 20*72=1440, Resulting Numbers: [1440] 1440,95 unequal: No Solution Exploring Operation: 20+72=92, Resulting Numbers: [92] 92,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 95:[41, 11], Operations: ['63-43=20', '31-20=11'] Exploring Operation: 41-11=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 41*11=451, Resulting Numbers: [451] 451,95 unequal: No Solution Exploring Operation: 41+11=52, Resulting Numbers: [52] 52,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 95:[31, 61], Operations: ['63-43=20', '41+20=61'] Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 31+61=92, Resulting Numbers: [92] 92,95 unequal: No Solution Exploring Operation: 31*61=1891, Resulting Numbers: [1891] 1891,95 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: 95:[43, 31, 22], Operations: ['63-41=22'] Exploring Operation: 43+22=65, Resulting Numbers: [31, 65] Generated Node #0,1,0: 95:[31, 65] Operation: 43+22=65 Exploring Operation: 31-22=9, Resulting Numbers: [43, 9] Generated Node #0,1,1: 95:[43, 9] Operation: 31-22=9 Exploring Operation: 43+31=74, Resulting Numbers: [22, 74] Generated Node #0,1,2: 95:[22, 74] Operation: 43+31=74 Exploring Operation: 43-31=12, Resulting Numbers: [22, 12] Generated Node #0,1,3: 95:[22, 12] Operation: 43-31=12 Exploring Operation: 43-22=21, Resulting Numbers: [31, 21] Generated Node #0,1,4: 95:[31, 21] Operation: 43-22=21 Moving to Node #0,0 Current State: 95:[41, 31, 106], Operations: ['43+63=106'] Exploring Operation: 106-41=65, Resulting Numbers: [31, 65] Generated Node #0,0,0: 95:[31, 65] Operation: 106-41=65 Exploring Operation: 41+106=147, Resulting Numbers: [31, 147] Generated Node #0,0,1: 95:[31, 147] Operation: 41+106=147 Exploring Operation: 106-31=75, Resulting Numbers: [41, 75] Generated Node #0,0,2: 95:[41, 75] Operation: 106-31=75 Exploring Operation: 41-31=10, Resulting Numbers: [106, 10] Generated Node #0,0,3: 95:[106, 10] Operation: 41-31=10 Exploring Operation: 41+31=72, Resulting Numbers: [106, 72] Generated Node #0,0,4: 95:[106, 72] Operation: 41+31=72 Moving to Node #0,3 Current State: 95:[43, 31, 104], Operations: ['63+41=104'] Exploring Operation: 43+31=74, Resulting Numbers: [104, 74] Generated Node #0,3,0: 95:[104, 74] Operation: 43+31=74 Exploring Operation: 104-31=73, Resulting Numbers: [43, 73] Generated Node #0,3,1: 95:[43, 73] Operation: 104-31=73 Exploring Operation: 43+104=147, Resulting Numbers: [31, 147] Generated Node #0,3,2: 95:[31, 147] Operation: 43+104=147 Exploring Operation: 43-31=12, Resulting Numbers: [104, 12] Generated Node #0,3,3: 95:[104, 12] Operation: 43-31=12 Exploring Operation: 104-43=61, Resulting Numbers: [31, 61] Generated Node #0,3,4: 95:[31, 61] Operation: 104-43=61 Moving to Node #0,2 Current State: 95:[63, 31, 2], Operations: ['43-41=2'] Exploring Operation: 63+31=94, Resulting Numbers: [2, 94] Generated Node #0,2,0: 95:[2, 94] Operation: 63+31=94 Exploring Operation: 31-2=29, Resulting Numbers: [63, 29] Generated Node #0,2,1: 95:[63, 29] Operation: 31-2=29 Exploring Operation: 63+2=65, Resulting Numbers: [31, 65] Generated Node #0,2,2: 95:[31, 65] Operation: 63+2=65 Exploring Operation: 63-31=32, Resulting Numbers: [2, 32] Generated Node #0,2,3: 95:[2, 32] Operation: 63-31=32 Exploring Operation: 63*2=126, Resulting Numbers: [31, 126] Generated Node #0,2,4: 95:[31, 126] Operation: 63*2=126 Moving to Node #0,2,0 Current State: 95:[2, 94], Operations: ['43-41=2', '63+31=94'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,95 unequal: No Solution Exploring Operation: 2*94=188, Resulting Numbers: [188] 188,95 unequal: No Solution Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,95 unequal: No Solution Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[22, 12], Operations: ['63-41=22', '43-31=12'] Exploring Operation: 22+12=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 22*12=264, Resulting Numbers: [264] 264,95 unequal: No Solution Exploring Operation: 22-12=10, Resulting Numbers: [10] 10,95 unequal: No Solution Moving to Node #0,1,4 Current State: 95:[31, 21], Operations: ['63-41=22', '43-22=21'] Exploring Operation: 31+21=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 31*21=651, Resulting Numbers: [651] 651,95 unequal: No Solution Moving to Node #0,0,3 Current State: 95:[106, 10], Operations: ['43+63=106', '41-31=10'] Exploring Operation: 106-10=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 106+10=116, Resulting Numbers: [116] 116,95 unequal: No Solution Exploring Operation: 106*10=1060, Resulting Numbers: [1060] 1060,95 unequal: No Solution Moving to Node #0,3,3 Current State: 95:[104, 12], Operations: ['63+41=104', '43-31=12'] Exploring Operation: 104-12=92, Resulting Numbers: [92] 92,95 unequal: No Solution Exploring Operation: 104+12=116, Resulting Numbers: [116] 116,95 unequal: No Solution Exploring Operation: 104*12=1248, Resulting Numbers: [1248] 1248,95 unequal: No Solution Moving to Node #0,2,3 Current State: 95:[2, 32], Operations: ['43-41=2', '63-31=32'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 2*32=64, Resulting Numbers: [64] 64,95 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,95 unequal: No Solution Exploring Operation: 2+32=34, Resulting Numbers: [34] 34,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[22, 74], Operations: ['63-41=22', '43+31=74'] Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 22*74=1628, Resulting Numbers: [1628] 1628,95 unequal: No Solution Exploring Operation: 22+74=96, Resulting Numbers: [96] 96,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[43, 9], Operations: ['63-41=22', '31-22=9'] Exploring Operation: 43+9=52, Resulting Numbers: [52] 52,95 unequal: No Solution Exploring Operation: 43*9=387, Resulting Numbers: [387] 387,95 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,95 unequal: No Solution Moving to Node #0,3,0 Current State: 95:[104, 74], Operations: ['63+41=104', '43+31=74'] Exploring Operation: 104-74=30, Resulting Numbers: [30] 30,95 unequal: No Solution Exploring Operation: 104*74=7696, Resulting Numbers: [7696] 7696,95 unequal: No Solution Exploring Operation: 104+74=178, Resulting Numbers: [178] 178,95 unequal: No Solution Moving to Node #0,0,4 Current State: 95:[106, 72], Operations: ['43+63=106', '41+31=72'] Exploring Operation: 106*72=7632, Resulting Numbers: [7632] 7632,95 unequal: No Solution Exploring Operation: 106+72=178, Resulting Numbers: [178] 178,95 unequal: No Solution Exploring Operation: 106-72=34, Resulting Numbers: [34] 34,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[63, 29], Operations: ['43-41=2', '31-2=29'] Exploring Operation: 63-29=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 63*29=1827, Resulting Numbers: [1827] 1827,95 unequal: No Solution Exploring Operation: 63+29=92, Resulting Numbers: [92] 92,95 unequal: No Solution Moving to Node #0,1,0 Current State: 95:[31, 65], Operations: ['63-41=22', '43+22=65'] Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 31+65=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 31*65=2015, Resulting Numbers: [2015] 2015,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[31, 65], Operations: ['43-41=2', '63+2=65'] Exploring Operation: 31*65=2015, Resulting Numbers: [2015] 2015,95 unequal: No Solution Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 31+65=96, Resulting Numbers: [96] 96,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[41, 75], Operations: ['43+63=106', '106-31=75'] Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,95 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[31, 65], Operations: ['43+63=106', '106-41=65'] Exploring Operation: 31*65=2015, Resulting Numbers: [2015] 2015,95 unequal: No Solution Exploring Operation: 31+65=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 65-31=34, Resulting Numbers: [34] 34,95 unequal: No Solution Moving to Node #0,2,4 Current State: 95:[31, 126], Operations: ['43-41=2', '63*2=126'] Exploring Operation: 126-31=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[43, 63, 41, 31], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [63, 31, 2] Generated Node #0,2: 95:[63, 31, 2] Operation: 43-41=2 Moving to Node #0,2 Current State: 95:[63, 31, 2], Operations: ['43-41=2'] Exploring Operation: 63*2=126, Resulting Numbers: [31, 126] Generated Node #0,2,4: 95:[31, 126] Operation: 63*2=126 Moving to Node #0,2,4 Current State: 95:[31, 126], Operations: ['43-41=2', '63*2=126'] Exploring Operation: 126-31=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
0.914931
hs_5
sum_heuristic
[ 43, 71, 26, 45 ]
58
[ "45-43=2", "26/2=13", "71-13=58" ]
Current State: 58:[43, 71, 26, 45], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [71, 26, 2] Generated Node #2: [71, 26, 2] from Operation: 45-43=2 Current State: 58:[71, 26, 2], Operations: ['45-43=2'] Exploring Operation: 26/2=13, Resulting Numbers: [71, 13] Generated Node #3: [71, 13] from Operation: 26/2=13 Current State: 58:[71, 13], Operations: ['45-43=2', '26/2=13'] Exploring Operation: 71-13=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[43, 71, 26, 45], Operations: [] Exploring Operation: 45-43=2, Resulting Numbers: [71, 26, 2] Generated Node #0,0: 58:[71, 26, 2] Operation: 45-43=2 Exploring Operation: 71-43=28, Resulting Numbers: [26, 45, 28] Generated Node #0,1: 58:[26, 45, 28] Operation: 71-43=28 Moving to Node #0,0 Current State: 58:[71, 26, 2], Operations: ['45-43=2'] Exploring Operation: 71-26=45, Resulting Numbers: [2, 45] Generated Node #0,0,0: 58:[2, 45] Operation: 71-26=45 Exploring Operation: 71-2=69, Resulting Numbers: [26, 69] Generated Node #0,0,1: 58:[26, 69] Operation: 71-2=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[2, 45], Operations: ['45-43=2', '71-26=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 58:[26, 69], Operations: ['45-43=2', '71-2=69'] Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 26+69=95, Resulting Numbers: [95] 95,58 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: 58:[26, 45, 28], Operations: ['71-43=28'] Exploring Operation: 28-26=2, Resulting Numbers: [45, 2] Generated Node #0,1,0: 58:[45, 2] Operation: 28-26=2 Exploring Operation: 45-26=19, Resulting Numbers: [28, 19] Generated Node #0,1,1: 58:[28, 19] Operation: 45-26=19 Moving to Node #0,1,1 Current State: 58:[28, 19], Operations: ['71-43=28', '45-26=19'] Exploring Operation: 28+19=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[45, 2], Operations: ['71-43=28', '28-26=2'] Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,58 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,58 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 75, 13, 58, 96 ]
66
[ "75+13=88", "58+96=154", "154-88=66" ]
Current State: 66:[75, 13, 58, 96], Operations: [] Exploring Operation: 75+13=88, Resulting Numbers: [58, 96, 88] Generated Node #2: [58, 96, 88] from Operation: 75+13=88 Current State: 66:[58, 96, 88], Operations: ['75+13=88'] Exploring Operation: 58+96=154, Resulting Numbers: [88, 154] Generated Node #3: [88, 154] from Operation: 58+96=154 Current State: 66:[88, 154], Operations: ['75+13=88', '58+96=154'] Exploring Operation: 154-88=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[75, 13, 58, 96], Operations: [] Exploring Operation: 96-75=21, Resulting Numbers: [13, 58, 21] Generated Node #0,0: 66:[13, 58, 21] Operation: 96-75=21 Exploring Operation: 75-13=62, Resulting Numbers: [58, 96, 62] Generated Node #0,1: 66:[58, 96, 62] Operation: 75-13=62 Exploring Operation: 75-58=17, Resulting Numbers: [13, 96, 17] Generated Node #0,2: 66:[13, 96, 17] Operation: 75-58=17 Exploring Operation: 96-58=38, Resulting Numbers: [75, 13, 38] Generated Node #0,3: 66:[75, 13, 38] Operation: 96-58=38 Exploring Operation: 96-13=83, Resulting Numbers: [75, 58, 83] Generated Node #0,4: 66:[75, 58, 83] Operation: 96-13=83 Moving to Node #0,0 Current State: 66:[13, 58, 21], Operations: ['96-75=21'] Exploring Operation: 58-13=45, Resulting Numbers: [21, 45] Generated Node #0,0,0: 66:[21, 45] Operation: 58-13=45 Exploring Operation: 58-21=37, Resulting Numbers: [13, 37] Generated Node #0,0,1: 66:[13, 37] Operation: 58-21=37 Exploring Operation: 21-13=8, Resulting Numbers: [58, 8] Generated Node #0,0,2: 66:[58, 8] Operation: 21-13=8 Exploring Operation: 13+58=71, Resulting Numbers: [21, 71] Generated Node #0,0,3: 66:[21, 71] Operation: 13+58=71 Exploring Operation: 13+21=34, Resulting Numbers: [58, 34] Generated Node #0,0,4: 66:[58, 34] Operation: 13+21=34 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 66:[13, 37], Operations: ['96-75=21', '58-21=37'] Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 13*37=481, Resulting Numbers: [481] 481,66 unequal: No Solution Exploring Operation: 13+37=50, Resulting Numbers: [50] 50,66 unequal: No Solution No 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: 66:[21, 71], Operations: ['96-75=21', '13+58=71'] Exploring Operation: 21+71=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 21*71=1491, Resulting Numbers: [1491] 1491,66 unequal: No Solution Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,66 unequal: No Solution No 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: 66:[58, 34], Operations: ['96-75=21', '13+21=34'] Exploring Operation: 58*34=1972, Resulting Numbers: [1972] 1972,66 unequal: No Solution Exploring Operation: 58+34=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 58-34=24, Resulting Numbers: [24] 24,66 unequal: No Solution No 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: 66:[58, 8], Operations: ['96-75=21', '21-13=8'] Exploring Operation: 58*8=464, Resulting Numbers: [464] 464,66 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[75, 13, 58, 96], Operations: [] Exploring Operation: 96-75=21, Resulting Numbers: [13, 58, 21] Generated Node #0,0: 66:[13, 58, 21] Operation: 96-75=21 Moving to Node #0,0 Current State: 66:[13, 58, 21], Operations: ['96-75=21'] Exploring Operation: 21-13=8, Resulting Numbers: [58, 8] Generated Node #0,0,2: 66:[58, 8] Operation: 21-13=8 Moving to Node #0,0,2 Current State: 66:[58, 8], Operations: ['96-75=21', '21-13=8'] Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
sum_heuristic
[ 9, 27, 82, 47 ]
59
[ "27/9=3", "47*3=141", "141-82=59" ]
Current State: 59:[9, 27, 82, 47], Operations: [] Exploring Operation: 27/9=3, Resulting Numbers: [82, 47, 3] Generated Node #2: [82, 47, 3] from Operation: 27/9=3 Current State: 59:[82, 47, 3], Operations: ['27/9=3'] Exploring Operation: 47*3=141, Resulting Numbers: [82, 141] Generated Node #3: [82, 141] from Operation: 47*3=141 Current State: 59:[82, 141], Operations: ['27/9=3', '47*3=141'] Exploring Operation: 141-82=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[9, 27, 82, 47], Operations: [] Exploring Operation: 82-27=55, Resulting Numbers: [9, 47, 55] Generated Node #0,0: 59:[9, 47, 55] Operation: 82-27=55 Exploring Operation: 27-9=18, Resulting Numbers: [82, 47, 18] Generated Node #0,1: 59:[82, 47, 18] Operation: 27-9=18 Exploring Operation: 9+27=36, Resulting Numbers: [82, 47, 36] Generated Node #0,2: 59:[82, 47, 36] Operation: 9+27=36 Exploring Operation: 82-9=73, Resulting Numbers: [27, 47, 73] Generated Node #0,3: 59:[27, 47, 73] Operation: 82-9=73 Exploring Operation: 9+47=56, Resulting Numbers: [27, 82, 56] Generated Node #0,4: 59:[27, 82, 56] Operation: 9+47=56 Moving to Node #0,2 Current State: 59:[82, 47, 36], Operations: ['9+27=36'] Exploring Operation: 82+36=118, Resulting Numbers: [47, 118] Generated Node #0,2,0: 59:[47, 118] Operation: 82+36=118 Exploring Operation: 47-36=11, Resulting Numbers: [82, 11] Generated Node #0,2,1: 59:[82, 11] Operation: 47-36=11 Exploring Operation: 82-47=35, Resulting Numbers: [36, 35] Generated Node #0,2,2: 59:[36, 35] Operation: 82-47=35 Exploring Operation: 82-36=46, Resulting Numbers: [47, 46] Generated Node #0,2,3: 59:[47, 46] Operation: 82-36=46 Exploring Operation: 47+36=83, Resulting Numbers: [82, 83] Generated Node #0,2,4: 59:[82, 83] Operation: 47+36=83 Moving to Node #0,4 Current State: 59:[27, 82, 56], Operations: ['9+47=56'] Exploring Operation: 27+82=109, Resulting Numbers: [56, 109] Generated Node #0,4,0: 59:[56, 109] Operation: 27+82=109 Exploring Operation: 82-27=55, Resulting Numbers: [56, 55] Generated Node #0,4,1: 59:[56, 55] Operation: 82-27=55 Exploring Operation: 56-27=29, Resulting Numbers: [82, 29] Generated Node #0,4,2: 59:[82, 29] Operation: 56-27=29 Exploring Operation: 82-56=26, Resulting Numbers: [27, 26] Generated Node #0,4,3: 59:[27, 26] Operation: 82-56=26 Exploring Operation: 27+56=83, Resulting Numbers: [82, 83] Generated Node #0,4,4: 59:[82, 83] Operation: 27+56=83 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 59:[56, 55], Operations: ['9+47=56', '82-27=55'] Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 56+55=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 56*55=3080, Resulting Numbers: [3080] 3080,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 59:[82, 83], Operations: ['9+47=56', '27+56=83'] Exploring Operation: 82+83=165, Resulting Numbers: [165] 165,59 unequal: No Solution Exploring Operation: 83-82=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 82*83=6806, Resulting Numbers: [6806] 6806,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 59:[56, 109], Operations: ['9+47=56', '27+82=109'] Exploring Operation: 56*109=6104, Resulting Numbers: [6104] 6104,59 unequal: No Solution Exploring Operation: 109-56=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 56+109=165, Resulting Numbers: [165] 165,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 59:[82, 29], Operations: ['9+47=56', '56-27=29'] Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,59 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 59:[27, 26], Operations: ['9+47=56', '82-56=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,59 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,59 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: 59:[27, 47, 73], Operations: ['82-9=73'] Exploring Operation: 47-27=20, Resulting Numbers: [73, 20] Generated Node #0,3,0: 59:[73, 20] Operation: 47-27=20 Exploring Operation: 73-27=46, Resulting Numbers: [47, 46] Generated Node #0,3,1: 59:[47, 46] Operation: 73-27=46 Exploring Operation: 27+73=100, Resulting Numbers: [47, 100] Generated Node #0,3,2: 59:[47, 100] Operation: 27+73=100 Exploring Operation: 73-47=26, Resulting Numbers: [27, 26] Generated Node #0,3,3: 59:[27, 26] Operation: 73-47=26 Exploring Operation: 27+47=74, Resulting Numbers: [73, 74] Generated Node #0,3,4: 59:[73, 74] Operation: 27+47=74 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 59:[47, 46], Operations: ['82-9=73', '73-27=46'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 47*46=2162, Resulting Numbers: [2162] 2162,59 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 #0,3,4 Current State: 59:[73, 74], Operations: ['82-9=73', '27+47=74'] Exploring Operation: 73*74=5402, Resulting Numbers: [5402] 5402,59 unequal: No Solution Exploring Operation: 73+74=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 74-73=1, Resulting Numbers: [1] 1,59 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:[73, 20], Operations: ['82-9=73', '47-27=20'] Exploring Operation: 73+20=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 73*20=1460, Resulting Numbers: [1460] 1460,59 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 #0,3,2 Current State: 59:[47, 100], Operations: ['82-9=73', '27+73=100'] Exploring Operation: 47+100=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 100-47=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 47*100=4700, Resulting Numbers: [4700] 4700,59 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 #0,3,3 Current State: 59:[27, 26], Operations: ['82-9=73', '73-47=26'] Exploring Operation: 27-26=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 27+26=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 27*26=702, Resulting Numbers: [702] 702,59 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: 59:[9, 47, 55], Operations: ['82-27=55'] Exploring Operation: 9+47=56, Resulting Numbers: [55, 56] Generated Node #0,0,0: 59:[55, 56] Operation: 9+47=56 Exploring Operation: 47+55=102, Resulting Numbers: [9, 102] Generated Node #0,0,1: 59:[9, 102] Operation: 47+55=102 Exploring Operation: 55-9=46, Resulting Numbers: [47, 46] Generated Node #0,0,2: 59:[47, 46] Operation: 55-9=46 Exploring Operation: 47-9=38, Resulting Numbers: [55, 38] Generated Node #0,0,3: 59:[55, 38] Operation: 47-9=38 Exploring Operation: 9+55=64, Resulting Numbers: [47, 64] Generated Node #0,0,4: 59:[47, 64] Operation: 9+55=64 Moving to Node #0,1 Current State: 59:[82, 47, 18], Operations: ['27-9=18'] Exploring Operation: 47+18=65, Resulting Numbers: [82, 65] Generated Node #0,1,0: 59:[82, 65] Operation: 47+18=65 Exploring Operation: 82-18=64, Resulting Numbers: [47, 64] Generated Node #0,1,1: 59:[47, 64] Operation: 82-18=64 Exploring Operation: 47-18=29, Resulting Numbers: [82, 29] Generated Node #0,1,2: 59:[82, 29] Operation: 47-18=29 Exploring Operation: 82+18=100, Resulting Numbers: [47, 100] Generated Node #0,1,3: 59:[47, 100] Operation: 82+18=100 Exploring Operation: 82-47=35, Resulting Numbers: [18, 35] Generated Node #0,1,4: 59:[18, 35] Operation: 82-47=35 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 59:[47, 64], Operations: ['27-9=18', '82-18=64'] Exploring Operation: 47*64=3008, Resulting Numbers: [3008] 3008,59 unequal: No Solution Exploring Operation: 47+64=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 64-47=17, Resulting Numbers: [17] 17,59 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 #0,1,0 Current State: 59:[82, 65], Operations: ['27-9=18', '47+18=65'] Exploring Operation: 82+65=147, Resulting Numbers: [147] 147,59 unequal: No Solution Exploring Operation: 82-65=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 82*65=5330, Resulting Numbers: [5330] 5330,59 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:[82, 29], Operations: ['27-9=18', '47-18=29'] Exploring Operation: 82*29=2378, Resulting Numbers: [2378] 2378,59 unequal: No Solution Exploring Operation: 82+29=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 82-29=53, Resulting Numbers: [53] 53,59 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 #0,1,3 Current State: 59:[47, 100], Operations: ['27-9=18', '82+18=100'] Exploring Operation: 100-47=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 47*100=4700, Resulting Numbers: [4700] 4700,59 unequal: No Solution Exploring Operation: 47+100=147, Resulting Numbers: [147] 147,59 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 #0,1,4 Current State: 59:[18, 35], Operations: ['27-9=18', '82-47=35'] Exploring Operation: 18+35=53, Resulting Numbers: [53] 53,59 unequal: No Solution Exploring Operation: 18*35=630, Resulting Numbers: [630] 630,59 unequal: No Solution Exploring Operation: 35-18=17, Resulting Numbers: [17] 17,59 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: 59:[55, 56], Operations: ['82-27=55', '9+47=56'] Exploring Operation: 55+56=111, Resulting Numbers: [111] 111,59 unequal: No Solution Exploring Operation: 56-55=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 55*56=3080, Resulting Numbers: [3080] 3080,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[47, 64], Operations: ['82-27=55', '9+55=64'] Exploring Operation: 47*64=3008, Resulting Numbers: [3008] 3008,59 unequal: No Solution Exploring Operation: 64-47=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 47+64=111, Resulting Numbers: [111] 111,59 unequal: No Solution Moving to Node #0,2,3 Current State: 59:[47, 46], Operations: ['9+27=36', '82-36=46'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 47*46=2162, Resulting Numbers: [2162] 2162,59 unequal: No Solution Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[47, 46], Operations: ['82-27=55', '55-9=46'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 47*46=2162, Resulting Numbers: [2162] 2162,59 unequal: No Solution Exploring Operation: 47+46=93, Resulting Numbers: [93] 93,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[55, 38], Operations: ['82-27=55', '47-9=38'] Exploring Operation: 55-38=17, Resulting Numbers: [17] 17,59 unequal: No Solution Exploring Operation: 55+38=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 55*38=2090, Resulting Numbers: [2090] 2090,59 unequal: No Solution Moving to Node #0,2,4 Current State: 59:[82, 83], Operations: ['9+27=36', '47+36=83'] Exploring Operation: 83-82=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 82*83=6806, Resulting Numbers: [6806] 6806,59 unequal: No Solution Exploring Operation: 82+83=165, Resulting Numbers: [165] 165,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[36, 35], Operations: ['9+27=36', '82-47=35'] Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,59 unequal: No Solution Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,59 unequal: No Solution Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[82, 11], Operations: ['9+27=36', '47-36=11'] Exploring Operation: 82*11=902, Resulting Numbers: [902] 902,59 unequal: No Solution Exploring Operation: 82+11=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[47, 118], Operations: ['9+27=36', '82+36=118'] Exploring Operation: 47+118=165, Resulting Numbers: [165] 165,59 unequal: No Solution Exploring Operation: 118-47=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 47*118=5546, Resulting Numbers: [5546] 5546,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[9, 102], Operations: ['82-27=55', '47+55=102'] Exploring Operation: 9*102=918, Resulting Numbers: [918] 918,59 unequal: No Solution Exploring Operation: 102-9=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 9+102=111, Resulting Numbers: [111] 111,59 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 84, 2, 21, 20 ]
18
[ "84/2=42", "42/21=2", "20-2=18" ]
Current State: 18:[84, 2, 21, 20], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [21, 20, 42] Generated Node #2: [21, 20, 42] from Operation: 84/2=42 Current State: 18:[21, 20, 42], Operations: ['84/2=42'] Exploring Operation: 42/21=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 42/21=2 Current State: 18:[20, 2], Operations: ['84/2=42', '42/21=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[84, 2, 21, 20], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [21, 20, 42] Generated Node #0,0: 18:[21, 20, 42] Operation: 84/2=42 Exploring Operation: 84/21=4, Resulting Numbers: [2, 20, 4] Generated Node #0,1: 18:[2, 20, 4] Operation: 84/21=4 Exploring Operation: 84-21=63, Resulting Numbers: [2, 20, 63] Generated Node #0,2: 18:[2, 20, 63] Operation: 84-21=63 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[2, 20, 4], Operations: ['84/21=4'] Exploring Operation: 20/2=10, Resulting Numbers: [4, 10] Generated Node #0,1,0: 18:[4, 10] Operation: 20/2=10 Exploring Operation: 20-2=18, Resulting Numbers: [4, 18] Generated Node #0,1,1: 18:[4, 18] Operation: 20-2=18 Exploring Operation: 20/4=5, Resulting Numbers: [2, 5] Generated Node #0,1,2: 18:[2, 5] Operation: 20/4=5 Moving to Node #0,1,1 Current State: 18:[4, 18], Operations: ['84/21=4', '20-2=18'] Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,18 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[2, 5], Operations: ['84/21=4', '20/4=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,18 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[4, 10], Operations: ['84/21=4', '20/2=10'] Exploring Operation: 4+10=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 10-4=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 4*10=40, Resulting Numbers: [40] 40,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[21, 20, 42], Operations: ['84/2=42'] Exploring Operation: 42-20=22, Resulting Numbers: [21, 22] Generated Node #0,0,0: 18:[21, 22] Operation: 42-20=22 Exploring Operation: 42-21=21, Resulting Numbers: [20, 21] Generated Node #0,0,1: 18:[20, 21] Operation: 42-21=21 Exploring Operation: 42/21=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 18:[20, 2] Operation: 42/21=2 Moving to Node #0,0,2 Current State: 18:[20, 2], Operations: ['84/2=42', '42/21=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[84, 2, 21, 20], Operations: [] Exploring Operation: 84/2=42, Resulting Numbers: [21, 20, 42] Generated Node #0,0: 18:[21, 20, 42] Operation: 84/2=42 Moving to Node #0,0 Current State: 18:[21, 20, 42], Operations: ['84/2=42'] Exploring Operation: 42/21=2, Resulting Numbers: [20, 2] Generated Node #0,0,2: 18:[20, 2] Operation: 42/21=2 Moving to Node #0,0,2 Current State: 18:[20, 2], Operations: ['84/2=42', '42/21=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 4, 68, 27, 28 ]
48
[ "28/4=7", "68-27=41", "7+41=48" ]
Current State: 48:[4, 68, 27, 28], Operations: [] Exploring Operation: 28/4=7, Resulting Numbers: [68, 27, 7] Generated Node #2: [68, 27, 7] from Operation: 28/4=7 Current State: 48:[68, 27, 7], Operations: ['28/4=7'] Exploring Operation: 68-27=41, Resulting Numbers: [7, 41] Generated Node #3: [7, 41] from Operation: 68-27=41 Current State: 48:[7, 41], Operations: ['28/4=7', '68-27=41'] Exploring Operation: 7+41=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[4, 68, 27, 28], Operations: [] Exploring Operation: 68/4=17, Resulting Numbers: [27, 28, 17] Generated Node #0,0: 48:[27, 28, 17] Operation: 68/4=17 Moving to Node #0,0 Current State: 48:[27, 28, 17], Operations: ['68/4=17'] Exploring Operation: 28-27=1, Resulting Numbers: [17, 1] Generated Node #0,0,0: 48:[17, 1] Operation: 28-27=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[17, 1], Operations: ['68/4=17', '28-27=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,48 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
[ 57, 90, 95, 57 ]
90
[ "57-57=0", "95*0=0", "90+0=90" ]
Current State: 90:[57, 90, 95, 57], Operations: [] Exploring Operation: 57-57=0, Resulting Numbers: [90, 95, 0] Generated Node #2: [90, 95, 0] from Operation: 57-57=0 Current State: 90:[90, 95, 0], Operations: ['57-57=0'] Exploring Operation: 95*0=0, Resulting Numbers: [90, 0] Generated Node #3: [90, 0] from Operation: 95*0=0 Current State: 90:[90, 0], Operations: ['57-57=0', '95*0=0'] Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[57, 90, 95, 57], Operations: [] Exploring Operation: 95-57=38, Resulting Numbers: [90, 57, 38] Generated Node #0,0: 90:[90, 57, 38] Operation: 95-57=38 Exploring Operation: 95-57=38, Resulting Numbers: [57, 90, 38] Generated Node #0,1: 90:[57, 90, 38] Operation: 95-57=38 Exploring Operation: 57/57=1, Resulting Numbers: [90, 95, 1] Generated Node #0,2: 90:[90, 95, 1] Operation: 57/57=1 Exploring Operation: 57-57=0, Resulting Numbers: [90, 95, 0] Generated Node #0,3: 90:[90, 95, 0] Operation: 57-57=0 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[90, 95, 1], Operations: ['57/57=1'] Exploring Operation: 90*1=90, Resulting Numbers: [95, 90] Generated Node #0,2,0: 90:[95, 90] Operation: 90*1=90 Exploring Operation: 95-1=94, Resulting Numbers: [90, 94] Generated Node #0,2,1: 90:[90, 94] Operation: 95-1=94 Exploring Operation: 90/1=90, Resulting Numbers: [95, 90] Generated Node #0,2,2: 90:[95, 90] Operation: 90/1=90 Exploring Operation: 95-90=5, Resulting Numbers: [1, 5] Generated Node #0,2,3: 90:[1, 5] Operation: 95-90=5 Moving to Node #0,2,3 Current State: 90:[1, 5], Operations: ['57/57=1', '95-90=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[90, 94], Operations: ['57/57=1', '95-1=94'] Exploring Operation: 90+94=184, Resulting Numbers: [184] 184,90 unequal: No Solution Exploring Operation: 94-90=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 90*94=8460, Resulting Numbers: [8460] 8460,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[95, 90], Operations: ['57/57=1', '90/1=90'] Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,90 unequal: No Solution Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,90 unequal: No Solution Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[95, 90], Operations: ['57/57=1', '90*1=90'] Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,90 unequal: No Solution Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[90, 95, 0], Operations: ['57-57=0'] Exploring Operation: 90-0=90, Resulting Numbers: [95, 90] Generated Node #0,3,0: 90:[95, 90] Operation: 90-0=90 Exploring Operation: 95-90=5, Resulting Numbers: [0, 5] Generated Node #0,3,1: 90:[0, 5] Operation: 95-90=5 Exploring Operation: 95*0=0, Resulting Numbers: [90, 0] Generated Node #0,3,2: 90:[90, 0] Operation: 95*0=0 Exploring Operation: 90+0=90, Resulting Numbers: [95, 90] Generated Node #0,3,3: 90:[95, 90] Operation: 90+0=90 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[0, 5], Operations: ['57-57=0', '95-90=5'] Exploring Operation: 5-0=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 0*5=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 0+5=5, Resulting Numbers: [5] 5,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[90, 0], Operations: ['57-57=0', '95*0=0'] Exploring Operation: 90*0=0, Resulting Numbers: [0] 0,90 unequal: No Solution Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[57, 90, 95, 57], Operations: [] Exploring Operation: 57-57=0, Resulting Numbers: [90, 95, 0] Generated Node #0,3: 90:[90, 95, 0] Operation: 57-57=0 Moving to Node #0,3 Current State: 90:[90, 95, 0], Operations: ['57-57=0'] Exploring Operation: 95*0=0, Resulting Numbers: [90, 0] Generated Node #0,3,2: 90:[90, 0] Operation: 95*0=0 Moving to Node #0,3,2 Current State: 90:[90, 0], Operations: ['57-57=0', '95*0=0'] Exploring Operation: 90+0=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 14, 56, 52, 45 ]
27
[ "14+56=70", "52+45=97", "97-70=27" ]
Current State: 27:[14, 56, 52, 45], Operations: [] Exploring Operation: 14+56=70, Resulting Numbers: [52, 45, 70] Generated Node #2: [52, 45, 70] from Operation: 14+56=70 Current State: 27:[52, 45, 70], Operations: ['14+56=70'] Exploring Operation: 52+45=97, Resulting Numbers: [70, 97] Generated Node #3: [70, 97] from Operation: 52+45=97 Current State: 27:[70, 97], Operations: ['14+56=70', '52+45=97'] Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[14, 56, 52, 45], Operations: [] Exploring Operation: 56-45=11, Resulting Numbers: [14, 52, 11] Generated Node #0,0: 27:[14, 52, 11] Operation: 56-45=11 Exploring Operation: 56-52=4, Resulting Numbers: [14, 45, 4] Generated Node #0,1: 27:[14, 45, 4] Operation: 56-52=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[14, 45, 4], Operations: ['56-52=4'] Exploring Operation: 45-14=31, Resulting Numbers: [4, 31] Generated Node #0,1,0: 27:[4, 31] Operation: 45-14=31 Exploring Operation: 14-4=10, Resulting Numbers: [45, 10] Generated Node #0,1,1: 27:[45, 10] Operation: 14-4=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[4, 31], Operations: ['56-52=4', '45-14=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[14, 56, 52, 45], Operations: [] Exploring Operation: 56-52=4, Resulting Numbers: [14, 45, 4] Generated Node #0,1: 27:[14, 45, 4] Operation: 56-52=4 Moving to Node #0,1 Current State: 27:[14, 45, 4], Operations: ['56-52=4'] Exploring Operation: 45-14=31, Resulting Numbers: [4, 31] Generated Node #0,1,0: 27:[4, 31] Operation: 45-14=31 Moving to Node #0,1,0 Current State: 27:[4, 31], Operations: ['56-52=4', '45-14=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 3, 50, 42, 49 ]
75
[ "50+49=99", "99/3=33", "42+33=75" ]
Current State: 75:[3, 50, 42, 49], Operations: [] Exploring Operation: 50+49=99, Resulting Numbers: [3, 42, 99] Generated Node #2: [3, 42, 99] from Operation: 50+49=99 Current State: 75:[3, 42, 99], Operations: ['50+49=99'] Exploring Operation: 99/3=33, Resulting Numbers: [42, 33] Generated Node #3: [42, 33] from Operation: 99/3=33 Current State: 75:[42, 33], Operations: ['50+49=99', '99/3=33'] Exploring Operation: 42+33=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[3, 50, 42, 49], Operations: [] Exploring Operation: 50-49=1, Resulting Numbers: [3, 42, 1] Generated Node #0,0: 75:[3, 42, 1] Operation: 50-49=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[3, 42, 1], Operations: ['50-49=1'] Exploring Operation: 42/3=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 75:[1, 14] Operation: 42/3=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[1, 14], Operations: ['50-49=1', '42/3=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 86, 37, 2, 91 ]
79
[ "91-86=5", "37*2=74", "5+74=79" ]
Current State: 79:[86, 37, 2, 91], Operations: [] Exploring Operation: 91-86=5, Resulting Numbers: [37, 2, 5] Generated Node #2: [37, 2, 5] from Operation: 91-86=5 Current State: 79:[37, 2, 5], Operations: ['91-86=5'] Exploring Operation: 37*2=74, Resulting Numbers: [5, 74] Generated Node #3: [5, 74] from Operation: 37*2=74 Current State: 79:[5, 74], Operations: ['91-86=5', '37*2=74'] Exploring Operation: 5+74=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[86, 37, 2, 91], Operations: [] Exploring Operation: 37*2=74, Resulting Numbers: [86, 91, 74] Generated Node #0,0: 79:[86, 91, 74] Operation: 37*2=74 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[86, 91, 74], Operations: ['37*2=74'] Exploring Operation: 91-74=17, Resulting Numbers: [86, 17] Generated Node #0,0,0: 79:[86, 17] Operation: 91-74=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[86, 17], Operations: ['37*2=74', '91-74=17'] Exploring Operation: 86-17=69, Resulting Numbers: [69] 69,79 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
[ 31, 53, 47, 8 ]
61
[ "53-31=22", "47-8=39", "22+39=61" ]
Current State: 61:[31, 53, 47, 8], Operations: [] Exploring Operation: 53-31=22, Resulting Numbers: [47, 8, 22] Generated Node #2: [47, 8, 22] from Operation: 53-31=22 Current State: 61:[47, 8, 22], Operations: ['53-31=22'] Exploring Operation: 47-8=39, Resulting Numbers: [22, 39] Generated Node #3: [22, 39] from Operation: 47-8=39 Current State: 61:[22, 39], Operations: ['53-31=22', '47-8=39'] Exploring Operation: 22+39=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[31, 53, 47, 8], Operations: [] Exploring Operation: 53-8=45, Resulting Numbers: [31, 47, 45] Generated Node #0,0: 61:[31, 47, 45] Operation: 53-8=45 Exploring Operation: 31-8=23, Resulting Numbers: [53, 47, 23] Generated Node #0,1: 61:[53, 47, 23] Operation: 31-8=23 Exploring Operation: 47+8=55, Resulting Numbers: [31, 53, 55] Generated Node #0,2: 61:[31, 53, 55] Operation: 47+8=55 Exploring Operation: 31+8=39, Resulting Numbers: [53, 47, 39] Generated Node #0,3: 61:[53, 47, 39] Operation: 31+8=39 Exploring Operation: 53+8=61, Resulting Numbers: [31, 47, 61] Generated Node #0,4: 61:[31, 47, 61] Operation: 53+8=61 Start Sub Search at level 1: Moving to Node #0,2 Current State: 61:[31, 53, 55], Operations: ['47+8=55'] Exploring Operation: 31+53=84, Resulting Numbers: [55, 84] Generated Node #0,2,0: 61:[55, 84] Operation: 31+53=84 Exploring Operation: 55-31=24, Resulting Numbers: [53, 24] Generated Node #0,2,1: 61:[53, 24] Operation: 55-31=24 Exploring Operation: 53+55=108, Resulting Numbers: [31, 108] Generated Node #0,2,2: 61:[31, 108] Operation: 53+55=108 Exploring Operation: 31+55=86, Resulting Numbers: [53, 86] Generated Node #0,2,3: 61:[53, 86] Operation: 31+55=86 Exploring Operation: 53-31=22, Resulting Numbers: [55, 22] Generated Node #0,2,4: 61:[55, 22] Operation: 53-31=22 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 61:[55, 84], Operations: ['47+8=55', '31+53=84'] Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 55+84=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 55*84=4620, Resulting Numbers: [4620] 4620,61 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:[53, 86], Operations: ['47+8=55', '31+55=86'] Exploring Operation: 53*86=4558, Resulting Numbers: [4558] 4558,61 unequal: No Solution Exploring Operation: 53+86=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 86-53=33, Resulting Numbers: [33] 33,61 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:[53, 24], Operations: ['47+8=55', '55-31=24'] Exploring Operation: 53*24=1272, Resulting Numbers: [1272] 1272,61 unequal: No Solution Exploring Operation: 53-24=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 53+24=77, Resulting Numbers: [77] 77,61 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 #0,2,4 Current State: 61:[55, 22], Operations: ['47+8=55', '53-31=22'] Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,61 unequal: No Solution Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,61 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:[31, 108], Operations: ['47+8=55', '53+55=108'] Exploring Operation: 31+108=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 31*108=3348, Resulting Numbers: [3348] 3348,61 unequal: No Solution Exploring Operation: 108-31=77, Resulting Numbers: [77] 77,61 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 #0,3 Current State: 61:[53, 47, 39], Operations: ['31+8=39'] Exploring Operation: 47+39=86, Resulting Numbers: [53, 86] Generated Node #0,3,0: 61:[53, 86] Operation: 47+39=86 Exploring Operation: 53+39=92, Resulting Numbers: [47, 92] Generated Node #0,3,1: 61:[47, 92] Operation: 53+39=92 Exploring Operation: 53-39=14, Resulting Numbers: [47, 14] Generated Node #0,3,2: 61:[47, 14] Operation: 53-39=14 Exploring Operation: 47-39=8, Resulting Numbers: [53, 8] Generated Node #0,3,3: 61:[53, 8] Operation: 47-39=8 Exploring Operation: 53+47=100, Resulting Numbers: [39, 100] Generated Node #0,3,4: 61:[39, 100] Operation: 53+47=100 Moving to Node #0,3,0 Current State: 61:[53, 86], Operations: ['31+8=39', '47+39=86'] Exploring Operation: 86-53=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 53*86=4558, Resulting Numbers: [4558] 4558,61 unequal: No Solution Exploring Operation: 53+86=139, Resulting Numbers: [139] 139,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[47, 92], Operations: ['31+8=39', '53+39=92'] Exploring Operation: 47*92=4324, Resulting Numbers: [4324] 4324,61 unequal: No Solution Exploring Operation: 47+92=139, Resulting Numbers: [139] 139,61 unequal: No Solution Exploring Operation: 92-47=45, Resulting Numbers: [45] 45,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[47, 14], Operations: ['31+8=39', '53-39=14'] Exploring Operation: 47*14=658, Resulting Numbers: [658] 658,61 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,61 unequal: No Solution Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[31, 53, 47, 8], Operations: [] Exploring Operation: 31+8=39, Resulting Numbers: [53, 47, 39] Generated Node #0,3: 61:[53, 47, 39] Operation: 31+8=39 Moving to Node #0,3 Current State: 61:[53, 47, 39], Operations: ['31+8=39'] Exploring Operation: 53-39=14, Resulting Numbers: [47, 14] Generated Node #0,3,2: 61:[47, 14] Operation: 53-39=14 Moving to Node #0,3,2 Current State: 61:[47, 14], Operations: ['31+8=39', '53-39=14'] Exploring Operation: 47+14=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
sum_heuristic
[ 62, 34, 68, 72 ]
98
[ "68/34=2", "72/2=36", "62+36=98" ]
Current State: 98:[62, 34, 68, 72], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [62, 72, 2] Generated Node #2: [62, 72, 2] from Operation: 68/34=2 Current State: 98:[62, 72, 2], Operations: ['68/34=2'] Exploring Operation: 72/2=36, Resulting Numbers: [62, 36] Generated Node #3: [62, 36] from Operation: 72/2=36 Current State: 98:[62, 36], Operations: ['68/34=2', '72/2=36'] Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[62, 34, 68, 72], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [62, 72, 2] Generated Node #0,0: 98:[62, 72, 2] Operation: 68/34=2 Exploring Operation: 72-68=4, Resulting Numbers: [62, 34, 4] Generated Node #0,1: 98:[62, 34, 4] Operation: 72-68=4 Moving to Node #0,1 Current State: 98:[62, 34, 4], Operations: ['72-68=4'] Exploring Operation: 62+34=96, Resulting Numbers: [4, 96] Generated Node #0,1,0: 98:[4, 96] Operation: 62+34=96 Exploring Operation: 62-34=28, Resulting Numbers: [4, 28] Generated Node #0,1,1: 98:[4, 28] Operation: 62-34=28 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 98:[4, 96], Operations: ['72-68=4', '62+34=96'] Exploring Operation: 4+96=100, Resulting Numbers: [100] 100,98 unequal: No Solution Exploring Operation: 96-4=92, Resulting Numbers: [92] 92,98 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 98:[4, 28], Operations: ['72-68=4', '62-34=28'] Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,98 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,98 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: 98:[62, 72, 2], Operations: ['68/34=2'] Exploring Operation: 72-62=10, Resulting Numbers: [2, 10] Generated Node #0,0,0: 98:[2, 10] Operation: 72-62=10 Exploring Operation: 72/2=36, Resulting Numbers: [62, 36] Generated Node #0,0,1: 98:[62, 36] Operation: 72/2=36 Moving to Node #0,0,0 Current State: 98:[2, 10], Operations: ['68/34=2', '72-62=10'] Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,98 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[62, 36], Operations: ['68/34=2', '72/2=36'] Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,98 equal: Goal Reached Moving to Node #0 Current State: 98:[62, 34, 68, 72], Operations: [] Exploring Operation: 68/34=2, Resulting Numbers: [62, 72, 2] Generated Node #0,0: 98:[62, 72, 2] Operation: 68/34=2 Moving to Node #0,0 Current State: 98:[62, 72, 2], Operations: ['68/34=2'] Exploring Operation: 72/2=36, Resulting Numbers: [62, 36] Generated Node #0,0,1: 98:[62, 36] Operation: 72/2=36 Moving to Node #0,0,1 Current State: 98:[62, 36], Operations: ['68/34=2', '72/2=36'] Exploring Operation: 62+36=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 94, 44, 44, 93 ]
89
[ "94+44=138", "93-44=49", "138-49=89" ]
Current State: 89:[94, 44, 44, 93], Operations: [] Exploring Operation: 94+44=138, Resulting Numbers: [93, 138] Generated Node #2: [93, 138] from Operation: 94+44=138 Current State: 89:[93, 138], Operations: ['94+44=138'] Exploring Operation: 93-44=49, Resulting Numbers: [138, 49] Generated Node #3: [138, 49] from Operation: 93-44=49 Current State: 89:[138, 49], Operations: ['94+44=138', '93-44=49'] Exploring Operation: 138-49=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[94, 44, 44, 93], Operations: [] Exploring Operation: 44+44=88, Resulting Numbers: [94, 93, 88] Generated Node #0,0: 89:[94, 93, 88] Operation: 44+44=88 Exploring Operation: 94-44=50, Resulting Numbers: [44, 93, 50] Generated Node #0,1: 89:[44, 93, 50] Operation: 94-44=50 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[94, 93, 88], Operations: ['44+44=88'] Exploring Operation: 94-88=6, Resulting Numbers: [93, 6] Generated Node #0,0,0: 89:[93, 6] Operation: 94-88=6 Exploring Operation: 94-93=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 89:[88, 1] Operation: 94-93=1 Moving to Node #0,0,0 Current State: 89:[93, 6], Operations: ['44+44=88', '94-88=6'] Exploring Operation: 93+6=99, Resulting Numbers: [99] 99,89 unequal: No Solution Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,89 unequal: No Solution Moving to Node #0,0,1 Current State: 89:[88, 1], Operations: ['44+44=88', '94-93=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[94, 44, 44, 93], Operations: [] Exploring Operation: 44+44=88, Resulting Numbers: [94, 93, 88] Generated Node #0,0: 89:[94, 93, 88] Operation: 44+44=88 Moving to Node #0,0 Current State: 89:[94, 93, 88], Operations: ['44+44=88'] Exploring Operation: 94-93=1, Resulting Numbers: [88, 1] Generated Node #0,0,1: 89:[88, 1] Operation: 94-93=1 Moving to Node #0,0,1 Current State: 89:[88, 1], Operations: ['44+44=88', '94-93=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 40, 48, 61, 15 ]
43
[ "48*15=720", "720/40=18", "61-18=43" ]
Current State: 43:[40, 48, 61, 15], Operations: [] Exploring Operation: 48*15=720, Resulting Numbers: [40, 61, 720] Generated Node #2: [40, 61, 720] from Operation: 48*15=720 Current State: 43:[40, 61, 720], Operations: ['48*15=720'] Exploring Operation: 720/40=18, Resulting Numbers: [61, 18] Generated Node #3: [61, 18] from Operation: 720/40=18 Current State: 43:[61, 18], Operations: ['48*15=720', '720/40=18'] Exploring Operation: 61-18=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[40, 48, 61, 15], Operations: [] Exploring Operation: 40+15=55, Resulting Numbers: [48, 61, 55] Generated Node #0,0: 43:[48, 61, 55] Operation: 40+15=55 Exploring Operation: 61-15=46, Resulting Numbers: [40, 48, 46] Generated Node #0,1: 43:[40, 48, 46] Operation: 61-15=46 Exploring Operation: 48-15=33, Resulting Numbers: [40, 61, 33] Generated Node #0,2: 43:[40, 61, 33] Operation: 48-15=33 Moving to Node #0,1 Current State: 43:[40, 48, 46], Operations: ['61-15=46'] Exploring Operation: 48-46=2, Resulting Numbers: [40, 2] Generated Node #0,1,0: 43:[40, 2] Operation: 48-46=2 Exploring Operation: 46-40=6, Resulting Numbers: [48, 6] Generated Node #0,1,1: 43:[48, 6] Operation: 46-40=6 Exploring Operation: 48-40=8, Resulting Numbers: [46, 8] Generated Node #0,1,2: 43:[46, 8] Operation: 48-40=8 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[46, 8], Operations: ['61-15=46', '48-40=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,43 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,43 unequal: No Solution No 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: 43:[48, 6], Operations: ['61-15=46', '46-40=6'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,43 unequal: No Solution No 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: 43:[40, 2], Operations: ['61-15=46', '48-46=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,43 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,43 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: 43:[40, 61, 33], Operations: ['48-15=33'] Exploring Operation: 61-40=21, Resulting Numbers: [33, 21] Generated Node #0,2,0: 43:[33, 21] Operation: 61-40=21 Exploring Operation: 61-33=28, Resulting Numbers: [40, 28] Generated Node #0,2,1: 43:[40, 28] Operation: 61-33=28 Exploring Operation: 40+33=73, Resulting Numbers: [61, 73] Generated Node #0,2,2: 43:[61, 73] Operation: 40+33=73 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[40, 28], Operations: ['48-15=33', '61-33=28'] Exploring Operation: 40-28=12, Resulting Numbers: [12] 12,43 unequal: No Solution Exploring Operation: 40*28=1120, Resulting Numbers: [1120] 1120,43 unequal: No Solution Exploring Operation: 40+28=68, Resulting Numbers: [68] 68,43 unequal: No Solution No 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: 43:[33, 21], Operations: ['48-15=33', '61-40=21'] Exploring Operation: 33+21=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 33*21=693, Resulting Numbers: [693] 693,43 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,43 unequal: No Solution No 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: 43:[61, 73], Operations: ['48-15=33', '40+33=73'] Exploring Operation: 61*73=4453, Resulting Numbers: [4453] 4453,43 unequal: No Solution Exploring Operation: 61+73=134, Resulting Numbers: [134] 134,43 unequal: No Solution Exploring Operation: 73-61=12, Resulting Numbers: [12] 12,43 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: 43:[48, 61, 55], Operations: ['40+15=55'] Exploring Operation: 55-48=7, Resulting Numbers: [61, 7] Generated Node #0,0,0: 43:[61, 7] Operation: 55-48=7 Exploring Operation: 61-55=6, Resulting Numbers: [48, 6] Generated Node #0,0,1: 43:[48, 6] Operation: 61-55=6 Exploring Operation: 61-48=13, Resulting Numbers: [55, 13] Generated Node #0,0,2: 43:[55, 13] Operation: 61-48=13 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 43:[48, 6], Operations: ['40+15=55', '61-55=6'] Exploring Operation: 48+6=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,43 unequal: No Solution No 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: 43:[55, 13], Operations: ['40+15=55', '61-48=13'] Exploring Operation: 55*13=715, Resulting Numbers: [715] 715,43 unequal: No Solution Exploring Operation: 55+13=68, Resulting Numbers: [68] 68,43 unequal: No Solution Exploring Operation: 55-13=42, Resulting Numbers: [42] 42,43 unequal: No Solution No 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: 43:[61, 7], Operations: ['40+15=55', '55-48=7'] Exploring Operation: 61-7=54, Resulting Numbers: [54] 54,43 unequal: No Solution Exploring Operation: 61*7=427, Resulting Numbers: [427] 427,43 unequal: No Solution Exploring Operation: 61+7=68, Resulting Numbers: [68] 68,43 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
[ 48, 46, 43, 49 ]
24
[ "48*46=2208", "43+49=92", "2208/92=24" ]
Current State: 24:[48, 46, 43, 49], Operations: [] Exploring Operation: 48*46=2208, Resulting Numbers: [43, 49, 2208] Generated Node #2: [43, 49, 2208] from Operation: 48*46=2208 Current State: 24:[43, 49, 2208], Operations: ['48*46=2208'] Exploring Operation: 43+49=92, Resulting Numbers: [2208, 92] Generated Node #3: [2208, 92] from Operation: 43+49=92 Current State: 24:[2208, 92], Operations: ['48*46=2208', '43+49=92'] Exploring Operation: 2208/92=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[48, 46, 43, 49], Operations: [] Exploring Operation: 49-48=1, Resulting Numbers: [46, 43, 1] Generated Node #0,0: 24:[46, 43, 1] Operation: 49-48=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[46, 43, 1], Operations: ['49-48=1'] Exploring Operation: 46-43=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 24:[1, 3] Operation: 46-43=3 Moving to Node #0,0,0 Current State: 24:[1, 3], Operations: ['49-48=1', '46-43=3'] Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,24 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
[ 77, 38, 8, 80 ]
14
[ "80-77=3", "8*3=24", "38-24=14" ]
Current State: 14:[77, 38, 8, 80], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [38, 8, 3] Generated Node #2: [38, 8, 3] from Operation: 80-77=3 Current State: 14:[38, 8, 3], Operations: ['80-77=3'] Exploring Operation: 8*3=24, Resulting Numbers: [38, 24] Generated Node #3: [38, 24] from Operation: 8*3=24 Current State: 14:[38, 24], Operations: ['80-77=3', '8*3=24'] Exploring Operation: 38-24=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[77, 38, 8, 80], Operations: [] Exploring Operation: 80/8=10, Resulting Numbers: [77, 38, 10] Generated Node #0,0: 14:[77, 38, 10] Operation: 80/8=10 Exploring Operation: 77-38=39, Resulting Numbers: [8, 80, 39] Generated Node #0,1: 14:[8, 80, 39] Operation: 77-38=39 Exploring Operation: 80-77=3, Resulting Numbers: [38, 8, 3] Generated Node #0,2: 14:[38, 8, 3] Operation: 80-77=3 Exploring Operation: 80-38=42, Resulting Numbers: [77, 8, 42] Generated Node #0,3: 14:[77, 8, 42] Operation: 80-38=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 14:[38, 8, 3], Operations: ['80-77=3'] Exploring Operation: 38-8=30, Resulting Numbers: [3, 30] Generated Node #0,2,0: 14:[3, 30] Operation: 38-8=30 Exploring Operation: 38-3=35, Resulting Numbers: [8, 35] Generated Node #0,2,1: 14:[8, 35] Operation: 38-3=35 Exploring Operation: 8-3=5, Resulting Numbers: [38, 5] Generated Node #0,2,2: 14:[38, 5] Operation: 8-3=5 Exploring Operation: 8+3=11, Resulting Numbers: [38, 11] Generated Node #0,2,3: 14:[38, 11] Operation: 8+3=11 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 14:[3, 30], Operations: ['80-77=3', '38-8=30'] Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,14 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,14 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 #0,2,1 Current State: 14:[8, 35], Operations: ['80-77=3', '38-3=35'] Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,14 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,14 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 #0,2,2 Current State: 14:[38, 5], Operations: ['80-77=3', '8-3=5'] Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,14 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,14 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 #0,2,3 Current State: 14:[38, 11], Operations: ['80-77=3', '8+3=11'] Exploring Operation: 38-11=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 38*11=418, Resulting Numbers: [418] 418,14 unequal: No Solution Exploring Operation: 38+11=49, Resulting Numbers: [49] 49,14 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: 14:[77, 38, 10], Operations: ['80/8=10'] Exploring Operation: 77+10=87, Resulting Numbers: [38, 87] Generated Node #0,0,0: 14:[38, 87] Operation: 77+10=87 Exploring Operation: 77-38=39, Resulting Numbers: [10, 39] Generated Node #0,0,1: 14:[10, 39] Operation: 77-38=39 Exploring Operation: 38-10=28, Resulting Numbers: [77, 28] Generated Node #0,0,2: 14:[77, 28] Operation: 38-10=28 Exploring Operation: 77-10=67, Resulting Numbers: [38, 67] Generated Node #0,0,3: 14:[38, 67] Operation: 77-10=67 Moving to Node #0,0,1 Current State: 14:[10, 39], Operations: ['80/8=10', '77-38=39'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 10*39=390, Resulting Numbers: [390] 390,14 unequal: No Solution Exploring Operation: 10+39=49, Resulting Numbers: [49] 49,14 unequal: No Solution Moving to Node #0,0,3 Current State: 14:[38, 67], Operations: ['80/8=10', '77-10=67'] Exploring Operation: 38+67=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 38*67=2546, Resulting Numbers: [2546] 2546,14 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,14 unequal: No Solution Moving to Node #0,0,2 Current State: 14:[77, 28], Operations: ['80/8=10', '38-10=28'] Exploring Operation: 77+28=105, Resulting Numbers: [105] 105,14 unequal: No Solution Exploring Operation: 77*28=2156, Resulting Numbers: [2156] 2156,14 unequal: No Solution Exploring Operation: 77-28=49, Resulting Numbers: [49] 49,14 unequal: No Solution Moving to Node #0,0,0 Current State: 14:[38, 87], Operations: ['80/8=10', '77+10=87'] Exploring Operation: 87-38=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 38+87=125, Resulting Numbers: [125] 125,14 unequal: No Solution Exploring Operation: 38*87=3306, Resulting Numbers: [3306] 3306,14 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 Current State: 14:[8, 80, 39], Operations: ['77-38=39'] Exploring Operation: 80-39=41, Resulting Numbers: [8, 41] Generated Node #0,1,0: 14:[8, 41] Operation: 80-39=41 Exploring Operation: 80-8=72, Resulting Numbers: [39, 72] Generated Node #0,1,1: 14:[39, 72] Operation: 80-8=72 Exploring Operation: 39-8=31, Resulting Numbers: [80, 31] Generated Node #0,1,2: 14:[80, 31] Operation: 39-8=31 Exploring Operation: 80/8=10, Resulting Numbers: [39, 10] Generated Node #0,1,3: 14:[39, 10] Operation: 80/8=10 Moving to Node #0,1,0 Current State: 14:[8, 41], Operations: ['77-38=39', '80-39=41'] Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,14 unequal: No Solution Moving to Node #0,1,3 Current State: 14:[39, 10], Operations: ['77-38=39', '80/8=10'] Exploring Operation: 39-10=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,14 unequal: No Solution Exploring Operation: 39*10=390, Resulting Numbers: [390] 390,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[80, 31], Operations: ['77-38=39', '39-8=31'] Exploring Operation: 80+31=111, Resulting Numbers: [111] 111,14 unequal: No Solution Exploring Operation: 80*31=2480, Resulting Numbers: [2480] 2480,14 unequal: No Solution Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[39, 72], Operations: ['77-38=39', '80-8=72'] Exploring Operation: 72-39=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 39*72=2808, Resulting Numbers: [2808] 2808,14 unequal: No Solution Exploring Operation: 39+72=111, Resulting Numbers: [111] 111,14 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 #0,3 Current State: 14:[77, 8, 42], Operations: ['80-38=42'] Exploring Operation: 77+8=85, Resulting Numbers: [42, 85] Generated Node #0,3,0: 14:[42, 85] Operation: 77+8=85 Exploring Operation: 77-8=69, Resulting Numbers: [42, 69] Generated Node #0,3,1: 14:[42, 69] Operation: 77-8=69 Exploring Operation: 42-8=34, Resulting Numbers: [77, 34] Generated Node #0,3,2: 14:[77, 34] Operation: 42-8=34 Exploring Operation: 77-42=35, Resulting Numbers: [8, 35] Generated Node #0,3,3: 14:[8, 35] Operation: 77-42=35 Moving to Node #0,3,3 Current State: 14:[8, 35], Operations: ['80-38=42', '77-42=35'] Exploring Operation: 8*35=280, Resulting Numbers: [280] 280,14 unequal: No Solution Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 8+35=43, Resulting Numbers: [43] 43,14 unequal: No Solution Moving to Node #0,3,2 Current State: 14:[77, 34], Operations: ['80-38=42', '42-8=34'] Exploring Operation: 77*34=2618, Resulting Numbers: [2618] 2618,14 unequal: No Solution Exploring Operation: 77-34=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 77+34=111, Resulting Numbers: [111] 111,14 unequal: No Solution Moving to Node #0,3,1 Current State: 14:[42, 69], Operations: ['80-38=42', '77-8=69'] Exploring Operation: 42+69=111, Resulting Numbers: [111] 111,14 unequal: No Solution Exploring Operation: 69-42=27, Resulting Numbers: [27] 27,14 unequal: No Solution Exploring Operation: 42*69=2898, Resulting Numbers: [2898] 2898,14 unequal: No Solution Moving to Node #0,3,0 Current State: 14:[42, 85], Operations: ['80-38=42', '77+8=85'] Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 42+85=127, Resulting Numbers: [127] 127,14 unequal: No Solution Exploring Operation: 42*85=3570, Resulting Numbers: [3570] 3570,14 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
[ 19, 15, 5, 2 ]
64
[ "5-2=3", "15*3=45", "19+45=64" ]
Current State: 64:[19, 15, 5, 2], Operations: [] Exploring Operation: 5-2=3, Resulting Numbers: [19, 15, 3] Generated Node #2: [19, 15, 3] from Operation: 5-2=3 Current State: 64:[19, 15, 3], Operations: ['5-2=3'] Exploring Operation: 15*3=45, Resulting Numbers: [19, 45] Generated Node #3: [19, 45] from Operation: 15*3=45 Current State: 64:[19, 45], Operations: ['5-2=3', '15*3=45'] Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[19, 15, 5, 2], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [5, 2, 4] Generated Node #0,0: 64:[5, 2, 4] Operation: 19-15=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[5, 2, 4], Operations: ['19-15=4'] Exploring Operation: 5+2=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 64:[4, 7] Operation: 5+2=7 Moving to Node #0,0,0 Current State: 64:[4, 7], Operations: ['19-15=4', '5+2=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 34, 17, 7, 21 ]
37
[ "34+17=51", "21-7=14", "51-14=37" ]
Current State: 37:[34, 17, 7, 21], Operations: [] Exploring Operation: 34+17=51, Resulting Numbers: [7, 21, 51] Generated Node #2: [7, 21, 51] from Operation: 34+17=51 Current State: 37:[7, 21, 51], Operations: ['34+17=51'] Exploring Operation: 21-7=14, Resulting Numbers: [51, 14] Generated Node #3: [51, 14] from Operation: 21-7=14 Current State: 37:[51, 14], Operations: ['34+17=51', '21-7=14'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[34, 17, 7, 21], Operations: [] Exploring Operation: 34+7=41, Resulting Numbers: [17, 21, 41] Generated Node #0,0: 37:[17, 21, 41] Operation: 34+7=41 Exploring Operation: 17+7=24, Resulting Numbers: [34, 21, 24] Generated Node #0,1: 37:[34, 21, 24] Operation: 17+7=24 Exploring Operation: 7+21=28, Resulting Numbers: [34, 17, 28] Generated Node #0,2: 37:[34, 17, 28] Operation: 7+21=28 Exploring Operation: 17+21=38, Resulting Numbers: [34, 7, 38] Generated Node #0,3: 37:[34, 7, 38] Operation: 17+21=38 Moving to Node #0,1 Current State: 37:[34, 21, 24], Operations: ['17+7=24'] Exploring Operation: 34-21=13, Resulting Numbers: [24, 13] Generated Node #0,1,0: 37:[24, 13] Operation: 34-21=13 Exploring Operation: 34+21=55, Resulting Numbers: [24, 55] Generated Node #0,1,1: 37:[24, 55] Operation: 34+21=55 Exploring Operation: 21+24=45, Resulting Numbers: [34, 45] Generated Node #0,1,2: 37:[34, 45] Operation: 21+24=45 Exploring Operation: 34+24=58, Resulting Numbers: [21, 58] Generated Node #0,1,3: 37:[21, 58] Operation: 34+24=58 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 37:[34, 45], Operations: ['17+7=24', '21+24=45'] Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,37 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 37:[24, 55], Operations: ['17+7=24', '34+21=55'] Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,37 unequal: No Solution Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[24, 13], Operations: ['17+7=24', '34-21=13'] Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[34, 17, 7, 21], Operations: [] Exploring Operation: 17+7=24, Resulting Numbers: [34, 21, 24] Generated Node #0,1: 37:[34, 21, 24] Operation: 17+7=24 Moving to Node #0,1 Current State: 37:[34, 21, 24], Operations: ['17+7=24'] Exploring Operation: 34-21=13, Resulting Numbers: [24, 13] Generated Node #0,1,0: 37:[24, 13] Operation: 34-21=13 Moving to Node #0,1,0 Current State: 37:[24, 13], Operations: ['17+7=24', '34-21=13'] Exploring Operation: 24+13=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 45, 97, 18, 7 ]
74
[ "97-45=52", "18*7=126", "126-52=74" ]
Current State: 74:[45, 97, 18, 7], Operations: [] Exploring Operation: 97-45=52, Resulting Numbers: [18, 7, 52] Generated Node #2: [18, 7, 52] from Operation: 97-45=52 Current State: 74:[18, 7, 52], Operations: ['97-45=52'] Exploring Operation: 18*7=126, Resulting Numbers: [52, 126] Generated Node #3: [52, 126] from Operation: 18*7=126 Current State: 74:[52, 126], Operations: ['97-45=52', '18*7=126'] Exploring Operation: 126-52=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[45, 97, 18, 7], Operations: [] Exploring Operation: 45-18=27, Resulting Numbers: [97, 7, 27] Generated Node #0,0: 74:[97, 7, 27] Operation: 45-18=27 Exploring Operation: 97-18=79, Resulting Numbers: [45, 7, 79] Generated Node #0,1: 74:[45, 7, 79] Operation: 97-18=79 Exploring Operation: 97-45=52, Resulting Numbers: [18, 7, 52] Generated Node #0,2: 74:[18, 7, 52] Operation: 97-45=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[45, 7, 79], Operations: ['97-18=79'] Exploring Operation: 79-45=34, Resulting Numbers: [7, 34] Generated Node #0,1,0: 74:[7, 34] Operation: 79-45=34 Exploring Operation: 45-7=38, Resulting Numbers: [79, 38] Generated Node #0,1,1: 74:[79, 38] Operation: 45-7=38 Exploring Operation: 79-7=72, Resulting Numbers: [45, 72] Generated Node #0,1,2: 74:[45, 72] Operation: 79-7=72 Moving to Node #0,1,1 Current State: 74:[79, 38], Operations: ['97-18=79', '45-7=38'] Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 79*38=3002, Resulting Numbers: [3002] 3002,74 unequal: No Solution Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[7, 34], Operations: ['97-18=79', '79-45=34'] Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,74 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,74 unequal: No Solution Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,74 unequal: No Solution Moving to Node #0,1,2 Current State: 74:[45, 72], Operations: ['97-18=79', '79-7=72'] Exploring Operation: 45+72=117, Resulting Numbers: [117] 117,74 unequal: No Solution Exploring Operation: 45*72=3240, Resulting Numbers: [3240] 3240,74 unequal: No Solution Exploring Operation: 72-45=27, Resulting Numbers: [27] 27,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[18, 7, 52], Operations: ['97-45=52'] Exploring Operation: 52-18=34, Resulting Numbers: [7, 34] Generated Node #0,2,0: 74:[7, 34] Operation: 52-18=34 Exploring Operation: 18-7=11, Resulting Numbers: [52, 11] Generated Node #0,2,1: 74:[52, 11] Operation: 18-7=11 Exploring Operation: 18+52=70, Resulting Numbers: [7, 70] Generated Node #0,2,2: 74:[7, 70] Operation: 18+52=70 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[7, 34], Operations: ['97-45=52', '52-18=34'] Exploring Operation: 7+34=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 34-7=27, Resulting Numbers: [27] 27,74 unequal: No Solution Exploring Operation: 7*34=238, Resulting Numbers: [238] 238,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 74:[7, 70], Operations: ['97-45=52', '18+52=70'] Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,74 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,74 unequal: No Solution Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[52, 11], Operations: ['97-45=52', '18-7=11'] Exploring Operation: 52*11=572, Resulting Numbers: [572] 572,74 unequal: No Solution Exploring Operation: 52-11=41, Resulting Numbers: [41] 41,74 unequal: No Solution Exploring Operation: 52+11=63, Resulting Numbers: [63] 63,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[97, 7, 27], Operations: ['45-18=27'] Exploring Operation: 7+27=34, Resulting Numbers: [97, 34] Generated Node #0,0,0: 74:[97, 34] Operation: 7+27=34 Exploring Operation: 97-7=90, Resulting Numbers: [27, 90] Generated Node #0,0,1: 74:[27, 90] Operation: 97-7=90 Exploring Operation: 97-27=70, Resulting Numbers: [7, 70] Generated Node #0,0,2: 74:[7, 70] Operation: 97-27=70 Moving to Node #0,0,2 Current State: 74:[7, 70], Operations: ['45-18=27', '97-27=70'] Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,74 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,74 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,74 unequal: No Solution Moving to Node #0,0,0 Current State: 74:[97, 34], Operations: ['45-18=27', '7+27=34'] Exploring Operation: 97+34=131, Resulting Numbers: [131] 131,74 unequal: No Solution Exploring Operation: 97*34=3298, Resulting Numbers: [3298] 3298,74 unequal: No Solution Exploring Operation: 97-34=63, Resulting Numbers: [63] 63,74 unequal: No Solution Moving to Node #0,0,1 Current State: 74:[27, 90], Operations: ['45-18=27', '97-7=90'] Exploring Operation: 27+90=117, Resulting Numbers: [117] 117,74 unequal: No Solution Exploring Operation: 90-27=63, Resulting Numbers: [63] 63,74 unequal: No Solution Exploring Operation: 27*90=2430, Resulting Numbers: [2430] 2430,74 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
[ 30, 83, 51, 10 ]
20
[ "83-30=53", "53-51=2", "10*2=20" ]
Current State: 20:[30, 83, 51, 10], Operations: [] Exploring Operation: 83-30=53, Resulting Numbers: [51, 10, 53] Generated Node #2: [51, 10, 53] from Operation: 83-30=53 Current State: 20:[51, 10, 53], Operations: ['83-30=53'] Exploring Operation: 53-51=2, Resulting Numbers: [10, 2] Generated Node #3: [10, 2] from Operation: 53-51=2 Current State: 20:[10, 2], Operations: ['83-30=53', '53-51=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[30, 83, 51, 10], Operations: [] Exploring Operation: 51-30=21, Resulting Numbers: [83, 10, 21] Generated Node #0,0: 20:[83, 10, 21] Operation: 51-30=21 Exploring Operation: 83-30=53, Resulting Numbers: [51, 10, 53] Generated Node #0,1: 20:[51, 10, 53] Operation: 83-30=53 Exploring Operation: 83-51=32, Resulting Numbers: [30, 10, 32] Generated Node #0,2: 20:[30, 10, 32] Operation: 83-51=32 Moving to Node #0,2 Current State: 20:[30, 10, 32], Operations: ['83-51=32'] Exploring Operation: 32-30=2, Resulting Numbers: [10, 2] Generated Node #0,2,0: 20:[10, 2] Operation: 32-30=2 Exploring Operation: 32-10=22, Resulting Numbers: [30, 22] Generated Node #0,2,1: 20:[30, 22] Operation: 32-10=22 Exploring Operation: 30-10=20, Resulting Numbers: [32, 20] Generated Node #0,2,2: 20:[32, 20] Operation: 30-10=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 20:[10, 2], Operations: ['83-51=32', '32-30=2'] Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,20 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[30, 83, 51, 10], Operations: [] Exploring Operation: 83-51=32, Resulting Numbers: [30, 10, 32] Generated Node #0,2: 20:[30, 10, 32] Operation: 83-51=32 Moving to Node #0,2 Current State: 20:[30, 10, 32], Operations: ['83-51=32'] Exploring Operation: 32-30=2, Resulting Numbers: [10, 2] Generated Node #0,2,0: 20:[10, 2] Operation: 32-30=2 Moving to Node #0,2,0 Current State: 20:[10, 2], Operations: ['83-51=32', '32-30=2'] Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 49, 5, 83, 33 ]
59
[ "83-33=50", "50/5=10", "49+10=59" ]
Current State: 59:[49, 5, 83, 33], Operations: [] Exploring Operation: 83-33=50, Resulting Numbers: [49, 5, 50] Generated Node #2: [49, 5, 50] from Operation: 83-33=50 Current State: 59:[49, 5, 50], Operations: ['83-33=50'] Exploring Operation: 50/5=10, Resulting Numbers: [49, 10] Generated Node #3: [49, 10] from Operation: 50/5=10 Current State: 59:[49, 10], Operations: ['83-33=50', '50/5=10'] Exploring Operation: 49+10=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[49, 5, 83, 33], Operations: [] Exploring Operation: 5+33=38, Resulting Numbers: [49, 83, 38] Generated Node #0,0: 59:[49, 83, 38] Operation: 5+33=38 Exploring Operation: 83-5=78, Resulting Numbers: [49, 33, 78] Generated Node #0,1: 59:[49, 33, 78] Operation: 83-5=78 Exploring Operation: 49+5=54, Resulting Numbers: [83, 33, 54] Generated Node #0,2: 59:[83, 33, 54] Operation: 49+5=54 Moving to Node #0,0 Current State: 59:[49, 83, 38], Operations: ['5+33=38'] Exploring Operation: 83-49=34, Resulting Numbers: [38, 34] Generated Node #0,0,0: 59:[38, 34] Operation: 83-49=34 Exploring Operation: 83-38=45, Resulting Numbers: [49, 45] Generated Node #0,0,1: 59:[49, 45] Operation: 83-38=45 Exploring Operation: 49+38=87, Resulting Numbers: [83, 87] Generated Node #0,0,2: 59:[83, 87] Operation: 49+38=87 Moving to Node #0,1 Current State: 59:[49, 33, 78], Operations: ['83-5=78'] Exploring Operation: 49+33=82, Resulting Numbers: [78, 82] Generated Node #0,1,0: 59:[78, 82] Operation: 49+33=82 Exploring Operation: 78-49=29, Resulting Numbers: [33, 29] Generated Node #0,1,1: 59:[33, 29] Operation: 78-49=29 Exploring Operation: 78-33=45, Resulting Numbers: [49, 45] Generated Node #0,1,2: 59:[49, 45] Operation: 78-33=45 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 59:[49, 45], Operations: ['83-5=78', '78-33=45'] Exploring Operation: 49*45=2205, Resulting Numbers: [2205] 2205,59 unequal: No Solution Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,59 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 #0,1,0 Current State: 59:[78, 82], Operations: ['83-5=78', '49+33=82'] Exploring Operation: 78*82=6396, Resulting Numbers: [6396] 6396,59 unequal: No Solution Exploring Operation: 78+82=160, Resulting Numbers: [160] 160,59 unequal: No Solution Exploring Operation: 82-78=4, Resulting Numbers: [4] 4,59 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 #0,1,1 Current State: 59:[33, 29], Operations: ['83-5=78', '78-49=29'] Exploring Operation: 33*29=957, Resulting Numbers: [957] 957,59 unequal: No Solution Exploring Operation: 33+29=62, Resulting Numbers: [62] 62,59 unequal: No Solution Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,59 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: 59:[83, 33, 54], Operations: ['49+5=54'] Exploring Operation: 83-33=50, Resulting Numbers: [54, 50] Generated Node #0,2,0: 59:[54, 50] Operation: 83-33=50 Exploring Operation: 33+54=87, Resulting Numbers: [83, 87] Generated Node #0,2,1: 59:[83, 87] Operation: 33+54=87 Exploring Operation: 83-54=29, Resulting Numbers: [33, 29] Generated Node #0,2,2: 59:[33, 29] Operation: 83-54=29 Moving to Node #0,2,0 Current State: 59:[54, 50], Operations: ['49+5=54', '83-33=50'] Exploring Operation: 54+50=104, Resulting Numbers: [104] 104,59 unequal: No Solution Exploring Operation: 54-50=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 54*50=2700, Resulting Numbers: [2700] 2700,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[49, 45], Operations: ['5+33=38', '83-38=45'] Exploring Operation: 49+45=94, Resulting Numbers: [94] 94,59 unequal: No Solution Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 49*45=2205, Resulting Numbers: [2205] 2205,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[38, 34], Operations: ['5+33=38', '83-49=34'] Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,59 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[83, 87], Operations: ['5+33=38', '49+38=87'] Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 83+87=170, Resulting Numbers: [170] 170,59 unequal: No Solution Exploring Operation: 83*87=7221, Resulting Numbers: [7221] 7221,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[83, 87], Operations: ['49+5=54', '33+54=87'] Exploring Operation: 83+87=170, Resulting Numbers: [170] 170,59 unequal: No Solution Exploring Operation: 87-83=4, Resulting Numbers: [4] 4,59 unequal: No Solution Exploring Operation: 83*87=7221, Resulting Numbers: [7221] 7221,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[33, 29], Operations: ['49+5=54', '83-54=29'] Exploring Operation: 33*29=957, Resulting Numbers: [957] 957,59 unequal: No Solution Exploring Operation: 33+29=62, Resulting Numbers: [62] 62,59 unequal: No Solution Exploring Operation: 33-29=4, Resulting Numbers: [4] 4,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 47, 12, 50, 16 ]
64
[ "50-47=3", "12*16=192", "192/3=64" ]
Current State: 64:[47, 12, 50, 16], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [12, 16, 3] Generated Node #2: [12, 16, 3] from Operation: 50-47=3 Current State: 64:[12, 16, 3], Operations: ['50-47=3'] Exploring Operation: 12*16=192, Resulting Numbers: [3, 192] Generated Node #3: [3, 192] from Operation: 12*16=192 Current State: 64:[3, 192], Operations: ['50-47=3', '12*16=192'] Exploring Operation: 192/3=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[47, 12, 50, 16], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [12, 16, 3] Generated Node #0,0: 64:[12, 16, 3] Operation: 50-47=3 Exploring Operation: 47-12=35, Resulting Numbers: [50, 16, 35] Generated Node #0,1: 64:[50, 16, 35] Operation: 47-12=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[12, 16, 3], Operations: ['50-47=3'] Exploring Operation: 16-12=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 64:[3, 4] Operation: 16-12=4 Exploring Operation: 12/3=4, Resulting Numbers: [16, 4] Generated Node #0,0,1: 64:[16, 4] Operation: 12/3=4 Moving to Node #0,0,1 Current State: 64:[16, 4], Operations: ['50-47=3', '12/3=4'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[47, 12, 50, 16], Operations: [] Exploring Operation: 50-47=3, Resulting Numbers: [12, 16, 3] Generated Node #0,0: 64:[12, 16, 3] Operation: 50-47=3 Moving to Node #0,0 Current State: 64:[12, 16, 3], Operations: ['50-47=3'] Exploring Operation: 12/3=4, Resulting Numbers: [16, 4] Generated Node #0,0,1: 64:[16, 4] Operation: 12/3=4 Moving to Node #0,0,1 Current State: 64:[16, 4], Operations: ['50-47=3', '12/3=4'] Exploring Operation: 16*4=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 54, 82, 24, 52 ]
29
[ "54-52=2", "82-24=58", "58/2=29" ]
Current State: 29:[54, 82, 24, 52], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [82, 24, 2] Generated Node #2: [82, 24, 2] from Operation: 54-52=2 Current State: 29:[82, 24, 2], Operations: ['54-52=2'] Exploring Operation: 82-24=58, Resulting Numbers: [2, 58] Generated Node #3: [2, 58] from Operation: 82-24=58 Current State: 29:[2, 58], Operations: ['54-52=2', '82-24=58'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[54, 82, 24, 52], Operations: [] Exploring Operation: 82-24=58, Resulting Numbers: [54, 52, 58] Generated Node #0,0: 29:[54, 52, 58] Operation: 82-24=58 Exploring Operation: 54-24=30, Resulting Numbers: [82, 52, 30] Generated Node #0,1: 29:[82, 52, 30] Operation: 54-24=30 Exploring Operation: 82-52=30, Resulting Numbers: [54, 24, 30] Generated Node #0,2: 29:[54, 24, 30] Operation: 82-52=30 Exploring Operation: 82-54=28, Resulting Numbers: [24, 52, 28] Generated Node #0,3: 29:[24, 52, 28] Operation: 82-54=28 Moving to Node #0,3 Current State: 29:[24, 52, 28], Operations: ['82-54=28'] Exploring Operation: 52-24=28, Resulting Numbers: [28, 28] Generated Node #0,3,0: 29:[28, 28] Operation: 52-24=28 Exploring Operation: 52-28=24, Resulting Numbers: [24, 24] Generated Node #0,3,1: 29:[24, 24] Operation: 52-28=24 Exploring Operation: 24+28=52, Resulting Numbers: [52, 52] Generated Node #0,3,2: 29:[52, 52] Operation: 24+28=52 Exploring Operation: 24+52=76, Resulting Numbers: [28, 76] Generated Node #0,3,3: 29:[28, 76] Operation: 24+52=76 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 29:[28, 28], Operations: ['82-54=28', '52-24=28'] Exploring Operation: 28-28=0, Resulting Numbers: [0] 0,29 unequal: No Solution Exploring Operation: 28*28=784, Resulting Numbers: [784] 784,29 unequal: No Solution Exploring Operation: 28/28=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 28+28=56, Resulting Numbers: [56] 56,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 29:[24, 24], Operations: ['82-54=28', '52-28=24'] Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,29 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 29:[52, 52], Operations: ['82-54=28', '24+28=52'] Exploring Operation: 52+52=104, Resulting Numbers: [104] 104,29 unequal: No Solution Exploring Operation: 52/52=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 52*52=2704, Resulting Numbers: [2704] 2704,29 unequal: No Solution Exploring Operation: 52-52=0, Resulting Numbers: [0] 0,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 29:[28, 76], Operations: ['82-54=28', '24+52=76'] Exploring Operation: 28+76=104, Resulting Numbers: [104] 104,29 unequal: No Solution Exploring Operation: 28*76=2128, Resulting Numbers: [2128] 2128,29 unequal: No Solution Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,29 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: 29:[54, 24, 30], Operations: ['82-52=30'] Exploring Operation: 30-24=6, Resulting Numbers: [54, 6] Generated Node #0,2,0: 29:[54, 6] Operation: 30-24=6 Exploring Operation: 54+24=78, Resulting Numbers: [30, 78] Generated Node #0,2,1: 29:[30, 78] Operation: 54+24=78 Exploring Operation: 54-24=30, Resulting Numbers: [30, 30] Generated Node #0,2,2: 29:[30, 30] Operation: 54-24=30 Exploring Operation: 54-30=24, Resulting Numbers: [24, 24] Generated Node #0,2,3: 29:[24, 24] Operation: 54-30=24 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[30, 30], Operations: ['82-52=30', '54-24=30'] Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,29 unequal: No Solution Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 29:[24, 24], Operations: ['82-52=30', '54-30=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,29 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,29 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[54, 6], Operations: ['82-52=30', '30-24=6'] Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,29 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,29 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[30, 78], Operations: ['82-52=30', '54+24=78'] Exploring Operation: 78-30=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 30*78=2340, Resulting Numbers: [2340] 2340,29 unequal: No Solution Exploring Operation: 30+78=108, Resulting Numbers: [108] 108,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 29:[82, 52, 30], Operations: ['54-24=30'] Exploring Operation: 82+52=134, Resulting Numbers: [30, 134] Generated Node #0,1,0: 29:[30, 134] Operation: 82+52=134 Exploring Operation: 52-30=22, Resulting Numbers: [82, 22] Generated Node #0,1,1: 29:[82, 22] Operation: 52-30=22 Exploring Operation: 82-30=52, Resulting Numbers: [52, 52] Generated Node #0,1,2: 29:[52, 52] Operation: 82-30=52 Exploring Operation: 82-52=30, Resulting Numbers: [30, 30] Generated Node #0,1,3: 29:[30, 30] Operation: 82-52=30 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 29:[30, 30], Operations: ['54-24=30', '82-52=30'] Exploring Operation: 30-30=0, Resulting Numbers: [0] 0,29 unequal: No Solution Exploring Operation: 30*30=900, Resulting Numbers: [900] 900,29 unequal: No Solution Exploring Operation: 30/30=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 30+30=60, Resulting Numbers: [60] 60,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 29:[52, 52], Operations: ['54-24=30', '82-30=52'] Exploring Operation: 52/52=1, Resulting Numbers: [1] 1,29 unequal: No Solution Exploring Operation: 52*52=2704, Resulting Numbers: [2704] 2704,29 unequal: No Solution Exploring Operation: 52-52=0, Resulting Numbers: [0] 0,29 unequal: No Solution Exploring Operation: 52+52=104, Resulting Numbers: [104] 104,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[82, 22], Operations: ['54-24=30', '52-30=22'] Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 82*22=1804, Resulting Numbers: [1804] 1804,29 unequal: No Solution Exploring Operation: 82+22=104, Resulting Numbers: [104] 104,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 29:[30, 134], Operations: ['54-24=30', '82+52=134'] Exploring Operation: 30*134=4020, Resulting Numbers: [4020] 4020,29 unequal: No Solution Exploring Operation: 30+134=164, Resulting Numbers: [164] 164,29 unequal: No Solution Exploring Operation: 134-30=104, Resulting Numbers: [104] 104,29 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: 29:[54, 52, 58], Operations: ['82-24=58'] Exploring Operation: 54+52=106, Resulting Numbers: [58, 106] Generated Node #0,0,0: 29:[58, 106] Operation: 54+52=106 Exploring Operation: 58-52=6, Resulting Numbers: [54, 6] Generated Node #0,0,1: 29:[54, 6] Operation: 58-52=6 Exploring Operation: 54-52=2, Resulting Numbers: [58, 2] Generated Node #0,0,2: 29:[58, 2] Operation: 54-52=2 Exploring Operation: 58-54=4, Resulting Numbers: [52, 4] Generated Node #0,0,3: 29:[52, 4] Operation: 58-54=4 Moving to Node #0,0,1 Current State: 29:[54, 6], Operations: ['82-24=58', '58-52=6'] Exploring Operation: 54*6=324, Resulting Numbers: [324] 324,29 unequal: No Solution Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[52, 4], Operations: ['82-24=58', '58-54=4'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 52+4=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,29 unequal: No Solution Exploring Operation: 52*4=208, Resulting Numbers: [208] 208,29 unequal: No Solution Moving to Node #0,0,2 Current State: 29:[58, 2], Operations: ['82-24=58', '54-52=2'] Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,29 unequal: No Solution Exploring Operation: 58*2=116, Resulting Numbers: [116] 116,29 unequal: No Solution Exploring Operation: 58+2=60, Resulting Numbers: [60] 60,29 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[54, 82, 24, 52], Operations: [] Exploring Operation: 82-24=58, Resulting Numbers: [54, 52, 58] Generated Node #0,0: 29:[54, 52, 58] Operation: 82-24=58 Moving to Node #0,0 Current State: 29:[54, 52, 58], Operations: ['82-24=58'] Exploring Operation: 54-52=2, Resulting Numbers: [58, 2] Generated Node #0,0,2: 29:[58, 2] Operation: 54-52=2 Moving to Node #0,0,2 Current State: 29:[58, 2], Operations: ['82-24=58', '54-52=2'] Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
0.930556
hs_4
sum_heuristic
[ 6, 60, 92, 77 ]
30
[ "92-77=15", "6*15=90", "90-60=30" ]
Current State: 30:[6, 60, 92, 77], Operations: [] Exploring Operation: 92-77=15, Resulting Numbers: [6, 60, 15] Generated Node #2: [6, 60, 15] from Operation: 92-77=15 Current State: 30:[6, 60, 15], Operations: ['92-77=15'] Exploring Operation: 6*15=90, Resulting Numbers: [60, 90] Generated Node #3: [60, 90] from Operation: 6*15=90 Current State: 30:[60, 90], Operations: ['92-77=15', '6*15=90'] Exploring Operation: 90-60=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[6, 60, 92, 77], Operations: [] Exploring Operation: 92-77=15, Resulting Numbers: [6, 60, 15] Generated Node #0,0: 30:[6, 60, 15] Operation: 92-77=15 Exploring Operation: 92-60=32, Resulting Numbers: [6, 77, 32] Generated Node #0,1: 30:[6, 77, 32] Operation: 92-60=32 Moving to Node #0,0 Current State: 30:[6, 60, 15], Operations: ['92-77=15'] Exploring Operation: 60/15=4, Resulting Numbers: [6, 4] Generated Node #0,0,0: 30:[6, 4] Operation: 60/15=4 Exploring Operation: 60/6=10, Resulting Numbers: [15, 10] Generated Node #0,0,1: 30:[15, 10] Operation: 60/6=10 Moving to Node #0,1 Current State: 30:[6, 77, 32], Operations: ['92-60=32'] Exploring Operation: 77-6=71, Resulting Numbers: [32, 71] Generated Node #0,1,0: 30:[32, 71] Operation: 77-6=71 Exploring Operation: 77-32=45, Resulting Numbers: [6, 45] Generated Node #0,1,1: 30:[6, 45] Operation: 77-32=45 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[6, 45], Operations: ['92-60=32', '77-32=45'] Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[32, 71], Operations: ['92-60=32', '77-6=71'] Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,30 unequal: No Solution Exploring Operation: 32+71=103, Resulting Numbers: [103] 103,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 30:[15, 10], Operations: ['92-77=15', '60/6=10'] Exploring Operation: 15-10=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 15+10=25, Resulting Numbers: [25] 25,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[6, 4], Operations: ['92-77=15', '60/15=4'] Exploring Operation: 6+4=10, Resulting Numbers: [10] 10,30 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,30 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 13, 36, 75, 75 ]
48
[ "13+36=49", "75/75=1", "49-1=48" ]
Current State: 48:[13, 36, 75, 75], Operations: [] Exploring Operation: 13+36=49, Resulting Numbers: [75, 75, 49] Generated Node #2: [75, 75, 49] from Operation: 13+36=49 Current State: 48:[75, 75, 49], Operations: ['13+36=49'] Exploring Operation: 75/75=1, Resulting Numbers: [49, 1] Generated Node #3: [49, 1] from Operation: 75/75=1 Current State: 48:[49, 1], Operations: ['13+36=49', '75/75=1'] Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[13, 36, 75, 75], Operations: [] Exploring Operation: 75-36=39, Resulting Numbers: [13, 75, 39] Generated Node #0,0: 48:[13, 75, 39] Operation: 75-36=39 Exploring Operation: 75-75=0, Resulting Numbers: [13, 36, 0] Generated Node #0,1: 48:[13, 36, 0] Operation: 75-75=0 Exploring Operation: 75-13=62, Resulting Numbers: [36, 75, 62] Generated Node #0,2: 48:[36, 75, 62] Operation: 75-13=62 Exploring Operation: 75/75=1, Resulting Numbers: [13, 36, 1] Generated Node #0,3: 48:[13, 36, 1] Operation: 75/75=1 Exploring Operation: 75-36=39, Resulting Numbers: [13, 75, 39] Generated Node #0,4: 48:[13, 75, 39] Operation: 75-36=39 Moving to Node #0,3 Current State: 48:[13, 36, 1], Operations: ['75/75=1'] Exploring Operation: 36+1=37, Resulting Numbers: [13, 37] Generated Node #0,3,0: 48:[13, 37] Operation: 36+1=37 Exploring Operation: 36-1=35, Resulting Numbers: [13, 35] Generated Node #0,3,1: 48:[13, 35] Operation: 36-1=35 Exploring Operation: 13-1=12, Resulting Numbers: [36, 12] Generated Node #0,3,2: 48:[36, 12] Operation: 13-1=12 Exploring Operation: 36-13=23, Resulting Numbers: [1, 23] Generated Node #0,3,3: 48:[1, 23] Operation: 36-13=23 Exploring Operation: 13+36=49, Resulting Numbers: [1, 49] Generated Node #0,3,4: 48:[1, 49] Operation: 13+36=49 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 48:[1, 23], Operations: ['75/75=1', '36-13=23'] Exploring Operation: 1*23=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,48 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,48 unequal: No Solution Exploring Operation: 1+23=24, Resulting Numbers: [24] 24,48 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 #0,3,4 Current State: 48:[1, 49], Operations: ['75/75=1', '13+36=49'] Exploring Operation: 1+49=50, Resulting Numbers: [50] 50,48 unequal: No Solution Exploring Operation: 49/1=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 1*49=49, Resulting Numbers: [49] 49,48 unequal: No Solution Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[13, 36, 75, 75], Operations: [] Exploring Operation: 75/75=1, Resulting Numbers: [13, 36, 1] Generated Node #0,3: 48:[13, 36, 1] Operation: 75/75=1 Moving to Node #0,3 Current State: 48:[13, 36, 1], Operations: ['75/75=1'] Exploring Operation: 13+36=49, Resulting Numbers: [1, 49] Generated Node #0,3,4: 48:[1, 49] Operation: 13+36=49 Moving to Node #0,3,4 Current State: 48:[1, 49], Operations: ['75/75=1', '13+36=49'] Exploring Operation: 49-1=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 90, 18, 5, 42 ]
32
[ "90/18=5", "42-5=37", "37-5=32" ]
Current State: 32:[90, 18, 5, 42], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [5, 42, 5] Generated Node #2: [5, 42, 5] from Operation: 90/18=5 Current State: 32:[5, 42, 5], Operations: ['90/18=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,32 equal: Goal Reached Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[90, 18, 5, 42], Operations: [] Exploring Operation: 90-18=72, Resulting Numbers: [5, 42, 72] Generated Node #0,0: 32:[5, 42, 72] Operation: 90-18=72 Exploring Operation: 90-5=85, Resulting Numbers: [18, 42, 85] Generated Node #0,1: 32:[18, 42, 85] Operation: 90-5=85 Exploring Operation: 90-42=48, Resulting Numbers: [18, 5, 48] Generated Node #0,2: 32:[18, 5, 48] Operation: 90-42=48 Exploring Operation: 90/5=18, Resulting Numbers: [18, 42, 18] Generated Node #0,3: 32:[18, 42, 18] Operation: 90/5=18 Exploring Operation: 90/18=5, Resulting Numbers: [5, 42, 5] Generated Node #0,4: 32:[5, 42, 5] Operation: 90/18=5 Moving to Node #0,4 Current State: 32:[5, 42, 5], Operations: ['90/18=5'] Exploring Operation: 5+5=10, Resulting Numbers: [42, 10] Generated Node #0,4,0: 32:[42, 10] Operation: 5+5=10 Exploring Operation: 42-5=37, Resulting Numbers: [5, 37] Generated Node #0,4,1: 32:[5, 37] Operation: 42-5=37 Exploring Operation: 42-5=37, Resulting Numbers: [5, 37] Generated Node #0,4,2: 32:[5, 37] Operation: 42-5=37 Exploring Operation: 5/5=1, Resulting Numbers: [42, 1] Generated Node #0,4,3: 32:[42, 1] Operation: 5/5=1 Exploring Operation: 5-5=0, Resulting Numbers: [42, 0] Generated Node #0,4,4: 32:[42, 0] Operation: 5-5=0 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 32:[5, 37], Operations: ['90/18=5', '42-5=37'] Exploring Operation: 5+37=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 5*37=185, Resulting Numbers: [185] 185,32 unequal: No Solution Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[90, 18, 5, 42], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [5, 42, 5] Generated Node #0,4: 32:[5, 42, 5] Operation: 90/18=5 Moving to Node #0,4 Current State: 32:[5, 42, 5], Operations: ['90/18=5'] Exploring Operation: 42-5=37, Resulting Numbers: [5, 37] Generated Node #0,4,1: 32:[5, 37] Operation: 42-5=37 Moving to Node #0,4,1 Current State: 32:[5, 37], Operations: ['90/18=5', '42-5=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 33, 10, 17, 58 ]
79
[ "33+58=91", "10*17=170", "170-91=79" ]
Current State: 79:[33, 10, 17, 58], Operations: [] Exploring Operation: 33+58=91, Resulting Numbers: [10, 17, 91] Generated Node #2: [10, 17, 91] from Operation: 33+58=91 Current State: 79:[10, 17, 91], Operations: ['33+58=91'] Exploring Operation: 10*17=170, Resulting Numbers: [91, 170] Generated Node #3: [91, 170] from Operation: 10*17=170 Current State: 79:[91, 170], Operations: ['33+58=91', '10*17=170'] Exploring Operation: 170-91=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[33, 10, 17, 58], Operations: [] Exploring Operation: 33+17=50, Resulting Numbers: [10, 58, 50] Generated Node #0,0: 79:[10, 58, 50] Operation: 33+17=50 Exploring Operation: 33+10=43, Resulting Numbers: [17, 58, 43] Generated Node #0,1: 79:[17, 58, 43] Operation: 33+10=43 Exploring Operation: 10+58=68, Resulting Numbers: [33, 17, 68] Generated Node #0,2: 79:[33, 17, 68] Operation: 10+58=68 Exploring Operation: 17+58=75, Resulting Numbers: [33, 10, 75] Generated Node #0,3: 79:[33, 10, 75] Operation: 17+58=75 Exploring Operation: 10+17=27, Resulting Numbers: [33, 58, 27] Generated Node #0,4: 79:[33, 58, 27] Operation: 10+17=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[10, 58, 50], Operations: ['33+17=50'] Exploring Operation: 58-10=48, Resulting Numbers: [50, 48] Generated Node #0,0,0: 79:[50, 48] Operation: 58-10=48 Exploring Operation: 50-10=40, Resulting Numbers: [58, 40] Generated Node #0,0,1: 79:[58, 40] Operation: 50-10=40 Exploring Operation: 50/10=5, Resulting Numbers: [58, 5] Generated Node #0,0,2: 79:[58, 5] Operation: 50/10=5 Exploring Operation: 10+58=68, Resulting Numbers: [50, 68] Generated Node #0,0,3: 79:[50, 68] Operation: 10+58=68 Exploring Operation: 10+50=60, Resulting Numbers: [58, 60] Generated Node #0,0,4: 79:[58, 60] Operation: 10+50=60 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 79:[50, 68], Operations: ['33+17=50', '10+58=68'] Exploring Operation: 50*68=3400, Resulting Numbers: [3400] 3400,79 unequal: No Solution Exploring Operation: 50+68=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,79 unequal: No Solution No 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: 79:[58, 60], Operations: ['33+17=50', '10+50=60'] Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,79 unequal: No Solution No 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: 79:[50, 48], Operations: ['33+17=50', '58-10=48'] Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,79 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,79 unequal: No Solution No 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: 79:[58, 40], Operations: ['33+17=50', '50-10=40'] Exploring Operation: 58-40=18, Resulting Numbers: [18] 18,79 unequal: No Solution Exploring Operation: 58*40=2320, Resulting Numbers: [2320] 2320,79 unequal: No Solution Exploring Operation: 58+40=98, Resulting Numbers: [98] 98,79 unequal: No Solution No 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: 79:[58, 5], Operations: ['33+17=50', '50/10=5'] Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,79 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,79 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,79 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: 79:[17, 58, 43], Operations: ['33+10=43'] Exploring Operation: 58-17=41, Resulting Numbers: [43, 41] Generated Node #0,1,0: 79:[43, 41] Operation: 58-17=41 Exploring Operation: 17+58=75, Resulting Numbers: [43, 75] Generated Node #0,1,1: 79:[43, 75] Operation: 17+58=75 Exploring Operation: 43-17=26, Resulting Numbers: [58, 26] Generated Node #0,1,2: 79:[58, 26] Operation: 43-17=26 Exploring Operation: 17+43=60, Resulting Numbers: [58, 60] Generated Node #0,1,3: 79:[58, 60] Operation: 17+43=60 Exploring Operation: 58+43=101, Resulting Numbers: [17, 101] Generated Node #0,1,4: 79:[17, 101] Operation: 58+43=101 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[43, 75], Operations: ['33+10=43', '17+58=75'] Exploring Operation: 43+75=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 43*75=3225, Resulting Numbers: [3225] 3225,79 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,79 unequal: No Solution No 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: 79:[58, 60], Operations: ['33+10=43', '17+43=60'] Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,79 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,79 unequal: No Solution No 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: 79:[43, 41], Operations: ['33+10=43', '58-17=41'] Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 43*41=1763, Resulting Numbers: [1763] 1763,79 unequal: No Solution Exploring Operation: 43+41=84, Resulting Numbers: [84] 84,79 unequal: No Solution No 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: 79:[58, 26], Operations: ['33+10=43', '43-17=26'] Exploring Operation: 58*26=1508, Resulting Numbers: [1508] 1508,79 unequal: No Solution Exploring Operation: 58-26=32, Resulting Numbers: [32] 32,79 unequal: No Solution Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,79 unequal: No Solution No 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: 79:[17, 101], Operations: ['33+10=43', '58+43=101'] Exploring Operation: 17+101=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 17*101=1717, Resulting Numbers: [1717] 1717,79 unequal: No Solution Exploring Operation: 101-17=84, Resulting Numbers: [84] 84,79 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: 79:[33, 17, 68], Operations: ['10+58=68'] Exploring Operation: 17+68=85, Resulting Numbers: [33, 85] Generated Node #0,2,0: 79:[33, 85] Operation: 17+68=85 Exploring Operation: 68-17=51, Resulting Numbers: [33, 51] Generated Node #0,2,1: 79:[33, 51] Operation: 68-17=51 Exploring Operation: 33+17=50, Resulting Numbers: [68, 50] Generated Node #0,2,2: 79:[68, 50] Operation: 33+17=50 Exploring Operation: 33+68=101, Resulting Numbers: [17, 101] Generated Node #0,2,3: 79:[17, 101] Operation: 33+68=101 Exploring Operation: 33-17=16, Resulting Numbers: [68, 16] Generated Node #0,2,4: 79:[68, 16] Operation: 33-17=16 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 79:[68, 50], Operations: ['10+58=68', '33+17=50'] Exploring Operation: 68-50=18, Resulting Numbers: [18] 18,79 unequal: No Solution Exploring Operation: 68+50=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 68*50=3400, Resulting Numbers: [3400] 3400,79 unequal: No Solution No 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: 79:[33, 85], Operations: ['10+58=68', '17+68=85'] Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,79 unequal: No Solution Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,79 unequal: No Solution No 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: 79:[33, 51], Operations: ['10+58=68', '68-17=51'] Exploring Operation: 33+51=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 51-33=18, Resulting Numbers: [18] 18,79 unequal: No Solution Exploring Operation: 33*51=1683, Resulting Numbers: [1683] 1683,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 79:[68, 16], Operations: ['10+58=68', '33-17=16'] Exploring Operation: 68+16=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 68-16=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 68*16=1088, Resulting Numbers: [1088] 1088,79 unequal: No Solution No 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: 79:[17, 101], Operations: ['10+58=68', '33+68=101'] Exploring Operation: 101-17=84, Resulting Numbers: [84] 84,79 unequal: No Solution Exploring Operation: 17*101=1717, Resulting Numbers: [1717] 1717,79 unequal: No Solution Exploring Operation: 17+101=118, Resulting Numbers: [118] 118,79 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: 79:[33, 10, 75], Operations: ['17+58=75'] Exploring Operation: 33+10=43, Resulting Numbers: [75, 43] Generated Node #0,3,0: 79:[75, 43] Operation: 33+10=43 Exploring Operation: 33-10=23, Resulting Numbers: [75, 23] Generated Node #0,3,1: 79:[75, 23] Operation: 33-10=23 Exploring Operation: 75-10=65, Resulting Numbers: [33, 65] Generated Node #0,3,2: 79:[33, 65] Operation: 75-10=65 Exploring Operation: 33+75=108, Resulting Numbers: [10, 108] Generated Node #0,3,3: 79:[10, 108] Operation: 33+75=108 Exploring Operation: 10+75=85, Resulting Numbers: [33, 85] Generated Node #0,3,4: 79:[33, 85] Operation: 10+75=85 Moving to Node #0,3,0 Current State: 79:[75, 43], Operations: ['17+58=75', '33+10=43'] Exploring Operation: 75+43=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 75-43=32, Resulting Numbers: [32] 32,79 unequal: No Solution Exploring Operation: 75*43=3225, Resulting Numbers: [3225] 3225,79 unequal: No Solution Moving to Node #0,3,4 Current State: 79:[33, 85], Operations: ['17+58=75', '10+75=85'] Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[75, 23], Operations: ['17+58=75', '33-10=23'] Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,79 unequal: No Solution Exploring Operation: 75*23=1725, Resulting Numbers: [1725] 1725,79 unequal: No Solution Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[33, 65], Operations: ['17+58=75', '75-10=65'] Exploring Operation: 33*65=2145, Resulting Numbers: [2145] 2145,79 unequal: No Solution Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,79 unequal: No Solution Exploring Operation: 33+65=98, Resulting Numbers: [98] 98,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[10, 108], Operations: ['17+58=75', '33+75=108'] Exploring Operation: 10*108=1080, Resulting Numbers: [1080] 1080,79 unequal: No Solution Exploring Operation: 10+108=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 108-10=98, Resulting Numbers: [98] 98,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 79:[33, 58, 27], Operations: ['10+17=27'] Exploring Operation: 33-27=6, Resulting Numbers: [58, 6] Generated Node #0,4,0: 79:[58, 6] Operation: 33-27=6 Exploring Operation: 58+27=85, Resulting Numbers: [33, 85] Generated Node #0,4,1: 79:[33, 85] Operation: 58+27=85 Exploring Operation: 58-27=31, Resulting Numbers: [33, 31] Generated Node #0,4,2: 79:[33, 31] Operation: 58-27=31 Exploring Operation: 33+58=91, Resulting Numbers: [27, 91] Generated Node #0,4,3: 79:[27, 91] Operation: 33+58=91 Exploring Operation: 33+27=60, Resulting Numbers: [58, 60] Generated Node #0,4,4: 79:[58, 60] Operation: 33+27=60 Moving to Node #0,4,4 Current State: 79:[58, 60], Operations: ['10+17=27', '33+27=60'] Exploring Operation: 58+60=118, Resulting Numbers: [118] 118,79 unequal: No Solution Exploring Operation: 58*60=3480, Resulting Numbers: [3480] 3480,79 unequal: No Solution Exploring Operation: 60-58=2, Resulting Numbers: [2] 2,79 unequal: No Solution Moving to Node #0,4,1 Current State: 79:[33, 85], Operations: ['10+17=27', '58+27=85'] Exploring Operation: 33*85=2805, Resulting Numbers: [2805] 2805,79 unequal: No Solution Exploring Operation: 85-33=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 33+85=118, Resulting Numbers: [118] 118,79 unequal: No Solution Moving to Node #0,4,3 Current State: 79:[27, 91], Operations: ['10+17=27', '33+58=91'] Exploring Operation: 27*91=2457, Resulting Numbers: [2457] 2457,79 unequal: No Solution Exploring Operation: 91-27=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 27+91=118, Resulting Numbers: [118] 118,79 unequal: No Solution Moving to Node #0,4,0 Current State: 79:[58, 6], Operations: ['10+17=27', '33-27=6'] Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,79 unequal: No Solution Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,79 unequal: No Solution Moving to Node #0,4,2 Current State: 79:[33, 31], Operations: ['10+17=27', '58-27=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,79 unequal: No Solution Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 79, 88, 7, 85 ]
87
[ "88-79=9", "85-7=78", "9+78=87" ]
Current State: 87:[79, 88, 7, 85], Operations: [] Exploring Operation: 88-79=9, Resulting Numbers: [7, 85, 9] Generated Node #2: [7, 85, 9] from Operation: 88-79=9 Current State: 87:[7, 85, 9], Operations: ['88-79=9'] Exploring Operation: 85-7=78, Resulting Numbers: [9, 78] Generated Node #3: [9, 78] from Operation: 85-7=78 Current State: 87:[9, 78], Operations: ['88-79=9', '85-7=78'] Exploring Operation: 9+78=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[79, 88, 7, 85], Operations: [] Exploring Operation: 79+7=86, Resulting Numbers: [88, 85, 86] Generated Node #0,0: 87:[88, 85, 86] Operation: 79+7=86 Moving to Node #0,0 Current State: 87:[88, 85, 86], Operations: ['79+7=86'] Exploring Operation: 88-85=3, Resulting Numbers: [86, 3] Generated Node #0,0,0: 87:[86, 3] Operation: 88-85=3 Moving to Node #0,0,0 Current State: 87:[86, 3], Operations: ['79+7=86', '88-85=3'] Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,87 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 52, 47, 95, 11 ]
21
[ "95*11=1045", "47+1045=1092", "1092/52=21" ]
Current State: 21:[52, 47, 95, 11], Operations: [] Exploring Operation: 95*11=1045, Resulting Numbers: [52, 47, 1045] Generated Node #2: [52, 47, 1045] from Operation: 95*11=1045 Current State: 21:[52, 47, 1045], Operations: ['95*11=1045'] Exploring Operation: 47+1045=1092, Resulting Numbers: [52, 1092] Generated Node #3: [52, 1092] from Operation: 47+1045=1092 Current State: 21:[52, 1092], Operations: ['95*11=1045', '47+1045=1092'] Exploring Operation: 1092/52=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[52, 47, 95, 11], Operations: [] Exploring Operation: 95-52=43, Resulting Numbers: [47, 11, 43] Generated Node #0,0: 21:[47, 11, 43] Operation: 95-52=43 Moving to Node #0,0 Current State: 21:[47, 11, 43], Operations: ['95-52=43'] Exploring Operation: 47-43=4, Resulting Numbers: [11, 4] Generated Node #0,0,0: 21:[11, 4] Operation: 47-43=4 Moving to Node #0,0,0 Current State: 21:[11, 4], Operations: ['95-52=43', '47-43=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,21 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 9, 45, 63, 13 ]
27
[ "13-9=4", "45+63=108", "108/4=27" ]
Current State: 27:[9, 45, 63, 13], Operations: [] Exploring Operation: 13-9=4, Resulting Numbers: [45, 63, 4] Generated Node #2: [45, 63, 4] from Operation: 13-9=4 Current State: 27:[45, 63, 4], Operations: ['13-9=4'] Exploring Operation: 45+63=108, Resulting Numbers: [4, 108] Generated Node #3: [4, 108] from Operation: 45+63=108 Current State: 27:[4, 108], Operations: ['13-9=4', '45+63=108'] Exploring Operation: 108/4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[9, 45, 63, 13], Operations: [] Exploring Operation: 63-45=18, Resulting Numbers: [9, 13, 18] Generated Node #0,0: 27:[9, 13, 18] Operation: 63-45=18 Exploring Operation: 63/9=7, Resulting Numbers: [45, 13, 7] Generated Node #0,1: 27:[45, 13, 7] Operation: 63/9=7 Exploring Operation: 45-13=32, Resulting Numbers: [9, 63, 32] Generated Node #0,2: 27:[9, 63, 32] Operation: 45-13=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[9, 13, 18], Operations: ['63-45=18'] Exploring Operation: 18-9=9, Resulting Numbers: [13, 9] Generated Node #0,0,0: 27:[13, 9] Operation: 18-9=9 Exploring Operation: 18-13=5, Resulting Numbers: [9, 5] Generated Node #0,0,1: 27:[9, 5] Operation: 18-13=5 Exploring Operation: 9+18=27, Resulting Numbers: [13, 27] Generated Node #0,0,2: 27:[13, 27] Operation: 9+18=27 Moving to Node #0,0,1 Current State: 27:[9, 5], Operations: ['63-45=18', '18-13=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[13, 9], Operations: ['63-45=18', '18-9=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 13*9=117, Resulting Numbers: [117] 117,27 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[13, 27], Operations: ['63-45=18', '9+18=27'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,27 unequal: No Solution Exploring Operation: 13*27=351, Resulting Numbers: [351] 351,27 unequal: No Solution Exploring Operation: 13+27=40, Resulting Numbers: [40] 40,27 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 Current State: 27:[45, 13, 7], Operations: ['63/9=7'] Exploring Operation: 13-7=6, Resulting Numbers: [45, 6] Generated Node #0,1,0: 27:[45, 6] Operation: 13-7=6 Exploring Operation: 45-13=32, Resulting Numbers: [7, 32] Generated Node #0,1,1: 27:[7, 32] Operation: 45-13=32 Exploring Operation: 45-7=38, Resulting Numbers: [13, 38] Generated Node #0,1,2: 27:[13, 38] Operation: 45-7=38 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[7, 32], Operations: ['63/9=7', '45-13=32'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,27 unequal: No Solution No 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: 27:[13, 38], Operations: ['63/9=7', '45-7=38'] Exploring Operation: 13*38=494, Resulting Numbers: [494] 494,27 unequal: No Solution Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,27 unequal: No Solution No 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: 27:[45, 6], Operations: ['63/9=7', '13-7=6'] Exploring Operation: 45+6=51, Resulting Numbers: [51] 51,27 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 45*6=270, Resulting Numbers: [270] 270,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[9, 63, 32], Operations: ['45-13=32'] Exploring Operation: 63-32=31, Resulting Numbers: [9, 31] Generated Node #0,2,0: 27:[9, 31] Operation: 63-32=31 Exploring Operation: 63/9=7, Resulting Numbers: [32, 7] Generated Node #0,2,1: 27:[32, 7] Operation: 63/9=7 Exploring Operation: 63-9=54, Resulting Numbers: [32, 54] Generated Node #0,2,2: 27:[32, 54] Operation: 63-9=54 Moving to Node #0,2,0 Current State: 27:[9, 31], Operations: ['45-13=32', '63-32=31'] Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,27 unequal: No Solution Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[32, 7], Operations: ['45-13=32', '63/9=7'] Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,27 unequal: No Solution Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,27 unequal: No Solution Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[32, 54], Operations: ['45-13=32', '63-9=54'] Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,27 unequal: No Solution Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 65, 18, 43, 36 ]
32
[ "65-18=47", "43+36=79", "79-47=32" ]
Current State: 32:[65, 18, 43, 36], Operations: [] Exploring Operation: 65-18=47, Resulting Numbers: [43, 36, 47] Generated Node #2: [43, 36, 47] from Operation: 65-18=47 Current State: 32:[43, 36, 47], Operations: ['65-18=47'] Exploring Operation: 43+36=79, Resulting Numbers: [47, 79] Generated Node #3: [47, 79] from Operation: 43+36=79 Current State: 32:[47, 79], Operations: ['65-18=47', '43+36=79'] Exploring Operation: 79-47=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[65, 18, 43, 36], Operations: [] Exploring Operation: 65-43=22, Resulting Numbers: [18, 36, 22] Generated Node #0,0: 32:[18, 36, 22] Operation: 65-43=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[18, 36, 22], Operations: ['65-43=22'] Exploring Operation: 22-18=4, Resulting Numbers: [36, 4] Generated Node #0,0,0: 32:[36, 4] Operation: 22-18=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[36, 4], Operations: ['65-43=22', '22-18=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[65, 18, 43, 36], Operations: [] Exploring Operation: 65-43=22, Resulting Numbers: [18, 36, 22] Generated Node #0,0: 32:[18, 36, 22] Operation: 65-43=22 Moving to Node #0,0 Current State: 32:[18, 36, 22], Operations: ['65-43=22'] Exploring Operation: 22-18=4, Resulting Numbers: [36, 4] Generated Node #0,0,0: 32:[36, 4] Operation: 22-18=4 Moving to Node #0,0,0 Current State: 32:[36, 4], Operations: ['65-43=22', '22-18=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 61, 2, 65, 2 ]
61
[ "61+2=63", "2*63=126", "126-65=61" ]
Current State: 61:[61, 2, 65, 2], Operations: [] Exploring Operation: 61+2=63, Resulting Numbers: [65, 63] Generated Node #2: [65, 63] from Operation: 61+2=63 Current State: 61:[65, 63], Operations: ['61+2=63'] Exploring Operation: 2*63=126, Resulting Numbers: [65, 126] Generated Node #3: [65, 126] from Operation: 2*63=126 Current State: 61:[65, 126], Operations: ['61+2=63', '2*63=126'] Exploring Operation: 126-65=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[61, 2, 65, 2], Operations: [] Exploring Operation: 65-2=63, Resulting Numbers: [61, 2, 63] Generated Node #0,0: 61:[61, 2, 63] Operation: 65-2=63 Exploring Operation: 2*2=4, Resulting Numbers: [61, 65, 4] Generated Node #0,1: 61:[61, 65, 4] Operation: 2*2=4 Exploring Operation: 2+2=4, Resulting Numbers: [61, 65, 4] Generated Node #0,2: 61:[61, 65, 4] Operation: 2+2=4 Exploring Operation: 65-2=63, Resulting Numbers: [61, 2, 63] Generated Node #0,3: 61:[61, 2, 63] Operation: 65-2=63 Exploring Operation: 2/2=1, Resulting Numbers: [61, 65, 1] Generated Node #0,4: 61:[61, 65, 1] Operation: 2/2=1 Moving to Node #0,0 Current State: 61:[61, 2, 63], Operations: ['65-2=63'] Exploring Operation: 61+2=63, Resulting Numbers: [63, 63] Generated Node #0,0,0: 61:[63, 63] Operation: 61+2=63 Exploring Operation: 63-2=61, Resulting Numbers: [61, 61] Generated Node #0,0,1: 61:[61, 61] Operation: 63-2=61 Exploring Operation: 61*2=122, Resulting Numbers: [63, 122] Generated Node #0,0,2: 61:[63, 122] Operation: 61*2=122 Exploring Operation: 61-2=59, Resulting Numbers: [63, 59] Generated Node #0,0,3: 61:[63, 59] Operation: 61-2=59 Exploring Operation: 2+63=65, Resulting Numbers: [61, 65] Generated Node #0,0,4: 61:[61, 65] Operation: 2+63=65 Moving to Node #0,2 Current State: 61:[61, 65, 4], Operations: ['2+2=4'] Exploring Operation: 65-4=61, Resulting Numbers: [61, 61] Generated Node #0,2,0: 61:[61, 61] Operation: 65-4=61 Exploring Operation: 61+4=65, Resulting Numbers: [65, 65] Generated Node #0,2,1: 61:[65, 65] Operation: 61+4=65 Exploring Operation: 61-4=57, Resulting Numbers: [65, 57] Generated Node #0,2,2: 61:[65, 57] Operation: 61-4=57 Exploring Operation: 65+4=69, Resulting Numbers: [61, 69] Generated Node #0,2,3: 61:[61, 69] Operation: 65+4=69 Exploring Operation: 65-61=4, Resulting Numbers: [4, 4] Generated Node #0,2,4: 61:[4, 4] Operation: 65-61=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[61, 61], Operations: ['2+2=4', '65-4=61'] Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 61*61=3721, Resulting Numbers: [3721] 3721,61 unequal: No Solution Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,61 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:[65, 65], Operations: ['2+2=4', '61+4=65'] Exploring Operation: 65-65=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 65+65=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 65/65=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 65*65=4225, Resulting Numbers: [4225] 4225,61 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 #0,2,2 Current State: 61:[65, 57], Operations: ['2+2=4', '61-4=57'] Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 65+57=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 65*57=3705, Resulting Numbers: [3705] 3705,61 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 #0,2,3 Current State: 61:[61, 69], Operations: ['2+2=4', '65+4=69'] Exploring Operation: 69-61=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 61+69=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 61*69=4209, Resulting Numbers: [4209] 4209,61 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 #0,2,4 Current State: 61:[4, 4], Operations: ['2+2=4', '65-61=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,61 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:[61, 65, 4], Operations: ['2*2=4'] Exploring Operation: 61-4=57, Resulting Numbers: [65, 57] Generated Node #0,1,0: 61:[65, 57] Operation: 61-4=57 Exploring Operation: 61+4=65, Resulting Numbers: [65, 65] Generated Node #0,1,1: 61:[65, 65] Operation: 61+4=65 Exploring Operation: 65-61=4, Resulting Numbers: [4, 4] Generated Node #0,1,2: 61:[4, 4] Operation: 65-61=4 Exploring Operation: 65-4=61, Resulting Numbers: [61, 61] Generated Node #0,1,3: 61:[61, 61] Operation: 65-4=61 Exploring Operation: 65+4=69, Resulting Numbers: [61, 69] Generated Node #0,1,4: 61:[61, 69] Operation: 65+4=69 Moving to Node #0,3 Current State: 61:[61, 2, 63], Operations: ['65-2=63'] Exploring Operation: 61+2=63, Resulting Numbers: [63, 63] Generated Node #0,3,0: 61:[63, 63] Operation: 61+2=63 Exploring Operation: 2+63=65, Resulting Numbers: [61, 65] Generated Node #0,3,1: 61:[61, 65] Operation: 2+63=65 Exploring Operation: 63-2=61, Resulting Numbers: [61, 61] Generated Node #0,3,2: 61:[61, 61] Operation: 63-2=61 Exploring Operation: 61*2=122, Resulting Numbers: [63, 122] Generated Node #0,3,3: 61:[63, 122] Operation: 61*2=122 Exploring Operation: 61-2=59, Resulting Numbers: [63, 59] Generated Node #0,3,4: 61:[63, 59] Operation: 61-2=59 Moving to Node #0,4 Current State: 61:[61, 65, 1], Operations: ['2/2=1'] Exploring Operation: 65/1=65, Resulting Numbers: [61, 65] Generated Node #0,4,0: 61:[61, 65] Operation: 65/1=65 Exploring Operation: 65*1=65, Resulting Numbers: [61, 65] Generated Node #0,4,1: 61:[61, 65] Operation: 65*1=65 Exploring Operation: 65-1=64, Resulting Numbers: [61, 64] Generated Node #0,4,2: 61:[61, 64] Operation: 65-1=64 Exploring Operation: 61/1=61, Resulting Numbers: [65, 61] Generated Node #0,4,3: 61:[65, 61] Operation: 61/1=61 Exploring Operation: 61*1=61, Resulting Numbers: [65, 61] Generated Node #0,4,4: 61:[65, 61] Operation: 61*1=61 Moving to Node #0,0,1 Current State: 61:[61, 61], Operations: ['65-2=63', '63-2=61'] Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 61*61=3721, Resulting Numbers: [3721] 3721,61 unequal: No Solution Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[61, 61], Operations: ['2*2=4', '65-4=61'] Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 61*61=3721, Resulting Numbers: [3721] 3721,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[61, 61], Operations: ['65-2=63', '63-2=61'] Exploring Operation: 61+61=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 61-61=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 61/61=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 61*61=3721, Resulting Numbers: [3721] 3721,61 unequal: No Solution Moving to Node #0,4,2 Current State: 61:[61, 64], Operations: ['2/2=1', '65-1=64'] Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,61 unequal: No Solution Exploring Operation: 61*64=3904, Resulting Numbers: [3904] 3904,61 unequal: No Solution Exploring Operation: 61+64=125, Resulting Numbers: [125] 125,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[63, 59], Operations: ['65-2=63', '61-2=59'] Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 63+59=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 63*59=3717, Resulting Numbers: [3717] 3717,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[63, 59], Operations: ['65-2=63', '61-2=59'] Exploring Operation: 63-59=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 63+59=122, Resulting Numbers: [122] 122,61 unequal: No Solution Exploring Operation: 63*59=3717, Resulting Numbers: [3717] 3717,61 unequal: No Solution Moving to Node #0,3,1 Current State: 61:[61, 65], Operations: ['65-2=63', '2+63=65'] Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 61*65=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,4,0 Current State: 61:[61, 65], Operations: ['2/2=1', '65/1=65'] Exploring Operation: 61*65=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[63, 63], Operations: ['65-2=63', '61+2=63'] Exploring Operation: 63/63=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 63-63=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 63*63=3969, Resulting Numbers: [3969] 3969,61 unequal: No Solution Exploring Operation: 63+63=126, Resulting Numbers: [126] 126,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[63, 63], Operations: ['65-2=63', '61+2=63'] Exploring Operation: 63-63=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 63+63=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 63/63=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 63*63=3969, Resulting Numbers: [3969] 3969,61 unequal: No Solution Moving to Node #0,4,4 Current State: 61:[65, 61], Operations: ['2/2=1', '61*1=61'] Exploring Operation: 65+61=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 65*61=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,4,1 Current State: 61:[61, 65], Operations: ['2/2=1', '65*1=65'] Exploring Operation: 61*65=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,61 unequal: No Solution Moving to Node #0,4,3 Current State: 61:[65, 61], Operations: ['2/2=1', '61/1=61'] Exploring Operation: 65+61=126, Resulting Numbers: [126] 126,61 unequal: No Solution Exploring Operation: 65*61=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Moving to Node #0,0,4 Current State: 61:[61, 65], Operations: ['65-2=63', '2+63=65'] Exploring Operation: 65-61=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 61*65=3965, Resulting Numbers: [3965] 3965,61 unequal: No Solution Exploring Operation: 61+65=126, Resulting Numbers: [126] 126,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[65, 57], Operations: ['2*2=4', '61-4=57'] Exploring Operation: 65*57=3705, Resulting Numbers: [3705] 3705,61 unequal: No Solution Exploring Operation: 65-57=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 65+57=122, Resulting Numbers: [122] 122,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[65, 65], Operations: ['2*2=4', '61+4=65'] Exploring Operation: 65*65=4225, Resulting Numbers: [4225] 4225,61 unequal: No Solution Exploring Operation: 65+65=130, Resulting Numbers: [130] 130,61 unequal: No Solution Exploring Operation: 65-65=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 65/65=1, Resulting Numbers: [1] 1,61 unequal: No Solution Moving to Node #0,1,4 Current State: 61:[61, 69], Operations: ['2*2=4', '65+4=69'] Exploring Operation: 69-61=8, Resulting Numbers: [8] 8,61 unequal: No Solution Exploring Operation: 61*69=4209, Resulting Numbers: [4209] 4209,61 unequal: No Solution Exploring Operation: 61+69=130, Resulting Numbers: [130] 130,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[63, 122], Operations: ['65-2=63', '61*2=122'] Exploring Operation: 63+122=185, Resulting Numbers: [185] 185,61 unequal: No Solution Exploring Operation: 63*122=7686, Resulting Numbers: [7686] 7686,61 unequal: No Solution Exploring Operation: 122-63=59, Resulting Numbers: [59] 59,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[63, 122], Operations: ['65-2=63', '61*2=122'] Exploring Operation: 63+122=185, Resulting Numbers: [185] 185,61 unequal: No Solution Exploring Operation: 122-63=59, Resulting Numbers: [59] 59,61 unequal: No Solution Exploring Operation: 63*122=7686, Resulting Numbers: [7686] 7686,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[4, 4], Operations: ['2*2=4', '65-61=4'] Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,61 unequal: No Solution Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,61 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,61 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,61 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 43, 34, 30, 61 ]
82
[ "43-34=9", "30+61=91", "91-9=82" ]
Current State: 82:[43, 34, 30, 61], Operations: [] Exploring Operation: 43-34=9, Resulting Numbers: [30, 61, 9] Generated Node #2: [30, 61, 9] from Operation: 43-34=9 Current State: 82:[30, 61, 9], Operations: ['43-34=9'] Exploring Operation: 30+61=91, Resulting Numbers: [9, 91] Generated Node #3: [9, 91] from Operation: 30+61=91 Current State: 82:[9, 91], Operations: ['43-34=9', '30+61=91'] Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[43, 34, 30, 61], Operations: [] Exploring Operation: 30+61=91, Resulting Numbers: [43, 34, 91] Generated Node #0,0: 82:[43, 34, 91] Operation: 30+61=91 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[43, 34, 91], Operations: ['30+61=91'] Exploring Operation: 43+34=77, Resulting Numbers: [91, 77] Generated Node #0,0,0: 82:[91, 77] Operation: 43+34=77 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[91, 77], Operations: ['30+61=91', '43+34=77'] Exploring Operation: 91-77=14, Resulting Numbers: [14] 14,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 81, 52, 63, 86 ]
23
[ "86-81=5", "52+63=115", "115/5=23" ]
Current State: 23:[81, 52, 63, 86], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [52, 63, 5] Generated Node #2: [52, 63, 5] from Operation: 86-81=5 Current State: 23:[52, 63, 5], Operations: ['86-81=5'] Exploring Operation: 52+63=115, Resulting Numbers: [5, 115] Generated Node #3: [5, 115] from Operation: 52+63=115 Current State: 23:[5, 115], Operations: ['86-81=5', '52+63=115'] Exploring Operation: 115/5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[81, 52, 63, 86], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [52, 63, 5] Generated Node #0,0: 23:[52, 63, 5] Operation: 86-81=5 Exploring Operation: 86-63=23, Resulting Numbers: [81, 52, 23] Generated Node #0,1: 23:[81, 52, 23] Operation: 86-63=23 Exploring Operation: 81-63=18, Resulting Numbers: [52, 86, 18] Generated Node #0,2: 23:[52, 86, 18] Operation: 81-63=18 Moving to Node #0,0 Current State: 23:[52, 63, 5], Operations: ['86-81=5'] Exploring Operation: 63-52=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 23:[5, 11] Operation: 63-52=11 Exploring Operation: 52-5=47, Resulting Numbers: [63, 47] Generated Node #0,0,1: 23:[63, 47] Operation: 52-5=47 Exploring Operation: 63-5=58, Resulting Numbers: [52, 58] Generated Node #0,0,2: 23:[52, 58] Operation: 63-5=58 Moving to Node #0,1 Current State: 23:[81, 52, 23], Operations: ['86-63=23'] Exploring Operation: 81-52=29, Resulting Numbers: [23, 29] Generated Node #0,1,0: 23:[23, 29] Operation: 81-52=29 Exploring Operation: 81-23=58, Resulting Numbers: [52, 58] Generated Node #0,1,1: 23:[52, 58] Operation: 81-23=58 Exploring Operation: 52-23=29, Resulting Numbers: [81, 29] Generated Node #0,1,2: 23:[81, 29] Operation: 52-23=29 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[23, 29], Operations: ['86-63=23', '81-52=29'] Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[52, 58], Operations: ['86-63=23', '81-23=58'] Exploring Operation: 52*58=3016, Resulting Numbers: [3016] 3016,23 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 52+58=110, Resulting Numbers: [110] 110,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 23:[81, 29], Operations: ['86-63=23', '52-23=29'] Exploring Operation: 81*29=2349, Resulting Numbers: [2349] 2349,23 unequal: No Solution Exploring Operation: 81-29=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 81+29=110, Resulting Numbers: [110] 110,23 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: 23:[52, 86, 18], Operations: ['81-63=18'] Exploring Operation: 86-18=68, Resulting Numbers: [52, 68] Generated Node #0,2,0: 23:[52, 68] Operation: 86-18=68 Exploring Operation: 86-52=34, Resulting Numbers: [18, 34] Generated Node #0,2,1: 23:[18, 34] Operation: 86-52=34 Exploring Operation: 52-18=34, Resulting Numbers: [86, 34] Generated Node #0,2,2: 23:[86, 34] Operation: 52-18=34 Moving to Node #0,2,1 Current State: 23:[18, 34], Operations: ['81-63=18', '86-52=34'] Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,23 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[5, 11], Operations: ['86-81=5', '63-52=11'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,23 unequal: No Solution Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[52, 58], Operations: ['86-81=5', '63-5=58'] Exploring Operation: 52+58=110, Resulting Numbers: [110] 110,23 unequal: No Solution Exploring Operation: 52*58=3016, Resulting Numbers: [3016] 3016,23 unequal: No Solution Exploring Operation: 58-52=6, Resulting Numbers: [6] 6,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[63, 47], Operations: ['86-81=5', '52-5=47'] Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 63*47=2961, Resulting Numbers: [2961] 2961,23 unequal: No Solution Exploring Operation: 63+47=110, Resulting Numbers: [110] 110,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[86, 34], Operations: ['81-63=18', '52-18=34'] Exploring Operation: 86*34=2924, Resulting Numbers: [2924] 2924,23 unequal: No Solution Exploring Operation: 86+34=120, Resulting Numbers: [120] 120,23 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[52, 68], Operations: ['81-63=18', '86-18=68'] Exploring Operation: 68-52=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 52*68=3536, Resulting Numbers: [3536] 3536,23 unequal: No Solution Exploring Operation: 52+68=120, Resulting Numbers: [120] 120,23 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 43, 88, 58, 31 ]
43
[ "88-58=30", "31-30=1", "43*1=43" ]
Current State: 43:[43, 88, 58, 31], Operations: [] Exploring Operation: 88-58=30, Resulting Numbers: [43, 31, 30] Generated Node #2: [43, 31, 30] from Operation: 88-58=30 Current State: 43:[43, 31, 30], Operations: ['88-58=30'] Exploring Operation: 31-30=1, Resulting Numbers: [43, 1] Generated Node #3: [43, 1] from Operation: 31-30=1 Current State: 43:[43, 1], Operations: ['88-58=30', '31-30=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[43, 88, 58, 31], Operations: [] Exploring Operation: 88-58=30, Resulting Numbers: [43, 31, 30] Generated Node #0,0: 43:[43, 31, 30] Operation: 88-58=30 Exploring Operation: 88-43=45, Resulting Numbers: [58, 31, 45] Generated Node #0,1: 43:[58, 31, 45] Operation: 88-43=45 Exploring Operation: 58-43=15, Resulting Numbers: [88, 31, 15] Generated Node #0,2: 43:[88, 31, 15] Operation: 58-43=15 Exploring Operation: 58-31=27, Resulting Numbers: [43, 88, 27] Generated Node #0,3: 43:[43, 88, 27] Operation: 58-31=27 Exploring Operation: 88-31=57, Resulting Numbers: [43, 58, 57] Generated Node #0,4: 43:[43, 58, 57] Operation: 88-31=57 Moving to Node #0,0 Current State: 43:[43, 31, 30], Operations: ['88-58=30'] Exploring Operation: 43-30=13, Resulting Numbers: [31, 13] Generated Node #0,0,0: 43:[31, 13] Operation: 43-30=13 Exploring Operation: 43+31=74, Resulting Numbers: [30, 74] Generated Node #0,0,1: 43:[30, 74] Operation: 43+31=74 Exploring Operation: 31+30=61, Resulting Numbers: [43, 61] Generated Node #0,0,2: 43:[43, 61] Operation: 31+30=61 Exploring Operation: 43+30=73, Resulting Numbers: [31, 73] Generated Node #0,0,3: 43:[31, 73] Operation: 43+30=73 Exploring Operation: 31-30=1, Resulting Numbers: [43, 1] Generated Node #0,0,4: 43:[43, 1] Operation: 31-30=1 Moving to Node #0,4 Current State: 43:[43, 58, 57], Operations: ['88-31=57'] Exploring Operation: 43+57=100, Resulting Numbers: [58, 100] Generated Node #0,4,0: 43:[58, 100] Operation: 43+57=100 Exploring Operation: 57-43=14, Resulting Numbers: [58, 14] Generated Node #0,4,1: 43:[58, 14] Operation: 57-43=14 Exploring Operation: 58-57=1, Resulting Numbers: [43, 1] Generated Node #0,4,2: 43:[43, 1] Operation: 58-57=1 Exploring Operation: 58-43=15, Resulting Numbers: [57, 15] Generated Node #0,4,3: 43:[57, 15] Operation: 58-43=15 Exploring Operation: 43+58=101, Resulting Numbers: [57, 101] Generated Node #0,4,4: 43:[57, 101] Operation: 43+58=101 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 43:[43, 1], Operations: ['88-31=57', '58-57=1'] Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,43 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,43 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[43, 88, 58, 31], Operations: [] Exploring Operation: 88-31=57, Resulting Numbers: [43, 58, 57] Generated Node #0,4: 43:[43, 58, 57] Operation: 88-31=57 Moving to Node #0,4 Current State: 43:[43, 58, 57], Operations: ['88-31=57'] Exploring Operation: 58-57=1, Resulting Numbers: [43, 1] Generated Node #0,4,2: 43:[43, 1] Operation: 58-57=1 Moving to Node #0,4,2 Current State: 43:[43, 1], Operations: ['88-31=57', '58-57=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 72, 32, 90, 8 ]
72
[ "90-72=18", "32/8=4", "18*4=72" ]
Current State: 72:[72, 32, 90, 8], Operations: [] Exploring Operation: 90-72=18, Resulting Numbers: [32, 8, 18] Generated Node #2: [32, 8, 18] from Operation: 90-72=18 Current State: 72:[32, 8, 18], Operations: ['90-72=18'] Exploring Operation: 32/8=4, Resulting Numbers: [18, 4] Generated Node #3: [18, 4] from Operation: 32/8=4 Current State: 72:[18, 4], Operations: ['90-72=18', '32/8=4'] Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[72, 32, 90, 8], Operations: [] Exploring Operation: 90-72=18, Resulting Numbers: [32, 8, 18] Generated Node #0,0: 72:[32, 8, 18] Operation: 90-72=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[32, 8, 18], Operations: ['90-72=18'] Exploring Operation: 32-8=24, Resulting Numbers: [18, 24] Generated Node #0,0,0: 72:[18, 24] Operation: 32-8=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[18, 24], Operations: ['90-72=18', '32-8=24'] Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 10, 50, 20, 95 ]
23
[ "50/10=5", "20+95=115", "115/5=23" ]
Current State: 23:[10, 50, 20, 95], Operations: [] Exploring Operation: 50/10=5, Resulting Numbers: [20, 95, 5] Generated Node #2: [20, 95, 5] from Operation: 50/10=5 Current State: 23:[20, 95, 5], Operations: ['50/10=5'] Exploring Operation: 20+95=115, Resulting Numbers: [5, 115] Generated Node #3: [5, 115] from Operation: 20+95=115 Current State: 23:[5, 115], Operations: ['50/10=5', '20+95=115'] Exploring Operation: 115/5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[10, 50, 20, 95], Operations: [] Exploring Operation: 95-50=45, Resulting Numbers: [10, 20, 45] Generated Node #0,0: 23:[10, 20, 45] Operation: 95-50=45 Exploring Operation: 50-10=40, Resulting Numbers: [20, 95, 40] Generated Node #0,1: 23:[20, 95, 40] Operation: 50-10=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[10, 20, 45], Operations: ['95-50=45'] Exploring Operation: 45-20=25, Resulting Numbers: [10, 25] Generated Node #0,0,0: 23:[10, 25] Operation: 45-20=25 Exploring Operation: 45-10=35, Resulting Numbers: [20, 35] Generated Node #0,0,1: 23:[20, 35] Operation: 45-10=35 Moving to Node #0,0,0 Current State: 23:[10, 25], Operations: ['95-50=45', '45-20=25'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 10+25=35, Resulting Numbers: [35] 35,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[20, 35], Operations: ['95-50=45', '45-10=35'] Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[20, 95, 40], Operations: ['50-10=40'] Exploring Operation: 95-40=55, Resulting Numbers: [20, 55] Generated Node #0,1,0: 23:[20, 55] Operation: 95-40=55 Exploring Operation: 95-20=75, Resulting Numbers: [40, 75] Generated Node #0,1,1: 23:[40, 75] Operation: 95-20=75 Moving to Node #0,1,0 Current State: 23:[20, 55], Operations: ['50-10=40', '95-40=55'] Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[40, 75], Operations: ['50-10=40', '95-20=75'] Exploring Operation: 75-40=35, Resulting Numbers: [35] 35,23 unequal: No Solution Exploring Operation: 40+75=115, Resulting Numbers: [115] 115,23 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
[ 43, 52, 63, 4 ]
11
[ "52-43=9", "63/9=7", "4+7=11" ]
Current State: 11:[43, 52, 63, 4], Operations: [] Exploring Operation: 52-43=9, Resulting Numbers: [63, 4, 9] Generated Node #2: [63, 4, 9] from Operation: 52-43=9 Current State: 11:[63, 4, 9], Operations: ['52-43=9'] Exploring Operation: 63/9=7, Resulting Numbers: [4, 7] Generated Node #3: [4, 7] from Operation: 63/9=7 Current State: 11:[4, 7], Operations: ['52-43=9', '63/9=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[43, 52, 63, 4], Operations: [] Exploring Operation: 63-52=11, Resulting Numbers: [43, 4, 11] Generated Node #0,0: 11:[43, 4, 11] Operation: 63-52=11 Exploring Operation: 63-43=20, Resulting Numbers: [52, 4, 20] Generated Node #0,1: 11:[52, 4, 20] Operation: 63-43=20 Moving to Node #0,0 Current State: 11:[43, 4, 11], Operations: ['63-52=11'] Exploring Operation: 43-4=39, Resulting Numbers: [11, 39] Generated Node #0,0,0: 11:[11, 39] Operation: 43-4=39 Exploring Operation: 43-11=32, Resulting Numbers: [4, 32] Generated Node #0,0,1: 11:[4, 32] Operation: 43-11=32 Moving to Node #0,1 Current State: 11:[52, 4, 20], Operations: ['63-43=20'] Exploring Operation: 52/4=13, Resulting Numbers: [20, 13] Generated Node #0,1,0: 11:[20, 13] Operation: 52/4=13 Exploring Operation: 52-20=32, Resulting Numbers: [4, 32] Generated Node #0,1,1: 11:[4, 32] Operation: 52-20=32 Moving to Node #0,1,0 Current State: 11:[20, 13], Operations: ['63-43=20', '52/4=13'] Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,11 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,11 unequal: No Solution Moving to Node #0,0,0 Current State: 11:[11, 39], Operations: ['63-52=11', '43-4=39'] Exploring Operation: 11+39=50, Resulting Numbers: [50] 50,11 unequal: No Solution Exploring Operation: 39-11=28, Resulting Numbers: [28] 28,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[4, 32], Operations: ['63-52=11', '43-11=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,11 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,11 unequal: No Solution Moving to Node #0,1,1 Current State: 11:[4, 32], Operations: ['63-43=20', '52-20=32'] Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,11 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,11 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 13, 89, 26, 25 ]
32
[ "26/13=2", "89-25=64", "64/2=32" ]
Current State: 32:[13, 89, 26, 25], Operations: [] Exploring Operation: 26/13=2, Resulting Numbers: [89, 25, 2] Generated Node #2: [89, 25, 2] from Operation: 26/13=2 Current State: 32:[89, 25, 2], Operations: ['26/13=2'] Exploring Operation: 89-25=64, Resulting Numbers: [2, 64] Generated Node #3: [2, 64] from Operation: 89-25=64 Current State: 32:[2, 64], Operations: ['26/13=2', '89-25=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[13, 89, 26, 25], Operations: [] Exploring Operation: 89-26=63, Resulting Numbers: [13, 25, 63] Generated Node #0,0: 32:[13, 25, 63] Operation: 89-26=63 Exploring Operation: 89-25=64, Resulting Numbers: [13, 26, 64] Generated Node #0,1: 32:[13, 26, 64] Operation: 89-25=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[13, 25, 63], Operations: ['89-26=63'] Exploring Operation: 63-25=38, Resulting Numbers: [13, 38] Generated Node #0,0,0: 32:[13, 38] Operation: 63-25=38 Exploring Operation: 63-13=50, Resulting Numbers: [25, 50] Generated Node #0,0,1: 32:[25, 50] Operation: 63-13=50 Moving to Node #0,0,0 Current State: 32:[13, 38], Operations: ['89-26=63', '63-25=38'] Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,32 unequal: No Solution Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,32 unequal: No Solution Moving to Node #0,0,1 Current State: 32:[25, 50], Operations: ['89-26=63', '63-13=50'] Exploring Operation: 50/25=2, Resulting Numbers: [2] 2,32 unequal: No Solution Exploring Operation: 50-25=25, Resulting Numbers: [25] 25,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 32:[13, 26, 64], Operations: ['89-25=64'] Exploring Operation: 64-26=38, Resulting Numbers: [13, 38] Generated Node #0,1,0: 32:[13, 38] Operation: 64-26=38 Exploring Operation: 64-13=51, Resulting Numbers: [26, 51] Generated Node #0,1,1: 32:[26, 51] Operation: 64-13=51 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 32:[13, 38], Operations: ['89-25=64', '64-26=38'] Exploring Operation: 13+38=51, Resulting Numbers: [51] 51,32 unequal: No Solution Exploring Operation: 38-13=25, Resulting Numbers: [25] 25,32 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:[26, 51], Operations: ['89-25=64', '64-13=51'] Exploring Operation: 26+51=77, Resulting Numbers: [77] 77,32 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,32 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_2
mult_heuristic