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
[ 72, 52, 5, 23 ]
73
[ "52-23=29", "5*29=145", "145-72=73" ]
Current State: 73:[72, 52, 5, 23], Operations: [] Exploring Operation: 52-23=29, Resulting Numbers: [72, 5, 29] Generated Node #2: [72, 5, 29] from Operation: 52-23=29 Current State: 73:[72, 5, 29], Operations: ['52-23=29'] Exploring Operation: 5*29=145, Resulting Numbers: [72, 145] Generated Node #3: [72, 145] from Operation: 5*29=145 Current State: 73:[72, 145], Operations: ['52-23=29', '5*29=145'] Exploring Operation: 145-72=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[72, 52, 5, 23], Operations: [] Exploring Operation: 52+5=57, Resulting Numbers: [72, 23, 57] Generated Node #0,0: 73:[72, 23, 57] Operation: 52+5=57 Exploring Operation: 5*23=115, Resulting Numbers: [72, 52, 115] Generated Node #0,1: 73:[72, 52, 115] Operation: 5*23=115 Exploring Operation: 5+23=28, Resulting Numbers: [72, 52, 28] Generated Node #0,2: 73:[72, 52, 28] Operation: 5+23=28 Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[72, 52, 115], Operations: ['5*23=115'] Exploring Operation: 115-52=63, Resulting Numbers: [72, 63] Generated Node #0,1,0: 73:[72, 63] Operation: 115-52=63 Exploring Operation: 72+52=124, Resulting Numbers: [115, 124] Generated Node #0,1,1: 73:[115, 124] Operation: 72+52=124 Exploring Operation: 115-72=43, Resulting Numbers: [52, 43] Generated Node #0,1,2: 73:[52, 43] Operation: 115-72=43 Moving to Node #0,1,0 Current State: 73:[72, 63], Operations: ['5*23=115', '115-52=63'] Exploring Operation: 72-63=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 72*63=4536, Resulting Numbers: [4536] 4536,73 unequal: No Solution Exploring Operation: 72+63=135, Resulting Numbers: [135] 135,73 unequal: No Solution Moving to Node #0,1,2 Current State: 73:[52, 43], Operations: ['5*23=115', '115-72=43'] Exploring Operation: 52-43=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 52+43=95, Resulting Numbers: [95] 95,73 unequal: No Solution Exploring Operation: 52*43=2236, Resulting Numbers: [2236] 2236,73 unequal: No Solution Moving to Node #0,1,1 Current State: 73:[115, 124], Operations: ['5*23=115', '72+52=124'] Exploring Operation: 115+124=239, Resulting Numbers: [239] 239,73 unequal: No Solution Exploring Operation: 124-115=9, Resulting Numbers: [9] 9,73 unequal: No Solution Exploring Operation: 115*124=14260, Resulting Numbers: [14260] 14260,73 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 Current State: 73:[72, 23, 57], Operations: ['52+5=57'] Exploring Operation: 72-23=49, Resulting Numbers: [57, 49] Generated Node #0,0,0: 73:[57, 49] Operation: 72-23=49 Exploring Operation: 72+23=95, Resulting Numbers: [57, 95] Generated Node #0,0,1: 73:[57, 95] Operation: 72+23=95 Exploring Operation: 23+57=80, Resulting Numbers: [72, 80] Generated Node #0,0,2: 73:[72, 80] Operation: 23+57=80 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[72, 80], Operations: ['52+5=57', '23+57=80'] Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,73 unequal: No Solution Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,73 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[57, 95], Operations: ['52+5=57', '72+23=95'] Exploring Operation: 57*95=5415, Resulting Numbers: [5415] 5415,73 unequal: No Solution Exploring Operation: 57+95=152, Resulting Numbers: [152] 152,73 unequal: No Solution Exploring Operation: 95-57=38, Resulting Numbers: [38] 38,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[57, 49], Operations: ['52+5=57', '72-23=49'] Exploring Operation: 57-49=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 57+49=106, Resulting Numbers: [106] 106,73 unequal: No Solution Exploring Operation: 57*49=2793, Resulting Numbers: [2793] 2793,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[72, 52, 28], Operations: ['5+23=28'] Exploring Operation: 72-28=44, Resulting Numbers: [52, 44] Generated Node #0,2,0: 73:[52, 44] Operation: 72-28=44 Exploring Operation: 72+28=100, Resulting Numbers: [52, 100] Generated Node #0,2,1: 73:[52, 100] Operation: 72+28=100 Exploring Operation: 52+28=80, Resulting Numbers: [72, 80] Generated Node #0,2,2: 73:[72, 80] Operation: 52+28=80 Moving to Node #0,2,2 Current State: 73:[72, 80], Operations: ['5+23=28', '52+28=80'] Exploring Operation: 72+80=152, Resulting Numbers: [152] 152,73 unequal: No Solution Exploring Operation: 72*80=5760, Resulting Numbers: [5760] 5760,73 unequal: No Solution Exploring Operation: 80-72=8, Resulting Numbers: [8] 8,73 unequal: No Solution Moving to Node #0,2,1 Current State: 73:[52, 100], Operations: ['5+23=28', '72+28=100'] Exploring Operation: 52*100=5200, Resulting Numbers: [5200] 5200,73 unequal: No Solution Exploring Operation: 100-52=48, Resulting Numbers: [48] 48,73 unequal: No Solution Exploring Operation: 52+100=152, Resulting Numbers: [152] 152,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[52, 44], Operations: ['5+23=28', '72-28=44'] Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,73 unequal: No Solution Exploring Operation: 52*44=2288, Resulting Numbers: [2288] 2288,73 unequal: No Solution Exploring Operation: 52+44=96, Resulting Numbers: [96] 96,73 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
[ 46, 42, 37, 6 ]
96
[ "46-37=9", "6*9=54", "42+54=96" ]
Current State: 96:[46, 42, 37, 6], Operations: [] Exploring Operation: 46-37=9, Resulting Numbers: [42, 6, 9] Generated Node #2: [42, 6, 9] from Operation: 46-37=9 Current State: 96:[42, 6, 9], Operations: ['46-37=9'] Exploring Operation: 6*9=54, Resulting Numbers: [42, 54] Generated Node #3: [42, 54] from Operation: 6*9=54 Current State: 96:[42, 54], Operations: ['46-37=9', '6*9=54'] Exploring Operation: 42+54=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[46, 42, 37, 6], Operations: [] Exploring Operation: 46-37=9, Resulting Numbers: [42, 6, 9] Generated Node #0,0: 96:[42, 6, 9] Operation: 46-37=9 Exploring Operation: 42/6=7, Resulting Numbers: [46, 37, 7] Generated Node #0,1: 96:[46, 37, 7] Operation: 42/6=7 Exploring Operation: 46-42=4, Resulting Numbers: [37, 6, 4] Generated Node #0,2: 96:[37, 6, 4] Operation: 46-42=4 Exploring Operation: 42+6=48, Resulting Numbers: [46, 37, 48] Generated Node #0,3: 96:[46, 37, 48] Operation: 42+6=48 Exploring Operation: 42-37=5, Resulting Numbers: [46, 6, 5] Generated Node #0,4: 96:[46, 6, 5] Operation: 42-37=5 Moving to Node #0,4 Current State: 96:[46, 6, 5], Operations: ['42-37=5'] Exploring Operation: 6-5=1, Resulting Numbers: [46, 1] Generated Node #0,4,0: 96:[46, 1] Operation: 6-5=1 Exploring Operation: 46+6=52, Resulting Numbers: [5, 52] Generated Node #0,4,1: 96:[5, 52] Operation: 46+6=52 Exploring Operation: 46+5=51, Resulting Numbers: [6, 51] Generated Node #0,4,2: 96:[6, 51] Operation: 46+5=51 Exploring Operation: 6+5=11, Resulting Numbers: [46, 11] Generated Node #0,4,3: 96:[46, 11] Operation: 6+5=11 Exploring Operation: 6*5=30, Resulting Numbers: [46, 30] Generated Node #0,4,4: 96:[46, 30] Operation: 6*5=30 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 96:[46, 1], Operations: ['42-37=5', '6-5=1'] Exploring Operation: 46*1=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 46/1=46, Resulting Numbers: [46] 46,96 unequal: No Solution Exploring Operation: 46-1=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 46+1=47, Resulting Numbers: [47] 47,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 96:[6, 51], Operations: ['42-37=5', '46+5=51'] Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 6*51=306, Resulting Numbers: [306] 306,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 96:[46, 11], Operations: ['42-37=5', '6+5=11'] Exploring Operation: 46*11=506, Resulting Numbers: [506] 506,96 unequal: No Solution Exploring Operation: 46+11=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 96:[46, 30], Operations: ['42-37=5', '6*5=30'] Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 96:[5, 52], Operations: ['42-37=5', '46+6=52'] Exploring Operation: 52-5=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 5+52=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 5*52=260, Resulting Numbers: [260] 260,96 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: 96:[37, 6, 4], Operations: ['46-42=4'] Exploring Operation: 37+6=43, Resulting Numbers: [4, 43] Generated Node #0,2,0: 96:[4, 43] Operation: 37+6=43 Exploring Operation: 6*4=24, Resulting Numbers: [37, 24] Generated Node #0,2,1: 96:[37, 24] Operation: 6*4=24 Exploring Operation: 37-4=33, Resulting Numbers: [6, 33] Generated Node #0,2,2: 96:[6, 33] Operation: 37-4=33 Exploring Operation: 6-4=2, Resulting Numbers: [37, 2] Generated Node #0,2,3: 96:[37, 2] Operation: 6-4=2 Exploring Operation: 37-6=31, Resulting Numbers: [4, 31] Generated Node #0,2,4: 96:[4, 31] Operation: 37-6=31 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 96:[6, 33], Operations: ['46-42=4', '37-4=33'] Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,96 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 96:[4, 31], Operations: ['46-42=4', '37-6=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,96 unequal: No Solution Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[4, 43], Operations: ['46-42=4', '37+6=43'] Exploring Operation: 4+43=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 4*43=172, Resulting Numbers: [172] 172,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 96:[37, 24], Operations: ['46-42=4', '6*4=24'] Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,96 unequal: No Solution Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,96 unequal: No Solution Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 96:[37, 2], Operations: ['46-42=4', '6-4=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,96 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: 96:[42, 6, 9], Operations: ['46-37=9'] Exploring Operation: 42-9=33, Resulting Numbers: [6, 33] Generated Node #0,0,0: 96:[6, 33] Operation: 42-9=33 Exploring Operation: 42/6=7, Resulting Numbers: [9, 7] Generated Node #0,0,1: 96:[9, 7] Operation: 42/6=7 Exploring Operation: 42-6=36, Resulting Numbers: [9, 36] Generated Node #0,0,2: 96:[9, 36] Operation: 42-6=36 Exploring Operation: 42+9=51, Resulting Numbers: [6, 51] Generated Node #0,0,3: 96:[6, 51] Operation: 42+9=51 Exploring Operation: 42+6=48, Resulting Numbers: [9, 48] Generated Node #0,0,4: 96:[9, 48] Operation: 42+6=48 Moving to Node #0,3 Current State: 96:[46, 37, 48], Operations: ['42+6=48'] Exploring Operation: 46+37=83, Resulting Numbers: [48, 83] Generated Node #0,3,0: 96:[48, 83] Operation: 46+37=83 Exploring Operation: 46-37=9, Resulting Numbers: [48, 9] Generated Node #0,3,1: 96:[48, 9] Operation: 46-37=9 Exploring Operation: 48-37=11, Resulting Numbers: [46, 11] Generated Node #0,3,2: 96:[46, 11] Operation: 48-37=11 Exploring Operation: 46+48=94, Resulting Numbers: [37, 94] Generated Node #0,3,3: 96:[37, 94] Operation: 46+48=94 Exploring Operation: 48-46=2, Resulting Numbers: [37, 2] Generated Node #0,3,4: 96:[37, 2] Operation: 48-46=2 Moving to Node #0,1 Current State: 96:[46, 37, 7], Operations: ['42/6=7'] Exploring Operation: 46-37=9, Resulting Numbers: [7, 9] Generated Node #0,1,0: 96:[7, 9] Operation: 46-37=9 Exploring Operation: 46+7=53, Resulting Numbers: [37, 53] Generated Node #0,1,1: 96:[37, 53] Operation: 46+7=53 Exploring Operation: 46-7=39, Resulting Numbers: [37, 39] Generated Node #0,1,2: 96:[37, 39] Operation: 46-7=39 Exploring Operation: 37-7=30, Resulting Numbers: [46, 30] Generated Node #0,1,3: 96:[46, 30] Operation: 37-7=30 Exploring Operation: 37+7=44, Resulting Numbers: [46, 44] Generated Node #0,1,4: 96:[46, 44] Operation: 37+7=44 Moving to Node #0,0,0 Current State: 96:[6, 33], Operations: ['46-37=9', '42-9=33'] Exploring Operation: 6+33=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,96 unequal: No Solution Exploring Operation: 6*33=198, Resulting Numbers: [198] 198,96 unequal: No Solution Moving to Node #0,3,1 Current State: 96:[48, 9], Operations: ['42+6=48', '46-37=9'] Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,96 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,96 unequal: No Solution Moving to Node #0,0,4 Current State: 96:[9, 48], Operations: ['46-37=9', '42+6=48'] Exploring Operation: 9+48=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 9*48=432, Resulting Numbers: [432] 432,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[9, 7], Operations: ['46-37=9', '42/6=7'] Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,96 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[7, 9], Operations: ['42/6=7', '46-37=9'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 7+9=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 7*9=63, Resulting Numbers: [63] 63,96 unequal: No Solution Moving to Node #0,3,2 Current State: 96:[46, 11], Operations: ['42+6=48', '48-37=11'] Exploring Operation: 46-11=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 46*11=506, Resulting Numbers: [506] 506,96 unequal: No Solution Exploring Operation: 46+11=57, Resulting Numbers: [57] 57,96 unequal: No Solution Moving to Node #0,0,3 Current State: 96:[6, 51], Operations: ['46-37=9', '42+9=51'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,96 unequal: No Solution Exploring Operation: 6+51=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 6*51=306, Resulting Numbers: [306] 306,96 unequal: No Solution Moving to Node #0,1,3 Current State: 96:[46, 30], Operations: ['42/6=7', '37-7=30'] Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,96 unequal: No Solution Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[9, 36], Operations: ['46-37=9', '42-6=36'] Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,96 unequal: No Solution Exploring Operation: 9*36=324, Resulting Numbers: [324] 324,96 unequal: No Solution Exploring Operation: 9+36=45, Resulting Numbers: [45] 45,96 unequal: No Solution Moving to Node #0,3,4 Current State: 96:[37, 2], Operations: ['42+6=48', '48-46=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,96 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,96 unequal: No Solution Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,96 unequal: No Solution Moving to Node #0,1,4 Current State: 96:[46, 44], Operations: ['42/6=7', '37+7=44'] Exploring Operation: 46-44=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 46*44=2024, Resulting Numbers: [2024] 2024,96 unequal: No Solution Exploring Operation: 46+44=90, Resulting Numbers: [90] 90,96 unequal: No Solution Moving to Node #0,3,3 Current State: 96:[37, 94], Operations: ['42+6=48', '46+48=94'] Exploring Operation: 37+94=131, Resulting Numbers: [131] 131,96 unequal: No Solution Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 37*94=3478, Resulting Numbers: [3478] 3478,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[37, 53], Operations: ['42/6=7', '46+7=53'] Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,96 unequal: No Solution Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,96 unequal: No Solution Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[37, 39], Operations: ['42/6=7', '46-7=39'] Exploring Operation: 37*39=1443, Resulting Numbers: [1443] 1443,96 unequal: No Solution Exploring Operation: 37+39=76, Resulting Numbers: [76] 76,96 unequal: No Solution Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,96 unequal: No Solution Moving to Node #0,3,0 Current State: 96:[48, 83], Operations: ['42+6=48', '46+37=83'] Exploring Operation: 48*83=3984, Resulting Numbers: [3984] 3984,96 unequal: No Solution Exploring Operation: 83-48=35, Resulting Numbers: [35] 35,96 unequal: No Solution Exploring Operation: 48+83=131, Resulting Numbers: [131] 131,96 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 80, 4, 19, 9 ]
63
[ "80+19=99", "4*9=36", "99-36=63" ]
Current State: 63:[80, 4, 19, 9], Operations: [] Exploring Operation: 80+19=99, Resulting Numbers: [4, 9, 99] Generated Node #2: [4, 9, 99] from Operation: 80+19=99 Current State: 63:[4, 9, 99], Operations: ['80+19=99'] Exploring Operation: 4*9=36, Resulting Numbers: [99, 36] Generated Node #3: [99, 36] from Operation: 4*9=36 Current State: 63:[99, 36], Operations: ['80+19=99', '4*9=36'] Exploring Operation: 99-36=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[80, 4, 19, 9], Operations: [] Exploring Operation: 80-19=61, Resulting Numbers: [4, 9, 61] Generated Node #0,0: 63:[4, 9, 61] Operation: 80-19=61 Exploring Operation: 80-9=71, Resulting Numbers: [4, 19, 71] Generated Node #0,1: 63:[4, 19, 71] Operation: 80-9=71 Exploring Operation: 80/4=20, Resulting Numbers: [19, 9, 20] Generated Node #0,2: 63:[19, 9, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [19, 9, 76] Generated Node #0,3: 63:[19, 9, 76] Operation: 80-4=76 Exploring Operation: 4+19=23, Resulting Numbers: [80, 9, 23] Generated Node #0,4: 63:[80, 9, 23] Operation: 4+19=23 Moving to Node #0,0 Current State: 63:[4, 9, 61], Operations: ['80-19=61'] Exploring Operation: 61-4=57, Resulting Numbers: [9, 57] Generated Node #0,0,0: 63:[9, 57] Operation: 61-4=57 Exploring Operation: 9+61=70, Resulting Numbers: [4, 70] Generated Node #0,0,1: 63:[4, 70] Operation: 9+61=70 Exploring Operation: 4+9=13, Resulting Numbers: [61, 13] Generated Node #0,0,2: 63:[61, 13] Operation: 4+9=13 Exploring Operation: 4+61=65, Resulting Numbers: [9, 65] Generated Node #0,0,3: 63:[9, 65] Operation: 4+61=65 Exploring Operation: 9-4=5, Resulting Numbers: [61, 5] Generated Node #0,0,4: 63:[61, 5] Operation: 9-4=5 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 63:[9, 65], Operations: ['80-19=61', '4+61=65'] Exploring Operation: 9+65=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 9*65=585, Resulting Numbers: [585] 585,63 unequal: No Solution Exploring Operation: 65-9=56, Resulting Numbers: [56] 56,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 63:[61, 5], Operations: ['80-19=61', '9-4=5'] Exploring Operation: 61+5=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 61-5=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 61*5=305, Resulting Numbers: [305] 305,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 63:[9, 57], Operations: ['80-19=61', '61-4=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 9*57=513, Resulting Numbers: [513] 513,63 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 63:[61, 13], Operations: ['80-19=61', '4+9=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 61-13=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 63:[4, 70], Operations: ['80-19=61', '9+61=70'] Exploring Operation: 4*70=280, Resulting Numbers: [280] 280,63 unequal: No Solution Exploring Operation: 4+70=74, Resulting Numbers: [74] 74,63 unequal: No Solution Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,63 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: 63:[19, 9, 20], Operations: ['80/4=20'] Exploring Operation: 19-9=10, Resulting Numbers: [20, 10] Generated Node #0,2,0: 63:[20, 10] Operation: 19-9=10 Exploring Operation: 19+9=28, Resulting Numbers: [20, 28] Generated Node #0,2,1: 63:[20, 28] Operation: 19+9=28 Exploring Operation: 20-19=1, Resulting Numbers: [9, 1] Generated Node #0,2,2: 63:[9, 1] Operation: 20-19=1 Exploring Operation: 20-9=11, Resulting Numbers: [19, 11] Generated Node #0,2,3: 63:[19, 11] Operation: 20-9=11 Exploring Operation: 9+20=29, Resulting Numbers: [19, 29] Generated Node #0,2,4: 63:[19, 29] Operation: 9+20=29 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 63:[20, 10], Operations: ['80/4=20', '19-9=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 63:[9, 1], Operations: ['80/4=20', '20-19=1'] Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 9/1=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 9*1=9, Resulting Numbers: [9] 9,63 unequal: No Solution Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 63:[19, 11], Operations: ['80/4=20', '20-9=11'] Exploring Operation: 19+11=30, Resulting Numbers: [30] 30,63 unequal: No Solution Exploring Operation: 19-11=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 19*11=209, Resulting Numbers: [209] 209,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 63:[20, 28], Operations: ['80/4=20', '19+9=28'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,63 unequal: No Solution Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,63 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 63:[19, 29], Operations: ['80/4=20', '9+20=29'] Exploring Operation: 29-19=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 19+29=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 19*29=551, Resulting Numbers: [551] 551,63 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: 63:[4, 19, 71], Operations: ['80-9=71'] Exploring Operation: 71-4=67, Resulting Numbers: [19, 67] Generated Node #0,1,0: 63:[19, 67] Operation: 71-4=67 Exploring Operation: 4+71=75, Resulting Numbers: [19, 75] Generated Node #0,1,1: 63:[19, 75] Operation: 4+71=75 Exploring Operation: 4+19=23, Resulting Numbers: [71, 23] Generated Node #0,1,2: 63:[71, 23] Operation: 4+19=23 Exploring Operation: 19-4=15, Resulting Numbers: [71, 15] Generated Node #0,1,3: 63:[71, 15] Operation: 19-4=15 Exploring Operation: 71-19=52, Resulting Numbers: [4, 52] Generated Node #0,1,4: 63:[4, 52] Operation: 71-19=52 Moving to Node #0,3 Current State: 63:[19, 9, 76], Operations: ['80-4=76'] Exploring Operation: 19+9=28, Resulting Numbers: [76, 28] Generated Node #0,3,0: 63:[76, 28] Operation: 19+9=28 Exploring Operation: 76-19=57, Resulting Numbers: [9, 57] Generated Node #0,3,1: 63:[9, 57] Operation: 76-19=57 Exploring Operation: 76/19=4, Resulting Numbers: [9, 4] Generated Node #0,3,2: 63:[9, 4] Operation: 76/19=4 Exploring Operation: 76-9=67, Resulting Numbers: [19, 67] Generated Node #0,3,3: 63:[19, 67] Operation: 76-9=67 Exploring Operation: 19-9=10, Resulting Numbers: [76, 10] Generated Node #0,3,4: 63:[76, 10] Operation: 19-9=10 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[9, 4], Operations: ['80-4=76', '76/19=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,63 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,63 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 63:[9, 57], Operations: ['80-4=76', '76-19=57'] Exploring Operation: 9*57=513, Resulting Numbers: [513] 513,63 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 63:[19, 67], Operations: ['80-4=76', '76-9=67'] Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 63:[76, 10], Operations: ['80-4=76', '19-9=10'] Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,63 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,63 unequal: No Solution Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 63:[76, 28], Operations: ['80-4=76', '19+9=28'] Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 76*28=2128, Resulting Numbers: [2128] 2128,63 unequal: No Solution Exploring Operation: 76+28=104, Resulting Numbers: [104] 104,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 63:[80, 9, 23], Operations: ['4+19=23'] Exploring Operation: 23-9=14, Resulting Numbers: [80, 14] Generated Node #0,4,0: 63:[80, 14] Operation: 23-9=14 Exploring Operation: 80+9=89, Resulting Numbers: [23, 89] Generated Node #0,4,1: 63:[23, 89] Operation: 80+9=89 Exploring Operation: 80-9=71, Resulting Numbers: [23, 71] Generated Node #0,4,2: 63:[23, 71] Operation: 80-9=71 Exploring Operation: 80-23=57, Resulting Numbers: [9, 57] Generated Node #0,4,3: 63:[9, 57] Operation: 80-23=57 Exploring Operation: 9+23=32, Resulting Numbers: [80, 32] Generated Node #0,4,4: 63:[80, 32] Operation: 9+23=32 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 63:[9, 57], Operations: ['4+19=23', '80-23=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,63 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 9*57=513, Resulting Numbers: [513] 513,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 63:[23, 71], Operations: ['4+19=23', '80-9=71'] Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,63 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 23*71=1633, Resulting Numbers: [1633] 1633,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 63:[80, 14], Operations: ['4+19=23', '23-9=14'] Exploring Operation: 80+14=94, Resulting Numbers: [94] 94,63 unequal: No Solution Exploring Operation: 80*14=1120, Resulting Numbers: [1120] 1120,63 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 63:[23, 89], Operations: ['4+19=23', '80+9=89'] Exploring Operation: 23+89=112, Resulting Numbers: [112] 112,63 unequal: No Solution Exploring Operation: 23*89=2047, Resulting Numbers: [2047] 2047,63 unequal: No Solution Exploring Operation: 89-23=66, Resulting Numbers: [66] 66,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 63:[80, 32], Operations: ['4+19=23', '9+23=32'] Exploring Operation: 80+32=112, Resulting Numbers: [112] 112,63 unequal: No Solution Exploring Operation: 80-32=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 80*32=2560, Resulting Numbers: [2560] 2560,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 63:[19, 67], Operations: ['80-9=71', '71-4=67'] Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,63 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[71, 23], Operations: ['80-9=71', '4+19=23'] Exploring Operation: 71*23=1633, Resulting Numbers: [1633] 1633,63 unequal: No Solution Exploring Operation: 71+23=94, Resulting Numbers: [94] 94,63 unequal: No Solution Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,63 unequal: No Solution Moving to Node #0,1,4 Current State: 63:[4, 52], Operations: ['80-9=71', '71-19=52'] Exploring Operation: 4*52=208, Resulting Numbers: [208] 208,63 unequal: No Solution Exploring Operation: 4+52=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 52-4=48, Resulting Numbers: [48] 48,63 unequal: No Solution Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[19, 75], Operations: ['80-9=71', '4+71=75'] Exploring Operation: 19+75=94, Resulting Numbers: [94] 94,63 unequal: No Solution Exploring Operation: 75-19=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 19*75=1425, Resulting Numbers: [1425] 1425,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[71, 15], Operations: ['80-9=71', '19-4=15'] Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,63 unequal: No Solution Exploring Operation: 71*15=1065, Resulting Numbers: [1065] 1065,63 unequal: No Solution Exploring Operation: 71+15=86, Resulting Numbers: [86] 86,63 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 73, 79, 60, 1 ]
65
[ "79-73=6", "60-1=59", "6+59=65" ]
Current State: 65:[73, 79, 60, 1], Operations: [] Exploring Operation: 79-73=6, Resulting Numbers: [60, 1, 6] Generated Node #2: [60, 1, 6] from Operation: 79-73=6 Current State: 65:[60, 1, 6], Operations: ['79-73=6'] Exploring Operation: 60-1=59, Resulting Numbers: [6, 59] Generated Node #3: [6, 59] from Operation: 60-1=59 Current State: 65:[6, 59], Operations: ['79-73=6', '60-1=59'] Exploring Operation: 6+59=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[73, 79, 60, 1], Operations: [] Exploring Operation: 79-1=78, Resulting Numbers: [73, 60, 78] Generated Node #0,0: 65:[73, 60, 78] Operation: 79-1=78 Exploring Operation: 73-1=72, Resulting Numbers: [79, 60, 72] Generated Node #0,1: 65:[79, 60, 72] Operation: 73-1=72 Exploring Operation: 79-60=19, Resulting Numbers: [73, 1, 19] Generated Node #0,2: 65:[73, 1, 19] Operation: 79-60=19 Exploring Operation: 73-60=13, Resulting Numbers: [79, 1, 13] Generated Node #0,3: 65:[79, 1, 13] Operation: 73-60=13 Exploring Operation: 79-73=6, Resulting Numbers: [60, 1, 6] Generated Node #0,4: 65:[60, 1, 6] Operation: 79-73=6 Moving to Node #0,4 Current State: 65:[60, 1, 6], Operations: ['79-73=6'] Exploring Operation: 60*1=60, Resulting Numbers: [6, 60] Generated Node #0,4,0: 65:[6, 60] Operation: 60*1=60 Exploring Operation: 60+1=61, Resulting Numbers: [6, 61] Generated Node #0,4,1: 65:[6, 61] Operation: 60+1=61 Exploring Operation: 6-1=5, Resulting Numbers: [60, 5] Generated Node #0,4,2: 65:[60, 5] Operation: 6-1=5 Exploring Operation: 60+6=66, Resulting Numbers: [1, 66] Generated Node #0,4,3: 65:[1, 66] Operation: 60+6=66 Exploring Operation: 60/1=60, Resulting Numbers: [6, 60] Generated Node #0,4,4: 65:[6, 60] Operation: 60/1=60 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[6, 61], Operations: ['79-73=6', '60+1=61'] Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,65 unequal: No Solution Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,65 unequal: No Solution Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,65 unequal: No Solution No 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: 65:[60, 5], Operations: ['79-73=6', '6-1=5'] Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[73, 79, 60, 1], Operations: [] Exploring Operation: 79-73=6, Resulting Numbers: [60, 1, 6] Generated Node #0,4: 65:[60, 1, 6] Operation: 79-73=6 Moving to Node #0,4 Current State: 65:[60, 1, 6], Operations: ['79-73=6'] Exploring Operation: 6-1=5, Resulting Numbers: [60, 5] Generated Node #0,4,2: 65:[60, 5] Operation: 6-1=5 Moving to Node #0,4,2 Current State: 65:[60, 5], Operations: ['79-73=6', '6-1=5'] Exploring Operation: 60+5=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_5
sum_heuristic
[ 23, 44, 12, 68 ]
25
[ "68-44=24", "24/12=2", "23+2=25" ]
Current State: 25:[23, 44, 12, 68], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [23, 12, 24] Generated Node #2: [23, 12, 24] from Operation: 68-44=24 Current State: 25:[23, 12, 24], Operations: ['68-44=24'] Exploring Operation: 24/12=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 24/12=2 Current State: 25:[23, 2], Operations: ['68-44=24', '24/12=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[23, 44, 12, 68], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [23, 12, 24] Generated Node #0,0: 25:[23, 12, 24] Operation: 68-44=24 Exploring Operation: 68-12=56, Resulting Numbers: [23, 44, 56] Generated Node #0,1: 25:[23, 44, 56] Operation: 68-12=56 Exploring Operation: 68-23=45, Resulting Numbers: [44, 12, 45] Generated Node #0,2: 25:[44, 12, 45] Operation: 68-23=45 Exploring Operation: 44-12=32, Resulting Numbers: [23, 68, 32] Generated Node #0,3: 25:[23, 68, 32] Operation: 44-12=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 25:[23, 12, 24], Operations: ['68-44=24'] Exploring Operation: 24-12=12, Resulting Numbers: [23, 12] Generated Node #0,0,0: 25:[23, 12] Operation: 24-12=12 Exploring Operation: 24/12=2, Resulting Numbers: [23, 2] Generated Node #0,0,1: 25:[23, 2] Operation: 24/12=2 Exploring Operation: 23+12=35, Resulting Numbers: [24, 35] Generated Node #0,0,2: 25:[24, 35] Operation: 23+12=35 Exploring Operation: 23-12=11, Resulting Numbers: [24, 11] Generated Node #0,0,3: 25:[24, 11] Operation: 23-12=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 25:[23, 2], Operations: ['68-44=24', '24/12=2'] Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,25 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,25 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[23, 44, 12, 68], Operations: [] Exploring Operation: 68-44=24, Resulting Numbers: [23, 12, 24] Generated Node #0,0: 25:[23, 12, 24] Operation: 68-44=24 Moving to Node #0,0 Current State: 25:[23, 12, 24], Operations: ['68-44=24'] Exploring Operation: 24/12=2, Resulting Numbers: [23, 2] Generated Node #0,0,1: 25:[23, 2] Operation: 24/12=2 Moving to Node #0,0,1 Current State: 25:[23, 2], Operations: ['68-44=24', '24/12=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 65, 32, 22, 86 ]
17
[ "65*22=1430", "32+1430=1462", "1462/86=17" ]
Current State: 17:[65, 32, 22, 86], Operations: [] Exploring Operation: 65*22=1430, Resulting Numbers: [32, 86, 1430] Generated Node #2: [32, 86, 1430] from Operation: 65*22=1430 Current State: 17:[32, 86, 1430], Operations: ['65*22=1430'] Exploring Operation: 32+1430=1462, Resulting Numbers: [86, 1462] Generated Node #3: [86, 1462] from Operation: 32+1430=1462 Current State: 17:[86, 1462], Operations: ['65*22=1430', '32+1430=1462'] Exploring Operation: 1462/86=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[65, 32, 22, 86], Operations: [] Exploring Operation: 65-22=43, Resulting Numbers: [32, 86, 43] Generated Node #0,0: 17:[32, 86, 43] Operation: 65-22=43 Exploring Operation: 65-32=33, Resulting Numbers: [22, 86, 33] Generated Node #0,1: 17:[22, 86, 33] Operation: 65-32=33 Exploring Operation: 86-65=21, Resulting Numbers: [32, 22, 21] Generated Node #0,2: 17:[32, 22, 21] Operation: 86-65=21 Exploring Operation: 86-32=54, Resulting Numbers: [65, 22, 54] Generated Node #0,3: 17:[65, 22, 54] Operation: 86-32=54 Moving to Node #0,2 Current State: 17:[32, 22, 21], Operations: ['86-65=21'] Exploring Operation: 22-21=1, Resulting Numbers: [32, 1] Generated Node #0,2,0: 17:[32, 1] Operation: 22-21=1 Exploring Operation: 32+22=54, Resulting Numbers: [21, 54] Generated Node #0,2,1: 17:[21, 54] Operation: 32+22=54 Exploring Operation: 32-21=11, Resulting Numbers: [22, 11] Generated Node #0,2,2: 17:[22, 11] Operation: 32-21=11 Exploring Operation: 32-22=10, Resulting Numbers: [21, 10] Generated Node #0,2,3: 17:[21, 10] Operation: 32-22=10 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 17:[22, 11], Operations: ['86-65=21', '32-21=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,17 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 17:[21, 10], Operations: ['86-65=21', '32-22=10'] Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,17 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 17:[32, 1], Operations: ['86-65=21', '22-21=1'] Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,17 unequal: No Solution Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 32+1=33, Resulting Numbers: [33] 33,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 17:[21, 54], Operations: ['86-65=21', '32+22=54'] Exploring Operation: 54-21=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 21+54=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 21*54=1134, Resulting Numbers: [1134] 1134,17 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: 17:[65, 22, 54], Operations: ['86-32=54'] Exploring Operation: 65+22=87, Resulting Numbers: [54, 87] Generated Node #0,3,0: 17:[54, 87] Operation: 65+22=87 Exploring Operation: 65-54=11, Resulting Numbers: [22, 11] Generated Node #0,3,1: 17:[22, 11] Operation: 65-54=11 Exploring Operation: 65-22=43, Resulting Numbers: [54, 43] Generated Node #0,3,2: 17:[54, 43] Operation: 65-22=43 Exploring Operation: 54-22=32, Resulting Numbers: [65, 32] Generated Node #0,3,3: 17:[65, 32] Operation: 54-22=32 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 17:[22, 11], Operations: ['86-32=54', '65-54=11'] Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,17 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[54, 43], Operations: ['86-32=54', '65-22=43'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 54*43=2322, Resulting Numbers: [2322] 2322,17 unequal: No Solution Exploring Operation: 54+43=97, Resulting Numbers: [97] 97,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 17:[65, 32], Operations: ['86-32=54', '54-22=32'] Exploring Operation: 65-32=33, Resulting Numbers: [33] 33,17 unequal: No Solution Exploring Operation: 65+32=97, Resulting Numbers: [97] 97,17 unequal: No Solution Exploring Operation: 65*32=2080, Resulting Numbers: [2080] 2080,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 17:[54, 87], Operations: ['86-32=54', '65+22=87'] Exploring Operation: 54+87=141, Resulting Numbers: [141] 141,17 unequal: No Solution Exploring Operation: 54*87=4698, Resulting Numbers: [4698] 4698,17 unequal: No Solution Exploring Operation: 87-54=33, Resulting Numbers: [33] 33,17 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: 17:[22, 86, 33], Operations: ['65-32=33'] Exploring Operation: 86-22=64, Resulting Numbers: [33, 64] Generated Node #0,1,0: 17:[33, 64] Operation: 86-22=64 Exploring Operation: 33-22=11, Resulting Numbers: [86, 11] Generated Node #0,1,1: 17:[86, 11] Operation: 33-22=11 Exploring Operation: 22+86=108, Resulting Numbers: [33, 108] Generated Node #0,1,2: 17:[33, 108] Operation: 22+86=108 Exploring Operation: 86-33=53, Resulting Numbers: [22, 53] Generated Node #0,1,3: 17:[22, 53] Operation: 86-33=53 Moving to Node #0,0 Current State: 17:[32, 86, 43], Operations: ['65-22=43'] Exploring Operation: 86/43=2, Resulting Numbers: [32, 2] Generated Node #0,0,0: 17:[32, 2] Operation: 86/43=2 Exploring Operation: 43-32=11, Resulting Numbers: [86, 11] Generated Node #0,0,1: 17:[86, 11] Operation: 43-32=11 Exploring Operation: 86-43=43, Resulting Numbers: [32, 43] Generated Node #0,0,2: 17:[32, 43] Operation: 86-43=43 Exploring Operation: 86-32=54, Resulting Numbers: [43, 54] Generated Node #0,0,3: 17:[43, 54] Operation: 86-32=54 Moving to Node #0,0,0 Current State: 17:[32, 2], Operations: ['65-22=43', '86/43=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,17 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,17 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,17 unequal: No Solution Moving to Node #0,0,2 Current State: 17:[32, 43], Operations: ['65-22=43', '86-43=43'] Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[22, 53], Operations: ['65-32=33', '86-33=53'] Exploring Operation: 22+53=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 53-22=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 22*53=1166, Resulting Numbers: [1166] 1166,17 unequal: No Solution Moving to Node #0,0,3 Current State: 17:[43, 54], Operations: ['65-22=43', '86-32=54'] Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,17 unequal: No Solution Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,17 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[33, 64], Operations: ['65-32=33', '86-22=64'] Exploring Operation: 64-33=31, Resulting Numbers: [31] 31,17 unequal: No Solution Exploring Operation: 33*64=2112, Resulting Numbers: [2112] 2112,17 unequal: No Solution Exploring Operation: 33+64=97, Resulting Numbers: [97] 97,17 unequal: No Solution Moving to Node #0,1,1 Current State: 17:[86, 11], Operations: ['65-32=33', '33-22=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,17 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[86, 11], Operations: ['65-22=43', '43-32=11'] Exploring Operation: 86-11=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 86+11=97, Resulting Numbers: [97] 97,17 unequal: No Solution Exploring Operation: 86*11=946, Resulting Numbers: [946] 946,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[33, 108], Operations: ['65-32=33', '22+86=108'] Exploring Operation: 108-33=75, Resulting Numbers: [75] 75,17 unequal: No Solution Exploring Operation: 33*108=3564, Resulting Numbers: [3564] 3564,17 unequal: No Solution Exploring Operation: 33+108=141, Resulting Numbers: [141] 141,17 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 43, 63, 3, 98 ]
68
[ "43+63=106", "98+106=204", "204/3=68" ]
Current State: 68:[43, 63, 3, 98], Operations: [] Exploring Operation: 43+63=106, Resulting Numbers: [3, 98, 106] Generated Node #2: [3, 98, 106] from Operation: 43+63=106 Current State: 68:[3, 98, 106], Operations: ['43+63=106'] Exploring Operation: 98+106=204, Resulting Numbers: [3, 204] Generated Node #3: [3, 204] from Operation: 98+106=204 Current State: 68:[3, 204], Operations: ['43+63=106', '98+106=204'] Exploring Operation: 204/3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[43, 63, 3, 98], Operations: [] Exploring Operation: 98-63=35, Resulting Numbers: [43, 3, 35] Generated Node #0,0: 68:[43, 3, 35] Operation: 98-63=35 Exploring Operation: 98-43=55, Resulting Numbers: [63, 3, 55] Generated Node #0,1: 68:[63, 3, 55] Operation: 98-43=55 Exploring Operation: 63-43=20, Resulting Numbers: [3, 98, 20] Generated Node #0,2: 68:[3, 98, 20] Operation: 63-43=20 Exploring Operation: 63+3=66, Resulting Numbers: [43, 98, 66] Generated Node #0,3: 68:[43, 98, 66] Operation: 63+3=66 Exploring Operation: 43-3=40, Resulting Numbers: [63, 98, 40] Generated Node #0,4: 68:[63, 98, 40] Operation: 43-3=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[43, 3, 35], Operations: ['98-63=35'] Exploring Operation: 35-3=32, Resulting Numbers: [43, 32] Generated Node #0,0,0: 68:[43, 32] Operation: 35-3=32 Exploring Operation: 43-35=8, Resulting Numbers: [3, 8] Generated Node #0,0,1: 68:[3, 8] Operation: 43-35=8 Exploring Operation: 43+35=78, Resulting Numbers: [3, 78] Generated Node #0,0,2: 68:[3, 78] Operation: 43+35=78 Exploring Operation: 43-3=40, Resulting Numbers: [35, 40] Generated Node #0,0,3: 68:[35, 40] Operation: 43-3=40 Exploring Operation: 43+3=46, Resulting Numbers: [35, 46] Generated Node #0,0,4: 68:[35, 46] Operation: 43+3=46 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 68:[3, 8], Operations: ['98-63=35', '43-35=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,68 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 #0,0,3 Current State: 68:[35, 40], Operations: ['98-63=35', '43-3=40'] Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 35*40=1400, Resulting Numbers: [1400] 1400,68 unequal: No Solution Exploring Operation: 35+40=75, Resulting Numbers: [75] 75,68 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 #0,0,0 Current State: 68:[43, 32], Operations: ['98-63=35', '35-3=32'] Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,68 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,68 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 #0,0,2 Current State: 68:[3, 78], Operations: ['98-63=35', '43+35=78'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,68 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,68 unequal: No Solution Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,68 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 #0,0,4 Current State: 68:[35, 46], Operations: ['98-63=35', '43+3=46'] Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,68 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[63, 3, 55], Operations: ['98-43=55'] Exploring Operation: 63/3=21, Resulting Numbers: [55, 21] Generated Node #0,1,0: 68:[55, 21] Operation: 63/3=21 Exploring Operation: 63+3=66, Resulting Numbers: [55, 66] Generated Node #0,1,1: 68:[55, 66] Operation: 63+3=66 Exploring Operation: 63-3=60, Resulting Numbers: [55, 60] Generated Node #0,1,2: 68:[55, 60] Operation: 63-3=60 Exploring Operation: 63-55=8, Resulting Numbers: [3, 8] Generated Node #0,1,3: 68:[3, 8] Operation: 63-55=8 Exploring Operation: 3+55=58, Resulting Numbers: [63, 58] Generated Node #0,1,4: 68:[63, 58] Operation: 3+55=58 Moving to Node #0,1,3 Current State: 68:[3, 8], Operations: ['98-43=55', '63-55=8'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,68 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,68 unequal: No Solution Moving to Node #0,1,4 Current State: 68:[63, 58], Operations: ['98-43=55', '3+55=58'] Exploring Operation: 63*58=3654, Resulting Numbers: [3654] 3654,68 unequal: No Solution Exploring Operation: 63+58=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[55, 66], Operations: ['98-43=55', '63+3=66'] Exploring Operation: 55+66=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 55*66=3630, Resulting Numbers: [3630] 3630,68 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[55, 21], Operations: ['98-43=55', '63/3=21'] Exploring Operation: 55*21=1155, Resulting Numbers: [1155] 1155,68 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 55+21=76, Resulting Numbers: [76] 76,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[55, 60], Operations: ['98-43=55', '63-3=60'] Exploring Operation: 60-55=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 55+60=115, Resulting Numbers: [115] 115,68 unequal: No Solution Exploring Operation: 55*60=3300, Resulting Numbers: [3300] 3300,68 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:[3, 98, 20], Operations: ['63-43=20'] Exploring Operation: 3+20=23, Resulting Numbers: [98, 23] Generated Node #0,2,0: 68:[98, 23] Operation: 3+20=23 Exploring Operation: 3+98=101, Resulting Numbers: [20, 101] Generated Node #0,2,1: 68:[20, 101] Operation: 3+98=101 Exploring Operation: 98-20=78, Resulting Numbers: [3, 78] Generated Node #0,2,2: 68:[3, 78] Operation: 98-20=78 Exploring Operation: 98-3=95, Resulting Numbers: [20, 95] Generated Node #0,2,3: 68:[20, 95] Operation: 98-3=95 Exploring Operation: 20-3=17, Resulting Numbers: [98, 17] Generated Node #0,2,4: 68:[98, 17] Operation: 20-3=17 Moving to Node #0,2,2 Current State: 68:[3, 78], Operations: ['63-43=20', '98-20=78'] Exploring Operation: 3+78=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 3*78=234, Resulting Numbers: [234] 234,68 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,68 unequal: No Solution Moving to Node #0,2,4 Current State: 68:[98, 17], Operations: ['63-43=20', '20-3=17'] Exploring Operation: 98+17=115, Resulting Numbers: [115] 115,68 unequal: No Solution Exploring Operation: 98-17=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 98*17=1666, Resulting Numbers: [1666] 1666,68 unequal: No Solution Moving to Node #0,2,3 Current State: 68:[20, 95], Operations: ['63-43=20', '98-3=95'] Exploring Operation: 20*95=1900, Resulting Numbers: [1900] 1900,68 unequal: No Solution Exploring Operation: 20+95=115, Resulting Numbers: [115] 115,68 unequal: No Solution Exploring Operation: 95-20=75, Resulting Numbers: [75] 75,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[98, 23], Operations: ['63-43=20', '3+20=23'] Exploring Operation: 98*23=2254, Resulting Numbers: [2254] 2254,68 unequal: No Solution Exploring Operation: 98-23=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 98+23=121, Resulting Numbers: [121] 121,68 unequal: No Solution Moving to Node #0,2,1 Current State: 68:[20, 101], Operations: ['63-43=20', '3+98=101'] Exploring Operation: 101-20=81, Resulting Numbers: [81] 81,68 unequal: No Solution Exploring Operation: 20+101=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 20*101=2020, Resulting Numbers: [2020] 2020,68 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 #0,3 Current State: 68:[43, 98, 66], Operations: ['63+3=66'] Exploring Operation: 43+66=109, Resulting Numbers: [98, 109] Generated Node #0,3,0: 68:[98, 109] Operation: 43+66=109 Exploring Operation: 98-43=55, Resulting Numbers: [66, 55] Generated Node #0,3,1: 68:[66, 55] Operation: 98-43=55 Exploring Operation: 43+98=141, Resulting Numbers: [66, 141] Generated Node #0,3,2: 68:[66, 141] Operation: 43+98=141 Exploring Operation: 98-66=32, Resulting Numbers: [43, 32] Generated Node #0,3,3: 68:[43, 32] Operation: 98-66=32 Exploring Operation: 66-43=23, Resulting Numbers: [98, 23] Generated Node #0,3,4: 68:[98, 23] Operation: 66-43=23 Moving to Node #0,3,3 Current State: 68:[43, 32], Operations: ['63+3=66', '98-66=32'] Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,68 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,68 unequal: No Solution Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,68 unequal: No Solution Moving to Node #0,3,1 Current State: 68:[66, 55], Operations: ['63+3=66', '98-43=55'] Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,68 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,68 unequal: No Solution Moving to Node #0,3,4 Current State: 68:[98, 23], Operations: ['63+3=66', '66-43=23'] Exploring Operation: 98*23=2254, Resulting Numbers: [2254] 2254,68 unequal: No Solution Exploring Operation: 98+23=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 98-23=75, Resulting Numbers: [75] 75,68 unequal: No Solution Moving to Node #0,3,0 Current State: 68:[98, 109], Operations: ['63+3=66', '43+66=109'] Exploring Operation: 98*109=10682, Resulting Numbers: [10682] 10682,68 unequal: No Solution Exploring Operation: 98+109=207, Resulting Numbers: [207] 207,68 unequal: No Solution Exploring Operation: 109-98=11, Resulting Numbers: [11] 11,68 unequal: No Solution Moving to Node #0,3,2 Current State: 68:[66, 141], Operations: ['63+3=66', '43+98=141'] Exploring Operation: 66*141=9306, Resulting Numbers: [9306] 9306,68 unequal: No Solution Exploring Operation: 66+141=207, Resulting Numbers: [207] 207,68 unequal: No Solution Exploring Operation: 141-66=75, Resulting Numbers: [75] 75,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 68:[63, 98, 40], Operations: ['43-3=40'] Exploring Operation: 98-63=35, Resulting Numbers: [40, 35] Generated Node #0,4,0: 68:[40, 35] Operation: 98-63=35 Exploring Operation: 63-40=23, Resulting Numbers: [98, 23] Generated Node #0,4,1: 68:[98, 23] Operation: 63-40=23 Exploring Operation: 98+40=138, Resulting Numbers: [63, 138] Generated Node #0,4,2: 68:[63, 138] Operation: 98+40=138 Exploring Operation: 98-40=58, Resulting Numbers: [63, 58] Generated Node #0,4,3: 68:[63, 58] Operation: 98-40=58 Exploring Operation: 63+40=103, Resulting Numbers: [98, 103] Generated Node #0,4,4: 68:[98, 103] Operation: 63+40=103 Moving to Node #0,4,0 Current State: 68:[40, 35], Operations: ['43-3=40', '98-63=35'] Exploring Operation: 40+35=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 40*35=1400, Resulting Numbers: [1400] 1400,68 unequal: No Solution Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,68 unequal: No Solution Moving to Node #0,4,3 Current State: 68:[63, 58], Operations: ['43-3=40', '98-40=58'] Exploring Operation: 63*58=3654, Resulting Numbers: [3654] 3654,68 unequal: No Solution Exploring Operation: 63+58=121, Resulting Numbers: [121] 121,68 unequal: No Solution Exploring Operation: 63-58=5, Resulting Numbers: [5] 5,68 unequal: No Solution Moving to Node #0,4,1 Current State: 68:[98, 23], Operations: ['43-3=40', '63-40=23'] Exploring Operation: 98-23=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 98*23=2254, Resulting Numbers: [2254] 2254,68 unequal: No Solution Exploring Operation: 98+23=121, Resulting Numbers: [121] 121,68 unequal: No Solution Moving to Node #0,4,4 Current State: 68:[98, 103], Operations: ['43-3=40', '63+40=103'] Exploring Operation: 103-98=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 98+103=201, Resulting Numbers: [201] 201,68 unequal: No Solution Exploring Operation: 98*103=10094, Resulting Numbers: [10094] 10094,68 unequal: No Solution Moving to Node #0,4,2 Current State: 68:[63, 138], Operations: ['43-3=40', '98+40=138'] Exploring Operation: 63+138=201, Resulting Numbers: [201] 201,68 unequal: No Solution Exploring Operation: 138-63=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 63*138=8694, Resulting Numbers: [8694] 8694,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 4, 59, 27, 49 ]
29
[ "49-27=22", "4*22=88", "88-59=29" ]
Current State: 29:[4, 59, 27, 49], Operations: [] Exploring Operation: 49-27=22, Resulting Numbers: [4, 59, 22] Generated Node #2: [4, 59, 22] from Operation: 49-27=22 Current State: 29:[4, 59, 22], Operations: ['49-27=22'] Exploring Operation: 4*22=88, Resulting Numbers: [59, 88] Generated Node #3: [59, 88] from Operation: 4*22=88 Current State: 29:[59, 88], Operations: ['49-27=22', '4*22=88'] Exploring Operation: 88-59=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[4, 59, 27, 49], Operations: [] Exploring Operation: 59-49=10, Resulting Numbers: [4, 27, 10] Generated Node #0,0: 29:[4, 27, 10] Operation: 59-49=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[4, 27, 10], Operations: ['59-49=10'] Exploring Operation: 4*10=40, Resulting Numbers: [27, 40] Generated Node #0,0,0: 29:[27, 40] Operation: 4*10=40 Moving to Node #0,0,0 Current State: 29:[27, 40], Operations: ['59-49=10', '4*10=40'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,29 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
[ 93, 94, 37, 21 ]
17
[ "94-93=1", "37-21=16", "1+16=17" ]
Current State: 17:[93, 94, 37, 21], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [37, 21, 1] Generated Node #2: [37, 21, 1] from Operation: 94-93=1 Current State: 17:[37, 21, 1], Operations: ['94-93=1'] Exploring Operation: 37-21=16, Resulting Numbers: [1, 16] Generated Node #3: [1, 16] from Operation: 37-21=16 Current State: 17:[1, 16], Operations: ['94-93=1', '37-21=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[93, 94, 37, 21], Operations: [] Exploring Operation: 93-37=56, Resulting Numbers: [94, 21, 56] Generated Node #0,0: 17:[94, 21, 56] Operation: 93-37=56 Exploring Operation: 94-93=1, Resulting Numbers: [37, 21, 1] Generated Node #0,1: 17:[37, 21, 1] Operation: 94-93=1 Moving to Node #0,1 Current State: 17:[37, 21, 1], Operations: ['94-93=1'] Exploring Operation: 37-21=16, Resulting Numbers: [1, 16] Generated Node #0,1,0: 17:[1, 16] Operation: 37-21=16 Exploring Operation: 37-1=36, Resulting Numbers: [21, 36] Generated Node #0,1,1: 17:[21, 36] Operation: 37-1=36 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[1, 16], Operations: ['94-93=1', '37-21=16'] Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[93, 94, 37, 21], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [37, 21, 1] Generated Node #0,1: 17:[37, 21, 1] Operation: 94-93=1 Moving to Node #0,1 Current State: 17:[37, 21, 1], Operations: ['94-93=1'] Exploring Operation: 37-21=16, Resulting Numbers: [1, 16] Generated Node #0,1,0: 17:[1, 16] Operation: 37-21=16 Moving to Node #0,1,0 Current State: 17:[1, 16], Operations: ['94-93=1', '37-21=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 54, 63, 29, 51 ]
81
[ "54*51=2754", "63-29=34", "2754/34=81" ]
Current State: 81:[54, 63, 29, 51], Operations: [] Exploring Operation: 54*51=2754, Resulting Numbers: [63, 29, 2754] Generated Node #2: [63, 29, 2754] from Operation: 54*51=2754 Current State: 81:[63, 29, 2754], Operations: ['54*51=2754'] Exploring Operation: 63-29=34, Resulting Numbers: [2754, 34] Generated Node #3: [2754, 34] from Operation: 63-29=34 Current State: 81:[2754, 34], Operations: ['54*51=2754', '63-29=34'] Exploring Operation: 2754/34=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[54, 63, 29, 51], Operations: [] Exploring Operation: 54-51=3, Resulting Numbers: [63, 29, 3] Generated Node #0,0: 81:[63, 29, 3] Operation: 54-51=3 Exploring Operation: 63-54=9, Resulting Numbers: [29, 51, 9] Generated Node #0,1: 81:[29, 51, 9] Operation: 63-54=9 Exploring Operation: 63-51=12, Resulting Numbers: [54, 29, 12] Generated Node #0,2: 81:[54, 29, 12] Operation: 63-51=12 Exploring Operation: 54-29=25, Resulting Numbers: [63, 51, 25] Generated Node #0,3: 81:[63, 51, 25] Operation: 54-29=25 Exploring Operation: 54+29=83, Resulting Numbers: [63, 51, 83] Generated Node #0,4: 81:[63, 51, 83] Operation: 54+29=83 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[63, 29, 3], Operations: ['54-51=3'] Exploring Operation: 63+3=66, Resulting Numbers: [29, 66] Generated Node #0,0,0: 81:[29, 66] Operation: 63+3=66 Exploring Operation: 63/3=21, Resulting Numbers: [29, 21] Generated Node #0,0,1: 81:[29, 21] Operation: 63/3=21 Exploring Operation: 63+29=92, Resulting Numbers: [3, 92] Generated Node #0,0,2: 81:[3, 92] Operation: 63+29=92 Exploring Operation: 29-3=26, Resulting Numbers: [63, 26] Generated Node #0,0,3: 81:[63, 26] Operation: 29-3=26 Exploring Operation: 63-29=34, Resulting Numbers: [3, 34] Generated Node #0,0,4: 81:[3, 34] Operation: 63-29=34 Moving to Node #0,0,4 Current State: 81:[3, 34], Operations: ['54-51=3', '63-29=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 3+34=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 3*34=102, Resulting Numbers: [102] 102,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[29, 21], Operations: ['54-51=3', '63/3=21'] Exploring Operation: 29*21=609, Resulting Numbers: [609] 609,81 unequal: No Solution Exploring Operation: 29+21=50, Resulting Numbers: [50] 50,81 unequal: No Solution Exploring Operation: 29-21=8, Resulting Numbers: [8] 8,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[3, 92], Operations: ['54-51=3', '63+29=92'] Exploring Operation: 92-3=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 3+92=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 3*92=276, Resulting Numbers: [276] 276,81 unequal: No Solution Moving to Node #0,0,0 Current State: 81:[29, 66], Operations: ['54-51=3', '63+3=66'] Exploring Operation: 66-29=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 29+66=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 29*66=1914, Resulting Numbers: [1914] 1914,81 unequal: No Solution Moving to Node #0,0,3 Current State: 81:[63, 26], Operations: ['54-51=3', '29-3=26'] Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,81 unequal: No Solution Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[29, 51, 9], Operations: ['63-54=9'] Exploring Operation: 51-9=42, Resulting Numbers: [29, 42] Generated Node #0,1,0: 81:[29, 42] Operation: 51-9=42 Exploring Operation: 29+51=80, Resulting Numbers: [9, 80] Generated Node #0,1,1: 81:[9, 80] Operation: 29+51=80 Exploring Operation: 51-29=22, Resulting Numbers: [9, 22] Generated Node #0,1,2: 81:[9, 22] Operation: 51-29=22 Exploring Operation: 51+9=60, Resulting Numbers: [29, 60] Generated Node #0,1,3: 81:[29, 60] Operation: 51+9=60 Exploring Operation: 29-9=20, Resulting Numbers: [51, 20] Generated Node #0,1,4: 81:[51, 20] Operation: 29-9=20 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[9, 80], Operations: ['63-54=9', '29+51=80'] Exploring Operation: 9+80=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 9*80=720, Resulting Numbers: [720] 720,81 unequal: No Solution No 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: 81:[9, 22], Operations: ['63-54=9', '51-29=22'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,81 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,81 unequal: No Solution No 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: 81:[29, 42], Operations: ['63-54=9', '51-9=42'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,81 unequal: No Solution Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,81 unequal: No Solution No 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: 81:[29, 60], Operations: ['63-54=9', '51+9=60'] Exploring Operation: 29*60=1740, Resulting Numbers: [1740] 1740,81 unequal: No Solution Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 29+60=89, Resulting Numbers: [89] 89,81 unequal: No Solution No 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: 81:[51, 20], Operations: ['63-54=9', '29-9=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,81 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[54, 29, 12], Operations: ['63-51=12'] Exploring Operation: 54+29=83, Resulting Numbers: [12, 83] Generated Node #0,2,0: 81:[12, 83] Operation: 54+29=83 Exploring Operation: 54-12=42, Resulting Numbers: [29, 42] Generated Node #0,2,1: 81:[29, 42] Operation: 54-12=42 Exploring Operation: 29-12=17, Resulting Numbers: [54, 17] Generated Node #0,2,2: 81:[54, 17] Operation: 29-12=17 Exploring Operation: 54-29=25, Resulting Numbers: [12, 25] Generated Node #0,2,3: 81:[12, 25] Operation: 54-29=25 Exploring Operation: 54+12=66, Resulting Numbers: [29, 66] Generated Node #0,2,4: 81:[29, 66] Operation: 54+12=66 Moving to Node #0,2,0 Current State: 81:[12, 83], Operations: ['63-51=12', '54+29=83'] Exploring Operation: 12*83=996, Resulting Numbers: [996] 996,81 unequal: No Solution Exploring Operation: 12+83=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[12, 25], Operations: ['63-51=12', '54-29=25'] Exploring Operation: 12*25=300, Resulting Numbers: [300] 300,81 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 12+25=37, Resulting Numbers: [37] 37,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[29, 42], Operations: ['63-51=12', '54-12=42'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,81 unequal: No Solution Moving to Node #0,2,4 Current State: 81:[29, 66], Operations: ['63-51=12', '54+12=66'] Exploring Operation: 29+66=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 66-29=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 29*66=1914, Resulting Numbers: [1914] 1914,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[54, 17], Operations: ['63-51=12', '29-12=17'] Exploring Operation: 54-17=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 54+17=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 54*17=918, Resulting Numbers: [918] 918,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[63, 51, 25], Operations: ['54-29=25'] Exploring Operation: 63-51=12, Resulting Numbers: [25, 12] Generated Node #0,3,0: 81:[25, 12] Operation: 63-51=12 Exploring Operation: 63+25=88, Resulting Numbers: [51, 88] Generated Node #0,3,1: 81:[51, 88] Operation: 63+25=88 Exploring Operation: 51+25=76, Resulting Numbers: [63, 76] Generated Node #0,3,2: 81:[63, 76] Operation: 51+25=76 Exploring Operation: 63+51=114, Resulting Numbers: [25, 114] Generated Node #0,3,3: 81:[25, 114] Operation: 63+51=114 Exploring Operation: 51-25=26, Resulting Numbers: [63, 26] Generated Node #0,3,4: 81:[63, 26] Operation: 51-25=26 Moving to Node #0,3,0 Current State: 81:[25, 12], Operations: ['54-29=25', '63-51=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,81 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,81 unequal: No Solution Moving to Node #0,3,4 Current State: 81:[63, 26], Operations: ['54-29=25', '51-25=26'] Exploring Operation: 63+26=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 63*26=1638, Resulting Numbers: [1638] 1638,81 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,81 unequal: No Solution Moving to Node #0,3,2 Current State: 81:[63, 76], Operations: ['54-29=25', '51+25=76'] Exploring Operation: 76-63=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 63+76=139, Resulting Numbers: [139] 139,81 unequal: No Solution Exploring Operation: 63*76=4788, Resulting Numbers: [4788] 4788,81 unequal: No Solution Moving to Node #0,3,1 Current State: 81:[51, 88], Operations: ['54-29=25', '63+25=88'] Exploring Operation: 51+88=139, Resulting Numbers: [139] 139,81 unequal: No Solution Exploring Operation: 51*88=4488, Resulting Numbers: [4488] 4488,81 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[25, 114], Operations: ['54-29=25', '63+51=114'] Exploring Operation: 25*114=2850, Resulting Numbers: [2850] 2850,81 unequal: No Solution Exploring Operation: 25+114=139, Resulting Numbers: [139] 139,81 unequal: No Solution Exploring Operation: 114-25=89, Resulting Numbers: [89] 89,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 81:[63, 51, 83], Operations: ['54+29=83'] Exploring Operation: 83-51=32, Resulting Numbers: [63, 32] Generated Node #0,4,0: 81:[63, 32] Operation: 83-51=32 Exploring Operation: 51+83=134, Resulting Numbers: [63, 134] Generated Node #0,4,1: 81:[63, 134] Operation: 51+83=134 Exploring Operation: 63+51=114, Resulting Numbers: [83, 114] Generated Node #0,4,2: 81:[83, 114] Operation: 63+51=114 Exploring Operation: 83-63=20, Resulting Numbers: [51, 20] Generated Node #0,4,3: 81:[51, 20] Operation: 83-63=20 Exploring Operation: 63-51=12, Resulting Numbers: [83, 12] Generated Node #0,4,4: 81:[83, 12] Operation: 63-51=12 Moving to Node #0,4,4 Current State: 81:[83, 12], Operations: ['54+29=83', '63-51=12'] Exploring Operation: 83-12=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 83*12=996, Resulting Numbers: [996] 996,81 unequal: No Solution Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,81 unequal: No Solution Moving to Node #0,4,0 Current State: 81:[63, 32], Operations: ['54+29=83', '83-51=32'] Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,81 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 63*32=2016, Resulting Numbers: [2016] 2016,81 unequal: No Solution Moving to Node #0,4,3 Current State: 81:[51, 20], Operations: ['54+29=83', '83-63=20'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 51+20=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 51*20=1020, Resulting Numbers: [1020] 1020,81 unequal: No Solution Moving to Node #0,4,2 Current State: 81:[83, 114], Operations: ['54+29=83', '63+51=114'] Exploring Operation: 83+114=197, Resulting Numbers: [197] 197,81 unequal: No Solution Exploring Operation: 114-83=31, Resulting Numbers: [31] 31,81 unequal: No Solution Exploring Operation: 83*114=9462, Resulting Numbers: [9462] 9462,81 unequal: No Solution Moving to Node #0,4,1 Current State: 81:[63, 134], Operations: ['54+29=83', '51+83=134'] Exploring Operation: 63*134=8442, Resulting Numbers: [8442] 8442,81 unequal: No Solution Exploring Operation: 63+134=197, Resulting Numbers: [197] 197,81 unequal: No Solution Exploring Operation: 134-63=71, Resulting Numbers: [71] 71,81 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
[ 37, 39, 64, 1 ]
64
[ "39-37=2", "2-1=1", "64*1=64" ]
Current State: 64:[37, 39, 64, 1], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [64, 1, 2] Generated Node #2: [64, 1, 2] from Operation: 39-37=2 Current State: 64:[64, 1, 2], Operations: ['39-37=2'] Exploring Operation: 2-1=1, Resulting Numbers: [64, 1] Generated Node #3: [64, 1] from Operation: 2-1=1 Current State: 64:[64, 1], Operations: ['39-37=2', '2-1=1'] Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[37, 39, 64, 1], Operations: [] Exploring Operation: 39-37=2, Resulting Numbers: [64, 1, 2] Generated Node #0,0: 64:[64, 1, 2] Operation: 39-37=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[64, 1, 2], Operations: ['39-37=2'] Exploring Operation: 64*1=64, Resulting Numbers: [2, 64] Generated Node #0,0,0: 64:[2, 64] Operation: 64*1=64 Moving to Node #0,0,0 Current State: 64:[2, 64], Operations: ['39-37=2', '64*1=64'] Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,64 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 7, 84, 22, 70 ]
24
[ "7+70=77", "84*22=1848", "1848/77=24" ]
Current State: 24:[7, 84, 22, 70], Operations: [] Exploring Operation: 7+70=77, Resulting Numbers: [84, 22, 77] Generated Node #2: [84, 22, 77] from Operation: 7+70=77 Current State: 24:[84, 22, 77], Operations: ['7+70=77'] Exploring Operation: 84*22=1848, Resulting Numbers: [77, 1848] Generated Node #3: [77, 1848] from Operation: 84*22=1848 Current State: 24:[77, 1848], Operations: ['7+70=77', '84*22=1848'] Exploring Operation: 1848/77=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[7, 84, 22, 70], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [7, 22, 14] Generated Node #0,0: 24:[7, 22, 14] Operation: 84-70=14 Exploring Operation: 84/7=12, Resulting Numbers: [22, 70, 12] Generated Node #0,1: 24:[22, 70, 12] Operation: 84/7=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[7, 22, 14], Operations: ['84-70=14'] Exploring Operation: 14/7=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 24:[22, 2] Operation: 14/7=2 Exploring Operation: 22-14=8, Resulting Numbers: [7, 8] Generated Node #0,0,1: 24:[7, 8] Operation: 22-14=8 Moving to Node #0,0,1 Current State: 24:[7, 8], Operations: ['84-70=14', '22-14=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,24 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,24 unequal: No Solution Moving to Node #0,0,0 Current State: 24:[22, 2], Operations: ['84-70=14', '14/7=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,24 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[7, 84, 22, 70], Operations: [] Exploring Operation: 84-70=14, Resulting Numbers: [7, 22, 14] Generated Node #0,0: 24:[7, 22, 14] Operation: 84-70=14 Moving to Node #0,0 Current State: 24:[7, 22, 14], Operations: ['84-70=14'] Exploring Operation: 14/7=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 24:[22, 2] Operation: 14/7=2 Moving to Node #0,0,0 Current State: 24:[22, 2], Operations: ['84-70=14', '14/7=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 24, 39, 14, 59 ]
60
[ "39-24=15", "59-14=45", "15+45=60" ]
Current State: 60:[24, 39, 14, 59], Operations: [] Exploring Operation: 39-24=15, Resulting Numbers: [14, 59, 15] Generated Node #2: [14, 59, 15] from Operation: 39-24=15 Current State: 60:[14, 59, 15], Operations: ['39-24=15'] Exploring Operation: 59-14=45, Resulting Numbers: [15, 45] Generated Node #3: [15, 45] from Operation: 59-14=45 Current State: 60:[15, 45], Operations: ['39-24=15', '59-14=45'] Exploring Operation: 15+45=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[24, 39, 14, 59], Operations: [] Exploring Operation: 24+39=63, Resulting Numbers: [14, 59, 63] Generated Node #0,0: 60:[14, 59, 63] Operation: 24+39=63 Exploring Operation: 59-39=20, Resulting Numbers: [24, 14, 20] Generated Node #0,1: 60:[24, 14, 20] Operation: 59-39=20 Exploring Operation: 39-24=15, Resulting Numbers: [14, 59, 15] Generated Node #0,2: 60:[14, 59, 15] Operation: 39-24=15 Exploring Operation: 24-14=10, Resulting Numbers: [39, 59, 10] Generated Node #0,3: 60:[39, 59, 10] Operation: 24-14=10 Exploring Operation: 39-14=25, Resulting Numbers: [24, 59, 25] Generated Node #0,4: 60:[24, 59, 25] Operation: 39-14=25 Start Sub Search at level 1: Moving to Node #0,2 Current State: 60:[14, 59, 15], Operations: ['39-24=15'] Exploring Operation: 59-14=45, Resulting Numbers: [15, 45] Generated Node #0,2,0: 60:[15, 45] Operation: 59-14=45 Exploring Operation: 14+15=29, Resulting Numbers: [59, 29] Generated Node #0,2,1: 60:[59, 29] Operation: 14+15=29 Exploring Operation: 59+15=74, Resulting Numbers: [14, 74] Generated Node #0,2,2: 60:[14, 74] Operation: 59+15=74 Exploring Operation: 14+59=73, Resulting Numbers: [15, 73] Generated Node #0,2,3: 60:[15, 73] Operation: 14+59=73 Exploring Operation: 15-14=1, Resulting Numbers: [59, 1] Generated Node #0,2,4: 60:[59, 1] Operation: 15-14=1 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 60:[59, 29], Operations: ['39-24=15', '14+15=29'] Exploring Operation: 59+29=88, Resulting Numbers: [88] 88,60 unequal: No Solution Exploring Operation: 59-29=30, Resulting Numbers: [30] 30,60 unequal: No Solution Exploring Operation: 59*29=1711, Resulting Numbers: [1711] 1711,60 unequal: No Solution No 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: 60:[59, 1], Operations: ['39-24=15', '15-14=1'] Exploring Operation: 59*1=59, Resulting Numbers: [59] 59,60 unequal: No Solution Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[24, 39, 14, 59], Operations: [] Exploring Operation: 39-24=15, Resulting Numbers: [14, 59, 15] Generated Node #0,2: 60:[14, 59, 15] Operation: 39-24=15 Moving to Node #0,2 Current State: 60:[14, 59, 15], Operations: ['39-24=15'] Exploring Operation: 15-14=1, Resulting Numbers: [59, 1] Generated Node #0,2,4: 60:[59, 1] Operation: 15-14=1 Moving to Node #0,2,4 Current State: 60:[59, 1], Operations: ['39-24=15', '15-14=1'] Exploring Operation: 59+1=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 60, 66, 76, 5 ]
65
[ "66-60=6", "76-5=71", "71-6=65" ]
Current State: 65:[60, 66, 76, 5], Operations: [] Exploring Operation: 66-60=6, Resulting Numbers: [76, 5, 6] Generated Node #2: [76, 5, 6] from Operation: 66-60=6 Current State: 65:[76, 5, 6], Operations: ['66-60=6'] Exploring Operation: 76-5=71, Resulting Numbers: [6, 71] Generated Node #3: [6, 71] from Operation: 76-5=71 Current State: 65:[6, 71], Operations: ['66-60=6', '76-5=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[60, 66, 76, 5], Operations: [] Exploring Operation: 76-60=16, Resulting Numbers: [66, 5, 16] Generated Node #0,0: 65:[66, 5, 16] Operation: 76-60=16 Moving to Node #0,0 Current State: 65:[66, 5, 16], Operations: ['76-60=16'] Exploring Operation: 16-5=11, Resulting Numbers: [66, 11] Generated Node #0,0,0: 65:[66, 11] Operation: 16-5=11 Moving to Node #0,0,0 Current State: 65:[66, 11], Operations: ['76-60=16', '16-5=11'] Exploring Operation: 66/11=6, Resulting Numbers: [6] 6,65 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 45, 36, 11, 4 ]
33
[ "11+4=15", "45/15=3", "36-3=33" ]
Current State: 33:[45, 36, 11, 4], Operations: [] Exploring Operation: 11+4=15, Resulting Numbers: [45, 36, 15] Generated Node #2: [45, 36, 15] from Operation: 11+4=15 Current State: 33:[45, 36, 15], Operations: ['11+4=15'] Exploring Operation: 45/15=3, Resulting Numbers: [36, 3] Generated Node #3: [36, 3] from Operation: 45/15=3 Current State: 33:[36, 3], Operations: ['11+4=15', '45/15=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[45, 36, 11, 4], Operations: [] Exploring Operation: 45-11=34, Resulting Numbers: [36, 4, 34] Generated Node #0,0: 33:[36, 4, 34] Operation: 45-11=34 Exploring Operation: 45-4=41, Resulting Numbers: [36, 11, 41] Generated Node #0,1: 33:[36, 11, 41] Operation: 45-4=41 Exploring Operation: 45-36=9, Resulting Numbers: [11, 4, 9] Generated Node #0,2: 33:[11, 4, 9] Operation: 45-36=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 33:[11, 4, 9], Operations: ['45-36=9'] Exploring Operation: 4+9=13, Resulting Numbers: [11, 13] Generated Node #0,2,0: 33:[11, 13] Operation: 4+9=13 Exploring Operation: 11-9=2, Resulting Numbers: [4, 2] Generated Node #0,2,1: 33:[4, 2] Operation: 11-9=2 Exploring Operation: 9-4=5, Resulting Numbers: [11, 5] Generated Node #0,2,2: 33:[11, 5] Operation: 9-4=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 33:[11, 13], Operations: ['45-36=9', '4+9=13'] Exploring Operation: 11+13=24, Resulting Numbers: [24] 24,33 unequal: No Solution Exploring Operation: 13-11=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 11*13=143, Resulting Numbers: [143] 143,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 33:[4, 2], Operations: ['45-36=9', '11-9=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 33:[11, 5], Operations: ['45-36=9', '9-4=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,33 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[36, 4, 34], Operations: ['45-11=34'] Exploring Operation: 36-34=2, Resulting Numbers: [4, 2] Generated Node #0,0,0: 33:[4, 2] Operation: 36-34=2 Exploring Operation: 36/4=9, Resulting Numbers: [34, 9] Generated Node #0,0,1: 33:[34, 9] Operation: 36/4=9 Exploring Operation: 36-4=32, Resulting Numbers: [34, 32] Generated Node #0,0,2: 33:[34, 32] Operation: 36-4=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[4, 2], Operations: ['45-11=34', '36-34=2'] Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 33:[34, 32], Operations: ['45-11=34', '36-4=32'] Exploring Operation: 34+32=66, Resulting Numbers: [66] 66,33 unequal: No Solution Exploring Operation: 34-32=2, Resulting Numbers: [2] 2,33 unequal: No Solution Exploring Operation: 34*32=1088, Resulting Numbers: [1088] 1088,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[34, 9], Operations: ['45-11=34', '36/4=9'] Exploring Operation: 34+9=43, Resulting Numbers: [43] 43,33 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,33 unequal: No Solution Exploring Operation: 34*9=306, Resulting Numbers: [306] 306,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[36, 11, 41], Operations: ['45-4=41'] Exploring Operation: 41-11=30, Resulting Numbers: [36, 30] Generated Node #0,1,0: 33:[36, 30] Operation: 41-11=30 Exploring Operation: 41-36=5, Resulting Numbers: [11, 5] Generated Node #0,1,1: 33:[11, 5] Operation: 41-36=5 Exploring Operation: 36-11=25, Resulting Numbers: [41, 25] Generated Node #0,1,2: 33:[41, 25] Operation: 36-11=25 Moving to Node #0,1,1 Current State: 33:[11, 5], Operations: ['45-4=41', '41-36=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,33 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[36, 30], Operations: ['45-4=41', '41-11=30'] Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,33 unequal: No Solution Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 36*30=1080, Resulting Numbers: [1080] 1080,33 unequal: No Solution Moving to Node #0,1,2 Current State: 33:[41, 25], Operations: ['45-4=41', '36-11=25'] Exploring Operation: 41+25=66, Resulting Numbers: [66] 66,33 unequal: No Solution Exploring Operation: 41*25=1025, Resulting Numbers: [1025] 1025,33 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,33 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
[ 47, 1, 80, 4 ]
29
[ "47*1=47", "80-4=76", "76-47=29" ]
Current State: 29:[47, 1, 80, 4], Operations: [] Exploring Operation: 47*1=47, Resulting Numbers: [80, 4, 47] Generated Node #2: [80, 4, 47] from Operation: 47*1=47 Current State: 29:[80, 4, 47], Operations: ['47*1=47'] Exploring Operation: 80-4=76, Resulting Numbers: [47, 76] Generated Node #3: [47, 76] from Operation: 80-4=76 Current State: 29:[47, 76], Operations: ['47*1=47', '80-4=76'] Exploring Operation: 76-47=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[47, 1, 80, 4], Operations: [] Exploring Operation: 80-47=33, Resulting Numbers: [1, 4, 33] Generated Node #0,0: 29:[1, 4, 33] Operation: 80-47=33 Exploring Operation: 80/4=20, Resulting Numbers: [47, 1, 20] Generated Node #0,1: 29:[47, 1, 20] Operation: 80/4=20 Exploring Operation: 47-1=46, Resulting Numbers: [80, 4, 46] Generated Node #0,2: 29:[80, 4, 46] Operation: 47-1=46 Moving to Node #0,1 Current State: 29:[47, 1, 20], Operations: ['80/4=20'] Exploring Operation: 47*1=47, Resulting Numbers: [20, 47] Generated Node #0,1,0: 29:[20, 47] Operation: 47*1=47 Exploring Operation: 47-1=46, Resulting Numbers: [20, 46] Generated Node #0,1,1: 29:[20, 46] Operation: 47-1=46 Exploring Operation: 1+20=21, Resulting Numbers: [47, 21] Generated Node #0,1,2: 29:[47, 21] Operation: 1+20=21 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 29:[20, 46], Operations: ['80/4=20', '47-1=46'] Exploring Operation: 20*46=920, Resulting Numbers: [920] 920,29 unequal: No Solution Exploring Operation: 20+46=66, Resulting Numbers: [66] 66,29 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,29 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:[47, 21], Operations: ['80/4=20', '1+20=21'] Exploring Operation: 47*21=987, Resulting Numbers: [987] 987,29 unequal: No Solution Exploring Operation: 47-21=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 47+21=68, Resulting Numbers: [68] 68,29 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:[20, 47], Operations: ['80/4=20', '47*1=47'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,29 unequal: No Solution Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,29 unequal: No Solution Exploring Operation: 20*47=940, Resulting Numbers: [940] 940,29 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:[1, 4, 33], Operations: ['80-47=33'] Exploring Operation: 1+4=5, Resulting Numbers: [33, 5] Generated Node #0,0,0: 29:[33, 5] Operation: 1+4=5 Exploring Operation: 33-4=29, Resulting Numbers: [1, 29] Generated Node #0,0,1: 29:[1, 29] Operation: 33-4=29 Exploring Operation: 33-1=32, Resulting Numbers: [4, 32] Generated Node #0,0,2: 29:[4, 32] Operation: 33-1=32 Moving to Node #0,2 Current State: 29:[80, 4, 46], Operations: ['47-1=46'] Exploring Operation: 80-46=34, Resulting Numbers: [4, 34] Generated Node #0,2,0: 29:[4, 34] Operation: 80-46=34 Exploring Operation: 80/4=20, Resulting Numbers: [46, 20] Generated Node #0,2,1: 29:[46, 20] Operation: 80/4=20 Exploring Operation: 80-4=76, Resulting Numbers: [46, 76] Generated Node #0,2,2: 29:[46, 76] Operation: 80-4=76 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[46, 20], Operations: ['47-1=46', '80/4=20'] Exploring Operation: 46*20=920, Resulting Numbers: [920] 920,29 unequal: No Solution Exploring Operation: 46-20=26, Resulting Numbers: [26] 26,29 unequal: No Solution Exploring Operation: 46+20=66, Resulting Numbers: [66] 66,29 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:[4, 34], Operations: ['47-1=46', '80-46=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,29 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,29 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 #0,2,2 Current State: 29:[46, 76], Operations: ['47-1=46', '80-4=76'] Exploring Operation: 46+76=122, Resulting Numbers: [122] 122,29 unequal: No Solution Exploring Operation: 46*76=3496, Resulting Numbers: [3496] 3496,29 unequal: No Solution Exploring Operation: 76-46=30, Resulting Numbers: [30] 30,29 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: 29:[33, 5], Operations: ['80-47=33', '1+4=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,29 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[1, 29], Operations: ['80-47=33', '33-4=29'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[47, 1, 80, 4], Operations: [] Exploring Operation: 80-47=33, Resulting Numbers: [1, 4, 33] Generated Node #0,0: 29:[1, 4, 33] Operation: 80-47=33 Moving to Node #0,0 Current State: 29:[1, 4, 33], Operations: ['80-47=33'] Exploring Operation: 33-4=29, Resulting Numbers: [1, 29] Generated Node #0,0,1: 29:[1, 29] Operation: 33-4=29 Moving to Node #0,0,1 Current State: 29:[1, 29], Operations: ['80-47=33', '33-4=29'] Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
0.967014
hs_3
sum_heuristic
[ 61, 8, 36, 6 ]
83
[ "61-8=53", "36-6=30", "53+30=83" ]
Current State: 83:[61, 8, 36, 6], Operations: [] Exploring Operation: 61-8=53, Resulting Numbers: [36, 6, 53] Generated Node #2: [36, 6, 53] from Operation: 61-8=53 Current State: 83:[36, 6, 53], Operations: ['61-8=53'] Exploring Operation: 36-6=30, Resulting Numbers: [53, 30] Generated Node #3: [53, 30] from Operation: 36-6=30 Current State: 83:[53, 30], Operations: ['61-8=53', '36-6=30'] Exploring Operation: 53+30=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[61, 8, 36, 6], Operations: [] Exploring Operation: 61+8=69, Resulting Numbers: [36, 6, 69] Generated Node #0,0: 83:[36, 6, 69] Operation: 61+8=69 Exploring Operation: 8*6=48, Resulting Numbers: [61, 36, 48] Generated Node #0,1: 83:[61, 36, 48] Operation: 8*6=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[61, 36, 48], Operations: ['8*6=48'] Exploring Operation: 36+48=84, Resulting Numbers: [61, 84] Generated Node #0,1,0: 83:[61, 84] Operation: 36+48=84 Exploring Operation: 61+36=97, Resulting Numbers: [48, 97] Generated Node #0,1,1: 83:[48, 97] Operation: 61+36=97 Moving to Node #0,1,0 Current State: 83:[61, 84], Operations: ['8*6=48', '36+48=84'] Exploring Operation: 84-61=23, Resulting Numbers: [23] 23,83 unequal: No Solution Exploring Operation: 61+84=145, Resulting Numbers: [145] 145,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[48, 97], Operations: ['8*6=48', '61+36=97'] Exploring Operation: 97-48=49, Resulting Numbers: [49] 49,83 unequal: No Solution Exploring Operation: 48+97=145, Resulting Numbers: [145] 145,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[36, 6, 69], Operations: ['61+8=69'] Exploring Operation: 6+69=75, Resulting Numbers: [36, 75] Generated Node #0,0,0: 83:[36, 75] Operation: 6+69=75 Exploring Operation: 36+6=42, Resulting Numbers: [69, 42] Generated Node #0,0,1: 83:[69, 42] Operation: 36+6=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[36, 75], Operations: ['61+8=69', '6+69=75'] Exploring Operation: 75-36=39, Resulting Numbers: [39] 39,83 unequal: No Solution Exploring Operation: 36+75=111, Resulting Numbers: [111] 111,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[69, 42], Operations: ['61+8=69', '36+6=42'] Exploring Operation: 69+42=111, Resulting Numbers: [111] 111,83 unequal: No Solution Exploring Operation: 69-42=27, Resulting Numbers: [27] 27,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 27, 46, 32, 28 ]
41
[ "46-27=19", "32+28=60", "60-19=41" ]
Current State: 41:[27, 46, 32, 28], Operations: [] Exploring Operation: 46-27=19, Resulting Numbers: [32, 28, 19] Generated Node #2: [32, 28, 19] from Operation: 46-27=19 Current State: 41:[32, 28, 19], Operations: ['46-27=19'] Exploring Operation: 32+28=60, Resulting Numbers: [19, 60] Generated Node #3: [19, 60] from Operation: 32+28=60 Current State: 41:[19, 60], Operations: ['46-27=19', '32+28=60'] Exploring Operation: 60-19=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[27, 46, 32, 28], Operations: [] Exploring Operation: 27+32=59, Resulting Numbers: [46, 28, 59] Generated Node #0,0: 41:[46, 28, 59] Operation: 27+32=59 Exploring Operation: 46-27=19, Resulting Numbers: [32, 28, 19] Generated Node #0,1: 41:[32, 28, 19] Operation: 46-27=19 Exploring Operation: 32+28=60, Resulting Numbers: [27, 46, 60] Generated Node #0,2: 41:[27, 46, 60] Operation: 32+28=60 Exploring Operation: 27+28=55, Resulting Numbers: [46, 32, 55] Generated Node #0,3: 41:[46, 32, 55] Operation: 27+28=55 Exploring Operation: 46-28=18, Resulting Numbers: [27, 32, 18] Generated Node #0,4: 41:[27, 32, 18] Operation: 46-28=18 Moving to Node #0,3 Current State: 41:[46, 32, 55], Operations: ['27+28=55'] Exploring Operation: 46+32=78, Resulting Numbers: [55, 78] Generated Node #0,3,0: 41:[55, 78] Operation: 46+32=78 Exploring Operation: 55-32=23, Resulting Numbers: [46, 23] Generated Node #0,3,1: 41:[46, 23] Operation: 55-32=23 Exploring Operation: 55-46=9, Resulting Numbers: [32, 9] Generated Node #0,3,2: 41:[32, 9] Operation: 55-46=9 Exploring Operation: 46-32=14, Resulting Numbers: [55, 14] Generated Node #0,3,3: 41:[55, 14] Operation: 46-32=14 Exploring Operation: 32+55=87, Resulting Numbers: [46, 87] Generated Node #0,3,4: 41:[46, 87] Operation: 32+55=87 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[46, 23], Operations: ['27+28=55', '55-32=23'] Exploring Operation: 46/23=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 46+23=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 46*23=1058, Resulting Numbers: [1058] 1058,41 unequal: No Solution Exploring Operation: 46-23=23, Resulting Numbers: [23] 23,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[32, 9], Operations: ['27+28=55', '55-46=9'] Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[27, 46, 32, 28], Operations: [] Exploring Operation: 27+28=55, Resulting Numbers: [46, 32, 55] Generated Node #0,3: 41:[46, 32, 55] Operation: 27+28=55 Moving to Node #0,3 Current State: 41:[46, 32, 55], Operations: ['27+28=55'] Exploring Operation: 55-46=9, Resulting Numbers: [32, 9] Generated Node #0,3,2: 41:[32, 9] Operation: 55-46=9 Moving to Node #0,3,2 Current State: 41:[32, 9], Operations: ['27+28=55', '55-46=9'] Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 13, 12, 93, 17 ]
98
[ "13+93=106", "12*17=204", "204-106=98" ]
Current State: 98:[13, 12, 93, 17], Operations: [] Exploring Operation: 13+93=106, Resulting Numbers: [12, 17, 106] Generated Node #2: [12, 17, 106] from Operation: 13+93=106 Current State: 98:[12, 17, 106], Operations: ['13+93=106'] Exploring Operation: 12*17=204, Resulting Numbers: [106, 204] Generated Node #3: [106, 204] from Operation: 12*17=204 Current State: 98:[106, 204], Operations: ['13+93=106', '12*17=204'] Exploring Operation: 204-106=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[13, 12, 93, 17], Operations: [] Exploring Operation: 17-12=5, Resulting Numbers: [13, 93, 5] Generated Node #0,0: 98:[13, 93, 5] Operation: 17-12=5 Moving to Node #0,0 Current State: 98:[13, 93, 5], Operations: ['17-12=5'] Exploring Operation: 93+5=98, Resulting Numbers: [13, 98] Generated Node #0,0,0: 98:[13, 98] Operation: 93+5=98 Moving to Node #0,0,0 Current State: 98:[13, 98], Operations: ['17-12=5', '93+5=98'] Exploring Operation: 13+98=111, Resulting Numbers: [111] 111,98 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 94, 80, 68, 57 ]
82
[ "94*57=5358", "80*68=5440", "5440-5358=82" ]
Current State: 82:[94, 80, 68, 57], Operations: [] Exploring Operation: 94*57=5358, Resulting Numbers: [80, 68, 5358] Generated Node #2: [80, 68, 5358] from Operation: 94*57=5358 Current State: 82:[80, 68, 5358], Operations: ['94*57=5358'] Exploring Operation: 80*68=5440, Resulting Numbers: [5358, 5440] Generated Node #3: [5358, 5440] from Operation: 80*68=5440 Current State: 82:[5358, 5440], Operations: ['94*57=5358', '80*68=5440'] Exploring Operation: 5440-5358=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[94, 80, 68, 57], Operations: [] Exploring Operation: 94-68=26, Resulting Numbers: [80, 57, 26] Generated Node #0,0: 82:[80, 57, 26] Operation: 94-68=26 Exploring Operation: 94-57=37, Resulting Numbers: [80, 68, 37] Generated Node #0,1: 82:[80, 68, 37] Operation: 94-57=37 Exploring Operation: 80-68=12, Resulting Numbers: [94, 57, 12] Generated Node #0,2: 82:[94, 57, 12] Operation: 80-68=12 Exploring Operation: 94-80=14, Resulting Numbers: [68, 57, 14] Generated Node #0,3: 82:[68, 57, 14] Operation: 94-80=14 Exploring Operation: 68-57=11, Resulting Numbers: [94, 80, 11] Generated Node #0,4: 82:[94, 80, 11] Operation: 68-57=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[80, 68, 37], Operations: ['94-57=37'] Exploring Operation: 80-37=43, Resulting Numbers: [68, 43] Generated Node #0,1,0: 82:[68, 43] Operation: 80-37=43 Exploring Operation: 80-68=12, Resulting Numbers: [37, 12] Generated Node #0,1,1: 82:[37, 12] Operation: 80-68=12 Exploring Operation: 80+37=117, Resulting Numbers: [68, 117] Generated Node #0,1,2: 82:[68, 117] Operation: 80+37=117 Exploring Operation: 68+37=105, Resulting Numbers: [80, 105] Generated Node #0,1,3: 82:[80, 105] Operation: 68+37=105 Exploring Operation: 68-37=31, Resulting Numbers: [80, 31] Generated Node #0,1,4: 82:[80, 31] Operation: 68-37=31 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 82:[80, 31], Operations: ['94-57=37', '68-37=31'] Exploring Operation: 80+31=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 80*31=2480, Resulting Numbers: [2480] 2480,82 unequal: No Solution Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[37, 12], Operations: ['94-57=37', '80-68=12'] Exploring Operation: 37*12=444, Resulting Numbers: [444] 444,82 unequal: No Solution Exploring Operation: 37+12=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[68, 43], Operations: ['94-57=37', '80-37=43'] Exploring Operation: 68+43=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,82 unequal: No Solution Exploring Operation: 68*43=2924, Resulting Numbers: [2924] 2924,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 82:[80, 105], Operations: ['94-57=37', '68+37=105'] Exploring Operation: 105-80=25, Resulting Numbers: [25] 25,82 unequal: No Solution Exploring Operation: 80*105=8400, Resulting Numbers: [8400] 8400,82 unequal: No Solution Exploring Operation: 80+105=185, Resulting Numbers: [185] 185,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 82:[68, 117], Operations: ['94-57=37', '80+37=117'] Exploring Operation: 68+117=185, Resulting Numbers: [185] 185,82 unequal: No Solution Exploring Operation: 117-68=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 68*117=7956, Resulting Numbers: [7956] 7956,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 82:[94, 80, 11], Operations: ['68-57=11'] Exploring Operation: 94-11=83, Resulting Numbers: [80, 83] Generated Node #0,4,0: 82:[80, 83] Operation: 94-11=83 Exploring Operation: 80-11=69, Resulting Numbers: [94, 69] Generated Node #0,4,1: 82:[94, 69] Operation: 80-11=69 Exploring Operation: 94-80=14, Resulting Numbers: [11, 14] Generated Node #0,4,2: 82:[11, 14] Operation: 94-80=14 Exploring Operation: 80+11=91, Resulting Numbers: [94, 91] Generated Node #0,4,3: 82:[94, 91] Operation: 80+11=91 Exploring Operation: 94+11=105, Resulting Numbers: [80, 105] Generated Node #0,4,4: 82:[80, 105] Operation: 94+11=105 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 82:[80, 83], Operations: ['68-57=11', '94-11=83'] Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,82 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,82 unequal: No Solution Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 82:[11, 14], Operations: ['68-57=11', '94-80=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,82 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 82:[94, 91], Operations: ['68-57=11', '80+11=91'] Exploring Operation: 94+91=185, Resulting Numbers: [185] 185,82 unequal: No Solution Exploring Operation: 94-91=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 94*91=8554, Resulting Numbers: [8554] 8554,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 82:[94, 69], Operations: ['68-57=11', '80-11=69'] Exploring Operation: 94*69=6486, Resulting Numbers: [6486] 6486,82 unequal: No Solution Exploring Operation: 94+69=163, Resulting Numbers: [163] 163,82 unequal: No Solution Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 82:[80, 105], Operations: ['68-57=11', '94+11=105'] Exploring Operation: 80+105=185, Resulting Numbers: [185] 185,82 unequal: No Solution Exploring Operation: 80*105=8400, Resulting Numbers: [8400] 8400,82 unequal: No Solution Exploring Operation: 105-80=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[80, 57, 26], Operations: ['94-68=26'] Exploring Operation: 57-26=31, Resulting Numbers: [80, 31] Generated Node #0,0,0: 82:[80, 31] Operation: 57-26=31 Exploring Operation: 80+26=106, Resulting Numbers: [57, 106] Generated Node #0,0,1: 82:[57, 106] Operation: 80+26=106 Exploring Operation: 57+26=83, Resulting Numbers: [80, 83] Generated Node #0,0,2: 82:[80, 83] Operation: 57+26=83 Exploring Operation: 80-26=54, Resulting Numbers: [57, 54] Generated Node #0,0,3: 82:[57, 54] Operation: 80-26=54 Exploring Operation: 80-57=23, Resulting Numbers: [26, 23] Generated Node #0,0,4: 82:[26, 23] Operation: 80-57=23 Moving to Node #0,0,2 Current State: 82:[80, 83], Operations: ['94-68=26', '57+26=83'] Exploring Operation: 83-80=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 80+83=163, Resulting Numbers: [163] 163,82 unequal: No Solution Exploring Operation: 80*83=6640, Resulting Numbers: [6640] 6640,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[80, 31], Operations: ['94-68=26', '57-26=31'] Exploring Operation: 80-31=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 80+31=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 80*31=2480, Resulting Numbers: [2480] 2480,82 unequal: No Solution Moving to Node #0,0,3 Current State: 82:[57, 54], Operations: ['94-68=26', '80-26=54'] Exploring Operation: 57*54=3078, Resulting Numbers: [3078] 3078,82 unequal: No Solution Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,82 unequal: No Solution Moving to Node #0,0,4 Current State: 82:[26, 23], Operations: ['94-68=26', '80-57=23'] Exploring Operation: 26-23=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 26*23=598, Resulting Numbers: [598] 598,82 unequal: No Solution Exploring Operation: 26+23=49, Resulting Numbers: [49] 49,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[57, 106], Operations: ['94-68=26', '80+26=106'] Exploring Operation: 106-57=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 57*106=6042, Resulting Numbers: [6042] 6042,82 unequal: No Solution Exploring Operation: 57+106=163, Resulting Numbers: [163] 163,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[94, 57, 12], Operations: ['80-68=12'] Exploring Operation: 94-12=82, Resulting Numbers: [57, 82] Generated Node #0,2,0: 82:[57, 82] Operation: 94-12=82 Exploring Operation: 94-57=37, Resulting Numbers: [12, 37] Generated Node #0,2,1: 82:[12, 37] Operation: 94-57=37 Exploring Operation: 94+12=106, Resulting Numbers: [57, 106] Generated Node #0,2,2: 82:[57, 106] Operation: 94+12=106 Exploring Operation: 57+12=69, Resulting Numbers: [94, 69] Generated Node #0,2,3: 82:[94, 69] Operation: 57+12=69 Exploring Operation: 57-12=45, Resulting Numbers: [94, 45] Generated Node #0,2,4: 82:[94, 45] Operation: 57-12=45 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[12, 37], Operations: ['80-68=12', '94-57=37'] Exploring Operation: 37-12=25, Resulting Numbers: [25] 25,82 unequal: No Solution Exploring Operation: 12+37=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 12*37=444, Resulting Numbers: [444] 444,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[57, 82], Operations: ['80-68=12', '94-12=82'] Exploring Operation: 57+82=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,82 unequal: No Solution Exploring Operation: 57*82=4674, Resulting Numbers: [4674] 4674,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 82:[94, 45], Operations: ['80-68=12', '57-12=45'] Exploring Operation: 94*45=4230, Resulting Numbers: [4230] 4230,82 unequal: No Solution Exploring Operation: 94-45=49, Resulting Numbers: [49] 49,82 unequal: No Solution Exploring Operation: 94+45=139, Resulting Numbers: [139] 139,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[94, 69], Operations: ['80-68=12', '57+12=69'] Exploring Operation: 94*69=6486, Resulting Numbers: [6486] 6486,82 unequal: No Solution Exploring Operation: 94+69=163, Resulting Numbers: [163] 163,82 unequal: No Solution Exploring Operation: 94-69=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[57, 106], Operations: ['80-68=12', '94+12=106'] Exploring Operation: 57*106=6042, Resulting Numbers: [6042] 6042,82 unequal: No Solution Exploring Operation: 57+106=163, Resulting Numbers: [163] 163,82 unequal: No Solution Exploring Operation: 106-57=49, Resulting Numbers: [49] 49,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[68, 57, 14], Operations: ['94-80=14'] Exploring Operation: 57+14=71, Resulting Numbers: [68, 71] Generated Node #0,3,0: 82:[68, 71] Operation: 57+14=71 Exploring Operation: 57-14=43, Resulting Numbers: [68, 43] Generated Node #0,3,1: 82:[68, 43] Operation: 57-14=43 Exploring Operation: 68-14=54, Resulting Numbers: [57, 54] Generated Node #0,3,2: 82:[57, 54] Operation: 68-14=54 Exploring Operation: 68+14=82, Resulting Numbers: [57, 82] Generated Node #0,3,3: 82:[57, 82] Operation: 68+14=82 Exploring Operation: 68-57=11, Resulting Numbers: [14, 11] Generated Node #0,3,4: 82:[14, 11] Operation: 68-57=11 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 82:[68, 43], Operations: ['94-80=14', '57-14=43'] Exploring Operation: 68*43=2924, Resulting Numbers: [2924] 2924,82 unequal: No Solution Exploring Operation: 68+43=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 68-43=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 82:[57, 82], Operations: ['94-80=14', '68+14=82'] Exploring Operation: 57+82=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 57*82=4674, Resulting Numbers: [4674] 4674,82 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 82:[14, 11], Operations: ['94-80=14', '68-57=11'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 14+11=25, Resulting Numbers: [25] 25,82 unequal: No Solution Exploring Operation: 14*11=154, Resulting Numbers: [154] 154,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 82:[68, 71], Operations: ['94-80=14', '57+14=71'] Exploring Operation: 68+71=139, Resulting Numbers: [139] 139,82 unequal: No Solution Exploring Operation: 71-68=3, Resulting Numbers: [3] 3,82 unequal: No Solution Exploring Operation: 68*71=4828, Resulting Numbers: [4828] 4828,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 82:[57, 54], Operations: ['94-80=14', '68-14=54'] Exploring Operation: 57*54=3078, Resulting Numbers: [3078] 3078,82 unequal: No Solution Exploring Operation: 57+54=111, Resulting Numbers: [111] 111,82 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,82 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_5
mult_heuristic
[ 45, 36, 51, 62 ]
33
[ "62-45=17", "51/17=3", "36-3=33" ]
Current State: 33:[45, 36, 51, 62], Operations: [] Exploring Operation: 62-45=17, Resulting Numbers: [36, 51, 17] Generated Node #2: [36, 51, 17] from Operation: 62-45=17 Current State: 33:[36, 51, 17], Operations: ['62-45=17'] Exploring Operation: 51/17=3, Resulting Numbers: [36, 3] Generated Node #3: [36, 3] from Operation: 51/17=3 Current State: 33:[36, 3], Operations: ['62-45=17', '51/17=3'] Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[45, 36, 51, 62], Operations: [] Exploring Operation: 62-51=11, Resulting Numbers: [45, 36, 11] Generated Node #0,0: 33:[45, 36, 11] Operation: 62-51=11 Moving to Node #0,0 Current State: 33:[45, 36, 11], Operations: ['62-51=11'] Exploring Operation: 45-36=9, Resulting Numbers: [11, 9] Generated Node #0,0,0: 33:[11, 9] Operation: 45-36=9 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 33:[11, 9], Operations: ['62-51=11', '45-36=9'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,33 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
[ 70, 13, 3, 76 ]
11
[ "70-3=67", "76+67=143", "143/13=11" ]
Current State: 11:[70, 13, 3, 76], Operations: [] Exploring Operation: 70-3=67, Resulting Numbers: [13, 76, 67] Generated Node #2: [13, 76, 67] from Operation: 70-3=67 Current State: 11:[13, 76, 67], Operations: ['70-3=67'] Exploring Operation: 76+67=143, Resulting Numbers: [13, 143] Generated Node #3: [13, 143] from Operation: 76+67=143 Current State: 11:[13, 143], Operations: ['70-3=67', '76+67=143'] Exploring Operation: 143/13=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[70, 13, 3, 76], Operations: [] Exploring Operation: 76-70=6, Resulting Numbers: [13, 3, 6] Generated Node #0,0: 11:[13, 3, 6] Operation: 76-70=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[13, 3, 6], Operations: ['76-70=6'] Exploring Operation: 3+6=9, Resulting Numbers: [13, 9] Generated Node #0,0,0: 11:[13, 9] Operation: 3+6=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[13, 9], Operations: ['76-70=6', '3+6=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 7, 5, 60, 18 ]
55
[ "7+18=25", "25/5=5", "60-5=55" ]
Current State: 55:[7, 5, 60, 18], Operations: [] Exploring Operation: 7+18=25, Resulting Numbers: [5, 60, 25] Generated Node #2: [5, 60, 25] from Operation: 7+18=25 Current State: 55:[5, 60, 25], Operations: ['7+18=25'] Exploring Operation: 25/5=5, Resulting Numbers: [60, 5] Generated Node #3: [60, 5] from Operation: 25/5=5 Current State: 55:[60, 5], Operations: ['7+18=25', '25/5=5'] Exploring Operation: 60-5=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[7, 5, 60, 18], Operations: [] Exploring Operation: 18-7=11, Resulting Numbers: [5, 60, 11] Generated Node #0,0: 55:[5, 60, 11] Operation: 18-7=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[5, 60, 11], Operations: ['18-7=11'] Exploring Operation: 60-5=55, Resulting Numbers: [11, 55] Generated Node #0,0,0: 55:[11, 55] Operation: 60-5=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[11, 55], Operations: ['18-7=11', '60-5=55'] Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 21, 30, 1, 66 ]
57
[ "30-21=9", "1*66=66", "66-9=57" ]
Current State: 57:[21, 30, 1, 66], Operations: [] Exploring Operation: 30-21=9, Resulting Numbers: [1, 66, 9] Generated Node #2: [1, 66, 9] from Operation: 30-21=9 Current State: 57:[1, 66, 9], Operations: ['30-21=9'] Exploring Operation: 1*66=66, Resulting Numbers: [9, 66] Generated Node #3: [9, 66] from Operation: 1*66=66 Current State: 57:[9, 66], Operations: ['30-21=9', '1*66=66'] Exploring Operation: 66-9=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[21, 30, 1, 66], Operations: [] Exploring Operation: 21-1=20, Resulting Numbers: [30, 66, 20] Generated Node #0,0: 57:[30, 66, 20] Operation: 21-1=20 Exploring Operation: 30-21=9, Resulting Numbers: [1, 66, 9] Generated Node #0,1: 57:[1, 66, 9] Operation: 30-21=9 Exploring Operation: 21+30=51, Resulting Numbers: [1, 66, 51] Generated Node #0,2: 57:[1, 66, 51] Operation: 21+30=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[1, 66, 9], Operations: ['30-21=9'] Exploring Operation: 66-1=65, Resulting Numbers: [9, 65] Generated Node #0,1,0: 57:[9, 65] Operation: 66-1=65 Exploring Operation: 9-1=8, Resulting Numbers: [66, 8] Generated Node #0,1,1: 57:[66, 8] Operation: 9-1=8 Exploring Operation: 66-9=57, Resulting Numbers: [1, 57] Generated Node #0,1,2: 57:[1, 57] Operation: 66-9=57 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 57:[1, 57], Operations: ['30-21=9', '66-9=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[21, 30, 1, 66], Operations: [] Exploring Operation: 30-21=9, Resulting Numbers: [1, 66, 9] Generated Node #0,1: 57:[1, 66, 9] Operation: 30-21=9 Moving to Node #0,1 Current State: 57:[1, 66, 9], Operations: ['30-21=9'] Exploring Operation: 66-9=57, Resulting Numbers: [1, 57] Generated Node #0,1,2: 57:[1, 57] Operation: 66-9=57 Moving to Node #0,1,2 Current State: 57:[1, 57], Operations: ['30-21=9', '66-9=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 46, 27, 35, 45 ]
61
[ "46-27=19", "35+45=80", "80-19=61" ]
Current State: 61:[46, 27, 35, 45], Operations: [] Exploring Operation: 46-27=19, Resulting Numbers: [35, 45, 19] Generated Node #2: [35, 45, 19] from Operation: 46-27=19 Current State: 61:[35, 45, 19], Operations: ['46-27=19'] Exploring Operation: 35+45=80, Resulting Numbers: [19, 80] Generated Node #3: [19, 80] from Operation: 35+45=80 Current State: 61:[19, 80], Operations: ['46-27=19', '35+45=80'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[46, 27, 35, 45], Operations: [] Exploring Operation: 27+35=62, Resulting Numbers: [46, 45, 62] Generated Node #0,0: 61:[46, 45, 62] Operation: 27+35=62 Exploring Operation: 27+45=72, Resulting Numbers: [46, 35, 72] Generated Node #0,1: 61:[46, 35, 72] Operation: 27+45=72 Exploring Operation: 46+27=73, Resulting Numbers: [35, 45, 73] Generated Node #0,2: 61:[35, 45, 73] Operation: 46+27=73 Moving to Node #0,0 Current State: 61:[46, 45, 62], Operations: ['27+35=62'] Exploring Operation: 62-45=17, Resulting Numbers: [46, 17] Generated Node #0,0,0: 61:[46, 17] Operation: 62-45=17 Exploring Operation: 46+45=91, Resulting Numbers: [62, 91] Generated Node #0,0,1: 61:[62, 91] Operation: 46+45=91 Exploring Operation: 46-45=1, Resulting Numbers: [62, 1] Generated Node #0,0,2: 61:[62, 1] Operation: 46-45=1 Moving to Node #0,1 Current State: 61:[46, 35, 72], Operations: ['27+45=72'] Exploring Operation: 72-35=37, Resulting Numbers: [46, 37] Generated Node #0,1,0: 61:[46, 37] Operation: 72-35=37 Exploring Operation: 46-35=11, Resulting Numbers: [72, 11] Generated Node #0,1,1: 61:[72, 11] Operation: 46-35=11 Exploring Operation: 46+35=81, Resulting Numbers: [72, 81] Generated Node #0,1,2: 61:[72, 81] Operation: 46+35=81 Moving to Node #0,2 Current State: 61:[35, 45, 73], Operations: ['46+27=73'] Exploring Operation: 73-35=38, Resulting Numbers: [45, 38] Generated Node #0,2,0: 61:[45, 38] Operation: 73-35=38 Exploring Operation: 35+45=80, Resulting Numbers: [73, 80] Generated Node #0,2,1: 61:[73, 80] Operation: 35+45=80 Exploring Operation: 73-45=28, Resulting Numbers: [35, 28] Generated Node #0,2,2: 61:[35, 28] Operation: 73-45=28 Moving to Node #0,0,1 Current State: 61:[62, 91], Operations: ['27+35=62', '46+45=91'] Exploring Operation: 62*91=5642, Resulting Numbers: [5642] 5642,61 unequal: No Solution Exploring Operation: 91-62=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 62+91=153, Resulting Numbers: [153] 153,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[73, 80], Operations: ['46+27=73', '35+45=80'] Exploring Operation: 73+80=153, Resulting Numbers: [153] 153,61 unequal: No Solution Exploring Operation: 80-73=7, Resulting Numbers: [7] 7,61 unequal: No Solution Exploring Operation: 73*80=5840, Resulting Numbers: [5840] 5840,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[72, 81], Operations: ['27+45=72', '46+35=81'] Exploring Operation: 81-72=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 72+81=153, Resulting Numbers: [153] 153,61 unequal: No Solution Exploring Operation: 72*81=5832, Resulting Numbers: [5832] 5832,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[46, 37], Operations: ['27+45=72', '72-35=37'] Exploring Operation: 46-37=9, Resulting Numbers: [9] 9,61 unequal: No Solution Exploring Operation: 46+37=83, Resulting Numbers: [83] 83,61 unequal: No Solution Exploring Operation: 46*37=1702, Resulting Numbers: [1702] 1702,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[45, 38], Operations: ['46+27=73', '73-35=38'] Exploring Operation: 45+38=83, Resulting Numbers: [83] 83,61 unequal: No Solution Exploring Operation: 45*38=1710, Resulting Numbers: [1710] 1710,61 unequal: No Solution Exploring Operation: 45-38=7, Resulting Numbers: [7] 7,61 unequal: No Solution Moving to Node #0,2,2 Current State: 61:[35, 28], Operations: ['46+27=73', '73-45=28'] Exploring Operation: 35*28=980, Resulting Numbers: [980] 980,61 unequal: No Solution Exploring Operation: 35+28=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[46, 17], Operations: ['27+35=62', '62-45=17'] Exploring Operation: 46*17=782, Resulting Numbers: [782] 782,61 unequal: No Solution Exploring Operation: 46-17=29, Resulting Numbers: [29] 29,61 unequal: No Solution Exploring Operation: 46+17=63, Resulting Numbers: [63] 63,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[62, 1], Operations: ['27+35=62', '46-45=1'] Exploring Operation: 62/1=62, Resulting Numbers: [62] 62,61 unequal: No Solution Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[46, 27, 35, 45], Operations: [] Exploring Operation: 27+35=62, Resulting Numbers: [46, 45, 62] Generated Node #0,0: 61:[46, 45, 62] Operation: 27+35=62 Moving to Node #0,0 Current State: 61:[46, 45, 62], Operations: ['27+35=62'] Exploring Operation: 46-45=1, Resulting Numbers: [62, 1] Generated Node #0,0,2: 61:[62, 1] Operation: 46-45=1 Moving to Node #0,0,2 Current State: 61:[62, 1], Operations: ['27+35=62', '46-45=1'] Exploring Operation: 62-1=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
0.966146
hs_3
sum_heuristic
[ 48, 35, 42, 10 ]
88
[ "48-35=13", "10*13=130", "130-42=88" ]
Current State: 88:[48, 35, 42, 10], Operations: [] Exploring Operation: 48-35=13, Resulting Numbers: [42, 10, 13] Generated Node #2: [42, 10, 13] from Operation: 48-35=13 Current State: 88:[42, 10, 13], Operations: ['48-35=13'] Exploring Operation: 10*13=130, Resulting Numbers: [42, 130] Generated Node #3: [42, 130] from Operation: 10*13=130 Current State: 88:[42, 130], Operations: ['48-35=13', '10*13=130'] Exploring Operation: 130-42=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[48, 35, 42, 10], Operations: [] Exploring Operation: 48-35=13, Resulting Numbers: [42, 10, 13] Generated Node #0,0: 88:[42, 10, 13] Operation: 48-35=13 Exploring Operation: 42-35=7, Resulting Numbers: [48, 10, 7] Generated Node #0,1: 88:[48, 10, 7] Operation: 42-35=7 Moving to Node #0,0 Current State: 88:[42, 10, 13], Operations: ['48-35=13'] Exploring Operation: 10+13=23, Resulting Numbers: [42, 23] Generated Node #0,0,0: 88:[42, 23] Operation: 10+13=23 Exploring Operation: 13-10=3, Resulting Numbers: [42, 3] Generated Node #0,0,1: 88:[42, 3] Operation: 13-10=3 Moving to Node #0,1 Current State: 88:[48, 10, 7], Operations: ['42-35=7'] Exploring Operation: 48-7=41, Resulting Numbers: [10, 41] Generated Node #0,1,0: 88:[10, 41] Operation: 48-7=41 Exploring Operation: 10-7=3, Resulting Numbers: [48, 3] Generated Node #0,1,1: 88:[48, 3] Operation: 10-7=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[10, 41], Operations: ['42-35=7', '48-7=41'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,88 unequal: No Solution Exploring Operation: 10+41=51, Resulting Numbers: [51] 51,88 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 #0,1,1 Current State: 88:[48, 3], Operations: ['42-35=7', '10-7=3'] Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,88 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: 88:[42, 23], Operations: ['48-35=13', '10+13=23'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,88 unequal: No Solution Exploring Operation: 42+23=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[42, 3], Operations: ['48-35=13', '13-10=3'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,88 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,88 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 16, 3, 4, 69 ]
97
[ "16+69=85", "3*4=12", "85+12=97" ]
Current State: 97:[16, 3, 4, 69], Operations: [] Exploring Operation: 16+69=85, Resulting Numbers: [3, 4, 85] Generated Node #2: [3, 4, 85] from Operation: 16+69=85 Current State: 97:[3, 4, 85], Operations: ['16+69=85'] Exploring Operation: 3*4=12, Resulting Numbers: [85, 12] Generated Node #3: [85, 12] from Operation: 3*4=12 Current State: 97:[85, 12], Operations: ['16+69=85', '3*4=12'] Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[16, 3, 4, 69], Operations: [] Exploring Operation: 16*4=64, Resulting Numbers: [3, 69, 64] Generated Node #0,0: 97:[3, 69, 64] Operation: 16*4=64 Moving to Node #0,0 Current State: 97:[3, 69, 64], Operations: ['16*4=64'] Exploring Operation: 3+69=72, Resulting Numbers: [64, 72] Generated Node #0,0,0: 97:[64, 72] Operation: 3+69=72 Moving to Node #0,0,0 Current State: 97:[64, 72], Operations: ['16*4=64', '3+69=72'] Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,97 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 14, 69, 86, 2 ]
29
[ "69-14=55", "86-2=84", "84-55=29" ]
Current State: 29:[14, 69, 86, 2], Operations: [] Exploring Operation: 69-14=55, Resulting Numbers: [86, 2, 55] Generated Node #2: [86, 2, 55] from Operation: 69-14=55 Current State: 29:[86, 2, 55], Operations: ['69-14=55'] Exploring Operation: 86-2=84, Resulting Numbers: [55, 84] Generated Node #3: [55, 84] from Operation: 86-2=84 Current State: 29:[55, 84], Operations: ['69-14=55', '86-2=84'] Exploring Operation: 84-55=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[14, 69, 86, 2], Operations: [] Exploring Operation: 86-69=17, Resulting Numbers: [14, 2, 17] Generated Node #0,0: 29:[14, 2, 17] Operation: 86-69=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[14, 2, 17], Operations: ['86-69=17'] Exploring Operation: 14*2=28, Resulting Numbers: [17, 28] Generated Node #0,0,0: 29:[17, 28] Operation: 14*2=28 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[17, 28], Operations: ['86-69=17', '14*2=28'] Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,29 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
[ 9, 90, 11, 75 ]
84
[ "9+90=99", "99/11=9", "75+9=84" ]
Current State: 84:[9, 90, 11, 75], Operations: [] Exploring Operation: 9+90=99, Resulting Numbers: [11, 75, 99] Generated Node #2: [11, 75, 99] from Operation: 9+90=99 Current State: 84:[11, 75, 99], Operations: ['9+90=99'] Exploring Operation: 99/11=9, Resulting Numbers: [75, 9] Generated Node #3: [75, 9] from Operation: 99/11=9 Current State: 84:[75, 9], Operations: ['9+90=99', '99/11=9'] Exploring Operation: 75+9=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[9, 90, 11, 75], Operations: [] Exploring Operation: 90-75=15, Resulting Numbers: [9, 11, 15] Generated Node #0,0: 84:[9, 11, 15] Operation: 90-75=15 Moving to Node #0,0 Current State: 84:[9, 11, 15], Operations: ['90-75=15'] Exploring Operation: 11-9=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 84:[15, 2] Operation: 11-9=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[15, 2], Operations: ['90-75=15', '11-9=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,84 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
[ 66, 46, 39, 5 ]
89
[ "66-39=27", "5*27=135", "135-46=89" ]
Current State: 89:[66, 46, 39, 5], Operations: [] Exploring Operation: 66-39=27, Resulting Numbers: [46, 5, 27] Generated Node #2: [46, 5, 27] from Operation: 66-39=27 Current State: 89:[46, 5, 27], Operations: ['66-39=27'] Exploring Operation: 5*27=135, Resulting Numbers: [46, 135] Generated Node #3: [46, 135] from Operation: 5*27=135 Current State: 89:[46, 135], Operations: ['66-39=27', '5*27=135'] Exploring Operation: 135-46=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[66, 46, 39, 5], Operations: [] Exploring Operation: 66+5=71, Resulting Numbers: [46, 39, 71] Generated Node #0,0: 89:[46, 39, 71] Operation: 66+5=71 Moving to Node #0,0 Current State: 89:[46, 39, 71], Operations: ['66+5=71'] Exploring Operation: 46+39=85, Resulting Numbers: [71, 85] Generated Node #0,0,0: 89:[71, 85] Operation: 46+39=85 Moving to Node #0,0,0 Current State: 89:[71, 85], Operations: ['66+5=71', '46+39=85'] Exploring Operation: 71+85=156, Resulting Numbers: [156] 156,89 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 87, 13, 52, 65 ]
30
[ "87-52=35", "65/13=5", "35-5=30" ]
Current State: 30:[87, 13, 52, 65], Operations: [] Exploring Operation: 87-52=35, Resulting Numbers: [13, 65, 35] Generated Node #2: [13, 65, 35] from Operation: 87-52=35 Current State: 30:[13, 65, 35], Operations: ['87-52=35'] Exploring Operation: 65/13=5, Resulting Numbers: [35, 5] Generated Node #3: [35, 5] from Operation: 65/13=5 Current State: 30:[35, 5], Operations: ['87-52=35', '65/13=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[87, 13, 52, 65], Operations: [] Exploring Operation: 87-52=35, Resulting Numbers: [13, 65, 35] Generated Node #0,0: 30:[13, 65, 35] Operation: 87-52=35 Exploring Operation: 52/13=4, Resulting Numbers: [87, 65, 4] Generated Node #0,1: 30:[87, 65, 4] Operation: 52/13=4 Exploring Operation: 65/13=5, Resulting Numbers: [87, 52, 5] Generated Node #0,2: 30:[87, 52, 5] Operation: 65/13=5 Exploring Operation: 65-52=13, Resulting Numbers: [87, 13, 13] Generated Node #0,3: 30:[87, 13, 13] Operation: 65-52=13 Exploring Operation: 87-65=22, Resulting Numbers: [13, 52, 22] Generated Node #0,4: 30:[13, 52, 22] Operation: 87-65=22 Start Sub Search at level 1: Moving to Node #0,4 Current State: 30:[13, 52, 22], Operations: ['87-65=22'] Exploring Operation: 22-13=9, Resulting Numbers: [52, 9] Generated Node #0,4,0: 30:[52, 9] Operation: 22-13=9 Exploring Operation: 13+22=35, Resulting Numbers: [52, 35] Generated Node #0,4,1: 30:[52, 35] Operation: 13+22=35 Exploring Operation: 52-13=39, Resulting Numbers: [22, 39] Generated Node #0,4,2: 30:[22, 39] Operation: 52-13=39 Exploring Operation: 52-22=30, Resulting Numbers: [13, 30] Generated Node #0,4,3: 30:[13, 30] Operation: 52-22=30 Exploring Operation: 52/13=4, Resulting Numbers: [22, 4] Generated Node #0,4,4: 30:[22, 4] Operation: 52/13=4 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 30:[13, 30], Operations: ['87-65=22', '52-22=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,30 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,30 unequal: No Solution No 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: 30:[22, 4], Operations: ['87-65=22', '52/13=4'] Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,30 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,30 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,30 unequal: No Solution No 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: 30:[22, 39], Operations: ['87-65=22', '52-13=39'] Exploring Operation: 22*39=858, Resulting Numbers: [858] 858,30 unequal: No Solution Exploring Operation: 39-22=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 22+39=61, Resulting Numbers: [61] 61,30 unequal: No Solution No 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: 30:[52, 9], Operations: ['87-65=22', '22-13=9'] Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,30 unequal: No Solution Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 30:[52, 35], Operations: ['87-65=22', '13+22=35'] Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 52*35=1820, Resulting Numbers: [1820] 1820,30 unequal: No Solution Exploring Operation: 52+35=87, Resulting Numbers: [87] 87,30 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: 30:[13, 65, 35], Operations: ['87-52=35'] Exploring Operation: 65/13=5, Resulting Numbers: [35, 5] Generated Node #0,0,0: 30:[35, 5] Operation: 65/13=5 Exploring Operation: 65-13=52, Resulting Numbers: [35, 52] Generated Node #0,0,1: 30:[35, 52] Operation: 65-13=52 Exploring Operation: 65-35=30, Resulting Numbers: [13, 30] Generated Node #0,0,2: 30:[13, 30] Operation: 65-35=30 Exploring Operation: 13+65=78, Resulting Numbers: [35, 78] Generated Node #0,0,3: 30:[35, 78] Operation: 13+65=78 Exploring Operation: 35-13=22, Resulting Numbers: [65, 22] Generated Node #0,0,4: 30:[65, 22] Operation: 35-13=22 Moving to Node #0,0,2 Current State: 30:[13, 30], Operations: ['87-52=35', '65-35=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[35, 5], Operations: ['87-52=35', '65/13=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[87, 13, 52, 65], Operations: [] Exploring Operation: 87-52=35, Resulting Numbers: [13, 65, 35] Generated Node #0,0: 30:[13, 65, 35] Operation: 87-52=35 Moving to Node #0,0 Current State: 30:[13, 65, 35], Operations: ['87-52=35'] Exploring Operation: 65/13=5, Resulting Numbers: [35, 5] Generated Node #0,0,0: 30:[35, 5] Operation: 65/13=5 Moving to Node #0,0,0 Current State: 30:[35, 5], Operations: ['87-52=35', '65/13=5'] Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 23, 39, 24, 11 ]
50
[ "24-23=1", "39+11=50", "1*50=50" ]
Current State: 50:[23, 39, 24, 11], Operations: [] Exploring Operation: 24-23=1, Resulting Numbers: [39, 11, 1] Generated Node #2: [39, 11, 1] from Operation: 24-23=1 Current State: 50:[39, 11, 1], Operations: ['24-23=1'] Exploring Operation: 39+11=50, Resulting Numbers: [1, 50] Generated Node #3: [1, 50] from Operation: 39+11=50 Current State: 50:[1, 50], Operations: ['24-23=1', '39+11=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[23, 39, 24, 11], Operations: [] Exploring Operation: 39+11=50, Resulting Numbers: [23, 24, 50] Generated Node #0,0: 50:[23, 24, 50] Operation: 39+11=50 Exploring Operation: 39-11=28, Resulting Numbers: [23, 24, 28] Generated Node #0,1: 50:[23, 24, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[23, 24, 50], Operations: ['39+11=50'] Exploring Operation: 24-23=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 50:[50, 1] Operation: 24-23=1 Exploring Operation: 23+24=47, Resulting Numbers: [50, 47] Generated Node #0,0,1: 50:[50, 47] Operation: 23+24=47 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[50, 1], Operations: ['39+11=50', '24-23=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[23, 39, 24, 11], Operations: [] Exploring Operation: 39+11=50, Resulting Numbers: [23, 24, 50] Generated Node #0,0: 50:[23, 24, 50] Operation: 39+11=50 Moving to Node #0,0 Current State: 50:[23, 24, 50], Operations: ['39+11=50'] Exploring Operation: 24-23=1, Resulting Numbers: [50, 1] Generated Node #0,0,0: 50:[50, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 50:[50, 1], Operations: ['39+11=50', '24-23=1'] Exploring Operation: 50*1=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 3, 73, 40, 44 ]
79
[ "73+44=117", "117/3=39", "40+39=79" ]
Current State: 79:[3, 73, 40, 44], Operations: [] Exploring Operation: 73+44=117, Resulting Numbers: [3, 40, 117] Generated Node #2: [3, 40, 117] from Operation: 73+44=117 Current State: 79:[3, 40, 117], Operations: ['73+44=117'] Exploring Operation: 117/3=39, Resulting Numbers: [40, 39] Generated Node #3: [40, 39] from Operation: 117/3=39 Current State: 79:[40, 39], Operations: ['73+44=117', '117/3=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[3, 73, 40, 44], Operations: [] Exploring Operation: 3+73=76, Resulting Numbers: [40, 44, 76] Generated Node #0,0: 79:[40, 44, 76] Operation: 3+73=76 Exploring Operation: 3+44=47, Resulting Numbers: [73, 40, 47] Generated Node #0,1: 79:[73, 40, 47] Operation: 3+44=47 Exploring Operation: 3+40=43, Resulting Numbers: [73, 44, 43] Generated Node #0,2: 79:[73, 44, 43] Operation: 3+40=43 Exploring Operation: 3*40=120, Resulting Numbers: [73, 44, 120] Generated Node #0,3: 79:[73, 44, 120] Operation: 3*40=120 Moving to Node #0,0 Current State: 79:[40, 44, 76], Operations: ['3+73=76'] Exploring Operation: 40+76=116, Resulting Numbers: [44, 116] Generated Node #0,0,0: 79:[44, 116] Operation: 40+76=116 Exploring Operation: 44-40=4, Resulting Numbers: [76, 4] Generated Node #0,0,1: 79:[76, 4] Operation: 44-40=4 Exploring Operation: 40+44=84, Resulting Numbers: [76, 84] Generated Node #0,0,2: 79:[76, 84] Operation: 40+44=84 Exploring Operation: 76-40=36, Resulting Numbers: [44, 36] Generated Node #0,0,3: 79:[44, 36] Operation: 76-40=36 Moving to Node #0,2 Current State: 79:[73, 44, 43], Operations: ['3+40=43'] Exploring Operation: 44+43=87, Resulting Numbers: [73, 87] Generated Node #0,2,0: 79:[73, 87] Operation: 44+43=87 Exploring Operation: 73-43=30, Resulting Numbers: [44, 30] Generated Node #0,2,1: 79:[44, 30] Operation: 73-43=30 Exploring Operation: 73+43=116, Resulting Numbers: [44, 116] Generated Node #0,2,2: 79:[44, 116] Operation: 73+43=116 Exploring Operation: 73+44=117, Resulting Numbers: [43, 117] Generated Node #0,2,3: 79:[43, 117] Operation: 73+44=117 Moving to Node #0,1 Current State: 79:[73, 40, 47], Operations: ['3+44=47'] Exploring Operation: 73-40=33, Resulting Numbers: [47, 33] Generated Node #0,1,0: 79:[47, 33] Operation: 73-40=33 Exploring Operation: 40+47=87, Resulting Numbers: [73, 87] Generated Node #0,1,1: 79:[73, 87] Operation: 40+47=87 Exploring Operation: 73+40=113, Resulting Numbers: [47, 113] Generated Node #0,1,2: 79:[47, 113] Operation: 73+40=113 Exploring Operation: 47-40=7, Resulting Numbers: [73, 7] Generated Node #0,1,3: 79:[73, 7] Operation: 47-40=7 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[73, 87], Operations: ['3+44=47', '40+47=87'] Exploring Operation: 73*87=6351, Resulting Numbers: [6351] 6351,79 unequal: No Solution Exploring Operation: 73+87=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 87-73=14, Resulting Numbers: [14] 14,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[47, 113], Operations: ['3+44=47', '73+40=113'] Exploring Operation: 47+113=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 113-47=66, Resulting Numbers: [66] 66,79 unequal: No Solution Exploring Operation: 47*113=5311, Resulting Numbers: [5311] 5311,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[47, 33], Operations: ['3+44=47', '73-40=33'] Exploring Operation: 47+33=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 47*33=1551, Resulting Numbers: [1551] 1551,79 unequal: No Solution Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[73, 7], Operations: ['3+44=47', '47-40=7'] Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,79 unequal: No Solution Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 73*7=511, Resulting Numbers: [511] 511,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 79:[73, 44, 120], Operations: ['3*40=120'] Exploring Operation: 73-44=29, Resulting Numbers: [120, 29] Generated Node #0,3,0: 79:[120, 29] Operation: 73-44=29 Exploring Operation: 120-44=76, Resulting Numbers: [73, 76] Generated Node #0,3,1: 79:[73, 76] Operation: 120-44=76 Exploring Operation: 73+44=117, Resulting Numbers: [120, 117] Generated Node #0,3,2: 79:[120, 117] Operation: 73+44=117 Exploring Operation: 120-73=47, Resulting Numbers: [44, 47] Generated Node #0,3,3: 79:[44, 47] Operation: 120-73=47 Moving to Node #0,0,2 Current State: 79:[76, 84], Operations: ['3+73=76', '40+44=84'] Exploring Operation: 84-76=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 76+84=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 76*84=6384, Resulting Numbers: [6384] 6384,79 unequal: No Solution Moving to Node #0,3,1 Current State: 79:[73, 76], Operations: ['3*40=120', '120-44=76'] Exploring Operation: 73*76=5548, Resulting Numbers: [5548] 5548,79 unequal: No Solution Exploring Operation: 73+76=149, Resulting Numbers: [149] 149,79 unequal: No Solution Exploring Operation: 76-73=3, Resulting Numbers: [3] 3,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[73, 87], Operations: ['3+40=43', '44+43=87'] Exploring Operation: 73*87=6351, Resulting Numbers: [6351] 6351,79 unequal: No Solution Exploring Operation: 87-73=14, Resulting Numbers: [14] 14,79 unequal: No Solution Exploring Operation: 73+87=160, Resulting Numbers: [160] 160,79 unequal: No Solution Moving to Node #0,3,3 Current State: 79:[44, 47], Operations: ['3*40=120', '120-73=47'] Exploring Operation: 44+47=91, Resulting Numbers: [91] 91,79 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 44*47=2068, Resulting Numbers: [2068] 2068,79 unequal: No Solution Moving to Node #0,2,2 Current State: 79:[44, 116], Operations: ['3+40=43', '73+43=116'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,79 unequal: No Solution Exploring Operation: 44+116=160, Resulting Numbers: [160] 160,79 unequal: No Solution Exploring Operation: 44*116=5104, Resulting Numbers: [5104] 5104,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[44, 116], Operations: ['3+73=76', '40+76=116'] Exploring Operation: 116-44=72, Resulting Numbers: [72] 72,79 unequal: No Solution Exploring Operation: 44*116=5104, Resulting Numbers: [5104] 5104,79 unequal: No Solution Exploring Operation: 44+116=160, Resulting Numbers: [160] 160,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[43, 117], Operations: ['3+40=43', '73+44=117'] Exploring Operation: 117-43=74, Resulting Numbers: [74] 74,79 unequal: No Solution Exploring Operation: 43*117=5031, Resulting Numbers: [5031] 5031,79 unequal: No Solution Exploring Operation: 43+117=160, Resulting Numbers: [160] 160,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[76, 4], Operations: ['3+73=76', '44-40=4'] Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,79 unequal: No Solution Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,79 unequal: No Solution Exploring Operation: 76+4=80, Resulting Numbers: [80] 80,79 unequal: No Solution Exploring Operation: 76*4=304, Resulting Numbers: [304] 304,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[44, 36], Operations: ['3+73=76', '76-40=36'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,79 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,79 unequal: No Solution Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[120, 117], Operations: ['3*40=120', '73+44=117'] Exploring Operation: 120*117=14040, Resulting Numbers: [14040] 14040,79 unequal: No Solution Exploring Operation: 120+117=237, Resulting Numbers: [237] 237,79 unequal: No Solution Exploring Operation: 120-117=3, Resulting Numbers: [3] 3,79 unequal: No Solution Moving to Node #0,2,1 Current State: 79:[44, 30], Operations: ['3+40=43', '73-43=30'] Exploring Operation: 44*30=1320, Resulting Numbers: [1320] 1320,79 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,79 unequal: No Solution Exploring Operation: 44+30=74, Resulting Numbers: [74] 74,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[120, 29], Operations: ['3*40=120', '73-44=29'] Exploring Operation: 120+29=149, Resulting Numbers: [149] 149,79 unequal: No Solution Exploring Operation: 120*29=3480, Resulting Numbers: [3480] 3480,79 unequal: No Solution Exploring Operation: 120-29=91, Resulting Numbers: [91] 91,79 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 67, 94, 99, 93 ]
32
[ "99-67=32", "94-93=1", "32*1=32" ]
Current State: 32:[67, 94, 99, 93], Operations: [] Exploring Operation: 99-67=32, Resulting Numbers: [94, 93, 32] Generated Node #2: [94, 93, 32] from Operation: 99-67=32 Current State: 32:[94, 93, 32], Operations: ['99-67=32'] Exploring Operation: 94-93=1, Resulting Numbers: [32, 1] Generated Node #3: [32, 1] from Operation: 94-93=1 Current State: 32:[32, 1], Operations: ['99-67=32', '94-93=1'] Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[67, 94, 99, 93], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [67, 93, 5] Generated Node #0,0: 32:[67, 93, 5] Operation: 99-94=5 Exploring Operation: 94-93=1, Resulting Numbers: [67, 99, 1] Generated Node #0,1: 32:[67, 99, 1] Operation: 94-93=1 Exploring Operation: 99-93=6, Resulting Numbers: [67, 94, 6] Generated Node #0,2: 32:[67, 94, 6] Operation: 99-93=6 Exploring Operation: 94-67=27, Resulting Numbers: [99, 93, 27] Generated Node #0,3: 32:[99, 93, 27] Operation: 94-67=27 Exploring Operation: 99-67=32, Resulting Numbers: [94, 93, 32] Generated Node #0,4: 32:[94, 93, 32] Operation: 99-67=32 Moving to Node #0,0 Current State: 32:[67, 93, 5], Operations: ['99-94=5'] Exploring Operation: 93+5=98, Resulting Numbers: [67, 98] Generated Node #0,0,0: 32:[67, 98] Operation: 93+5=98 Exploring Operation: 67+5=72, Resulting Numbers: [93, 72] Generated Node #0,0,1: 32:[93, 72] Operation: 67+5=72 Exploring Operation: 93-67=26, Resulting Numbers: [5, 26] Generated Node #0,0,2: 32:[5, 26] Operation: 93-67=26 Exploring Operation: 93-5=88, Resulting Numbers: [67, 88] Generated Node #0,0,3: 32:[67, 88] Operation: 93-5=88 Exploring Operation: 67-5=62, Resulting Numbers: [93, 62] Generated Node #0,0,4: 32:[93, 62] Operation: 67-5=62 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[5, 26], Operations: ['99-94=5', '93-67=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[67, 88], Operations: ['99-94=5', '93-5=88'] Exploring Operation: 88-67=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 67+88=155, Resulting Numbers: [155] 155,32 unequal: No Solution Exploring Operation: 67*88=5896, Resulting Numbers: [5896] 5896,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 32:[93, 62], Operations: ['99-94=5', '67-5=62'] Exploring Operation: 93*62=5766, Resulting Numbers: [5766] 5766,32 unequal: No Solution Exploring Operation: 93-62=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 93+62=155, Resulting Numbers: [155] 155,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[67, 98], Operations: ['99-94=5', '93+5=98'] Exploring Operation: 98-67=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 67+98=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 67*98=6566, Resulting Numbers: [6566] 6566,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[93, 72], Operations: ['99-94=5', '67+5=72'] Exploring Operation: 93*72=6696, Resulting Numbers: [6696] 6696,32 unequal: No Solution Exploring Operation: 93+72=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 93-72=21, Resulting Numbers: [21] 21,32 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: 32:[67, 94, 6], Operations: ['99-93=6'] Exploring Operation: 94-67=27, Resulting Numbers: [6, 27] Generated Node #0,2,0: 32:[6, 27] Operation: 94-67=27 Exploring Operation: 67-6=61, Resulting Numbers: [94, 61] Generated Node #0,2,1: 32:[94, 61] Operation: 67-6=61 Exploring Operation: 94-6=88, Resulting Numbers: [67, 88] Generated Node #0,2,2: 32:[67, 88] Operation: 94-6=88 Exploring Operation: 94+6=100, Resulting Numbers: [67, 100] Generated Node #0,2,3: 32:[67, 100] Operation: 94+6=100 Exploring Operation: 67+6=73, Resulting Numbers: [94, 73] Generated Node #0,2,4: 32:[94, 73] Operation: 67+6=73 Moving to Node #0,1 Current State: 32:[67, 99, 1], Operations: ['94-93=1'] Exploring Operation: 67/1=67, Resulting Numbers: [99, 67] Generated Node #0,1,0: 32:[99, 67] Operation: 67/1=67 Exploring Operation: 99-67=32, Resulting Numbers: [1, 32] Generated Node #0,1,1: 32:[1, 32] Operation: 99-67=32 Exploring Operation: 67*1=67, Resulting Numbers: [99, 67] Generated Node #0,1,2: 32:[99, 67] Operation: 67*1=67 Exploring Operation: 67-1=66, Resulting Numbers: [99, 66] Generated Node #0,1,3: 32:[99, 66] Operation: 67-1=66 Exploring Operation: 99-1=98, Resulting Numbers: [67, 98] Generated Node #0,1,4: 32:[67, 98] Operation: 99-1=98 Moving to Node #0,4 Current State: 32:[94, 93, 32], Operations: ['99-67=32'] Exploring Operation: 94-32=62, Resulting Numbers: [93, 62] Generated Node #0,4,0: 32:[93, 62] Operation: 94-32=62 Exploring Operation: 94-93=1, Resulting Numbers: [32, 1] Generated Node #0,4,1: 32:[32, 1] Operation: 94-93=1 Exploring Operation: 94+32=126, Resulting Numbers: [93, 126] Generated Node #0,4,2: 32:[93, 126] Operation: 94+32=126 Exploring Operation: 94+93=187, Resulting Numbers: [32, 187] Generated Node #0,4,3: 32:[32, 187] Operation: 94+93=187 Exploring Operation: 93-32=61, Resulting Numbers: [94, 61] Generated Node #0,4,4: 32:[94, 61] Operation: 93-32=61 Moving to Node #0,3 Current State: 32:[99, 93, 27], Operations: ['94-67=27'] Exploring Operation: 99-93=6, Resulting Numbers: [27, 6] Generated Node #0,3,0: 32:[27, 6] Operation: 99-93=6 Exploring Operation: 93-27=66, Resulting Numbers: [99, 66] Generated Node #0,3,1: 32:[99, 66] Operation: 93-27=66 Exploring Operation: 93+27=120, Resulting Numbers: [99, 120] Generated Node #0,3,2: 32:[99, 120] Operation: 93+27=120 Exploring Operation: 99-27=72, Resulting Numbers: [93, 72] Generated Node #0,3,3: 32:[93, 72] Operation: 99-27=72 Exploring Operation: 99+27=126, Resulting Numbers: [93, 126] Generated Node #0,3,4: 32:[93, 126] Operation: 99+27=126 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 32:[27, 6], Operations: ['94-67=27', '99-93=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,32 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,32 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 #0,3,1 Current State: 32:[99, 66], Operations: ['94-67=27', '93-27=66'] Exploring Operation: 99-66=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 99*66=6534, Resulting Numbers: [6534] 6534,32 unequal: No Solution Exploring Operation: 99+66=165, Resulting Numbers: [165] 165,32 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 #0,3,3 Current State: 32:[93, 72], Operations: ['94-67=27', '99-27=72'] Exploring Operation: 93+72=165, Resulting Numbers: [165] 165,32 unequal: No Solution Exploring Operation: 93*72=6696, Resulting Numbers: [6696] 6696,32 unequal: No Solution Exploring Operation: 93-72=21, Resulting Numbers: [21] 21,32 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 #0,3,2 Current State: 32:[99, 120], Operations: ['94-67=27', '93+27=120'] Exploring Operation: 99+120=219, Resulting Numbers: [219] 219,32 unequal: No Solution Exploring Operation: 120-99=21, Resulting Numbers: [21] 21,32 unequal: No Solution Exploring Operation: 99*120=11880, Resulting Numbers: [11880] 11880,32 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 #0,3,4 Current State: 32:[93, 126], Operations: ['94-67=27', '99+27=126'] Exploring Operation: 93*126=11718, Resulting Numbers: [11718] 11718,32 unequal: No Solution Exploring Operation: 93+126=219, Resulting Numbers: [219] 219,32 unequal: No Solution Exploring Operation: 126-93=33, Resulting Numbers: [33] 33,32 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: 32:[1, 32], Operations: ['94-93=1', '99-67=32'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,32 unequal: No Solution Exploring Operation: 1+32=33, Resulting Numbers: [33] 33,32 unequal: No Solution Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[67, 94, 99, 93], Operations: [] Exploring Operation: 94-93=1, Resulting Numbers: [67, 99, 1] Generated Node #0,1: 32:[67, 99, 1] Operation: 94-93=1 Moving to Node #0,1 Current State: 32:[67, 99, 1], Operations: ['94-93=1'] Exploring Operation: 99-67=32, Resulting Numbers: [1, 32] Generated Node #0,1,1: 32:[1, 32] Operation: 99-67=32 Moving to Node #0,1,1 Current State: 32:[1, 32], Operations: ['94-93=1', '99-67=32'] Exploring Operation: 32/1=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.94184
hs_5
mult_heuristic
[ 14, 98, 69, 1 ]
61
[ "98/14=7", "69-1=68", "68-7=61" ]
Current State: 61:[14, 98, 69, 1], Operations: [] Exploring Operation: 98/14=7, Resulting Numbers: [69, 1, 7] Generated Node #2: [69, 1, 7] from Operation: 98/14=7 Current State: 61:[69, 1, 7], Operations: ['98/14=7'] Exploring Operation: 69-1=68, Resulting Numbers: [7, 68] Generated Node #3: [7, 68] from Operation: 69-1=68 Current State: 61:[7, 68], Operations: ['98/14=7', '69-1=68'] Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[14, 98, 69, 1], Operations: [] Exploring Operation: 14+1=15, Resulting Numbers: [98, 69, 15] Generated Node #0,0: 61:[98, 69, 15] Operation: 14+1=15 Exploring Operation: 98-14=84, Resulting Numbers: [69, 1, 84] Generated Node #0,1: 61:[69, 1, 84] Operation: 98-14=84 Moving to Node #0,0 Current State: 61:[98, 69, 15], Operations: ['14+1=15'] Exploring Operation: 69-15=54, Resulting Numbers: [98, 54] Generated Node #0,0,0: 61:[98, 54] Operation: 69-15=54 Exploring Operation: 98-15=83, Resulting Numbers: [69, 83] Generated Node #0,0,1: 61:[69, 83] Operation: 98-15=83 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[69, 83], Operations: ['14+1=15', '98-15=83'] Exploring Operation: 69+83=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,61 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:[98, 54], Operations: ['14+1=15', '69-15=54'] Exploring Operation: 98-54=44, Resulting Numbers: [44] 44,61 unequal: No Solution Exploring Operation: 98+54=152, Resulting Numbers: [152] 152,61 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:[69, 1, 84], Operations: ['98-14=84'] Exploring Operation: 69-1=68, Resulting Numbers: [84, 68] Generated Node #0,1,0: 61:[84, 68] Operation: 69-1=68 Exploring Operation: 84-1=83, Resulting Numbers: [69, 83] Generated Node #0,1,1: 61:[69, 83] Operation: 84-1=83 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 61:[84, 68], Operations: ['98-14=84', '69-1=68'] Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,61 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 61:[69, 83], Operations: ['98-14=84', '84-1=83'] Exploring Operation: 83-69=14, Resulting Numbers: [14] 14,61 unequal: No Solution Exploring Operation: 69+83=152, Resulting Numbers: [152] 152,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 83, 24, 56, 59 ]
62
[ "83-24=59", "59-56=3", "59+3=62" ]
Current State: 62:[83, 24, 56, 59], Operations: [] Exploring Operation: 83-24=59, Resulting Numbers: [56, 59, 59] Generated Node #2: [56, 59, 59] from Operation: 83-24=59 Current State: 62:[56, 59, 59], Operations: ['83-24=59'] Exploring Operation: 59-56=3, Resulting Numbers: [3] 3,62 equal: Goal Reached Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[83, 24, 56, 59], Operations: [] Exploring Operation: 83-56=27, Resulting Numbers: [24, 59, 27] Generated Node #0,0: 62:[24, 59, 27] Operation: 83-56=27 Exploring Operation: 56-24=32, Resulting Numbers: [83, 59, 32] Generated Node #0,1: 62:[83, 59, 32] Operation: 56-24=32 Exploring Operation: 83-59=24, Resulting Numbers: [24, 56, 24] Generated Node #0,2: 62:[24, 56, 24] Operation: 83-59=24 Exploring Operation: 83-24=59, Resulting Numbers: [56, 59, 59] Generated Node #0,3: 62:[56, 59, 59] Operation: 83-24=59 Moving to Node #0,3 Current State: 62:[56, 59, 59], Operations: ['83-24=59'] Exploring Operation: 59-56=3, Resulting Numbers: [59, 3] Generated Node #0,3,0: 62:[59, 3] Operation: 59-56=3 Exploring Operation: 59/59=1, Resulting Numbers: [56, 1] Generated Node #0,3,1: 62:[56, 1] Operation: 59/59=1 Exploring Operation: 59-56=3, Resulting Numbers: [59, 3] Generated Node #0,3,2: 62:[59, 3] Operation: 59-56=3 Exploring Operation: 59-59=0, Resulting Numbers: [56, 0] Generated Node #0,3,3: 62:[56, 0] Operation: 59-59=0 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 62:[59, 3], Operations: ['83-24=59', '59-56=3'] Exploring Operation: 59*3=177, Resulting Numbers: [177] 177,62 unequal: No Solution Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[83, 24, 56, 59], Operations: [] Exploring Operation: 83-24=59, Resulting Numbers: [56, 59, 59] Generated Node #0,3: 62:[56, 59, 59] Operation: 83-24=59 Moving to Node #0,3 Current State: 62:[56, 59, 59], Operations: ['83-24=59'] Exploring Operation: 59-56=3, Resulting Numbers: [59, 3] Generated Node #0,3,0: 62:[59, 3] Operation: 59-56=3 Moving to Node #0,3,0 Current State: 62:[59, 3], Operations: ['83-24=59', '59-56=3'] Exploring Operation: 59+3=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 15, 76, 25, 5 ]
79
[ "15*5=75", "75/25=3", "76+3=79" ]
Current State: 79:[15, 76, 25, 5], Operations: [] Exploring Operation: 15*5=75, Resulting Numbers: [76, 25, 75] Generated Node #2: [76, 25, 75] from Operation: 15*5=75 Current State: 79:[76, 25, 75], Operations: ['15*5=75'] Exploring Operation: 75/25=3, Resulting Numbers: [76, 3] Generated Node #3: [76, 3] from Operation: 75/25=3 Current State: 79:[76, 3], Operations: ['15*5=75', '75/25=3'] Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[15, 76, 25, 5], Operations: [] Exploring Operation: 15+25=40, Resulting Numbers: [76, 5, 40] Generated Node #0,0: 79:[76, 5, 40] Operation: 15+25=40 Exploring Operation: 15+5=20, Resulting Numbers: [76, 25, 20] Generated Node #0,1: 79:[76, 25, 20] Operation: 15+5=20 Exploring Operation: 25*5=125, Resulting Numbers: [15, 76, 125] Generated Node #0,2: 79:[15, 76, 125] Operation: 25*5=125 Exploring Operation: 15*5=75, Resulting Numbers: [76, 25, 75] Generated Node #0,3: 79:[76, 25, 75] Operation: 15*5=75 Moving to Node #0,3 Current State: 79:[76, 25, 75], Operations: ['15*5=75'] Exploring Operation: 76-25=51, Resulting Numbers: [75, 51] Generated Node #0,3,0: 79:[75, 51] Operation: 76-25=51 Exploring Operation: 76+25=101, Resulting Numbers: [75, 101] Generated Node #0,3,1: 79:[75, 101] Operation: 76+25=101 Exploring Operation: 75-25=50, Resulting Numbers: [76, 50] Generated Node #0,3,2: 79:[76, 50] Operation: 75-25=50 Exploring Operation: 25+75=100, Resulting Numbers: [76, 100] Generated Node #0,3,3: 79:[76, 100] Operation: 25+75=100 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 79:[76, 100], Operations: ['15*5=75', '25+75=100'] Exploring Operation: 76+100=176, Resulting Numbers: [176] 176,79 unequal: No Solution Exploring Operation: 76*100=7600, Resulting Numbers: [7600] 7600,79 unequal: No Solution Exploring Operation: 100-76=24, Resulting Numbers: [24] 24,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 79:[75, 101], Operations: ['15*5=75', '76+25=101'] Exploring Operation: 75+101=176, Resulting Numbers: [176] 176,79 unequal: No Solution Exploring Operation: 101-75=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 75*101=7575, Resulting Numbers: [7575] 7575,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 79:[75, 51], Operations: ['15*5=75', '76-25=51'] Exploring Operation: 75+51=126, Resulting Numbers: [126] 126,79 unequal: No Solution Exploring Operation: 75*51=3825, Resulting Numbers: [3825] 3825,79 unequal: No Solution Exploring Operation: 75-51=24, Resulting Numbers: [24] 24,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 79:[76, 50], Operations: ['15*5=75', '75-25=50'] Exploring Operation: 76-50=26, Resulting Numbers: [26] 26,79 unequal: No Solution Exploring Operation: 76*50=3800, Resulting Numbers: [3800] 3800,79 unequal: No Solution Exploring Operation: 76+50=126, Resulting Numbers: [126] 126,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 79:[15, 76, 125], Operations: ['25*5=125'] Exploring Operation: 15+125=140, Resulting Numbers: [76, 140] Generated Node #0,2,0: 79:[76, 140] Operation: 15+125=140 Exploring Operation: 76-15=61, Resulting Numbers: [125, 61] Generated Node #0,2,1: 79:[125, 61] Operation: 76-15=61 Exploring Operation: 125-15=110, Resulting Numbers: [76, 110] Generated Node #0,2,2: 79:[76, 110] Operation: 125-15=110 Exploring Operation: 15+76=91, Resulting Numbers: [125, 91] Generated Node #0,2,3: 79:[125, 91] Operation: 15+76=91 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[76, 110], Operations: ['25*5=125', '125-15=110'] Exploring Operation: 110-76=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 76+110=186, Resulting Numbers: [186] 186,79 unequal: No Solution Exploring Operation: 76*110=8360, Resulting Numbers: [8360] 8360,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 79:[125, 91], Operations: ['25*5=125', '15+76=91'] Exploring Operation: 125*91=11375, Resulting Numbers: [11375] 11375,79 unequal: No Solution Exploring Operation: 125-91=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 125+91=216, Resulting Numbers: [216] 216,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[76, 140], Operations: ['25*5=125', '15+125=140'] Exploring Operation: 76+140=216, Resulting Numbers: [216] 216,79 unequal: No Solution Exploring Operation: 140-76=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 76*140=10640, Resulting Numbers: [10640] 10640,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[125, 61], Operations: ['25*5=125', '76-15=61'] Exploring Operation: 125+61=186, Resulting Numbers: [186] 186,79 unequal: No Solution Exploring Operation: 125-61=64, Resulting Numbers: [64] 64,79 unequal: No Solution Exploring Operation: 125*61=7625, Resulting Numbers: [7625] 7625,79 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: 79:[76, 25, 20], Operations: ['15+5=20'] Exploring Operation: 76-20=56, Resulting Numbers: [25, 56] Generated Node #0,1,0: 79:[25, 56] Operation: 76-20=56 Exploring Operation: 25-20=5, Resulting Numbers: [76, 5] Generated Node #0,1,1: 79:[76, 5] Operation: 25-20=5 Exploring Operation: 25+20=45, Resulting Numbers: [76, 45] Generated Node #0,1,2: 79:[76, 45] Operation: 25+20=45 Exploring Operation: 76+20=96, Resulting Numbers: [25, 96] Generated Node #0,1,3: 79:[25, 96] Operation: 76+20=96 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[76, 45], Operations: ['15+5=20', '25+20=45'] Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,79 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 79:[25, 96], Operations: ['15+5=20', '76+20=96'] Exploring Operation: 25*96=2400, Resulting Numbers: [2400] 2400,79 unequal: No Solution Exploring Operation: 25+96=121, Resulting Numbers: [121] 121,79 unequal: No Solution Exploring Operation: 96-25=71, Resulting Numbers: [71] 71,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[25, 56], Operations: ['15+5=20', '76-20=56'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,79 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[76, 5], Operations: ['15+5=20', '25-20=5'] Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,79 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,79 unequal: No Solution Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 79:[76, 5, 40], Operations: ['15+25=40'] Exploring Operation: 40-5=35, Resulting Numbers: [76, 35] Generated Node #0,0,0: 79:[76, 35] Operation: 40-5=35 Exploring Operation: 5+40=45, Resulting Numbers: [76, 45] Generated Node #0,0,1: 79:[76, 45] Operation: 5+40=45 Exploring Operation: 76-5=71, Resulting Numbers: [40, 71] Generated Node #0,0,2: 79:[40, 71] Operation: 76-5=71 Exploring Operation: 76+5=81, Resulting Numbers: [40, 81] Generated Node #0,0,3: 79:[40, 81] Operation: 76+5=81 Moving to Node #0,0,1 Current State: 79:[76, 45], Operations: ['15+25=40', '5+40=45'] Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,79 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,79 unequal: No Solution Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[40, 81], Operations: ['15+25=40', '76+5=81'] Exploring Operation: 40*81=3240, Resulting Numbers: [3240] 3240,79 unequal: No Solution Exploring Operation: 40+81=121, Resulting Numbers: [121] 121,79 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,79 unequal: No Solution Moving to Node #0,0,2 Current State: 79:[40, 71], Operations: ['15+25=40', '76-5=71'] Exploring Operation: 40*71=2840, Resulting Numbers: [2840] 2840,79 unequal: No Solution Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 40+71=111, Resulting Numbers: [111] 111,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[76, 35], Operations: ['15+25=40', '40-5=35'] Exploring Operation: 76-35=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 76*35=2660, Resulting Numbers: [2660] 2660,79 unequal: No Solution Exploring Operation: 76+35=111, Resulting Numbers: [111] 111,79 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 35, 35, 32, 56 ]
89
[ "35/35=1", "32+56=88", "1+88=89" ]
Current State: 89:[35, 35, 32, 56], Operations: [] Exploring Operation: 35/35=1, Resulting Numbers: [32, 56, 1] Generated Node #2: [32, 56, 1] from Operation: 35/35=1 Current State: 89:[32, 56, 1], Operations: ['35/35=1'] Exploring Operation: 32+56=88, Resulting Numbers: [1, 88] Generated Node #3: [1, 88] from Operation: 32+56=88 Current State: 89:[1, 88], Operations: ['35/35=1', '32+56=88'] Exploring Operation: 1+88=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[35, 35, 32, 56], Operations: [] Exploring Operation: 35+32=67, Resulting Numbers: [35, 56, 67] Generated Node #0,0: 89:[35, 56, 67] Operation: 35+32=67 Exploring Operation: 35+32=67, Resulting Numbers: [35, 56, 67] Generated Node #0,1: 89:[35, 56, 67] Operation: 35+32=67 Exploring Operation: 35+35=70, Resulting Numbers: [32, 56, 70] Generated Node #0,2: 89:[32, 56, 70] Operation: 35+35=70 Start Sub Search at level 1: Moving to Node #0,0 Current State: 89:[35, 56, 67], Operations: ['35+32=67'] Exploring Operation: 56+67=123, Resulting Numbers: [35, 123] Generated Node #0,0,0: 89:[35, 123] Operation: 56+67=123 Exploring Operation: 35+67=102, Resulting Numbers: [56, 102] Generated Node #0,0,1: 89:[56, 102] Operation: 35+67=102 Exploring Operation: 35+56=91, Resulting Numbers: [67, 91] Generated Node #0,0,2: 89:[67, 91] Operation: 35+56=91 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 89:[67, 91], Operations: ['35+32=67', '35+56=91'] Exploring Operation: 67+91=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 67*91=6097, Resulting Numbers: [6097] 6097,89 unequal: No Solution Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 89:[56, 102], Operations: ['35+32=67', '35+67=102'] Exploring Operation: 56*102=5712, Resulting Numbers: [5712] 5712,89 unequal: No Solution Exploring Operation: 102-56=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 56+102=158, Resulting Numbers: [158] 158,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 89:[35, 123], Operations: ['35+32=67', '56+67=123'] Exploring Operation: 35+123=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 35*123=4305, Resulting Numbers: [4305] 4305,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 89:[35, 56, 67], Operations: ['35+32=67'] Exploring Operation: 35+56=91, Resulting Numbers: [67, 91] Generated Node #0,1,0: 89:[67, 91] Operation: 35+56=91 Exploring Operation: 56+67=123, Resulting Numbers: [35, 123] Generated Node #0,1,1: 89:[35, 123] Operation: 56+67=123 Exploring Operation: 35+67=102, Resulting Numbers: [56, 102] Generated Node #0,1,2: 89:[56, 102] Operation: 35+67=102 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 89:[67, 91], Operations: ['35+32=67', '35+56=91'] Exploring Operation: 67+91=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 91-67=24, Resulting Numbers: [24] 24,89 unequal: No Solution Exploring Operation: 67*91=6097, Resulting Numbers: [6097] 6097,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 89:[56, 102], Operations: ['35+32=67', '35+67=102'] Exploring Operation: 56*102=5712, Resulting Numbers: [5712] 5712,89 unequal: No Solution Exploring Operation: 56+102=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 102-56=46, Resulting Numbers: [46] 46,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 89:[35, 123], Operations: ['35+32=67', '56+67=123'] Exploring Operation: 35*123=4305, Resulting Numbers: [4305] 4305,89 unequal: No Solution Exploring Operation: 123-35=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 35+123=158, Resulting Numbers: [158] 158,89 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 89:[32, 56, 70], Operations: ['35+35=70'] Exploring Operation: 32+56=88, Resulting Numbers: [70, 88] Generated Node #0,2,0: 89:[70, 88] Operation: 32+56=88 Exploring Operation: 32+70=102, Resulting Numbers: [56, 102] Generated Node #0,2,1: 89:[56, 102] Operation: 32+70=102 Exploring Operation: 56-32=24, Resulting Numbers: [70, 24] Generated Node #0,2,2: 89:[70, 24] Operation: 56-32=24 Moving to Node #0,2,0 Current State: 89:[70, 88], Operations: ['35+35=70', '32+56=88'] Exploring Operation: 70*88=6160, Resulting Numbers: [6160] 6160,89 unequal: No Solution Exploring Operation: 70+88=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 88-70=18, Resulting Numbers: [18] 18,89 unequal: No Solution Moving to Node #0,2,1 Current State: 89:[56, 102], Operations: ['35+35=70', '32+70=102'] Exploring Operation: 56+102=158, Resulting Numbers: [158] 158,89 unequal: No Solution Exploring Operation: 102-56=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 56*102=5712, Resulting Numbers: [5712] 5712,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[70, 24], Operations: ['35+35=70', '56-32=24'] Exploring Operation: 70*24=1680, Resulting Numbers: [1680] 1680,89 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,89 unequal: No Solution Exploring Operation: 70+24=94, Resulting Numbers: [94] 94,89 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
[ 23, 33, 62, 11 ]
62
[ "33-23=10", "11-10=1", "62*1=62" ]
Current State: 62:[23, 33, 62, 11], Operations: [] Exploring Operation: 33-23=10, Resulting Numbers: [62, 11, 10] Generated Node #2: [62, 11, 10] from Operation: 33-23=10 Current State: 62:[62, 11, 10], Operations: ['33-23=10'] Exploring Operation: 11-10=1, Resulting Numbers: [62, 1] Generated Node #3: [62, 1] from Operation: 11-10=1 Current State: 62:[62, 1], Operations: ['33-23=10', '11-10=1'] Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[23, 33, 62, 11], Operations: [] Exploring Operation: 33/11=3, Resulting Numbers: [23, 62, 3] Generated Node #0,0: 62:[23, 62, 3] Operation: 33/11=3 Exploring Operation: 23+11=34, Resulting Numbers: [33, 62, 34] Generated Node #0,1: 62:[33, 62, 34] Operation: 23+11=34 Exploring Operation: 23+33=56, Resulting Numbers: [62, 11, 56] Generated Node #0,2: 62:[62, 11, 56] Operation: 23+33=56 Exploring Operation: 23-11=12, Resulting Numbers: [33, 62, 12] Generated Node #0,3: 62:[33, 62, 12] Operation: 23-11=12 Start Sub Search at level 1: Moving to Node #0,1 Current State: 62:[33, 62, 34], Operations: ['23+11=34'] Exploring Operation: 33+34=67, Resulting Numbers: [62, 67] Generated Node #0,1,0: 62:[62, 67] Operation: 33+34=67 Exploring Operation: 62-33=29, Resulting Numbers: [34, 29] Generated Node #0,1,1: 62:[34, 29] Operation: 62-33=29 Exploring Operation: 34-33=1, Resulting Numbers: [62, 1] Generated Node #0,1,2: 62:[62, 1] Operation: 34-33=1 Exploring Operation: 62-34=28, Resulting Numbers: [33, 28] Generated Node #0,1,3: 62:[33, 28] Operation: 62-34=28 Moving to Node #0,1,2 Current State: 62:[62, 1], Operations: ['23+11=34', '34-33=1'] Exploring Operation: 62+1=63, Resulting Numbers: [63] 63,62 unequal: No Solution Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[23, 33, 62, 11], Operations: [] Exploring Operation: 23+11=34, Resulting Numbers: [33, 62, 34] Generated Node #0,1: 62:[33, 62, 34] Operation: 23+11=34 Moving to Node #0,1 Current State: 62:[33, 62, 34], Operations: ['23+11=34'] Exploring Operation: 34-33=1, Resulting Numbers: [62, 1] Generated Node #0,1,2: 62:[62, 1] Operation: 34-33=1 Moving to Node #0,1,2 Current State: 62:[62, 1], Operations: ['23+11=34', '34-33=1'] Exploring Operation: 62*1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 56, 62, 69, 31 ]
23
[ "69-62=7", "56/7=8", "31-8=23" ]
Current State: 23:[56, 62, 69, 31], Operations: [] Exploring Operation: 69-62=7, Resulting Numbers: [56, 31, 7] Generated Node #2: [56, 31, 7] from Operation: 69-62=7 Current State: 23:[56, 31, 7], Operations: ['69-62=7'] Exploring Operation: 56/7=8, Resulting Numbers: [31, 8] Generated Node #3: [31, 8] from Operation: 56/7=8 Current State: 23:[31, 8], Operations: ['69-62=7', '56/7=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[56, 62, 69, 31], Operations: [] Exploring Operation: 69-62=7, Resulting Numbers: [56, 31, 7] Generated Node #0,0: 23:[56, 31, 7] Operation: 69-62=7 Exploring Operation: 62-56=6, Resulting Numbers: [69, 31, 6] Generated Node #0,1: 23:[69, 31, 6] Operation: 62-56=6 Exploring Operation: 69-56=13, Resulting Numbers: [62, 31, 13] Generated Node #0,2: 23:[62, 31, 13] Operation: 69-56=13 Moving to Node #0,0 Current State: 23:[56, 31, 7], Operations: ['69-62=7'] Exploring Operation: 56-31=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 23:[7, 25] Operation: 56-31=25 Exploring Operation: 56-7=49, Resulting Numbers: [31, 49] Generated Node #0,0,1: 23:[31, 49] Operation: 56-7=49 Exploring Operation: 56/7=8, Resulting Numbers: [31, 8] Generated Node #0,0,2: 23:[31, 8] Operation: 56/7=8 Moving to Node #0,2 Current State: 23:[62, 31, 13], Operations: ['69-56=13'] Exploring Operation: 62/31=2, Resulting Numbers: [13, 2] Generated Node #0,2,0: 23:[13, 2] Operation: 62/31=2 Exploring Operation: 62-31=31, Resulting Numbers: [13, 31] Generated Node #0,2,1: 23:[13, 31] Operation: 62-31=31 Exploring Operation: 62-13=49, Resulting Numbers: [31, 49] Generated Node #0,2,2: 23:[31, 49] Operation: 62-13=49 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 23:[13, 31], Operations: ['69-56=13', '62-31=31'] Exploring Operation: 13+31=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 13*31=403, Resulting Numbers: [403] 403,23 unequal: No Solution Exploring Operation: 31-13=18, Resulting Numbers: [18] 18,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[13, 2], Operations: ['69-56=13', '62/31=2'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,23 unequal: No Solution Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[31, 49], Operations: ['69-56=13', '62-13=49'] Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 31*49=1519, Resulting Numbers: [1519] 1519,23 unequal: No Solution Exploring Operation: 31+49=80, Resulting Numbers: [80] 80,23 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: 23:[69, 31, 6], Operations: ['62-56=6'] Exploring Operation: 69-31=38, Resulting Numbers: [6, 38] Generated Node #0,1,0: 23:[6, 38] Operation: 69-31=38 Exploring Operation: 69-6=63, Resulting Numbers: [31, 63] Generated Node #0,1,1: 23:[31, 63] Operation: 69-6=63 Exploring Operation: 31-6=25, Resulting Numbers: [69, 25] Generated Node #0,1,2: 23:[69, 25] Operation: 31-6=25 Moving to Node #0,0,0 Current State: 23:[7, 25], Operations: ['69-62=7', '56-31=25'] Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,23 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[31, 8], Operations: ['69-62=7', '56/7=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[56, 62, 69, 31], Operations: [] Exploring Operation: 69-62=7, Resulting Numbers: [56, 31, 7] Generated Node #0,0: 23:[56, 31, 7] Operation: 69-62=7 Moving to Node #0,0 Current State: 23:[56, 31, 7], Operations: ['69-62=7'] Exploring Operation: 56/7=8, Resulting Numbers: [31, 8] Generated Node #0,0,2: 23:[31, 8] Operation: 56/7=8 Moving to Node #0,0,2 Current State: 23:[31, 8], Operations: ['69-62=7', '56/7=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.974826
hs_3
sum_heuristic
[ 5, 39, 45, 3 ]
82
[ "39-5=34", "45+3=48", "34+48=82" ]
Current State: 82:[5, 39, 45, 3], Operations: [] Exploring Operation: 39-5=34, Resulting Numbers: [45, 3, 34] Generated Node #2: [45, 3, 34] from Operation: 39-5=34 Current State: 82:[45, 3, 34], Operations: ['39-5=34'] Exploring Operation: 45+3=48, Resulting Numbers: [34, 48] Generated Node #3: [34, 48] from Operation: 45+3=48 Current State: 82:[34, 48], Operations: ['39-5=34', '45+3=48'] Exploring Operation: 34+48=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[5, 39, 45, 3], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [39, 3, 40] Generated Node #0,0: 82:[39, 3, 40] Operation: 45-5=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[39, 3, 40], Operations: ['45-5=40'] Exploring Operation: 39+3=42, Resulting Numbers: [40, 42] Generated Node #0,0,0: 82:[40, 42] Operation: 39+3=42 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[40, 42], Operations: ['45-5=40', '39+3=42'] Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[5, 39, 45, 3], Operations: [] Exploring Operation: 45-5=40, Resulting Numbers: [39, 3, 40] Generated Node #0,0: 82:[39, 3, 40] Operation: 45-5=40 Moving to Node #0,0 Current State: 82:[39, 3, 40], Operations: ['45-5=40'] Exploring Operation: 39+3=42, Resulting Numbers: [40, 42] Generated Node #0,0,0: 82:[40, 42] Operation: 39+3=42 Moving to Node #0,0,0 Current State: 82:[40, 42], Operations: ['45-5=40', '39+3=42'] Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 7, 25, 13, 1 ]
18
[ "7+25=32", "13+1=14", "32-14=18" ]
Current State: 18:[7, 25, 13, 1], Operations: [] Exploring Operation: 7+25=32, Resulting Numbers: [13, 1, 32] Generated Node #2: [13, 1, 32] from Operation: 7+25=32 Current State: 18:[13, 1, 32], Operations: ['7+25=32'] Exploring Operation: 13+1=14, Resulting Numbers: [32, 14] Generated Node #3: [32, 14] from Operation: 13+1=14 Current State: 18:[32, 14], Operations: ['7+25=32', '13+1=14'] Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[7, 25, 13, 1], Operations: [] Exploring Operation: 13-7=6, Resulting Numbers: [25, 1, 6] Generated Node #0,0: 18:[25, 1, 6] Operation: 13-7=6 Exploring Operation: 7+13=20, Resulting Numbers: [25, 1, 20] Generated Node #0,1: 18:[25, 1, 20] Operation: 7+13=20 Exploring Operation: 25-7=18, Resulting Numbers: [13, 1, 18] Generated Node #0,2: 18:[13, 1, 18] Operation: 25-7=18 Exploring Operation: 25-13=12, Resulting Numbers: [7, 1, 12] Generated Node #0,3: 18:[7, 1, 12] Operation: 25-13=12 Moving to Node #0,2 Current State: 18:[13, 1, 18], Operations: ['25-7=18'] Exploring Operation: 18-13=5, Resulting Numbers: [1, 5] Generated Node #0,2,0: 18:[1, 5] Operation: 18-13=5 Exploring Operation: 13+1=14, Resulting Numbers: [18, 14] Generated Node #0,2,1: 18:[18, 14] Operation: 13+1=14 Exploring Operation: 13-1=12, Resulting Numbers: [18, 12] Generated Node #0,2,2: 18:[18, 12] Operation: 13-1=12 Exploring Operation: 13*1=13, Resulting Numbers: [18, 13] Generated Node #0,2,3: 18:[18, 13] Operation: 13*1=13 Moving to Node #0,3 Current State: 18:[7, 1, 12], Operations: ['25-13=12'] Exploring Operation: 12-1=11, Resulting Numbers: [7, 11] Generated Node #0,3,0: 18:[7, 11] Operation: 12-1=11 Exploring Operation: 7+12=19, Resulting Numbers: [1, 19] Generated Node #0,3,1: 18:[1, 19] Operation: 7+12=19 Exploring Operation: 7-1=6, Resulting Numbers: [12, 6] Generated Node #0,3,2: 18:[12, 6] Operation: 7-1=6 Exploring Operation: 12-7=5, Resulting Numbers: [1, 5] Generated Node #0,3,3: 18:[1, 5] Operation: 12-7=5 Moving to Node #0,0 Current State: 18:[25, 1, 6], Operations: ['13-7=6'] Exploring Operation: 25*1=25, Resulting Numbers: [6, 25] Generated Node #0,0,0: 18:[6, 25] Operation: 25*1=25 Exploring Operation: 25-6=19, Resulting Numbers: [1, 19] Generated Node #0,0,1: 18:[1, 19] Operation: 25-6=19 Exploring Operation: 25-1=24, Resulting Numbers: [6, 24] Generated Node #0,0,2: 18:[6, 24] Operation: 25-1=24 Exploring Operation: 25/1=25, Resulting Numbers: [6, 25] Generated Node #0,0,3: 18:[6, 25] Operation: 25/1=25 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[1, 19], Operations: ['13-7=6', '25-6=19'] Exploring Operation: 1+19=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 19/1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 1*19=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[7, 25, 13, 1], Operations: [] Exploring Operation: 13-7=6, Resulting Numbers: [25, 1, 6] Generated Node #0,0: 18:[25, 1, 6] Operation: 13-7=6 Moving to Node #0,0 Current State: 18:[25, 1, 6], Operations: ['13-7=6'] Exploring Operation: 25-6=19, Resulting Numbers: [1, 19] Generated Node #0,0,1: 18:[1, 19] Operation: 25-6=19 Moving to Node #0,0,1 Current State: 18:[1, 19], Operations: ['13-7=6', '25-6=19'] Exploring Operation: 19-1=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_4
mult_heuristic
[ 83, 87, 5, 4 ]
30
[ "83+87=170", "170/5=34", "34-4=30" ]
Current State: 30:[83, 87, 5, 4], Operations: [] Exploring Operation: 83+87=170, Resulting Numbers: [5, 4, 170] Generated Node #2: [5, 4, 170] from Operation: 83+87=170 Current State: 30:[5, 4, 170], Operations: ['83+87=170'] Exploring Operation: 170/5=34, Resulting Numbers: [4, 34] Generated Node #3: [4, 34] from Operation: 170/5=34 Current State: 30:[4, 34], Operations: ['83+87=170', '170/5=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[83, 87, 5, 4], Operations: [] Exploring Operation: 83-5=78, Resulting Numbers: [87, 4, 78] Generated Node #0,0: 30:[87, 4, 78] Operation: 83-5=78 Exploring Operation: 83-4=79, Resulting Numbers: [87, 5, 79] Generated Node #0,1: 30:[87, 5, 79] Operation: 83-4=79 Exploring Operation: 87-83=4, Resulting Numbers: [5, 4, 4] Generated Node #0,2: 30:[5, 4, 4] Operation: 87-83=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[5, 4, 4], Operations: ['87-83=4'] Exploring Operation: 4/4=1, Resulting Numbers: [5, 1] Generated Node #0,2,0: 30:[5, 1] Operation: 4/4=1 Exploring Operation: 4*4=16, Resulting Numbers: [5, 16] Generated Node #0,2,1: 30:[5, 16] Operation: 4*4=16 Exploring Operation: 5+4=9, Resulting Numbers: [4, 9] Generated Node #0,2,2: 30:[4, 9] Operation: 5+4=9 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 30:[5, 1], Operations: ['87-83=4', '4/4=1'] Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,30 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,30 unequal: No Solution No 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: 30:[5, 16], Operations: ['87-83=4', '4*4=16'] Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,30 unequal: No Solution Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,30 unequal: No Solution No 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: 30:[4, 9], Operations: ['87-83=4', '5+4=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,30 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: 30:[87, 4, 78], Operations: ['83-5=78'] Exploring Operation: 78-4=74, Resulting Numbers: [87, 74] Generated Node #0,0,0: 30:[87, 74] Operation: 78-4=74 Exploring Operation: 87-78=9, Resulting Numbers: [4, 9] Generated Node #0,0,1: 30:[4, 9] Operation: 87-78=9 Exploring Operation: 87-4=83, Resulting Numbers: [78, 83] Generated Node #0,0,2: 30:[78, 83] Operation: 87-4=83 Moving to Node #0,0,1 Current State: 30:[4, 9], Operations: ['83-5=78', '87-78=9'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[87, 74], Operations: ['83-5=78', '78-4=74'] Exploring Operation: 87+74=161, Resulting Numbers: [161] 161,30 unequal: No Solution Exploring Operation: 87*74=6438, Resulting Numbers: [6438] 6438,30 unequal: No Solution Exploring Operation: 87-74=13, Resulting Numbers: [13] 13,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[78, 83], Operations: ['83-5=78', '87-4=83'] Exploring Operation: 78+83=161, Resulting Numbers: [161] 161,30 unequal: No Solution Exploring Operation: 78*83=6474, Resulting Numbers: [6474] 6474,30 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,30 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 Current State: 30:[87, 5, 79], Operations: ['83-4=79'] Exploring Operation: 87-79=8, Resulting Numbers: [5, 8] Generated Node #0,1,0: 30:[5, 8] Operation: 87-79=8 Exploring Operation: 87-5=82, Resulting Numbers: [79, 82] Generated Node #0,1,1: 30:[79, 82] Operation: 87-5=82 Exploring Operation: 79-5=74, Resulting Numbers: [87, 74] Generated Node #0,1,2: 30:[87, 74] Operation: 79-5=74 Moving to Node #0,1,0 Current State: 30:[5, 8], Operations: ['83-4=79', '87-79=8'] Exploring Operation: 5*8=40, Resulting Numbers: [40] 40,30 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,30 unequal: No Solution Exploring Operation: 5+8=13, Resulting Numbers: [13] 13,30 unequal: No Solution Moving to Node #0,1,1 Current State: 30:[79, 82], Operations: ['83-4=79', '87-5=82'] Exploring Operation: 79*82=6478, Resulting Numbers: [6478] 6478,30 unequal: No Solution Exploring Operation: 79+82=161, Resulting Numbers: [161] 161,30 unequal: No Solution Exploring Operation: 82-79=3, Resulting Numbers: [3] 3,30 unequal: No Solution Moving to Node #0,1,2 Current State: 30:[87, 74], Operations: ['83-4=79', '79-5=74'] Exploring Operation: 87*74=6438, Resulting Numbers: [6438] 6438,30 unequal: No Solution Exploring Operation: 87-74=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 87+74=161, Resulting Numbers: [161] 161,30 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
[ 70, 6, 11, 27 ]
92
[ "70+6=76", "27-11=16", "76+16=92" ]
Current State: 92:[70, 6, 11, 27], Operations: [] Exploring Operation: 70+6=76, Resulting Numbers: [11, 27, 76] Generated Node #2: [11, 27, 76] from Operation: 70+6=76 Current State: 92:[11, 27, 76], Operations: ['70+6=76'] Exploring Operation: 27-11=16, Resulting Numbers: [76, 16] Generated Node #3: [76, 16] from Operation: 27-11=16 Current State: 92:[76, 16], Operations: ['70+6=76', '27-11=16'] Exploring Operation: 76+16=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[70, 6, 11, 27], Operations: [] Exploring Operation: 70-27=43, Resulting Numbers: [6, 11, 43] Generated Node #0,0: 92:[6, 11, 43] Operation: 70-27=43 Moving to Node #0,0 Current State: 92:[6, 11, 43], Operations: ['70-27=43'] Exploring Operation: 11-6=5, Resulting Numbers: [43, 5] Generated Node #0,0,0: 92:[43, 5] Operation: 11-6=5 Moving to Node #0,0,0 Current State: 92:[43, 5], Operations: ['70-27=43', '11-6=5'] Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,92 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 90, 37, 35, 28 ]
45
[ "37-28=9", "90/9=10", "35+10=45" ]
Current State: 45:[90, 37, 35, 28], Operations: [] Exploring Operation: 37-28=9, Resulting Numbers: [90, 35, 9] Generated Node #2: [90, 35, 9] from Operation: 37-28=9 Current State: 45:[90, 35, 9], Operations: ['37-28=9'] Exploring Operation: 90/9=10, Resulting Numbers: [35, 10] Generated Node #3: [35, 10] from Operation: 90/9=10 Current State: 45:[35, 10], Operations: ['37-28=9', '90/9=10'] Exploring Operation: 35+10=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[90, 37, 35, 28], Operations: [] Exploring Operation: 90-35=55, Resulting Numbers: [37, 28, 55] Generated Node #0,0: 45:[37, 28, 55] Operation: 90-35=55 Exploring Operation: 90-37=53, Resulting Numbers: [35, 28, 53] Generated Node #0,1: 45:[35, 28, 53] Operation: 90-37=53 Exploring Operation: 90-28=62, Resulting Numbers: [37, 35, 62] Generated Node #0,2: 45:[37, 35, 62] Operation: 90-28=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 45:[37, 28, 55], Operations: ['90-35=55'] Exploring Operation: 55-28=27, Resulting Numbers: [37, 27] Generated Node #0,0,0: 45:[37, 27] Operation: 55-28=27 Exploring Operation: 55-37=18, Resulting Numbers: [28, 18] Generated Node #0,0,1: 45:[28, 18] Operation: 55-37=18 Exploring Operation: 37-28=9, Resulting Numbers: [55, 9] Generated Node #0,0,2: 45:[55, 9] Operation: 37-28=9 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 45:[55, 9], Operations: ['90-35=55', '37-28=9'] Exploring Operation: 55*9=495, Resulting Numbers: [495] 495,45 unequal: No Solution Exploring Operation: 55-9=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 55+9=64, Resulting Numbers: [64] 64,45 unequal: No Solution No 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: 45:[28, 18], Operations: ['90-35=55', '55-37=18'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,45 unequal: No Solution Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,45 unequal: No Solution No 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: 45:[37, 27], Operations: ['90-35=55', '55-28=27'] Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,45 unequal: No Solution Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,45 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: 45:[35, 28, 53], Operations: ['90-37=53'] Exploring Operation: 35-28=7, Resulting Numbers: [53, 7] Generated Node #0,1,0: 45:[53, 7] Operation: 35-28=7 Exploring Operation: 53-35=18, Resulting Numbers: [28, 18] Generated Node #0,1,1: 45:[28, 18] Operation: 53-35=18 Exploring Operation: 53-28=25, Resulting Numbers: [35, 25] Generated Node #0,1,2: 45:[35, 25] Operation: 53-28=25 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 45:[53, 7], Operations: ['90-37=53', '35-28=7'] Exploring Operation: 53*7=371, Resulting Numbers: [371] 371,45 unequal: No Solution Exploring Operation: 53+7=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,45 unequal: No Solution No 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: 45:[28, 18], Operations: ['90-37=53', '53-35=18'] Exploring Operation: 28-18=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 28*18=504, Resulting Numbers: [504] 504,45 unequal: No Solution Exploring Operation: 28+18=46, Resulting Numbers: [46] 46,45 unequal: No Solution No 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: 45:[35, 25], Operations: ['90-37=53', '53-28=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,45 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,45 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: 45:[37, 35, 62], Operations: ['90-28=62'] Exploring Operation: 62-35=27, Resulting Numbers: [37, 27] Generated Node #0,2,0: 45:[37, 27] Operation: 62-35=27 Exploring Operation: 62-37=25, Resulting Numbers: [35, 25] Generated Node #0,2,1: 45:[35, 25] Operation: 62-37=25 Exploring Operation: 37-35=2, Resulting Numbers: [62, 2] Generated Node #0,2,2: 45:[62, 2] Operation: 37-35=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 45:[62, 2], Operations: ['90-28=62', '37-35=2'] Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,45 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,45 unequal: No Solution Exploring Operation: 62+2=64, Resulting Numbers: [64] 64,45 unequal: No Solution No 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: 45:[37, 27], Operations: ['90-28=62', '62-35=27'] Exploring Operation: 37+27=64, Resulting Numbers: [64] 64,45 unequal: No Solution Exploring Operation: 37-27=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 37*27=999, Resulting Numbers: [999] 999,45 unequal: No Solution No 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: 45:[35, 25], Operations: ['90-28=62', '62-37=25'] Exploring Operation: 35*25=875, Resulting Numbers: [875] 875,45 unequal: No Solution Exploring Operation: 35-25=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 35+25=60, Resulting Numbers: [60] 60,45 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
[ 81, 32, 57, 23 ]
60
[ "81*23=1863", "57+1863=1920", "1920/32=60" ]
Current State: 60:[81, 32, 57, 23], Operations: [] Exploring Operation: 81*23=1863, Resulting Numbers: [32, 57, 1863] Generated Node #2: [32, 57, 1863] from Operation: 81*23=1863 Current State: 60:[32, 57, 1863], Operations: ['81*23=1863'] Exploring Operation: 57+1863=1920, Resulting Numbers: [32, 1920] Generated Node #3: [32, 1920] from Operation: 57+1863=1920 Current State: 60:[32, 1920], Operations: ['81*23=1863', '57+1863=1920'] Exploring Operation: 1920/32=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[81, 32, 57, 23], Operations: [] Exploring Operation: 81-57=24, Resulting Numbers: [32, 23, 24] Generated Node #0,0: 60:[32, 23, 24] Operation: 81-57=24 Exploring Operation: 81-23=58, Resulting Numbers: [32, 57, 58] Generated Node #0,1: 60:[32, 57, 58] Operation: 81-23=58 Moving to Node #0,1 Current State: 60:[32, 57, 58], Operations: ['81-23=58'] Exploring Operation: 58-57=1, Resulting Numbers: [32, 1] Generated Node #0,1,0: 60:[32, 1] Operation: 58-57=1 Exploring Operation: 57-32=25, Resulting Numbers: [58, 25] Generated Node #0,1,1: 60:[58, 25] Operation: 57-32=25 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[32, 1], Operations: ['81-23=58', '58-57=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,60 unequal: No Solution Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[58, 25], Operations: ['81-23=58', '57-32=25'] Exploring Operation: 58-25=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 58+25=83, Resulting Numbers: [83] 83,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 60:[32, 23, 24], Operations: ['81-57=24'] Exploring Operation: 32-23=9, Resulting Numbers: [24, 9] Generated Node #0,0,0: 60:[24, 9] Operation: 32-23=9 Exploring Operation: 24-23=1, Resulting Numbers: [32, 1] Generated Node #0,0,1: 60:[32, 1] Operation: 24-23=1 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 60:[32, 1], Operations: ['81-57=24', '24-23=1'] Exploring Operation: 32-1=31, Resulting Numbers: [31] 31,60 unequal: No Solution Exploring Operation: 32*1=32, Resulting Numbers: [32] 32,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[24, 9], Operations: ['81-57=24', '32-23=9'] Exploring Operation: 24+9=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,60 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
[ 26, 75, 44, 65 ]
60
[ "75-26=49", "44+65=109", "109-49=60" ]
Current State: 60:[26, 75, 44, 65], Operations: [] Exploring Operation: 75-26=49, Resulting Numbers: [44, 65, 49] Generated Node #2: [44, 65, 49] from Operation: 75-26=49 Current State: 60:[44, 65, 49], Operations: ['75-26=49'] Exploring Operation: 44+65=109, Resulting Numbers: [49, 109] Generated Node #3: [49, 109] from Operation: 44+65=109 Current State: 60:[49, 109], Operations: ['75-26=49', '44+65=109'] Exploring Operation: 109-49=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[26, 75, 44, 65], Operations: [] Exploring Operation: 75-44=31, Resulting Numbers: [26, 65, 31] Generated Node #0,0: 60:[26, 65, 31] Operation: 75-44=31 Exploring Operation: 75-65=10, Resulting Numbers: [26, 44, 10] Generated Node #0,1: 60:[26, 44, 10] Operation: 75-65=10 Moving to Node #0,0 Current State: 60:[26, 65, 31], Operations: ['75-44=31'] Exploring Operation: 26+31=57, Resulting Numbers: [65, 57] Generated Node #0,0,0: 60:[65, 57] Operation: 26+31=57 Exploring Operation: 31-26=5, Resulting Numbers: [65, 5] Generated Node #0,0,1: 60:[65, 5] Operation: 31-26=5 Moving to Node #0,1 Current State: 60:[26, 44, 10], Operations: ['75-65=10'] Exploring Operation: 44-26=18, Resulting Numbers: [10, 18] Generated Node #0,1,0: 60:[10, 18] Operation: 44-26=18 Exploring Operation: 44-10=34, Resulting Numbers: [26, 34] Generated Node #0,1,1: 60:[26, 34] Operation: 44-10=34 Moving to Node #0,1,0 Current State: 60:[10, 18], Operations: ['75-65=10', '44-26=18'] Exploring Operation: 18-10=8, Resulting Numbers: [8] 8,60 unequal: No Solution Exploring Operation: 10+18=28, Resulting Numbers: [28] 28,60 unequal: No Solution Moving to Node #0,0,1 Current State: 60:[65, 5], Operations: ['75-44=31', '31-26=5'] Exploring Operation: 65/5=13, Resulting Numbers: [13] 13,60 unequal: No Solution Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[26, 75, 44, 65], Operations: [] Exploring Operation: 75-44=31, Resulting Numbers: [26, 65, 31] Generated Node #0,0: 60:[26, 65, 31] Operation: 75-44=31 Moving to Node #0,0 Current State: 60:[26, 65, 31], Operations: ['75-44=31'] Exploring Operation: 31-26=5, Resulting Numbers: [65, 5] Generated Node #0,0,1: 60:[65, 5] Operation: 31-26=5 Moving to Node #0,0,1 Current State: 60:[65, 5], Operations: ['75-44=31', '31-26=5'] Exploring Operation: 65-5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.987847
hs_2
mult_heuristic
[ 91, 31, 58, 66 ]
62
[ "91-58=33", "31*66=2046", "2046/33=62" ]
Current State: 62:[91, 31, 58, 66], Operations: [] Exploring Operation: 91-58=33, Resulting Numbers: [31, 66, 33] Generated Node #2: [31, 66, 33] from Operation: 91-58=33 Current State: 62:[31, 66, 33], Operations: ['91-58=33'] Exploring Operation: 31*66=2046, Resulting Numbers: [33, 2046] Generated Node #3: [33, 2046] from Operation: 31*66=2046 Current State: 62:[33, 2046], Operations: ['91-58=33', '31*66=2046'] Exploring Operation: 2046/33=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[91, 31, 58, 66], Operations: [] Exploring Operation: 91-58=33, Resulting Numbers: [31, 66, 33] Generated Node #0,0: 62:[31, 66, 33] Operation: 91-58=33 Moving to Node #0,0 Current State: 62:[31, 66, 33], Operations: ['91-58=33'] Exploring Operation: 66/33=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 66/33=2 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['91-58=33', '66/33=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[91, 31, 58, 66], Operations: [] Exploring Operation: 91-58=33, Resulting Numbers: [31, 66, 33] Generated Node #0,0: 62:[31, 66, 33] Operation: 91-58=33 Moving to Node #0,0 Current State: 62:[31, 66, 33], Operations: ['91-58=33'] Exploring Operation: 66/33=2, Resulting Numbers: [31, 2] Generated Node #0,0,0: 62:[31, 2] Operation: 66/33=2 Moving to Node #0,0,0 Current State: 62:[31, 2], Operations: ['91-58=33', '66/33=2'] Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 67, 84, 43, 13 ]
39
[ "84-67=17", "43+13=56", "56-17=39" ]
Current State: 39:[67, 84, 43, 13], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [43, 13, 17] Generated Node #2: [43, 13, 17] from Operation: 84-67=17 Current State: 39:[43, 13, 17], Operations: ['84-67=17'] Exploring Operation: 43+13=56, Resulting Numbers: [17, 56] Generated Node #3: [17, 56] from Operation: 43+13=56 Current State: 39:[17, 56], Operations: ['84-67=17', '43+13=56'] Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[67, 84, 43, 13], Operations: [] Exploring Operation: 67-13=54, Resulting Numbers: [84, 43, 54] Generated Node #0,0: 39:[84, 43, 54] Operation: 67-13=54 Exploring Operation: 67-43=24, Resulting Numbers: [84, 13, 24] Generated Node #0,1: 39:[84, 13, 24] Operation: 67-43=24 Exploring Operation: 84-43=41, Resulting Numbers: [67, 13, 41] Generated Node #0,2: 39:[67, 13, 41] Operation: 84-43=41 Exploring Operation: 84-67=17, Resulting Numbers: [43, 13, 17] Generated Node #0,3: 39:[43, 13, 17] Operation: 84-67=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[43, 13, 17], Operations: ['84-67=17'] Exploring Operation: 17-13=4, Resulting Numbers: [43, 4] Generated Node #0,3,0: 39:[43, 4] Operation: 17-13=4 Exploring Operation: 13+17=30, Resulting Numbers: [43, 30] Generated Node #0,3,1: 39:[43, 30] Operation: 13+17=30 Exploring Operation: 43-13=30, Resulting Numbers: [17, 30] Generated Node #0,3,2: 39:[17, 30] Operation: 43-13=30 Exploring Operation: 43-17=26, Resulting Numbers: [13, 26] Generated Node #0,3,3: 39:[13, 26] Operation: 43-17=26 Moving to Node #0,3,0 Current State: 39:[43, 4], Operations: ['84-67=17', '17-13=4'] Exploring Operation: 43+4=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 43*4=172, Resulting Numbers: [172] 172,39 unequal: No Solution Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[67, 84, 43, 13], Operations: [] Exploring Operation: 84-67=17, Resulting Numbers: [43, 13, 17] Generated Node #0,3: 39:[43, 13, 17] Operation: 84-67=17 Moving to Node #0,3 Current State: 39:[43, 13, 17], Operations: ['84-67=17'] Exploring Operation: 17-13=4, Resulting Numbers: [43, 4] Generated Node #0,3,0: 39:[43, 4] Operation: 17-13=4 Moving to Node #0,3,0 Current State: 39:[43, 4], Operations: ['84-67=17', '17-13=4'] Exploring Operation: 43-4=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 45, 86, 38, 73 ]
17
[ "45*73=3285", "86*38=3268", "3285-3268=17" ]
Current State: 17:[45, 86, 38, 73], Operations: [] Exploring Operation: 45*73=3285, Resulting Numbers: [86, 38, 3285] Generated Node #2: [86, 38, 3285] from Operation: 45*73=3285 Current State: 17:[86, 38, 3285], Operations: ['45*73=3285'] Exploring Operation: 86*38=3268, Resulting Numbers: [3285, 3268] Generated Node #3: [3285, 3268] from Operation: 86*38=3268 Current State: 17:[3285, 3268], Operations: ['45*73=3285', '86*38=3268'] Exploring Operation: 3285-3268=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[45, 86, 38, 73], Operations: [] Exploring Operation: 86-73=13, Resulting Numbers: [45, 38, 13] Generated Node #0,0: 17:[45, 38, 13] Operation: 86-73=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[45, 38, 13], Operations: ['86-73=13'] Exploring Operation: 45-38=7, Resulting Numbers: [13, 7] Generated Node #0,0,0: 17:[13, 7] Operation: 45-38=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[13, 7], Operations: ['86-73=13', '45-38=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 20, 74, 51, 9 ]
57
[ "74-20=54", "54/9=6", "51+6=57" ]
Current State: 57:[20, 74, 51, 9], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [51, 9, 54] Generated Node #2: [51, 9, 54] from Operation: 74-20=54 Current State: 57:[51, 9, 54], Operations: ['74-20=54'] Exploring Operation: 54/9=6, Resulting Numbers: [51, 6] Generated Node #3: [51, 6] from Operation: 54/9=6 Current State: 57:[51, 6], Operations: ['74-20=54', '54/9=6'] Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[20, 74, 51, 9], Operations: [] Exploring Operation: 74-9=65, Resulting Numbers: [20, 51, 65] Generated Node #0,0: 57:[20, 51, 65] Operation: 74-9=65 Exploring Operation: 74-51=23, Resulting Numbers: [20, 9, 23] Generated Node #0,1: 57:[20, 9, 23] Operation: 74-51=23 Exploring Operation: 20-9=11, Resulting Numbers: [74, 51, 11] Generated Node #0,2: 57:[74, 51, 11] Operation: 20-9=11 Exploring Operation: 74-20=54, Resulting Numbers: [51, 9, 54] Generated Node #0,3: 57:[51, 9, 54] Operation: 74-20=54 Exploring Operation: 51+9=60, Resulting Numbers: [20, 74, 60] Generated Node #0,4: 57:[20, 74, 60] Operation: 51+9=60 Moving to Node #0,1 Current State: 57:[20, 9, 23], Operations: ['74-51=23'] Exploring Operation: 20+9=29, Resulting Numbers: [23, 29] Generated Node #0,1,0: 57:[23, 29] Operation: 20+9=29 Exploring Operation: 9+23=32, Resulting Numbers: [20, 32] Generated Node #0,1,1: 57:[20, 32] Operation: 9+23=32 Exploring Operation: 23-9=14, Resulting Numbers: [20, 14] Generated Node #0,1,2: 57:[20, 14] Operation: 23-9=14 Exploring Operation: 20-9=11, Resulting Numbers: [23, 11] Generated Node #0,1,3: 57:[23, 11] Operation: 20-9=11 Exploring Operation: 23-20=3, Resulting Numbers: [9, 3] Generated Node #0,1,4: 57:[9, 3] Operation: 23-20=3 Moving to Node #0,3 Current State: 57:[51, 9, 54], Operations: ['74-20=54'] Exploring Operation: 51+9=60, Resulting Numbers: [54, 60] Generated Node #0,3,0: 57:[54, 60] Operation: 51+9=60 Exploring Operation: 54-51=3, Resulting Numbers: [9, 3] Generated Node #0,3,1: 57:[9, 3] Operation: 54-51=3 Exploring Operation: 51-9=42, Resulting Numbers: [54, 42] Generated Node #0,3,2: 57:[54, 42] Operation: 51-9=42 Exploring Operation: 9+54=63, Resulting Numbers: [51, 63] Generated Node #0,3,3: 57:[51, 63] Operation: 9+54=63 Exploring Operation: 54/9=6, Resulting Numbers: [51, 6] Generated Node #0,3,4: 57:[51, 6] Operation: 54/9=6 Moving to Node #0,0 Current State: 57:[20, 51, 65], Operations: ['74-9=65'] Exploring Operation: 20+65=85, Resulting Numbers: [51, 85] Generated Node #0,0,0: 57:[51, 85] Operation: 20+65=85 Exploring Operation: 20+51=71, Resulting Numbers: [65, 71] Generated Node #0,0,1: 57:[65, 71] Operation: 20+51=71 Exploring Operation: 65-51=14, Resulting Numbers: [20, 14] Generated Node #0,0,2: 57:[20, 14] Operation: 65-51=14 Exploring Operation: 65-20=45, Resulting Numbers: [51, 45] Generated Node #0,0,3: 57:[51, 45] Operation: 65-20=45 Exploring Operation: 51-20=31, Resulting Numbers: [65, 31] Generated Node #0,0,4: 57:[65, 31] Operation: 51-20=31 Moving to Node #0,4 Current State: 57:[20, 74, 60], Operations: ['51+9=60'] Exploring Operation: 60/20=3, Resulting Numbers: [74, 3] Generated Node #0,4,0: 57:[74, 3] Operation: 60/20=3 Exploring Operation: 74-20=54, Resulting Numbers: [60, 54] Generated Node #0,4,1: 57:[60, 54] Operation: 74-20=54 Exploring Operation: 20+74=94, Resulting Numbers: [60, 94] Generated Node #0,4,2: 57:[60, 94] Operation: 20+74=94 Exploring Operation: 60-20=40, Resulting Numbers: [74, 40] Generated Node #0,4,3: 57:[74, 40] Operation: 60-20=40 Exploring Operation: 74-60=14, Resulting Numbers: [20, 14] Generated Node #0,4,4: 57:[20, 14] Operation: 74-60=14 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 57:[60, 54], Operations: ['51+9=60', '74-20=54'] Exploring Operation: 60*54=3240, Resulting Numbers: [3240] 3240,57 unequal: No Solution Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 60+54=114, Resulting Numbers: [114] 114,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 57:[20, 14], Operations: ['51+9=60', '74-60=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,57 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 57:[74, 3], Operations: ['51+9=60', '60/20=3'] Exploring Operation: 74*3=222, Resulting Numbers: [222] 222,57 unequal: No Solution Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,57 unequal: No Solution Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 57:[74, 40], Operations: ['51+9=60', '60-20=40'] Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,57 unequal: No Solution Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 57:[60, 94], Operations: ['51+9=60', '20+74=94'] Exploring Operation: 94-60=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 60*94=5640, Resulting Numbers: [5640] 5640,57 unequal: No Solution Exploring Operation: 60+94=154, Resulting Numbers: [154] 154,57 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: 57:[74, 51, 11], Operations: ['20-9=11'] Exploring Operation: 74-51=23, Resulting Numbers: [11, 23] Generated Node #0,2,0: 57:[11, 23] Operation: 74-51=23 Exploring Operation: 51+11=62, Resulting Numbers: [74, 62] Generated Node #0,2,1: 57:[74, 62] Operation: 51+11=62 Exploring Operation: 74+11=85, Resulting Numbers: [51, 85] Generated Node #0,2,2: 57:[51, 85] Operation: 74+11=85 Exploring Operation: 51-11=40, Resulting Numbers: [74, 40] Generated Node #0,2,3: 57:[74, 40] Operation: 51-11=40 Exploring Operation: 74-11=63, Resulting Numbers: [51, 63] Generated Node #0,2,4: 57:[51, 63] Operation: 74-11=63 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 57:[11, 23], Operations: ['20-9=11', '74-51=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 57:[51, 63], Operations: ['20-9=11', '74-11=63'] Exploring Operation: 51+63=114, Resulting Numbers: [114] 114,57 unequal: No Solution Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 51*63=3213, Resulting Numbers: [3213] 3213,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 57:[74, 62], Operations: ['20-9=11', '51+11=62'] Exploring Operation: 74-62=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 74+62=136, Resulting Numbers: [136] 136,57 unequal: No Solution Exploring Operation: 74*62=4588, Resulting Numbers: [4588] 4588,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 57:[51, 85], Operations: ['20-9=11', '74+11=85'] Exploring Operation: 51*85=4335, Resulting Numbers: [4335] 4335,57 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,57 unequal: No Solution Exploring Operation: 51+85=136, Resulting Numbers: [136] 136,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 57:[74, 40], Operations: ['20-9=11', '51-11=40'] Exploring Operation: 74*40=2960, Resulting Numbers: [2960] 2960,57 unequal: No Solution Exploring Operation: 74+40=114, Resulting Numbers: [114] 114,57 unequal: No Solution Exploring Operation: 74-40=34, Resulting Numbers: [34] 34,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 57:[20, 14], Operations: ['74-51=23', '23-9=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,57 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,57 unequal: No Solution Moving to Node #0,3,0 Current State: 57:[54, 60], Operations: ['74-20=54', '51+9=60'] Exploring Operation: 60-54=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 54+60=114, Resulting Numbers: [114] 114,57 unequal: No Solution Exploring Operation: 54*60=3240, Resulting Numbers: [3240] 3240,57 unequal: No Solution Moving to Node #0,3,1 Current State: 57:[9, 3], Operations: ['74-20=54', '54-51=3'] Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,57 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,1,4 Current State: 57:[9, 3], Operations: ['74-51=23', '23-20=3'] Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 9+3=12, Resulting Numbers: [12] 12,57 unequal: No Solution Exploring Operation: 9*3=27, Resulting Numbers: [27] 27,57 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[20, 14], Operations: ['74-9=65', '65-51=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,57 unequal: No Solution Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,57 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,57 unequal: No Solution Moving to Node #0,3,4 Current State: 57:[51, 6], Operations: ['74-20=54', '54/9=6'] Exploring Operation: 51*6=306, Resulting Numbers: [306] 306,57 unequal: No Solution Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,57 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[20, 74, 51, 9], Operations: [] Exploring Operation: 74-20=54, Resulting Numbers: [51, 9, 54] Generated Node #0,3: 57:[51, 9, 54] Operation: 74-20=54 Moving to Node #0,3 Current State: 57:[51, 9, 54], Operations: ['74-20=54'] Exploring Operation: 54/9=6, Resulting Numbers: [51, 6] Generated Node #0,3,4: 57:[51, 6] Operation: 54/9=6 Moving to Node #0,3,4 Current State: 57:[51, 6], Operations: ['74-20=54', '54/9=6'] Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.927083
hs_5
mult_heuristic
[ 48, 34, 39, 57 ]
64
[ "48+34=82", "57-39=18", "82-18=64" ]
Current State: 64:[48, 34, 39, 57], Operations: [] Exploring Operation: 48+34=82, Resulting Numbers: [39, 57, 82] Generated Node #2: [39, 57, 82] from Operation: 48+34=82 Current State: 64:[39, 57, 82], Operations: ['48+34=82'] Exploring Operation: 57-39=18, Resulting Numbers: [82, 18] Generated Node #3: [82, 18] from Operation: 57-39=18 Current State: 64:[82, 18], Operations: ['48+34=82', '57-39=18'] Exploring Operation: 82-18=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[48, 34, 39, 57], Operations: [] Exploring Operation: 57-48=9, Resulting Numbers: [34, 39, 9] Generated Node #0,0: 64:[34, 39, 9] Operation: 57-48=9 Exploring Operation: 48-39=9, Resulting Numbers: [34, 57, 9] Generated Node #0,1: 64:[34, 57, 9] Operation: 48-39=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 64:[34, 39, 9], Operations: ['57-48=9'] Exploring Operation: 39-34=5, Resulting Numbers: [9, 5] Generated Node #0,0,0: 64:[9, 5] Operation: 39-34=5 Exploring Operation: 39-9=30, Resulting Numbers: [34, 30] Generated Node #0,0,1: 64:[34, 30] Operation: 39-9=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 64:[9, 5], Operations: ['57-48=9', '39-34=5'] Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,64 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:[34, 30], Operations: ['57-48=9', '39-9=30'] Exploring Operation: 34-30=4, Resulting Numbers: [4] 4,64 unequal: No Solution Exploring Operation: 34+30=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[48, 34, 39, 57], Operations: [] Exploring Operation: 57-48=9, Resulting Numbers: [34, 39, 9] Generated Node #0,0: 64:[34, 39, 9] Operation: 57-48=9 Moving to Node #0,0 Current State: 64:[34, 39, 9], Operations: ['57-48=9'] Exploring Operation: 39-9=30, Resulting Numbers: [34, 30] Generated Node #0,0,1: 64:[34, 30] Operation: 39-9=30 Moving to Node #0,0,1 Current State: 64:[34, 30], Operations: ['57-48=9', '39-9=30'] Exploring Operation: 34+30=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 46, 70, 45, 52 ]
36
[ "52-45=7", "70/7=10", "46-10=36" ]
Current State: 36:[46, 70, 45, 52], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [46, 70, 7] Generated Node #2: [46, 70, 7] from Operation: 52-45=7 Current State: 36:[46, 70, 7], Operations: ['52-45=7'] Exploring Operation: 70/7=10, Resulting Numbers: [46, 10] Generated Node #3: [46, 10] from Operation: 70/7=10 Current State: 36:[46, 10], Operations: ['52-45=7', '70/7=10'] Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[46, 70, 45, 52], Operations: [] Exploring Operation: 70-46=24, Resulting Numbers: [45, 52, 24] Generated Node #0,0: 36:[45, 52, 24] Operation: 70-46=24 Exploring Operation: 70-52=18, Resulting Numbers: [46, 45, 18] Generated Node #0,1: 36:[46, 45, 18] Operation: 70-52=18 Moving to Node #0,1 Current State: 36:[46, 45, 18], Operations: ['70-52=18'] Exploring Operation: 46-45=1, Resulting Numbers: [18, 1] Generated Node #0,1,0: 36:[18, 1] Operation: 46-45=1 Exploring Operation: 46-18=28, Resulting Numbers: [45, 28] Generated Node #0,1,1: 36:[45, 28] Operation: 46-18=28 Moving to Node #0,0 Current State: 36:[45, 52, 24], Operations: ['70-46=24'] Exploring Operation: 52-45=7, Resulting Numbers: [24, 7] Generated Node #0,0,0: 36:[24, 7] Operation: 52-45=7 Exploring Operation: 52-24=28, Resulting Numbers: [45, 28] Generated Node #0,0,1: 36:[45, 28] Operation: 52-24=28 Moving to Node #0,1,0 Current State: 36:[18, 1], Operations: ['70-52=18', '46-45=1'] Exploring Operation: 18*1=18, Resulting Numbers: [18] 18,36 unequal: No Solution Exploring Operation: 18/1=18, Resulting Numbers: [18] 18,36 unequal: No Solution Moving to Node #0,0,0 Current State: 36:[24, 7], Operations: ['70-46=24', '52-45=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,36 unequal: No Solution Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[45, 28], Operations: ['70-52=18', '46-18=28'] Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,36 unequal: No Solution Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,36 unequal: No Solution Moving to Node #0,0,1 Current State: 36:[45, 28], Operations: ['70-46=24', '52-24=28'] Exploring Operation: 45-28=17, Resulting Numbers: [17] 17,36 unequal: No Solution Exploring Operation: 45+28=73, Resulting Numbers: [73] 73,36 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 23, 63, 96, 51 ]
15
[ "63-51=12", "96/12=8", "23-8=15" ]
Current State: 15:[23, 63, 96, 51], Operations: [] Exploring Operation: 63-51=12, Resulting Numbers: [23, 96, 12] Generated Node #2: [23, 96, 12] from Operation: 63-51=12 Current State: 15:[23, 96, 12], Operations: ['63-51=12'] Exploring Operation: 96/12=8, Resulting Numbers: [23, 8] Generated Node #3: [23, 8] from Operation: 96/12=8 Current State: 15:[23, 8], Operations: ['63-51=12', '96/12=8'] Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[23, 63, 96, 51], Operations: [] Exploring Operation: 96-63=33, Resulting Numbers: [23, 51, 33] Generated Node #0,0: 15:[23, 51, 33] Operation: 96-63=33 Moving to Node #0,0 Current State: 15:[23, 51, 33], Operations: ['96-63=33'] Exploring Operation: 51-33=18, Resulting Numbers: [23, 18] Generated Node #0,0,0: 15:[23, 18] Operation: 51-33=18 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[23, 18], Operations: ['96-63=33', '51-33=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,15 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
[ 39, 13, 17, 13 ]
57
[ "39+17=56", "13/13=1", "56+1=57" ]
Current State: 57:[39, 13, 17, 13], Operations: [] Exploring Operation: 39+17=56, Resulting Numbers: [13, 13, 56] Generated Node #2: [13, 13, 56] from Operation: 39+17=56 Current State: 57:[13, 13, 56], Operations: ['39+17=56'] Exploring Operation: 13/13=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 13/13=1 Current State: 57:[56, 1], Operations: ['39+17=56', '13/13=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[39, 13, 17, 13], Operations: [] Exploring Operation: 39/13=3, Resulting Numbers: [17, 13, 3] Generated Node #0,0: 57:[17, 13, 3] Operation: 39/13=3 Moving to Node #0,0 Current State: 57:[17, 13, 3], Operations: ['39/13=3'] Exploring Operation: 17-13=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 57:[3, 4] Operation: 17-13=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[3, 4], Operations: ['39/13=3', '17-13=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,57 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
[ 15, 52, 85, 3 ]
16
[ "52-15=37", "85-37=48", "48/3=16" ]
Current State: 16:[15, 52, 85, 3], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [85, 3, 37] Generated Node #2: [85, 3, 37] from Operation: 52-15=37 Current State: 16:[85, 3, 37], Operations: ['52-15=37'] Exploring Operation: 85-37=48, Resulting Numbers: [3, 48] Generated Node #3: [3, 48] from Operation: 85-37=48 Current State: 16:[3, 48], Operations: ['52-15=37', '85-37=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[15, 52, 85, 3], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [85, 3, 37] Generated Node #0,0: 16:[85, 3, 37] Operation: 52-15=37 Exploring Operation: 85-52=33, Resulting Numbers: [15, 3, 33] Generated Node #0,1: 16:[15, 3, 33] Operation: 85-52=33 Exploring Operation: 85-15=70, Resulting Numbers: [52, 3, 70] Generated Node #0,2: 16:[52, 3, 70] Operation: 85-15=70 Exploring Operation: 52-3=49, Resulting Numbers: [15, 85, 49] Generated Node #0,3: 16:[15, 85, 49] Operation: 52-3=49 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[15, 3, 33], Operations: ['85-52=33'] Exploring Operation: 15/3=5, Resulting Numbers: [33, 5] Generated Node #0,1,0: 16:[33, 5] Operation: 15/3=5 Exploring Operation: 33-15=18, Resulting Numbers: [3, 18] Generated Node #0,1,1: 16:[3, 18] Operation: 33-15=18 Exploring Operation: 33/3=11, Resulting Numbers: [15, 11] Generated Node #0,1,2: 16:[15, 11] Operation: 33/3=11 Exploring Operation: 33-3=30, Resulting Numbers: [15, 30] Generated Node #0,1,3: 16:[15, 30] Operation: 33-3=30 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[3, 18], Operations: ['85-52=33', '33-15=18'] Exploring Operation: 3+18=21, Resulting Numbers: [21] 21,16 unequal: No Solution Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,16 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[15, 11], Operations: ['85-52=33', '33/3=11'] Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,16 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,16 unequal: No Solution Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[15, 30], Operations: ['85-52=33', '33-3=30'] Exploring Operation: 30/15=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,16 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 15*30=450, Resulting Numbers: [450] 450,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[33, 5], Operations: ['85-52=33', '15/3=5'] Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,16 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,16 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: 16:[85, 3, 37], Operations: ['52-15=37'] Exploring Operation: 37-3=34, Resulting Numbers: [85, 34] Generated Node #0,0,0: 16:[85, 34] Operation: 37-3=34 Exploring Operation: 85-37=48, Resulting Numbers: [3, 48] Generated Node #0,0,1: 16:[3, 48] Operation: 85-37=48 Exploring Operation: 85-3=82, Resulting Numbers: [37, 82] Generated Node #0,0,2: 16:[37, 82] Operation: 85-3=82 Exploring Operation: 85+3=88, Resulting Numbers: [37, 88] Generated Node #0,0,3: 16:[37, 88] Operation: 85+3=88 Moving to Node #0,0,1 Current State: 16:[3, 48], Operations: ['52-15=37', '85-37=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,16 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,16 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[15, 52, 85, 3], Operations: [] Exploring Operation: 52-15=37, Resulting Numbers: [85, 3, 37] Generated Node #0,0: 16:[85, 3, 37] Operation: 52-15=37 Moving to Node #0,0 Current State: 16:[85, 3, 37], Operations: ['52-15=37'] Exploring Operation: 85-37=48, Resulting Numbers: [3, 48] Generated Node #0,0,1: 16:[3, 48] Operation: 85-37=48 Moving to Node #0,0,1 Current State: 16:[3, 48], Operations: ['52-15=37', '85-37=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 54, 23, 64, 2 ]
90
[ "54+23=77", "2*77=154", "154-64=90" ]
Current State: 90:[54, 23, 64, 2], Operations: [] Exploring Operation: 54+23=77, Resulting Numbers: [64, 2, 77] Generated Node #2: [64, 2, 77] from Operation: 54+23=77 Current State: 90:[64, 2, 77], Operations: ['54+23=77'] Exploring Operation: 2*77=154, Resulting Numbers: [64, 154] Generated Node #3: [64, 154] from Operation: 2*77=154 Current State: 90:[64, 154], Operations: ['54+23=77', '2*77=154'] Exploring Operation: 154-64=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[54, 23, 64, 2], Operations: [] Exploring Operation: 64-23=41, Resulting Numbers: [54, 2, 41] Generated Node #0,0: 90:[54, 2, 41] Operation: 64-23=41 Exploring Operation: 23+64=87, Resulting Numbers: [54, 2, 87] Generated Node #0,1: 90:[54, 2, 87] Operation: 23+64=87 Exploring Operation: 64/2=32, Resulting Numbers: [54, 23, 32] Generated Node #0,2: 90:[54, 23, 32] Operation: 64/2=32 Exploring Operation: 64-54=10, Resulting Numbers: [23, 2, 10] Generated Node #0,3: 90:[23, 2, 10] Operation: 64-54=10 Moving to Node #0,3 Current State: 90:[23, 2, 10], Operations: ['64-54=10'] Exploring Operation: 23-10=13, Resulting Numbers: [2, 13] Generated Node #0,3,0: 90:[2, 13] Operation: 23-10=13 Exploring Operation: 23+10=33, Resulting Numbers: [2, 33] Generated Node #0,3,1: 90:[2, 33] Operation: 23+10=33 Exploring Operation: 23-2=21, Resulting Numbers: [10, 21] Generated Node #0,3,2: 90:[10, 21] Operation: 23-2=21 Exploring Operation: 23*2=46, Resulting Numbers: [10, 46] Generated Node #0,3,3: 90:[10, 46] Operation: 23*2=46 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 90:[10, 46], Operations: ['64-54=10', '23*2=46'] Exploring Operation: 10+46=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 46-10=36, Resulting Numbers: [36] 36,90 unequal: No Solution Exploring Operation: 10*46=460, Resulting Numbers: [460] 460,90 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 #0,3,0 Current State: 90:[2, 13], Operations: ['64-54=10', '23-10=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,90 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 #0,3,1 Current State: 90:[2, 33], Operations: ['64-54=10', '23+10=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,90 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 #0,3,2 Current State: 90:[10, 21], Operations: ['64-54=10', '23-2=21'] Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,90 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,90 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: 90:[54, 2, 87], Operations: ['23+64=87'] Exploring Operation: 54/2=27, Resulting Numbers: [87, 27] Generated Node #0,1,0: 90:[87, 27] Operation: 54/2=27 Exploring Operation: 2+87=89, Resulting Numbers: [54, 89] Generated Node #0,1,1: 90:[54, 89] Operation: 2+87=89 Exploring Operation: 54-2=52, Resulting Numbers: [87, 52] Generated Node #0,1,2: 90:[87, 52] Operation: 54-2=52 Exploring Operation: 87-54=33, Resulting Numbers: [2, 33] Generated Node #0,1,3: 90:[2, 33] Operation: 87-54=33 Moving to Node #0,0 Current State: 90:[54, 2, 41], Operations: ['64-23=41'] Exploring Operation: 54+41=95, Resulting Numbers: [2, 95] Generated Node #0,0,0: 90:[2, 95] Operation: 54+41=95 Exploring Operation: 54-41=13, Resulting Numbers: [2, 13] Generated Node #0,0,1: 90:[2, 13] Operation: 54-41=13 Exploring Operation: 54/2=27, Resulting Numbers: [41, 27] Generated Node #0,0,2: 90:[41, 27] Operation: 54/2=27 Exploring Operation: 54-2=52, Resulting Numbers: [41, 52] Generated Node #0,0,3: 90:[41, 52] Operation: 54-2=52 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[2, 13], Operations: ['64-23=41', '54-41=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,90 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[2, 95], Operations: ['64-23=41', '54+41=95'] Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,90 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 2*95=190, Resulting Numbers: [190] 190,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[41, 27], Operations: ['64-23=41', '54/2=27'] Exploring Operation: 41-27=14, Resulting Numbers: [14] 14,90 unequal: No Solution Exploring Operation: 41+27=68, Resulting Numbers: [68] 68,90 unequal: No Solution Exploring Operation: 41*27=1107, Resulting Numbers: [1107] 1107,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[41, 52], Operations: ['64-23=41', '54-2=52'] Exploring Operation: 41+52=93, Resulting Numbers: [93] 93,90 unequal: No Solution Exploring Operation: 52-41=11, Resulting Numbers: [11] 11,90 unequal: No Solution Exploring Operation: 41*52=2132, Resulting Numbers: [2132] 2132,90 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: 90:[54, 23, 32], Operations: ['64/2=32'] Exploring Operation: 54-32=22, Resulting Numbers: [23, 22] Generated Node #0,2,0: 90:[23, 22] Operation: 54-32=22 Exploring Operation: 54+32=86, Resulting Numbers: [23, 86] Generated Node #0,2,1: 90:[23, 86] Operation: 54+32=86 Exploring Operation: 32-23=9, Resulting Numbers: [54, 9] Generated Node #0,2,2: 90:[54, 9] Operation: 32-23=9 Exploring Operation: 54-23=31, Resulting Numbers: [32, 31] Generated Node #0,2,3: 90:[32, 31] Operation: 54-23=31 Moving to Node #0,1,3 Current State: 90:[2, 33], Operations: ['23+64=87', '87-54=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[32, 31], Operations: ['64/2=32', '54-23=31'] Exploring Operation: 32+31=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 32-31=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 32*31=992, Resulting Numbers: [992] 992,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[87, 27], Operations: ['23+64=87', '54/2=27'] Exploring Operation: 87+27=114, Resulting Numbers: [114] 114,90 unequal: No Solution Exploring Operation: 87*27=2349, Resulting Numbers: [2349] 2349,90 unequal: No Solution Exploring Operation: 87-27=60, Resulting Numbers: [60] 60,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[23, 22], Operations: ['64/2=32', '54-32=22'] Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[54, 9], Operations: ['64/2=32', '32-23=9'] Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 54*9=486, Resulting Numbers: [486] 486,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[23, 86], Operations: ['64/2=32', '54+32=86'] Exploring Operation: 86-23=63, Resulting Numbers: [63] 63,90 unequal: No Solution Exploring Operation: 23*86=1978, Resulting Numbers: [1978] 1978,90 unequal: No Solution Exploring Operation: 23+86=109, Resulting Numbers: [109] 109,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[87, 52], Operations: ['23+64=87', '54-2=52'] Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,90 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[54, 89], Operations: ['23+64=87', '2+87=89'] Exploring Operation: 54*89=4806, Resulting Numbers: [4806] 4806,90 unequal: No Solution Exploring Operation: 89-54=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 54+89=143, Resulting Numbers: [143] 143,90 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 49, 86, 40, 24 ]
81
[ "49+86=135", "24*135=3240", "3240/40=81" ]
Current State: 81:[49, 86, 40, 24], Operations: [] Exploring Operation: 49+86=135, Resulting Numbers: [40, 24, 135] Generated Node #2: [40, 24, 135] from Operation: 49+86=135 Current State: 81:[40, 24, 135], Operations: ['49+86=135'] Exploring Operation: 24*135=3240, Resulting Numbers: [40, 3240] Generated Node #3: [40, 3240] from Operation: 24*135=3240 Current State: 81:[40, 3240], Operations: ['49+86=135', '24*135=3240'] Exploring Operation: 3240/40=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[49, 86, 40, 24], Operations: [] Exploring Operation: 49+40=89, Resulting Numbers: [86, 24, 89] Generated Node #0,0: 81:[86, 24, 89] Operation: 49+40=89 Exploring Operation: 49-24=25, Resulting Numbers: [86, 40, 25] Generated Node #0,1: 81:[86, 40, 25] Operation: 49-24=25 Exploring Operation: 49-40=9, Resulting Numbers: [86, 24, 9] Generated Node #0,2: 81:[86, 24, 9] Operation: 49-40=9 Moving to Node #0,2 Current State: 81:[86, 24, 9], Operations: ['49-40=9'] Exploring Operation: 24+9=33, Resulting Numbers: [86, 33] Generated Node #0,2,0: 81:[86, 33] Operation: 24+9=33 Exploring Operation: 24-9=15, Resulting Numbers: [86, 15] Generated Node #0,2,1: 81:[86, 15] Operation: 24-9=15 Exploring Operation: 86-9=77, Resulting Numbers: [24, 77] Generated Node #0,2,2: 81:[24, 77] Operation: 86-9=77 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[24, 77], Operations: ['49-40=9', '86-9=77'] Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,81 unequal: No Solution Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[86, 33], Operations: ['49-40=9', '24+9=33'] Exploring Operation: 86*33=2838, Resulting Numbers: [2838] 2838,81 unequal: No Solution Exploring Operation: 86-33=53, Resulting Numbers: [53] 53,81 unequal: No Solution Exploring Operation: 86+33=119, Resulting Numbers: [119] 119,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[86, 15], Operations: ['49-40=9', '24-9=15'] Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,81 unequal: No Solution Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,81 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,81 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: 81:[86, 24, 89], Operations: ['49+40=89'] Exploring Operation: 89-86=3, Resulting Numbers: [24, 3] Generated Node #0,0,0: 81:[24, 3] Operation: 89-86=3 Exploring Operation: 89-24=65, Resulting Numbers: [86, 65] Generated Node #0,0,1: 81:[86, 65] Operation: 89-24=65 Exploring Operation: 86-24=62, Resulting Numbers: [89, 62] Generated Node #0,0,2: 81:[89, 62] Operation: 86-24=62 Moving to Node #0,1 Current State: 81:[86, 40, 25], Operations: ['49-24=25'] Exploring Operation: 40-25=15, Resulting Numbers: [86, 15] Generated Node #0,1,0: 81:[86, 15] Operation: 40-25=15 Exploring Operation: 86-40=46, Resulting Numbers: [25, 46] Generated Node #0,1,1: 81:[25, 46] Operation: 86-40=46 Exploring Operation: 40+25=65, Resulting Numbers: [86, 65] Generated Node #0,1,2: 81:[86, 65] Operation: 40+25=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[86, 15], Operations: ['49-24=25', '40-25=15'] Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,81 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[25, 46], Operations: ['49-24=25', '86-40=46'] Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,81 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 81:[86, 65], Operations: ['49-24=25', '40+25=65'] Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,81 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,81 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,81 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: 81:[24, 3], Operations: ['49+40=89', '89-86=3'] Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,81 unequal: No Solution Exploring Operation: 24+3=27, Resulting Numbers: [27] 27,81 unequal: No Solution Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[86, 65], Operations: ['49+40=89', '89-24=65'] Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,81 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,81 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[89, 62], Operations: ['49+40=89', '86-24=62'] Exploring Operation: 89-62=27, Resulting Numbers: [27] 27,81 unequal: No Solution Exploring Operation: 89*62=5518, Resulting Numbers: [5518] 5518,81 unequal: No Solution Exploring Operation: 89+62=151, Resulting Numbers: [151] 151,81 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 64, 40, 82, 64 ]
40
[ "64-64=0", "82*0=0", "40+0=40" ]
Current State: 40:[64, 40, 82, 64], Operations: [] Exploring Operation: 64-64=0, Resulting Numbers: [40, 82, 0] Generated Node #2: [40, 82, 0] from Operation: 64-64=0 Current State: 40:[40, 82, 0], Operations: ['64-64=0'] Exploring Operation: 82*0=0, Resulting Numbers: [40, 0] Generated Node #3: [40, 0] from Operation: 82*0=0 Current State: 40:[40, 0], Operations: ['64-64=0', '82*0=0'] Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[64, 40, 82, 64], Operations: [] Exploring Operation: 64-64=0, Resulting Numbers: [40, 82, 0] Generated Node #0,0: 40:[40, 82, 0] Operation: 64-64=0 Exploring Operation: 64/64=1, Resulting Numbers: [40, 82, 1] Generated Node #0,1: 40:[40, 82, 1] Operation: 64/64=1 Exploring Operation: 82-64=18, Resulting Numbers: [40, 64, 18] Generated Node #0,2: 40:[40, 64, 18] Operation: 82-64=18 Exploring Operation: 82-64=18, Resulting Numbers: [64, 40, 18] Generated Node #0,3: 40:[64, 40, 18] Operation: 82-64=18 Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[40, 64, 18], Operations: ['82-64=18'] Exploring Operation: 40+18=58, Resulting Numbers: [64, 58] Generated Node #0,2,0: 40:[64, 58] Operation: 40+18=58 Exploring Operation: 40-18=22, Resulting Numbers: [64, 22] Generated Node #0,2,1: 40:[64, 22] Operation: 40-18=22 Exploring Operation: 64-40=24, Resulting Numbers: [18, 24] Generated Node #0,2,2: 40:[18, 24] Operation: 64-40=24 Exploring Operation: 64-18=46, Resulting Numbers: [40, 46] Generated Node #0,2,3: 40:[40, 46] Operation: 64-18=46 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 40:[18, 24], Operations: ['82-64=18', '64-40=24'] Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 40:[40, 46], Operations: ['82-64=18', '64-18=46'] Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,40 unequal: No Solution Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[64, 22], Operations: ['82-64=18', '40-18=22'] Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,40 unequal: No Solution Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[64, 58], Operations: ['82-64=18', '40+18=58'] Exploring Operation: 64+58=122, Resulting Numbers: [122] 122,40 unequal: No Solution Exploring Operation: 64-58=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 64*58=3712, Resulting Numbers: [3712] 3712,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[64, 40, 18], Operations: ['82-64=18'] Exploring Operation: 40-18=22, Resulting Numbers: [64, 22] Generated Node #0,3,0: 40:[64, 22] Operation: 40-18=22 Exploring Operation: 64-18=46, Resulting Numbers: [40, 46] Generated Node #0,3,1: 40:[40, 46] Operation: 64-18=46 Exploring Operation: 64+18=82, Resulting Numbers: [40, 82] Generated Node #0,3,2: 40:[40, 82] Operation: 64+18=82 Exploring Operation: 64-40=24, Resulting Numbers: [18, 24] Generated Node #0,3,3: 40:[18, 24] Operation: 64-40=24 Moving to Node #0,3,1 Current State: 40:[40, 46], Operations: ['82-64=18', '64-18=46'] Exploring Operation: 46-40=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 40+46=86, Resulting Numbers: [86] 86,40 unequal: No Solution Exploring Operation: 40*46=1840, Resulting Numbers: [1840] 1840,40 unequal: No Solution Moving to Node #0,3,3 Current State: 40:[18, 24], Operations: ['82-64=18', '64-40=24'] Exploring Operation: 18+24=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 18*24=432, Resulting Numbers: [432] 432,40 unequal: No Solution Exploring Operation: 24-18=6, Resulting Numbers: [6] 6,40 unequal: No Solution Moving to Node #0,3,0 Current State: 40:[64, 22], Operations: ['82-64=18', '40-18=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,40 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,40 unequal: No Solution Moving to Node #0,3,2 Current State: 40:[40, 82], Operations: ['82-64=18', '64+18=82'] Exploring Operation: 40+82=122, Resulting Numbers: [122] 122,40 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 40*82=3280, Resulting Numbers: [3280] 3280,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[40, 82, 1], Operations: ['64/64=1'] Exploring Operation: 82-40=42, Resulting Numbers: [1, 42] Generated Node #0,1,0: 40:[1, 42] Operation: 82-40=42 Exploring Operation: 82-1=81, Resulting Numbers: [40, 81] Generated Node #0,1,1: 40:[40, 81] Operation: 82-1=81 Exploring Operation: 40/1=40, Resulting Numbers: [82, 40] Generated Node #0,1,2: 40:[82, 40] Operation: 40/1=40 Exploring Operation: 40*1=40, Resulting Numbers: [82, 40] Generated Node #0,1,3: 40:[82, 40] Operation: 40*1=40 Moving to Node #0,1,0 Current State: 40:[1, 42], Operations: ['64/64=1', '82-40=42'] Exploring Operation: 1+42=43, Resulting Numbers: [43] 43,40 unequal: No Solution Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,40 unequal: No Solution Exploring Operation: 1*42=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,40 unequal: No Solution Moving to Node #0,1,1 Current State: 40:[40, 81], Operations: ['64/64=1', '82-1=81'] Exploring Operation: 40*81=3240, Resulting Numbers: [3240] 3240,40 unequal: No Solution Exploring Operation: 40+81=121, Resulting Numbers: [121] 121,40 unequal: No Solution Exploring Operation: 81-40=41, Resulting Numbers: [41] 41,40 unequal: No Solution Moving to Node #0,1,3 Current State: 40:[82, 40], Operations: ['64/64=1', '40*1=40'] Exploring Operation: 82*40=3280, Resulting Numbers: [3280] 3280,40 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 82+40=122, Resulting Numbers: [122] 122,40 unequal: No Solution Moving to Node #0,1,2 Current State: 40:[82, 40], Operations: ['64/64=1', '40/1=40'] Exploring Operation: 82+40=122, Resulting Numbers: [122] 122,40 unequal: No Solution Exploring Operation: 82-40=42, Resulting Numbers: [42] 42,40 unequal: No Solution Exploring Operation: 82*40=3280, Resulting Numbers: [3280] 3280,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[40, 82, 0], Operations: ['64-64=0'] Exploring Operation: 40+0=40, Resulting Numbers: [82, 40] Generated Node #0,0,0: 40:[82, 40] Operation: 40+0=40 Exploring Operation: 82*0=0, Resulting Numbers: [40, 0] Generated Node #0,0,1: 40:[40, 0] Operation: 82*0=0 Exploring Operation: 82-40=42, Resulting Numbers: [0, 42] Generated Node #0,0,2: 40:[0, 42] Operation: 82-40=42 Exploring Operation: 40-0=40, Resulting Numbers: [82, 40] Generated Node #0,0,3: 40:[82, 40] Operation: 40-0=40 Moving to Node #0,0,1 Current State: 40:[40, 0], Operations: ['64-64=0', '82*0=0'] Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[64, 40, 82, 64], Operations: [] Exploring Operation: 64-64=0, Resulting Numbers: [40, 82, 0] Generated Node #0,0: 40:[40, 82, 0] Operation: 64-64=0 Moving to Node #0,0 Current State: 40:[40, 82, 0], Operations: ['64-64=0'] Exploring Operation: 82*0=0, Resulting Numbers: [40, 0] Generated Node #0,0,1: 40:[40, 0] Operation: 82*0=0 Moving to Node #0,0,1 Current State: 40:[40, 0], Operations: ['64-64=0', '82*0=0'] Exploring Operation: 40+0=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_4
sum_heuristic
[ 80, 45, 56, 25 ]
61
[ "80+45=125", "125/25=5", "56+5=61" ]
Current State: 61:[80, 45, 56, 25], Operations: [] Exploring Operation: 80+45=125, Resulting Numbers: [56, 25, 125] Generated Node #2: [56, 25, 125] from Operation: 80+45=125 Current State: 61:[56, 25, 125], Operations: ['80+45=125'] Exploring Operation: 125/25=5, Resulting Numbers: [56, 5] Generated Node #3: [56, 5] from Operation: 125/25=5 Current State: 61:[56, 5], Operations: ['80+45=125', '125/25=5'] Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[80, 45, 56, 25], Operations: [] Exploring Operation: 56+25=81, Resulting Numbers: [80, 45, 81] Generated Node #0,0: 61:[80, 45, 81] Operation: 56+25=81 Exploring Operation: 45+25=70, Resulting Numbers: [80, 56, 70] Generated Node #0,1: 61:[80, 56, 70] Operation: 45+25=70 Exploring Operation: 80+25=105, Resulting Numbers: [45, 56, 105] Generated Node #0,2: 61:[45, 56, 105] Operation: 80+25=105 Exploring Operation: 80-25=55, Resulting Numbers: [45, 56, 55] Generated Node #0,3: 61:[45, 56, 55] Operation: 80-25=55 Moving to Node #0,3 Current State: 61:[45, 56, 55], Operations: ['80-25=55'] Exploring Operation: 55-45=10, Resulting Numbers: [56, 10] Generated Node #0,3,0: 61:[56, 10] Operation: 55-45=10 Exploring Operation: 45+55=100, Resulting Numbers: [56, 100] Generated Node #0,3,1: 61:[56, 100] Operation: 45+55=100 Exploring Operation: 56-45=11, Resulting Numbers: [55, 11] Generated Node #0,3,2: 61:[55, 11] Operation: 56-45=11 Exploring Operation: 45+56=101, Resulting Numbers: [55, 101] Generated Node #0,3,3: 61:[55, 101] Operation: 45+56=101 Moving to Node #0,1 Current State: 61:[80, 56, 70], Operations: ['45+25=70'] Exploring Operation: 70-56=14, Resulting Numbers: [80, 14] Generated Node #0,1,0: 61:[80, 14] Operation: 70-56=14 Exploring Operation: 80-70=10, Resulting Numbers: [56, 10] Generated Node #0,1,1: 61:[56, 10] Operation: 80-70=10 Exploring Operation: 80-56=24, Resulting Numbers: [70, 24] Generated Node #0,1,2: 61:[70, 24] Operation: 80-56=24 Exploring Operation: 80+56=136, Resulting Numbers: [70, 136] Generated Node #0,1,3: 61:[70, 136] Operation: 80+56=136 Moving to Node #0,0 Current State: 61:[80, 45, 81], Operations: ['56+25=81'] Exploring Operation: 80+45=125, Resulting Numbers: [81, 125] Generated Node #0,0,0: 61:[81, 125] Operation: 80+45=125 Exploring Operation: 80-45=35, Resulting Numbers: [81, 35] Generated Node #0,0,1: 61:[81, 35] Operation: 80-45=35 Exploring Operation: 81-45=36, Resulting Numbers: [80, 36] Generated Node #0,0,2: 61:[80, 36] Operation: 81-45=36 Exploring Operation: 81-80=1, Resulting Numbers: [45, 1] Generated Node #0,0,3: 61:[45, 1] Operation: 81-80=1 Moving to Node #0,2 Current State: 61:[45, 56, 105], Operations: ['80+25=105'] Exploring Operation: 56-45=11, Resulting Numbers: [105, 11] Generated Node #0,2,0: 61:[105, 11] Operation: 56-45=11 Exploring Operation: 45+56=101, Resulting Numbers: [105, 101] Generated Node #0,2,1: 61:[105, 101] Operation: 45+56=101 Exploring Operation: 105-45=60, Resulting Numbers: [56, 60] Generated Node #0,2,2: 61:[56, 60] Operation: 105-45=60 Exploring Operation: 105-56=49, Resulting Numbers: [45, 49] Generated Node #0,2,3: 61:[45, 49] Operation: 105-56=49 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 61:[56, 60], Operations: ['80+25=105', '105-45=60'] Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,61 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:[45, 49], Operations: ['80+25=105', '105-56=49'] Exploring Operation: 45+49=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 49-45=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 45*49=2205, Resulting Numbers: [2205] 2205,61 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:[105, 101], Operations: ['80+25=105', '45+56=101'] Exploring Operation: 105*101=10605, Resulting Numbers: [10605] 10605,61 unequal: No Solution Exploring Operation: 105-101=4, Resulting Numbers: [4] 4,61 unequal: No Solution Exploring Operation: 105+101=206, Resulting Numbers: [206] 206,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 61:[105, 11], Operations: ['80+25=105', '56-45=11'] Exploring Operation: 105+11=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 105-11=94, Resulting Numbers: [94] 94,61 unequal: No Solution Exploring Operation: 105*11=1155, Resulting Numbers: [1155] 1155,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,1 Current State: 61:[56, 100], Operations: ['80-25=55', '45+55=100'] Exploring Operation: 56*100=5600, Resulting Numbers: [5600] 5600,61 unequal: No Solution Exploring Operation: 56+100=156, Resulting Numbers: [156] 156,61 unequal: No Solution Exploring Operation: 100-56=44, Resulting Numbers: [44] 44,61 unequal: No Solution Moving to Node #0,0,2 Current State: 61:[80, 36], Operations: ['56+25=81', '81-45=36'] Exploring Operation: 80-36=44, Resulting Numbers: [44] 44,61 unequal: No Solution Exploring Operation: 80+36=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 80*36=2880, Resulting Numbers: [2880] 2880,61 unequal: No Solution Moving to Node #0,1,2 Current State: 61:[70, 24], Operations: ['45+25=70', '80-56=24'] Exploring Operation: 70*24=1680, Resulting Numbers: [1680] 1680,61 unequal: No Solution Exploring Operation: 70-24=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 70+24=94, Resulting Numbers: [94] 94,61 unequal: No Solution Moving to Node #0,0,1 Current State: 61:[81, 35], Operations: ['56+25=81', '80-45=35'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,61 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,61 unequal: No Solution Moving to Node #0,3,3 Current State: 61:[55, 101], Operations: ['80-25=55', '45+56=101'] Exploring Operation: 101-55=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 55*101=5555, Resulting Numbers: [5555] 5555,61 unequal: No Solution Exploring Operation: 55+101=156, Resulting Numbers: [156] 156,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[56, 10], Operations: ['80-25=55', '55-45=10'] Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,61 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[56, 10], Operations: ['45+25=70', '80-70=10'] Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,61 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,61 unequal: No Solution Moving to Node #0,3,2 Current State: 61:[55, 11], Operations: ['80-25=55', '56-45=11'] Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,61 unequal: No Solution Exploring Operation: 55+11=66, Resulting Numbers: [66] 66,61 unequal: No Solution Exploring Operation: 55*11=605, Resulting Numbers: [605] 605,61 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,61 unequal: No Solution Moving to Node #0,1,0 Current State: 61:[80, 14], Operations: ['45+25=70', '70-56=14'] Exploring Operation: 80*14=1120, Resulting Numbers: [1120] 1120,61 unequal: No Solution Exploring Operation: 80-14=66, Resulting Numbers: [66] 66,61 unequal: No Solution Exploring Operation: 80+14=94, Resulting Numbers: [94] 94,61 unequal: No Solution Moving to Node #0,0,3 Current State: 61:[45, 1], Operations: ['56+25=81', '81-80=1'] Exploring Operation: 45+1=46, Resulting Numbers: [46] 46,61 unequal: No Solution Exploring Operation: 45/1=45, Resulting Numbers: [45] 45,61 unequal: No Solution Exploring Operation: 45-1=44, Resulting Numbers: [44] 44,61 unequal: No Solution Exploring Operation: 45*1=45, Resulting Numbers: [45] 45,61 unequal: No Solution Moving to Node #0,1,3 Current State: 61:[70, 136], Operations: ['45+25=70', '80+56=136'] Exploring Operation: 70*136=9520, Resulting Numbers: [9520] 9520,61 unequal: No Solution Exploring Operation: 70+136=206, Resulting Numbers: [206] 206,61 unequal: No Solution Exploring Operation: 136-70=66, Resulting Numbers: [66] 66,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[81, 125], Operations: ['56+25=81', '80+45=125'] Exploring Operation: 81*125=10125, Resulting Numbers: [10125] 10125,61 unequal: No Solution Exploring Operation: 81+125=206, Resulting Numbers: [206] 206,61 unequal: No Solution Exploring Operation: 125-81=44, Resulting Numbers: [44] 44,61 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 48, 53, 50, 21 ]
31
[ "53-48=5", "50/5=10", "21+10=31" ]
Current State: 31:[48, 53, 50, 21], Operations: [] Exploring Operation: 53-48=5, Resulting Numbers: [50, 21, 5] Generated Node #2: [50, 21, 5] from Operation: 53-48=5 Current State: 31:[50, 21, 5], Operations: ['53-48=5'] Exploring Operation: 50/5=10, Resulting Numbers: [21, 10] Generated Node #3: [21, 10] from Operation: 50/5=10 Current State: 31:[21, 10], Operations: ['53-48=5', '50/5=10'] Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[48, 53, 50, 21], Operations: [] Exploring Operation: 50-21=29, Resulting Numbers: [48, 53, 29] Generated Node #0,0: 31:[48, 53, 29] Operation: 50-21=29 Exploring Operation: 48-21=27, Resulting Numbers: [53, 50, 27] Generated Node #0,1: 31:[53, 50, 27] Operation: 48-21=27 Exploring Operation: 53-48=5, Resulting Numbers: [50, 21, 5] Generated Node #0,2: 31:[50, 21, 5] Operation: 53-48=5 Exploring Operation: 53-21=32, Resulting Numbers: [48, 50, 32] Generated Node #0,3: 31:[48, 50, 32] Operation: 53-21=32 Moving to Node #0,3 Current State: 31:[48, 50, 32], Operations: ['53-21=32'] Exploring Operation: 48+50=98, Resulting Numbers: [32, 98] Generated Node #0,3,0: 31:[32, 98] Operation: 48+50=98 Exploring Operation: 50-48=2, Resulting Numbers: [32, 2] Generated Node #0,3,1: 31:[32, 2] Operation: 50-48=2 Exploring Operation: 50-32=18, Resulting Numbers: [48, 18] Generated Node #0,3,2: 31:[48, 18] Operation: 50-32=18 Exploring Operation: 48-32=16, Resulting Numbers: [50, 16] Generated Node #0,3,3: 31:[50, 16] Operation: 48-32=16 Moving to Node #0,0 Current State: 31:[48, 53, 29], Operations: ['50-21=29'] Exploring Operation: 53-29=24, Resulting Numbers: [48, 24] Generated Node #0,0,0: 31:[48, 24] Operation: 53-29=24 Exploring Operation: 48-29=19, Resulting Numbers: [53, 19] Generated Node #0,0,1: 31:[53, 19] Operation: 48-29=19 Exploring Operation: 53-48=5, Resulting Numbers: [29, 5] Generated Node #0,0,2: 31:[29, 5] Operation: 53-48=5 Exploring Operation: 48+29=77, Resulting Numbers: [53, 77] Generated Node #0,0,3: 31:[53, 77] Operation: 48+29=77 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[48, 24], Operations: ['50-21=29', '53-29=24'] Exploring Operation: 48+24=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 48/24=2, Resulting Numbers: [2] 2,31 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 48*24=1152, Resulting Numbers: [1152] 1152,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 31:[29, 5], Operations: ['50-21=29', '53-48=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,31 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 31:[53, 19], Operations: ['50-21=29', '48-29=19'] Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,31 unequal: No Solution Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,31 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 31:[53, 77], Operations: ['50-21=29', '48+29=77'] Exploring Operation: 53+77=130, Resulting Numbers: [130] 130,31 unequal: No Solution Exploring Operation: 53*77=4081, Resulting Numbers: [4081] 4081,31 unequal: No Solution Exploring Operation: 77-53=24, Resulting Numbers: [24] 24,31 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: 31:[53, 50, 27], Operations: ['48-21=27'] Exploring Operation: 50-27=23, Resulting Numbers: [53, 23] Generated Node #0,1,0: 31:[53, 23] Operation: 50-27=23 Exploring Operation: 53-27=26, Resulting Numbers: [50, 26] Generated Node #0,1,1: 31:[50, 26] Operation: 53-27=26 Exploring Operation: 53-50=3, Resulting Numbers: [27, 3] Generated Node #0,1,2: 31:[27, 3] Operation: 53-50=3 Exploring Operation: 53+27=80, Resulting Numbers: [50, 80] Generated Node #0,1,3: 31:[50, 80] Operation: 53+27=80 Moving to Node #0,2 Current State: 31:[50, 21, 5], Operations: ['53-48=5'] Exploring Operation: 21+5=26, Resulting Numbers: [50, 26] Generated Node #0,2,0: 31:[50, 26] Operation: 21+5=26 Exploring Operation: 50-5=45, Resulting Numbers: [21, 45] Generated Node #0,2,1: 31:[21, 45] Operation: 50-5=45 Exploring Operation: 50-21=29, Resulting Numbers: [5, 29] Generated Node #0,2,2: 31:[5, 29] Operation: 50-21=29 Exploring Operation: 50/5=10, Resulting Numbers: [21, 10] Generated Node #0,2,3: 31:[21, 10] Operation: 50/5=10 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 31:[50, 26], Operations: ['53-48=5', '21+5=26'] Exploring Operation: 50*26=1300, Resulting Numbers: [1300] 1300,31 unequal: No Solution Exploring Operation: 50+26=76, Resulting Numbers: [76] 76,31 unequal: No Solution Exploring Operation: 50-26=24, Resulting Numbers: [24] 24,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[21, 45], Operations: ['53-48=5', '50-5=45'] Exploring Operation: 21*45=945, Resulting Numbers: [945] 945,31 unequal: No Solution Exploring Operation: 45-21=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 21+45=66, Resulting Numbers: [66] 66,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 31:[5, 29], Operations: ['53-48=5', '50-21=29'] Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,31 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 31:[21, 10], Operations: ['53-48=5', '50/5=10'] Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[48, 53, 50, 21], Operations: [] Exploring Operation: 53-48=5, Resulting Numbers: [50, 21, 5] Generated Node #0,2: 31:[50, 21, 5] Operation: 53-48=5 Moving to Node #0,2 Current State: 31:[50, 21, 5], Operations: ['53-48=5'] Exploring Operation: 50/5=10, Resulting Numbers: [21, 10] Generated Node #0,2,3: 31:[21, 10] Operation: 50/5=10 Moving to Node #0,2,3 Current State: 31:[21, 10], Operations: ['53-48=5', '50/5=10'] Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_4
sum_heuristic
[ 78, 27, 82, 44 ]
46
[ "78*27=2106", "2106-82=2024", "2024/44=46" ]
Current State: 46:[78, 27, 82, 44], Operations: [] Exploring Operation: 78*27=2106, Resulting Numbers: [82, 44, 2106] Generated Node #2: [82, 44, 2106] from Operation: 78*27=2106 Current State: 46:[82, 44, 2106], Operations: ['78*27=2106'] Exploring Operation: 2106-82=2024, Resulting Numbers: [44, 2024] Generated Node #3: [44, 2024] from Operation: 2106-82=2024 Current State: 46:[44, 2024], Operations: ['78*27=2106', '2106-82=2024'] Exploring Operation: 2024/44=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[78, 27, 82, 44], Operations: [] Exploring Operation: 78-27=51, Resulting Numbers: [82, 44, 51] Generated Node #0,0: 46:[82, 44, 51] Operation: 78-27=51 Exploring Operation: 82-78=4, Resulting Numbers: [27, 44, 4] Generated Node #0,1: 46:[27, 44, 4] Operation: 82-78=4 Moving to Node #0,1 Current State: 46:[27, 44, 4], Operations: ['82-78=4'] Exploring Operation: 27-4=23, Resulting Numbers: [44, 23] Generated Node #0,1,0: 46:[44, 23] Operation: 27-4=23 Exploring Operation: 44+4=48, Resulting Numbers: [27, 48] Generated Node #0,1,1: 46:[27, 48] Operation: 44+4=48 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[44, 23], Operations: ['82-78=4', '27-4=23'] Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[27, 48], Operations: ['82-78=4', '44+4=48'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,46 unequal: No Solution Exploring Operation: 27+48=75, Resulting Numbers: [75] 75,46 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: 46:[82, 44, 51], Operations: ['78-27=51'] Exploring Operation: 82-44=38, Resulting Numbers: [51, 38] Generated Node #0,0,0: 46:[51, 38] Operation: 82-44=38 Exploring Operation: 82-51=31, Resulting Numbers: [44, 31] Generated Node #0,0,1: 46:[44, 31] Operation: 82-51=31 Moving to Node #0,0,1 Current State: 46:[44, 31], Operations: ['78-27=51', '82-51=31'] Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 44+31=75, Resulting Numbers: [75] 75,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[51, 38], Operations: ['78-27=51', '82-44=38'] Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 51+38=89, Resulting Numbers: [89] 89,46 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 16, 52, 6, 24 ]
84
[ "52*24=1248", "1248/16=78", "6+78=84" ]
Current State: 84:[16, 52, 6, 24], Operations: [] Exploring Operation: 52*24=1248, Resulting Numbers: [16, 6, 1248] Generated Node #2: [16, 6, 1248] from Operation: 52*24=1248 Current State: 84:[16, 6, 1248], Operations: ['52*24=1248'] Exploring Operation: 1248/16=78, Resulting Numbers: [6, 78] Generated Node #3: [6, 78] from Operation: 1248/16=78 Current State: 84:[6, 78], Operations: ['52*24=1248', '1248/16=78'] Exploring Operation: 6+78=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[16, 52, 6, 24], Operations: [] Exploring Operation: 52-24=28, Resulting Numbers: [16, 6, 28] Generated Node #0,0: 84:[16, 6, 28] Operation: 52-24=28 Exploring Operation: 52-16=36, Resulting Numbers: [6, 24, 36] Generated Node #0,1: 84:[6, 24, 36] Operation: 52-16=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[16, 6, 28], Operations: ['52-24=28'] Exploring Operation: 16+6=22, Resulting Numbers: [28, 22] Generated Node #0,0,0: 84:[28, 22] Operation: 16+6=22 Exploring Operation: 28-16=12, Resulting Numbers: [6, 12] Generated Node #0,0,1: 84:[6, 12] Operation: 28-16=12 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 84:[6, 12], Operations: ['52-24=28', '28-16=12'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,84 unequal: No Solution No 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: 84:[28, 22], Operations: ['52-24=28', '16+6=22'] Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,84 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: 84:[6, 24, 36], Operations: ['52-16=36'] Exploring Operation: 6+36=42, Resulting Numbers: [24, 42] Generated Node #0,1,0: 84:[24, 42] Operation: 6+36=42 Exploring Operation: 36-24=12, Resulting Numbers: [6, 12] Generated Node #0,1,1: 84:[6, 12] Operation: 36-24=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 84:[6, 12], Operations: ['52-16=36', '36-24=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,84 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,84 unequal: No Solution No 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: 84:[24, 42], Operations: ['52-16=36', '6+36=42'] Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,84 unequal: No Solution Exploring Operation: 24+42=66, Resulting Numbers: [66] 66,84 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
[ 90, 13, 38, 74 ]
70
[ "90-38=52", "52/13=4", "74-4=70" ]
Current State: 70:[90, 13, 38, 74], Operations: [] Exploring Operation: 90-38=52, Resulting Numbers: [13, 74, 52] Generated Node #2: [13, 74, 52] from Operation: 90-38=52 Current State: 70:[13, 74, 52], Operations: ['90-38=52'] Exploring Operation: 52/13=4, Resulting Numbers: [74, 4] Generated Node #3: [74, 4] from Operation: 52/13=4 Current State: 70:[74, 4], Operations: ['90-38=52', '52/13=4'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[90, 13, 38, 74], Operations: [] Exploring Operation: 90-13=77, Resulting Numbers: [38, 74, 77] Generated Node #0,0: 70:[38, 74, 77] Operation: 90-13=77 Exploring Operation: 90-74=16, Resulting Numbers: [13, 38, 16] Generated Node #0,1: 70:[13, 38, 16] Operation: 90-74=16 Exploring Operation: 74-38=36, Resulting Numbers: [90, 13, 36] Generated Node #0,2: 70:[90, 13, 36] Operation: 74-38=36 Exploring Operation: 90-38=52, Resulting Numbers: [13, 74, 52] Generated Node #0,3: 70:[13, 74, 52] Operation: 90-38=52 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[13, 38, 16], Operations: ['90-74=16'] Exploring Operation: 13+16=29, Resulting Numbers: [38, 29] Generated Node #0,1,0: 70:[38, 29] Operation: 13+16=29 Exploring Operation: 38-16=22, Resulting Numbers: [13, 22] Generated Node #0,1,1: 70:[13, 22] Operation: 38-16=22 Exploring Operation: 38-13=25, Resulting Numbers: [16, 25] Generated Node #0,1,2: 70:[16, 25] Operation: 38-13=25 Exploring Operation: 16-13=3, Resulting Numbers: [38, 3] Generated Node #0,1,3: 70:[38, 3] Operation: 16-13=3 Moving to Node #0,1,3 Current State: 70:[38, 3], Operations: ['90-74=16', '16-13=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[13, 22], Operations: ['90-74=16', '38-16=22'] Exploring Operation: 13*22=286, Resulting Numbers: [286] 286,70 unequal: No Solution Exploring Operation: 22-13=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 13+22=35, Resulting Numbers: [35] 35,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[38, 29], Operations: ['90-74=16', '13+16=29'] Exploring Operation: 38+29=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 38*29=1102, Resulting Numbers: [1102] 1102,70 unequal: No Solution Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,70 unequal: No Solution Moving to Node #0,1,2 Current State: 70:[16, 25], Operations: ['90-74=16', '38-13=25'] Exploring Operation: 16*25=400, Resulting Numbers: [400] 400,70 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 16+25=41, Resulting Numbers: [41] 41,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[38, 74, 77], Operations: ['90-13=77'] Exploring Operation: 38+74=112, Resulting Numbers: [77, 112] Generated Node #0,0,0: 70:[77, 112] Operation: 38+74=112 Exploring Operation: 77-74=3, Resulting Numbers: [38, 3] Generated Node #0,0,1: 70:[38, 3] Operation: 77-74=3 Exploring Operation: 74-38=36, Resulting Numbers: [77, 36] Generated Node #0,0,2: 70:[77, 36] Operation: 74-38=36 Exploring Operation: 77-38=39, Resulting Numbers: [74, 39] Generated Node #0,0,3: 70:[74, 39] Operation: 77-38=39 Moving to Node #0,0,1 Current State: 70:[38, 3], Operations: ['90-13=77', '77-74=3'] Exploring Operation: 38-3=35, Resulting Numbers: [35] 35,70 unequal: No Solution Exploring Operation: 38+3=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 38*3=114, Resulting Numbers: [114] 114,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[74, 39], Operations: ['90-13=77', '77-38=39'] Exploring Operation: 74+39=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 74*39=2886, Resulting Numbers: [2886] 2886,70 unequal: No Solution Exploring Operation: 74-39=35, Resulting Numbers: [35] 35,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[77, 36], Operations: ['90-13=77', '74-38=36'] Exploring Operation: 77*36=2772, Resulting Numbers: [2772] 2772,70 unequal: No Solution Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 77+36=113, Resulting Numbers: [113] 113,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[77, 112], Operations: ['90-13=77', '38+74=112'] Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,70 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,70 unequal: No Solution Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[90, 13, 36], Operations: ['74-38=36'] Exploring Operation: 90+13=103, Resulting Numbers: [36, 103] Generated Node #0,2,0: 70:[36, 103] Operation: 90+13=103 Exploring Operation: 90-36=54, Resulting Numbers: [13, 54] Generated Node #0,2,1: 70:[13, 54] Operation: 90-36=54 Exploring Operation: 36-13=23, Resulting Numbers: [90, 23] Generated Node #0,2,2: 70:[90, 23] Operation: 36-13=23 Exploring Operation: 90-13=77, Resulting Numbers: [36, 77] Generated Node #0,2,3: 70:[36, 77] Operation: 90-13=77 Moving to Node #0,2,3 Current State: 70:[36, 77], Operations: ['74-38=36', '90-13=77'] Exploring Operation: 36*77=2772, Resulting Numbers: [2772] 2772,70 unequal: No Solution Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,70 unequal: No Solution Exploring Operation: 36+77=113, Resulting Numbers: [113] 113,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[13, 54], Operations: ['74-38=36', '90-36=54'] Exploring Operation: 13+54=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 13*54=702, Resulting Numbers: [702] 702,70 unequal: No Solution Exploring Operation: 54-13=41, Resulting Numbers: [41] 41,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[90, 23], Operations: ['74-38=36', '36-13=23'] Exploring Operation: 90+23=113, Resulting Numbers: [113] 113,70 unequal: No Solution Exploring Operation: 90-23=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 90*23=2070, Resulting Numbers: [2070] 2070,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[36, 103], Operations: ['74-38=36', '90+13=103'] Exploring Operation: 36*103=3708, Resulting Numbers: [3708] 3708,70 unequal: No Solution Exploring Operation: 103-36=67, Resulting Numbers: [67] 67,70 unequal: No Solution Exploring Operation: 36+103=139, Resulting Numbers: [139] 139,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 70:[13, 74, 52], Operations: ['90-38=52'] Exploring Operation: 52/13=4, Resulting Numbers: [74, 4] Generated Node #0,3,0: 70:[74, 4] Operation: 52/13=4 Exploring Operation: 13+52=65, Resulting Numbers: [74, 65] Generated Node #0,3,1: 70:[74, 65] Operation: 13+52=65 Exploring Operation: 74-52=22, Resulting Numbers: [13, 22] Generated Node #0,3,2: 70:[13, 22] Operation: 74-52=22 Exploring Operation: 52-13=39, Resulting Numbers: [74, 39] Generated Node #0,3,3: 70:[74, 39] Operation: 52-13=39 Moving to Node #0,3,0 Current State: 70:[74, 4], Operations: ['90-38=52', '52/13=4'] Exploring Operation: 74+4=78, Resulting Numbers: [78] 78,70 unequal: No Solution Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[90, 13, 38, 74], Operations: [] Exploring Operation: 90-38=52, Resulting Numbers: [13, 74, 52] Generated Node #0,3: 70:[13, 74, 52] Operation: 90-38=52 Moving to Node #0,3 Current State: 70:[13, 74, 52], Operations: ['90-38=52'] Exploring Operation: 52/13=4, Resulting Numbers: [74, 4] Generated Node #0,3,0: 70:[74, 4] Operation: 52/13=4 Moving to Node #0,3,0 Current State: 70:[74, 4], Operations: ['90-38=52', '52/13=4'] Exploring Operation: 74-4=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_4
mult_heuristic
[ 14, 18, 1, 69 ]
73
[ "18-14=4", "1*69=69", "4+69=73" ]
Current State: 73:[14, 18, 1, 69], Operations: [] Exploring Operation: 18-14=4, Resulting Numbers: [1, 69, 4] Generated Node #2: [1, 69, 4] from Operation: 18-14=4 Current State: 73:[1, 69, 4], Operations: ['18-14=4'] Exploring Operation: 1*69=69, Resulting Numbers: [4, 69] Generated Node #3: [4, 69] from Operation: 1*69=69 Current State: 73:[4, 69], Operations: ['18-14=4', '1*69=69'] Exploring Operation: 4+69=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[14, 18, 1, 69], Operations: [] Exploring Operation: 1+69=70, Resulting Numbers: [14, 18, 70] Generated Node #0,0: 73:[14, 18, 70] Operation: 1+69=70 Exploring Operation: 14+18=32, Resulting Numbers: [1, 69, 32] Generated Node #0,1: 73:[1, 69, 32] Operation: 14+18=32 Exploring Operation: 18+1=19, Resulting Numbers: [14, 69, 19] Generated Node #0,2: 73:[14, 69, 19] Operation: 18+1=19 Exploring Operation: 14+1=15, Resulting Numbers: [18, 69, 15] Generated Node #0,3: 73:[18, 69, 15] Operation: 14+1=15 Exploring Operation: 14*1=14, Resulting Numbers: [18, 69, 14] Generated Node #0,4: 73:[18, 69, 14] Operation: 14*1=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[14, 18, 70], Operations: ['1+69=70'] Exploring Operation: 14+70=84, Resulting Numbers: [18, 84] Generated Node #0,0,0: 73:[18, 84] Operation: 14+70=84 Exploring Operation: 14+18=32, Resulting Numbers: [70, 32] Generated Node #0,0,1: 73:[70, 32] Operation: 14+18=32 Exploring Operation: 70-14=56, Resulting Numbers: [18, 56] Generated Node #0,0,2: 73:[18, 56] Operation: 70-14=56 Exploring Operation: 18+70=88, Resulting Numbers: [14, 88] Generated Node #0,0,3: 73:[14, 88] Operation: 18+70=88 Exploring Operation: 18-14=4, Resulting Numbers: [70, 4] Generated Node #0,0,4: 73:[70, 4] Operation: 18-14=4 Moving to Node #0,0,1 Current State: 73:[70, 32], Operations: ['1+69=70', '14+18=32'] Exploring Operation: 70*32=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Exploring Operation: 70+32=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[18, 84], Operations: ['1+69=70', '14+70=84'] Exploring Operation: 18*84=1512, Resulting Numbers: [1512] 1512,73 unequal: No Solution Exploring Operation: 18+84=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,73 unequal: No Solution Moving to Node #0,0,2 Current State: 73:[18, 56], Operations: ['1+69=70', '70-14=56'] Exploring Operation: 18*56=1008, Resulting Numbers: [1008] 1008,73 unequal: No Solution Exploring Operation: 18+56=74, Resulting Numbers: [74] 74,73 unequal: No Solution Exploring Operation: 56-18=38, Resulting Numbers: [38] 38,73 unequal: No Solution Moving to Node #0,0,4 Current State: 73:[70, 4], Operations: ['1+69=70', '18-14=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,73 unequal: No Solution Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,73 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,73 unequal: No Solution Moving to Node #0,0,3 Current State: 73:[14, 88], Operations: ['1+69=70', '18+70=88'] Exploring Operation: 14*88=1232, Resulting Numbers: [1232] 1232,73 unequal: No Solution Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,73 unequal: No Solution Exploring Operation: 14+88=102, Resulting Numbers: [102] 102,73 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 Current State: 73:[1, 69, 32], Operations: ['14+18=32'] Exploring Operation: 69/1=69, Resulting Numbers: [32, 69] Generated Node #0,1,0: 73:[32, 69] Operation: 69/1=69 Exploring Operation: 1*32=32, Resulting Numbers: [69, 32] Generated Node #0,1,1: 73:[69, 32] Operation: 1*32=32 Exploring Operation: 1*69=69, Resulting Numbers: [32, 69] Generated Node #0,1,2: 73:[32, 69] Operation: 1*69=69 Exploring Operation: 1+69=70, Resulting Numbers: [32, 70] Generated Node #0,1,3: 73:[32, 70] Operation: 1+69=70 Exploring Operation: 1+32=33, Resulting Numbers: [69, 33] Generated Node #0,1,4: 73:[69, 33] Operation: 1+32=33 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 73:[32, 70], Operations: ['14+18=32', '1+69=70'] Exploring Operation: 32*70=2240, Resulting Numbers: [2240] 2240,73 unequal: No Solution Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,73 unequal: No Solution Exploring Operation: 32+70=102, Resulting Numbers: [102] 102,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 73:[69, 33], Operations: ['14+18=32', '1+32=33'] Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,73 unequal: No Solution Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[32, 69], Operations: ['14+18=32', '69/1=69'] Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[69, 32], Operations: ['14+18=32', '1*32=32'] Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,73 unequal: No Solution Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 73:[32, 69], Operations: ['14+18=32', '1*69=69'] Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 32*69=2208, Resulting Numbers: [2208] 2208,73 unequal: No Solution Exploring Operation: 32+69=101, Resulting Numbers: [101] 101,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 73:[14, 69, 19], Operations: ['18+1=19'] Exploring Operation: 69-14=55, Resulting Numbers: [19, 55] Generated Node #0,2,0: 73:[19, 55] Operation: 69-14=55 Exploring Operation: 14+19=33, Resulting Numbers: [69, 33] Generated Node #0,2,1: 73:[69, 33] Operation: 14+19=33 Exploring Operation: 19-14=5, Resulting Numbers: [69, 5] Generated Node #0,2,2: 73:[69, 5] Operation: 19-14=5 Exploring Operation: 14+69=83, Resulting Numbers: [19, 83] Generated Node #0,2,3: 73:[19, 83] Operation: 14+69=83 Exploring Operation: 69+19=88, Resulting Numbers: [14, 88] Generated Node #0,2,4: 73:[14, 88] Operation: 69+19=88 Moving to Node #0,2,1 Current State: 73:[69, 33], Operations: ['18+1=19', '14+19=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,73 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,73 unequal: No Solution Moving to Node #0,2,3 Current State: 73:[19, 83], Operations: ['18+1=19', '14+69=83'] Exploring Operation: 19*83=1577, Resulting Numbers: [1577] 1577,73 unequal: No Solution Exploring Operation: 19+83=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 83-19=64, Resulting Numbers: [64] 64,73 unequal: No Solution Moving to Node #0,2,0 Current State: 73:[19, 55], Operations: ['18+1=19', '69-14=55'] Exploring Operation: 19+55=74, Resulting Numbers: [74] 74,73 unequal: No Solution Exploring Operation: 55-19=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 19*55=1045, Resulting Numbers: [1045] 1045,73 unequal: No Solution Moving to Node #0,2,2 Current State: 73:[69, 5], Operations: ['18+1=19', '19-14=5'] Exploring Operation: 69*5=345, Resulting Numbers: [345] 345,73 unequal: No Solution Exploring Operation: 69+5=74, Resulting Numbers: [74] 74,73 unequal: No Solution Exploring Operation: 69-5=64, Resulting Numbers: [64] 64,73 unequal: No Solution Moving to Node #0,2,4 Current State: 73:[14, 88], Operations: ['18+1=19', '69+19=88'] Exploring Operation: 14*88=1232, Resulting Numbers: [1232] 1232,73 unequal: No Solution Exploring Operation: 14+88=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 88-14=74, Resulting Numbers: [74] 74,73 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 Current State: 73:[18, 69, 15], Operations: ['14+1=15'] Exploring Operation: 69-15=54, Resulting Numbers: [18, 54] Generated Node #0,3,0: 73:[18, 54] Operation: 69-15=54 Exploring Operation: 18+15=33, Resulting Numbers: [69, 33] Generated Node #0,3,1: 73:[69, 33] Operation: 18+15=33 Exploring Operation: 18+69=87, Resulting Numbers: [15, 87] Generated Node #0,3,2: 73:[15, 87] Operation: 18+69=87 Exploring Operation: 69+15=84, Resulting Numbers: [18, 84] Generated Node #0,3,3: 73:[18, 84] Operation: 69+15=84 Exploring Operation: 18-15=3, Resulting Numbers: [69, 3] Generated Node #0,3,4: 73:[69, 3] Operation: 18-15=3 Moving to Node #0,3,1 Current State: 73:[69, 33], Operations: ['14+1=15', '18+15=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,73 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,73 unequal: No Solution Moving to Node #0,3,3 Current State: 73:[18, 84], Operations: ['14+1=15', '69+15=84'] Exploring Operation: 18+84=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 84-18=66, Resulting Numbers: [66] 66,73 unequal: No Solution Exploring Operation: 18*84=1512, Resulting Numbers: [1512] 1512,73 unequal: No Solution Moving to Node #0,3,2 Current State: 73:[15, 87], Operations: ['14+1=15', '18+69=87'] Exploring Operation: 15+87=102, Resulting Numbers: [102] 102,73 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 15*87=1305, Resulting Numbers: [1305] 1305,73 unequal: No Solution Moving to Node #0,3,0 Current State: 73:[18, 54], Operations: ['14+1=15', '69-15=54'] Exploring Operation: 18+54=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 18*54=972, Resulting Numbers: [972] 972,73 unequal: No Solution Exploring Operation: 54/18=3, Resulting Numbers: [3] 3,73 unequal: No Solution Exploring Operation: 54-18=36, Resulting Numbers: [36] 36,73 unequal: No Solution Moving to Node #0,3,4 Current State: 73:[69, 3], Operations: ['14+1=15', '18-15=3'] Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,73 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,73 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,73 unequal: No Solution Exploring Operation: 69*3=207, Resulting Numbers: [207] 207,73 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 #0,4 Current State: 73:[18, 69, 14], Operations: ['14*1=14'] Exploring Operation: 18-14=4, Resulting Numbers: [69, 4] Generated Node #0,4,0: 73:[69, 4] Operation: 18-14=4 Exploring Operation: 18+14=32, Resulting Numbers: [69, 32] Generated Node #0,4,1: 73:[69, 32] Operation: 18+14=32 Exploring Operation: 69-14=55, Resulting Numbers: [18, 55] Generated Node #0,4,2: 73:[18, 55] Operation: 69-14=55 Exploring Operation: 69+14=83, Resulting Numbers: [18, 83] Generated Node #0,4,3: 73:[18, 83] Operation: 69+14=83 Exploring Operation: 18+69=87, Resulting Numbers: [14, 87] Generated Node #0,4,4: 73:[14, 87] Operation: 18+69=87 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 73:[69, 32], Operations: ['14*1=14', '18+14=32'] Exploring Operation: 69-32=37, Resulting Numbers: [37] 37,73 unequal: No Solution Exploring Operation: 69*32=2208, Resulting Numbers: [2208] 2208,73 unequal: No Solution Exploring Operation: 69+32=101, Resulting Numbers: [101] 101,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 73:[18, 83], Operations: ['14*1=14', '69+14=83'] Exploring Operation: 18*83=1494, Resulting Numbers: [1494] 1494,73 unequal: No Solution Exploring Operation: 18+83=101, Resulting Numbers: [101] 101,73 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 73:[69, 4], Operations: ['14*1=14', '18-14=4'] Exploring Operation: 69*4=276, Resulting Numbers: [276] 276,73 unequal: No Solution Exploring Operation: 69-4=65, Resulting Numbers: [65] 65,73 unequal: No Solution Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[14, 18, 1, 69], Operations: [] Exploring Operation: 14*1=14, Resulting Numbers: [18, 69, 14] Generated Node #0,4: 73:[18, 69, 14] Operation: 14*1=14 Moving to Node #0,4 Current State: 73:[18, 69, 14], Operations: ['14*1=14'] Exploring Operation: 18-14=4, Resulting Numbers: [69, 4] Generated Node #0,4,0: 73:[69, 4] Operation: 18-14=4 Moving to Node #0,4,0 Current State: 73:[69, 4], Operations: ['14*1=14', '18-14=4'] Exploring Operation: 69+4=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.908854
hs_5
sum_heuristic
[ 5, 21, 7, 89 ]
97
[ "5+89=94", "21/7=3", "94+3=97" ]
Current State: 97:[5, 21, 7, 89], Operations: [] Exploring Operation: 5+89=94, Resulting Numbers: [21, 7, 94] Generated Node #2: [21, 7, 94] from Operation: 5+89=94 Current State: 97:[21, 7, 94], Operations: ['5+89=94'] Exploring Operation: 21/7=3, Resulting Numbers: [94, 3] Generated Node #3: [94, 3] from Operation: 21/7=3 Current State: 97:[94, 3], Operations: ['5+89=94', '21/7=3'] Exploring Operation: 94+3=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[5, 21, 7, 89], Operations: [] Exploring Operation: 5*21=105, Resulting Numbers: [7, 89, 105] Generated Node #0,0: 97:[7, 89, 105] Operation: 5*21=105 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[7, 89, 105], Operations: ['5*21=105'] Exploring Operation: 7+89=96, Resulting Numbers: [105, 96] Generated Node #0,0,0: 97:[105, 96] Operation: 7+89=96 Moving to Node #0,0,0 Current State: 97:[105, 96], Operations: ['5*21=105', '7+89=96'] Exploring Operation: 105-96=9, Resulting Numbers: [9] 9,97 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
[ 14, 34, 91, 9 ]
34
[ "14+34=48", "91-9=82", "82-48=34" ]
Current State: 34:[14, 34, 91, 9], Operations: [] Exploring Operation: 14+34=48, Resulting Numbers: [91, 9, 48] Generated Node #2: [91, 9, 48] from Operation: 14+34=48 Current State: 34:[91, 9, 48], Operations: ['14+34=48'] Exploring Operation: 91-9=82, Resulting Numbers: [48, 82] Generated Node #3: [48, 82] from Operation: 91-9=82 Current State: 34:[48, 82], Operations: ['14+34=48', '91-9=82'] Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[14, 34, 91, 9], Operations: [] Exploring Operation: 91-34=57, Resulting Numbers: [14, 9, 57] Generated Node #0,0: 34:[14, 9, 57] Operation: 91-34=57 Moving to Node #0,0 Current State: 34:[14, 9, 57], Operations: ['91-34=57'] Exploring Operation: 57-14=43, Resulting Numbers: [9, 43] Generated Node #0,0,0: 34:[9, 43] Operation: 57-14=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 34:[9, 43], Operations: ['91-34=57', '57-14=43'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[14, 34, 91, 9], Operations: [] Exploring Operation: 91-34=57, Resulting Numbers: [14, 9, 57] Generated Node #0,0: 34:[14, 9, 57] Operation: 91-34=57 Moving to Node #0,0 Current State: 34:[14, 9, 57], Operations: ['91-34=57'] Exploring Operation: 57-14=43, Resulting Numbers: [9, 43] Generated Node #0,0,0: 34:[9, 43] Operation: 57-14=43 Moving to Node #0,0,0 Current State: 34:[9, 43], Operations: ['91-34=57', '57-14=43'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 50, 52, 2, 31 ]
90
[ "50-31=19", "2*19=38", "52+38=90" ]
Current State: 90:[50, 52, 2, 31], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [52, 2, 19] Generated Node #2: [52, 2, 19] from Operation: 50-31=19 Current State: 90:[52, 2, 19], Operations: ['50-31=19'] Exploring Operation: 2*19=38, Resulting Numbers: [52, 38] Generated Node #3: [52, 38] from Operation: 2*19=38 Current State: 90:[52, 38], Operations: ['50-31=19', '2*19=38'] Exploring Operation: 52+38=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[50, 52, 2, 31], Operations: [] Exploring Operation: 50-31=19, Resulting Numbers: [52, 2, 19] Generated Node #0,0: 90:[52, 2, 19] Operation: 50-31=19 Exploring Operation: 52-31=21, Resulting Numbers: [50, 2, 21] Generated Node #0,1: 90:[50, 2, 21] Operation: 52-31=21 Exploring Operation: 52-50=2, Resulting Numbers: [2, 31, 2] Generated Node #0,2: 90:[2, 31, 2] Operation: 52-50=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[2, 31, 2], Operations: ['52-50=2'] Exploring Operation: 2+2=4, Resulting Numbers: [31, 4] Generated Node #0,2,0: 90:[31, 4] Operation: 2+2=4 Exploring Operation: 31-2=29, Resulting Numbers: [2, 29] Generated Node #0,2,1: 90:[2, 29] Operation: 31-2=29 Exploring Operation: 31-2=29, Resulting Numbers: [2, 29] Generated Node #0,2,2: 90:[2, 29] Operation: 31-2=29 Moving to Node #0,2,1 Current State: 90:[2, 29], Operations: ['52-50=2', '31-2=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[2, 29], Operations: ['52-50=2', '31-2=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[31, 4], Operations: ['52-50=2', '2+2=4'] Exploring Operation: 31*4=124, Resulting Numbers: [124] 124,90 unequal: No Solution Exploring Operation: 31+4=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[52, 2, 19], Operations: ['50-31=19'] Exploring Operation: 52/2=26, Resulting Numbers: [19, 26] Generated Node #0,0,0: 90:[19, 26] Operation: 52/2=26 Exploring Operation: 52-2=50, Resulting Numbers: [19, 50] Generated Node #0,0,1: 90:[19, 50] Operation: 52-2=50 Exploring Operation: 52-19=33, Resulting Numbers: [2, 33] Generated Node #0,0,2: 90:[2, 33] Operation: 52-19=33 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[2, 33], Operations: ['50-31=19', '52-19=33'] Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,90 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,90 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 #0,0,0 Current State: 90:[19, 26], Operations: ['50-31=19', '52/2=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,90 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,90 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[19, 50], Operations: ['50-31=19', '52-2=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,90 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[50, 2, 21], Operations: ['52-31=21'] Exploring Operation: 21-2=19, Resulting Numbers: [50, 19] Generated Node #0,1,0: 90:[50, 19] Operation: 21-2=19 Exploring Operation: 50-21=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 90:[2, 29] Operation: 50-21=29 Exploring Operation: 50-2=48, Resulting Numbers: [21, 48] Generated Node #0,1,2: 90:[21, 48] Operation: 50-2=48 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[2, 29], Operations: ['52-31=21', '50-21=29'] Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,90 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 #0,1,0 Current State: 90:[50, 19], Operations: ['52-31=21', '21-2=19'] Exploring Operation: 50*19=950, Resulting Numbers: [950] 950,90 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,90 unequal: No Solution Exploring Operation: 50+19=69, Resulting Numbers: [69] 69,90 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 #0,1,2 Current State: 90:[21, 48], Operations: ['52-31=21', '50-2=48'] Exploring Operation: 21*48=1008, Resulting Numbers: [1008] 1008,90 unequal: No Solution Exploring Operation: 21+48=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,90 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_3
mult_heuristic
[ 89, 2, 80, 40 ]
88
[ "80/2=40", "40/40=1", "89-1=88" ]
Current State: 88:[89, 2, 80, 40], Operations: [] Exploring Operation: 80/2=40, Resulting Numbers: [89, 40, 40] Generated Node #2: [89, 40, 40] from Operation: 80/2=40 Current State: 88:[89, 40, 40], Operations: ['80/2=40'] Exploring Operation: 40/40=1, Resulting Numbers: [89, 1] Generated Node #3: [89, 1] from Operation: 40/40=1 Current State: 88:[89, 1], Operations: ['80/2=40', '40/40=1'] Exploring Operation: 89-1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[89, 2, 80, 40], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [89, 2, 2] Generated Node #0,0: 88:[89, 2, 2] Operation: 80/40=2 Moving to Node #0,0 Current State: 88:[89, 2, 2], Operations: ['80/40=2'] Exploring Operation: 89-2=87, Resulting Numbers: [2, 87] Generated Node #0,0,0: 88:[2, 87] Operation: 89-2=87 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[2, 87], Operations: ['80/40=2', '89-2=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,88 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
[ 68, 97, 61, 91 ]
84
[ "68-61=7", "91/7=13", "97-13=84" ]
Current State: 84:[68, 97, 61, 91], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [97, 91, 7] Generated Node #2: [97, 91, 7] from Operation: 68-61=7 Current State: 84:[97, 91, 7], Operations: ['68-61=7'] Exploring Operation: 91/7=13, Resulting Numbers: [97, 13] Generated Node #3: [97, 13] from Operation: 91/7=13 Current State: 84:[97, 13], Operations: ['68-61=7', '91/7=13'] Exploring Operation: 97-13=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[68, 97, 61, 91], Operations: [] Exploring Operation: 97-61=36, Resulting Numbers: [68, 91, 36] Generated Node #0,0: 84:[68, 91, 36] Operation: 97-61=36 Exploring Operation: 68-61=7, Resulting Numbers: [97, 91, 7] Generated Node #0,1: 84:[97, 91, 7] Operation: 68-61=7 Exploring Operation: 97-68=29, Resulting Numbers: [61, 91, 29] Generated Node #0,2: 84:[61, 91, 29] Operation: 97-68=29 Moving to Node #0,1 Current State: 84:[97, 91, 7], Operations: ['68-61=7'] Exploring Operation: 97-91=6, Resulting Numbers: [7, 6] Generated Node #0,1,0: 84:[7, 6] Operation: 97-91=6 Exploring Operation: 97-7=90, Resulting Numbers: [91, 90] Generated Node #0,1,1: 84:[91, 90] Operation: 97-7=90 Exploring Operation: 91-7=84, Resulting Numbers: [97, 84] Generated Node #0,1,2: 84:[97, 84] Operation: 91-7=84 Moving to Node #0,2 Current State: 84:[61, 91, 29], Operations: ['97-68=29'] Exploring Operation: 61+29=90, Resulting Numbers: [91, 90] Generated Node #0,2,0: 84:[91, 90] Operation: 61+29=90 Exploring Operation: 61-29=32, Resulting Numbers: [91, 32] Generated Node #0,2,1: 84:[91, 32] Operation: 61-29=32 Exploring Operation: 91-61=30, Resulting Numbers: [29, 30] Generated Node #0,2,2: 84:[29, 30] Operation: 91-61=30 Moving to Node #0,0 Current State: 84:[68, 91, 36], Operations: ['97-61=36'] Exploring Operation: 68-36=32, Resulting Numbers: [91, 32] Generated Node #0,0,0: 84:[91, 32] Operation: 68-36=32 Exploring Operation: 91-68=23, Resulting Numbers: [36, 23] Generated Node #0,0,1: 84:[36, 23] Operation: 91-68=23 Exploring Operation: 68+36=104, Resulting Numbers: [91, 104] Generated Node #0,0,2: 84:[91, 104] Operation: 68+36=104 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[36, 23], Operations: ['97-61=36', '91-68=23'] Exploring Operation: 36+23=59, Resulting Numbers: [59] 59,84 unequal: No Solution Exploring Operation: 36*23=828, Resulting Numbers: [828] 828,84 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[91, 32], Operations: ['97-61=36', '68-36=32'] Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,84 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[91, 104], Operations: ['97-61=36', '68+36=104'] Exploring Operation: 104-91=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 91*104=9464, Resulting Numbers: [9464] 9464,84 unequal: No Solution Exploring Operation: 91+104=195, Resulting Numbers: [195] 195,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 84:[7, 6], Operations: ['68-61=7', '97-91=6'] Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,84 unequal: No Solution Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[29, 30], Operations: ['97-68=29', '91-61=30'] Exploring Operation: 29*30=870, Resulting Numbers: [870] 870,84 unequal: No Solution Exploring Operation: 30-29=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 29+30=59, Resulting Numbers: [59] 59,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[91, 32], Operations: ['97-68=29', '61-29=32'] Exploring Operation: 91*32=2912, Resulting Numbers: [2912] 2912,84 unequal: No Solution Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,84 unequal: No Solution Exploring Operation: 91+32=123, Resulting Numbers: [123] 123,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[97, 84], Operations: ['68-61=7', '91-7=84'] Exploring Operation: 97*84=8148, Resulting Numbers: [8148] 8148,84 unequal: No Solution Exploring Operation: 97+84=181, Resulting Numbers: [181] 181,84 unequal: No Solution Exploring Operation: 97-84=13, Resulting Numbers: [13] 13,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[91, 90], Operations: ['68-61=7', '97-7=90'] Exploring Operation: 91-90=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 91*90=8190, Resulting Numbers: [8190] 8190,84 unequal: No Solution Exploring Operation: 91+90=181, Resulting Numbers: [181] 181,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[91, 90], Operations: ['97-68=29', '61+29=90'] Exploring Operation: 91-90=1, Resulting Numbers: [1] 1,84 unequal: No Solution Exploring Operation: 91*90=8190, Resulting Numbers: [8190] 8190,84 unequal: No Solution Exploring Operation: 91+90=181, Resulting Numbers: [181] 181,84 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 89, 2, 38, 28 ]
98
[ "89+28=117", "38/2=19", "117-19=98" ]
Current State: 98:[89, 2, 38, 28], Operations: [] Exploring Operation: 89+28=117, Resulting Numbers: [2, 38, 117] Generated Node #2: [2, 38, 117] from Operation: 89+28=117 Current State: 98:[2, 38, 117], Operations: ['89+28=117'] Exploring Operation: 38/2=19, Resulting Numbers: [117, 19] Generated Node #3: [117, 19] from Operation: 38/2=19 Current State: 98:[117, 19], Operations: ['89+28=117', '38/2=19'] Exploring Operation: 117-19=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[89, 2, 38, 28], Operations: [] Exploring Operation: 89-38=51, Resulting Numbers: [2, 28, 51] Generated Node #0,0: 98:[2, 28, 51] Operation: 89-38=51 Exploring Operation: 38-28=10, Resulting Numbers: [89, 2, 10] Generated Node #0,1: 98:[89, 2, 10] Operation: 38-28=10 Exploring Operation: 28/2=14, Resulting Numbers: [89, 38, 14] Generated Node #0,2: 98:[89, 38, 14] Operation: 28/2=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 98:[89, 2, 10], Operations: ['38-28=10'] Exploring Operation: 89+2=91, Resulting Numbers: [10, 91] Generated Node #0,1,0: 98:[10, 91] Operation: 89+2=91 Exploring Operation: 10-2=8, Resulting Numbers: [89, 8] Generated Node #0,1,1: 98:[89, 8] Operation: 10-2=8 Exploring Operation: 89+10=99, Resulting Numbers: [2, 99] Generated Node #0,1,2: 98:[2, 99] Operation: 89+10=99 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 98:[2, 99], Operations: ['38-28=10', '89+10=99'] Exploring Operation: 2*99=198, Resulting Numbers: [198] 198,98 unequal: No Solution Exploring Operation: 2+99=101, Resulting Numbers: [101] 101,98 unequal: No Solution Exploring Operation: 99-2=97, Resulting Numbers: [97] 97,98 unequal: No Solution No 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: 98:[10, 91], Operations: ['38-28=10', '89+2=91'] Exploring Operation: 91-10=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 10*91=910, Resulting Numbers: [910] 910,98 unequal: No Solution Exploring Operation: 10+91=101, Resulting Numbers: [101] 101,98 unequal: No Solution No 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: 98:[89, 8], Operations: ['38-28=10', '10-2=8'] Exploring Operation: 89*8=712, Resulting Numbers: [712] 712,98 unequal: No Solution Exploring Operation: 89-8=81, Resulting Numbers: [81] 81,98 unequal: No Solution Exploring Operation: 89+8=97, Resulting Numbers: [97] 97,98 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: 98:[2, 28, 51], Operations: ['89-38=51'] Exploring Operation: 28/2=14, Resulting Numbers: [51, 14] Generated Node #0,0,0: 98:[51, 14] Operation: 28/2=14 Exploring Operation: 2*28=56, Resulting Numbers: [51, 56] Generated Node #0,0,1: 98:[51, 56] Operation: 2*28=56 Exploring Operation: 51-28=23, Resulting Numbers: [2, 23] Generated Node #0,0,2: 98:[2, 23] Operation: 51-28=23 Moving to Node #0,0,0 Current State: 98:[51, 14], Operations: ['89-38=51', '28/2=14'] Exploring Operation: 51*14=714, Resulting Numbers: [714] 714,98 unequal: No Solution Exploring Operation: 51+14=65, Resulting Numbers: [65] 65,98 unequal: No Solution Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,98 unequal: No Solution Moving to Node #0,0,1 Current State: 98:[51, 56], Operations: ['89-38=51', '2*28=56'] Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,98 unequal: No Solution Exploring Operation: 51*56=2856, Resulting Numbers: [2856] 2856,98 unequal: No Solution Exploring Operation: 51+56=107, Resulting Numbers: [107] 107,98 unequal: No Solution Moving to Node #0,0,2 Current State: 98:[2, 23], Operations: ['89-38=51', '51-28=23'] Exploring Operation: 2*23=46, Resulting Numbers: [46] 46,98 unequal: No Solution Exploring Operation: 2+23=25, Resulting Numbers: [25] 25,98 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,98 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 #0,2 Current State: 98:[89, 38, 14], Operations: ['28/2=14'] Exploring Operation: 89-38=51, Resulting Numbers: [14, 51] Generated Node #0,2,0: 98:[14, 51] Operation: 89-38=51 Exploring Operation: 38+14=52, Resulting Numbers: [89, 52] Generated Node #0,2,1: 98:[89, 52] Operation: 38+14=52 Exploring Operation: 89+14=103, Resulting Numbers: [38, 103] Generated Node #0,2,2: 98:[38, 103] Operation: 89+14=103 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 98:[14, 51], Operations: ['28/2=14', '89-38=51'] Exploring Operation: 51-14=37, Resulting Numbers: [37] 37,98 unequal: No Solution Exploring Operation: 14*51=714, Resulting Numbers: [714] 714,98 unequal: No Solution Exploring Operation: 14+51=65, Resulting Numbers: [65] 65,98 unequal: No Solution No 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: 98:[89, 52], Operations: ['28/2=14', '38+14=52'] Exploring Operation: 89+52=141, Resulting Numbers: [141] 141,98 unequal: No Solution Exploring Operation: 89*52=4628, Resulting Numbers: [4628] 4628,98 unequal: No Solution Exploring Operation: 89-52=37, Resulting Numbers: [37] 37,98 unequal: No Solution No 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: 98:[38, 103], Operations: ['28/2=14', '89+14=103'] Exploring Operation: 38+103=141, Resulting Numbers: [141] 141,98 unequal: No Solution Exploring Operation: 38*103=3914, Resulting Numbers: [3914] 3914,98 unequal: No Solution Exploring Operation: 103-38=65, Resulting Numbers: [65] 65,98 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
[ 32, 49, 88, 98 ]
27
[ "49-32=17", "98-88=10", "17+10=27" ]
Current State: 27:[32, 49, 88, 98], Operations: [] Exploring Operation: 49-32=17, Resulting Numbers: [88, 98, 17] Generated Node #2: [88, 98, 17] from Operation: 49-32=17 Current State: 27:[88, 98, 17], Operations: ['49-32=17'] Exploring Operation: 98-88=10, Resulting Numbers: [17, 10] Generated Node #3: [17, 10] from Operation: 98-88=10 Current State: 27:[17, 10], Operations: ['49-32=17', '98-88=10'] Exploring Operation: 17+10=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[32, 49, 88, 98], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [32, 49, 10] Generated Node #0,0: 27:[32, 49, 10] Operation: 98-88=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[32, 49, 10], Operations: ['98-88=10'] Exploring Operation: 49-32=17, Resulting Numbers: [10, 17] Generated Node #0,0,0: 27:[10, 17] Operation: 49-32=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[10, 17], Operations: ['98-88=10', '49-32=17'] Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[32, 49, 88, 98], Operations: [] Exploring Operation: 98-88=10, Resulting Numbers: [32, 49, 10] Generated Node #0,0: 27:[32, 49, 10] Operation: 98-88=10 Moving to Node #0,0 Current State: 27:[32, 49, 10], Operations: ['98-88=10'] Exploring Operation: 49-32=17, Resulting Numbers: [10, 17] Generated Node #0,0,0: 27:[10, 17] Operation: 49-32=17 Moving to Node #0,0,0 Current State: 27:[10, 17], Operations: ['98-88=10', '49-32=17'] Exploring Operation: 10+17=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 49, 13, 16, 87 ]
67
[ "49-13=36", "16+87=103", "103-36=67" ]
Current State: 67:[49, 13, 16, 87], Operations: [] Exploring Operation: 49-13=36, Resulting Numbers: [16, 87, 36] Generated Node #2: [16, 87, 36] from Operation: 49-13=36 Current State: 67:[16, 87, 36], Operations: ['49-13=36'] Exploring Operation: 16+87=103, Resulting Numbers: [36, 103] Generated Node #3: [36, 103] from Operation: 16+87=103 Current State: 67:[36, 103], Operations: ['49-13=36', '16+87=103'] Exploring Operation: 103-36=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[49, 13, 16, 87], Operations: [] Exploring Operation: 87-13=74, Resulting Numbers: [49, 16, 74] Generated Node #0,0: 67:[49, 16, 74] Operation: 87-13=74 Exploring Operation: 49+16=65, Resulting Numbers: [13, 87, 65] Generated Node #0,1: 67:[13, 87, 65] Operation: 49+16=65 Exploring Operation: 49+13=62, Resulting Numbers: [16, 87, 62] Generated Node #0,2: 67:[16, 87, 62] Operation: 49+13=62 Exploring Operation: 13+16=29, Resulting Numbers: [49, 87, 29] Generated Node #0,3: 67:[49, 87, 29] Operation: 13+16=29 Moving to Node #0,0 Current State: 67:[49, 16, 74], Operations: ['87-13=74'] Exploring Operation: 49+16=65, Resulting Numbers: [74, 65] Generated Node #0,0,0: 67:[74, 65] Operation: 49+16=65 Exploring Operation: 74-16=58, Resulting Numbers: [49, 58] Generated Node #0,0,1: 67:[49, 58] Operation: 74-16=58 Exploring Operation: 49-16=33, Resulting Numbers: [74, 33] Generated Node #0,0,2: 67:[74, 33] Operation: 49-16=33 Exploring Operation: 16+74=90, Resulting Numbers: [49, 90] Generated Node #0,0,3: 67:[49, 90] Operation: 16+74=90 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 67:[74, 65], Operations: ['87-13=74', '49+16=65'] Exploring Operation: 74+65=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 74*65=4810, Resulting Numbers: [4810] 4810,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 67:[49, 58], Operations: ['87-13=74', '74-16=58'] Exploring Operation: 49*58=2842, Resulting Numbers: [2842] 2842,67 unequal: No Solution Exploring Operation: 49+58=107, Resulting Numbers: [107] 107,67 unequal: No Solution Exploring Operation: 58-49=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 67:[74, 33], Operations: ['87-13=74', '49-16=33'] Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,67 unequal: No Solution Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 67:[49, 90], Operations: ['87-13=74', '16+74=90'] Exploring Operation: 49+90=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 90-49=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 49*90=4410, Resulting Numbers: [4410] 4410,67 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: 67:[16, 87, 62], Operations: ['49+13=62'] Exploring Operation: 62-16=46, Resulting Numbers: [87, 46] Generated Node #0,2,0: 67:[87, 46] Operation: 62-16=46 Exploring Operation: 16+87=103, Resulting Numbers: [62, 103] Generated Node #0,2,1: 67:[62, 103] Operation: 16+87=103 Exploring Operation: 16+62=78, Resulting Numbers: [87, 78] Generated Node #0,2,2: 67:[87, 78] Operation: 16+62=78 Exploring Operation: 87-16=71, Resulting Numbers: [62, 71] Generated Node #0,2,3: 67:[62, 71] Operation: 87-16=71 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 67:[62, 71], Operations: ['49+13=62', '87-16=71'] Exploring Operation: 62+71=133, Resulting Numbers: [133] 133,67 unequal: No Solution Exploring Operation: 62*71=4402, Resulting Numbers: [4402] 4402,67 unequal: No Solution Exploring Operation: 71-62=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[87, 78], Operations: ['49+13=62', '16+62=78'] Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,67 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,67 unequal: No Solution Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[87, 46], Operations: ['49+13=62', '62-16=46'] Exploring Operation: 87*46=4002, Resulting Numbers: [4002] 4002,67 unequal: No Solution Exploring Operation: 87-46=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 87+46=133, Resulting Numbers: [133] 133,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[62, 103], Operations: ['49+13=62', '16+87=103'] Exploring Operation: 62*103=6386, Resulting Numbers: [6386] 6386,67 unequal: No Solution Exploring Operation: 103-62=41, Resulting Numbers: [41] 41,67 unequal: No Solution Exploring Operation: 62+103=165, Resulting Numbers: [165] 165,67 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: 67:[13, 87, 65], Operations: ['49+16=65'] Exploring Operation: 65-13=52, Resulting Numbers: [87, 52] Generated Node #0,1,0: 67:[87, 52] Operation: 65-13=52 Exploring Operation: 87-13=74, Resulting Numbers: [65, 74] Generated Node #0,1,1: 67:[65, 74] Operation: 87-13=74 Exploring Operation: 13+65=78, Resulting Numbers: [87, 78] Generated Node #0,1,2: 67:[87, 78] Operation: 13+65=78 Exploring Operation: 13+87=100, Resulting Numbers: [65, 100] Generated Node #0,1,3: 67:[65, 100] Operation: 13+87=100 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[65, 74], Operations: ['49+16=65', '87-13=74'] Exploring Operation: 74-65=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 65*74=4810, Resulting Numbers: [4810] 4810,67 unequal: No Solution Exploring Operation: 65+74=139, Resulting Numbers: [139] 139,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 67:[87, 78], Operations: ['49+16=65', '13+65=78'] Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,67 unequal: No Solution Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[87, 52], Operations: ['49+16=65', '65-13=52'] Exploring Operation: 87+52=139, Resulting Numbers: [139] 139,67 unequal: No Solution Exploring Operation: 87*52=4524, Resulting Numbers: [4524] 4524,67 unequal: No Solution Exploring Operation: 87-52=35, Resulting Numbers: [35] 35,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 67:[65, 100], Operations: ['49+16=65', '13+87=100'] Exploring Operation: 65+100=165, Resulting Numbers: [165] 165,67 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 65*100=6500, Resulting Numbers: [6500] 6500,67 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: 67:[49, 87, 29], Operations: ['13+16=29'] Exploring Operation: 49+29=78, Resulting Numbers: [87, 78] Generated Node #0,3,0: 67:[87, 78] Operation: 49+29=78 Exploring Operation: 49-29=20, Resulting Numbers: [87, 20] Generated Node #0,3,1: 67:[87, 20] Operation: 49-29=20 Exploring Operation: 87-49=38, Resulting Numbers: [29, 38] Generated Node #0,3,2: 67:[29, 38] Operation: 87-49=38 Exploring Operation: 87-29=58, Resulting Numbers: [49, 58] Generated Node #0,3,3: 67:[49, 58] Operation: 87-29=58 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 67:[49, 58], Operations: ['13+16=29', '87-29=58'] Exploring Operation: 49*58=2842, Resulting Numbers: [2842] 2842,67 unequal: No Solution Exploring Operation: 49+58=107, Resulting Numbers: [107] 107,67 unequal: No Solution Exploring Operation: 58-49=9, Resulting Numbers: [9] 9,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 67:[87, 78], Operations: ['13+16=29', '49+29=78'] Exploring Operation: 87-78=9, Resulting Numbers: [9] 9,67 unequal: No Solution Exploring Operation: 87+78=165, Resulting Numbers: [165] 165,67 unequal: No Solution Exploring Operation: 87*78=6786, Resulting Numbers: [6786] 6786,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 67:[87, 20], Operations: ['13+16=29', '49-29=20'] Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,67 unequal: No Solution Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[49, 13, 16, 87], Operations: [] Exploring Operation: 13+16=29, Resulting Numbers: [49, 87, 29] Generated Node #0,3: 67:[49, 87, 29] Operation: 13+16=29 Moving to Node #0,3 Current State: 67:[49, 87, 29], Operations: ['13+16=29'] Exploring Operation: 49-29=20, Resulting Numbers: [87, 20] Generated Node #0,3,1: 67:[87, 20] Operation: 49-29=20 Moving to Node #0,3,1 Current State: 67:[87, 20], Operations: ['13+16=29', '49-29=20'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 62, 10, 3, 11 ]
44
[ "62-10=52", "11-3=8", "52-8=44" ]
Current State: 44:[62, 10, 3, 11], Operations: [] Exploring Operation: 62-10=52, Resulting Numbers: [3, 11, 52] Generated Node #2: [3, 11, 52] from Operation: 62-10=52 Current State: 44:[3, 11, 52], Operations: ['62-10=52'] Exploring Operation: 11-3=8, Resulting Numbers: [52, 8] Generated Node #3: [52, 8] from Operation: 11-3=8 Current State: 44:[52, 8], Operations: ['62-10=52', '11-3=8'] Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[62, 10, 3, 11], Operations: [] Exploring Operation: 10+3=13, Resulting Numbers: [62, 11, 13] Generated Node #0,0: 44:[62, 11, 13] Operation: 10+3=13 Exploring Operation: 10+11=21, Resulting Numbers: [62, 3, 21] Generated Node #0,1: 44:[62, 3, 21] Operation: 10+11=21 Exploring Operation: 62-11=51, Resulting Numbers: [10, 3, 51] Generated Node #0,2: 44:[10, 3, 51] Operation: 62-11=51 Exploring Operation: 62-10=52, Resulting Numbers: [3, 11, 52] Generated Node #0,3: 44:[3, 11, 52] Operation: 62-10=52 Exploring Operation: 62-3=59, Resulting Numbers: [10, 11, 59] Generated Node #0,4: 44:[10, 11, 59] Operation: 62-3=59 Moving to Node #0,2 Current State: 44:[10, 3, 51], Operations: ['62-11=51'] Exploring Operation: 10+3=13, Resulting Numbers: [51, 13] Generated Node #0,2,0: 44:[51, 13] Operation: 10+3=13 Exploring Operation: 51-10=41, Resulting Numbers: [3, 41] Generated Node #0,2,1: 44:[3, 41] Operation: 51-10=41 Exploring Operation: 51/3=17, Resulting Numbers: [10, 17] Generated Node #0,2,2: 44:[10, 17] Operation: 51/3=17 Exploring Operation: 51-3=48, Resulting Numbers: [10, 48] Generated Node #0,2,3: 44:[10, 48] Operation: 51-3=48 Exploring Operation: 10-3=7, Resulting Numbers: [51, 7] Generated Node #0,2,4: 44:[51, 7] Operation: 10-3=7 Moving to Node #0,3 Current State: 44:[3, 11, 52], Operations: ['62-10=52'] Exploring Operation: 3+11=14, Resulting Numbers: [52, 14] Generated Node #0,3,0: 44:[52, 14] Operation: 3+11=14 Exploring Operation: 52-11=41, Resulting Numbers: [3, 41] Generated Node #0,3,1: 44:[3, 41] Operation: 52-11=41 Exploring Operation: 52-3=49, Resulting Numbers: [11, 49] Generated Node #0,3,2: 44:[11, 49] Operation: 52-3=49 Exploring Operation: 11-3=8, Resulting Numbers: [52, 8] Generated Node #0,3,3: 44:[52, 8] Operation: 11-3=8 Exploring Operation: 3+52=55, Resulting Numbers: [11, 55] Generated Node #0,3,4: 44:[11, 55] Operation: 3+52=55 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 44:[3, 41], Operations: ['62-10=52', '52-11=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[62, 10, 3, 11], Operations: [] Exploring Operation: 62-10=52, Resulting Numbers: [3, 11, 52] Generated Node #0,3: 44:[3, 11, 52] Operation: 62-10=52 Moving to Node #0,3 Current State: 44:[3, 11, 52], Operations: ['62-10=52'] Exploring Operation: 52-11=41, Resulting Numbers: [3, 41] Generated Node #0,3,1: 44:[3, 41] Operation: 52-11=41 Moving to Node #0,3,1 Current State: 44:[3, 41], Operations: ['62-10=52', '52-11=41'] Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 75, 26, 65, 35 ]
16
[ "75-35=40", "26*40=1040", "1040/65=16" ]
Current State: 16:[75, 26, 65, 35], Operations: [] Exploring Operation: 75-35=40, Resulting Numbers: [26, 65, 40] Generated Node #2: [26, 65, 40] from Operation: 75-35=40 Current State: 16:[26, 65, 40], Operations: ['75-35=40'] Exploring Operation: 26*40=1040, Resulting Numbers: [65, 1040] Generated Node #3: [65, 1040] from Operation: 26*40=1040 Current State: 16:[65, 1040], Operations: ['75-35=40', '26*40=1040'] Exploring Operation: 1040/65=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[75, 26, 65, 35], Operations: [] Exploring Operation: 65-26=39, Resulting Numbers: [75, 35, 39] Generated Node #0,0: 16:[75, 35, 39] Operation: 65-26=39 Exploring Operation: 75-65=10, Resulting Numbers: [26, 35, 10] Generated Node #0,1: 16:[26, 35, 10] Operation: 75-65=10 Exploring Operation: 65-35=30, Resulting Numbers: [75, 26, 30] Generated Node #0,2: 16:[75, 26, 30] Operation: 65-35=30 Exploring Operation: 75-35=40, Resulting Numbers: [26, 65, 40] Generated Node #0,3: 16:[26, 65, 40] Operation: 75-35=40 Exploring Operation: 75-26=49, Resulting Numbers: [65, 35, 49] Generated Node #0,4: 16:[65, 35, 49] Operation: 75-26=49 Moving to Node #0,1 Current State: 16:[26, 35, 10], Operations: ['75-65=10'] Exploring Operation: 26+10=36, Resulting Numbers: [35, 36] Generated Node #0,1,0: 16:[35, 36] Operation: 26+10=36 Exploring Operation: 26-10=16, Resulting Numbers: [35, 16] Generated Node #0,1,1: 16:[35, 16] Operation: 26-10=16 Exploring Operation: 35-10=25, Resulting Numbers: [26, 25] Generated Node #0,1,2: 16:[26, 25] Operation: 35-10=25 Exploring Operation: 35-26=9, Resulting Numbers: [10, 9] Generated Node #0,1,3: 16:[10, 9] Operation: 35-26=9 Exploring Operation: 35+10=45, Resulting Numbers: [26, 45] Generated Node #0,1,4: 16:[26, 45] Operation: 35+10=45 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 16:[10, 9], Operations: ['75-65=10', '35-26=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,16 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 16:[35, 16], Operations: ['75-65=10', '26-10=16'] Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,16 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 16:[26, 25], Operations: ['75-65=10', '35-10=25'] Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 26+25=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 26*25=650, Resulting Numbers: [650] 650,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 16:[35, 36], Operations: ['75-65=10', '26+10=36'] Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,16 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 16:[26, 45], Operations: ['75-65=10', '35+10=45'] Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,16 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,16 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: 16:[26, 65, 40], Operations: ['75-35=40'] Exploring Operation: 26+65=91, Resulting Numbers: [40, 91] Generated Node #0,3,0: 16:[40, 91] Operation: 26+65=91 Exploring Operation: 65-40=25, Resulting Numbers: [26, 25] Generated Node #0,3,1: 16:[26, 25] Operation: 65-40=25 Exploring Operation: 26+40=66, Resulting Numbers: [65, 66] Generated Node #0,3,2: 16:[65, 66] Operation: 26+40=66 Exploring Operation: 40-26=14, Resulting Numbers: [65, 14] Generated Node #0,3,3: 16:[65, 14] Operation: 40-26=14 Exploring Operation: 65-26=39, Resulting Numbers: [40, 39] Generated Node #0,3,4: 16:[40, 39] Operation: 65-26=39 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 16:[26, 25], Operations: ['75-35=40', '65-40=25'] Exploring Operation: 26*25=650, Resulting Numbers: [650] 650,16 unequal: No Solution Exploring Operation: 26+25=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 26-25=1, Resulting Numbers: [1] 1,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 16:[40, 39], Operations: ['75-35=40', '65-26=39'] Exploring Operation: 40+39=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 40*39=1560, Resulting Numbers: [1560] 1560,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 16:[65, 14], Operations: ['75-35=40', '40-26=14'] Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,16 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 16:[40, 91], Operations: ['75-35=40', '26+65=91'] Exploring Operation: 40+91=131, Resulting Numbers: [131] 131,16 unequal: No Solution Exploring Operation: 40*91=3640, Resulting Numbers: [3640] 3640,16 unequal: No Solution Exploring Operation: 91-40=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 16:[65, 66], Operations: ['75-35=40', '26+40=66'] Exploring Operation: 65*66=4290, Resulting Numbers: [4290] 4290,16 unequal: No Solution Exploring Operation: 66-65=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 65+66=131, Resulting Numbers: [131] 131,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 16:[75, 26, 30], Operations: ['65-35=30'] Exploring Operation: 30-26=4, Resulting Numbers: [75, 4] Generated Node #0,2,0: 16:[75, 4] Operation: 30-26=4 Exploring Operation: 75-30=45, Resulting Numbers: [26, 45] Generated Node #0,2,1: 16:[26, 45] Operation: 75-30=45 Exploring Operation: 75+26=101, Resulting Numbers: [30, 101] Generated Node #0,2,2: 16:[30, 101] Operation: 75+26=101 Exploring Operation: 75+30=105, Resulting Numbers: [26, 105] Generated Node #0,2,3: 16:[26, 105] Operation: 75+30=105 Exploring Operation: 75-26=49, Resulting Numbers: [30, 49] Generated Node #0,2,4: 16:[30, 49] Operation: 75-26=49 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 16:[26, 45], Operations: ['65-35=30', '75-30=45'] Exploring Operation: 26+45=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 45-26=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 26*45=1170, Resulting Numbers: [1170] 1170,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 16:[30, 49], Operations: ['65-35=30', '75-26=49'] Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,16 unequal: No Solution Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 16:[75, 4], Operations: ['65-35=30', '30-26=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 75*4=300, Resulting Numbers: [300] 300,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 16:[30, 101], Operations: ['65-35=30', '75+26=101'] Exploring Operation: 30+101=131, Resulting Numbers: [131] 131,16 unequal: No Solution Exploring Operation: 30*101=3030, Resulting Numbers: [3030] 3030,16 unequal: No Solution Exploring Operation: 101-30=71, Resulting Numbers: [71] 71,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 16:[26, 105], Operations: ['65-35=30', '75+30=105'] Exploring Operation: 26+105=131, Resulting Numbers: [131] 131,16 unequal: No Solution Exploring Operation: 105-26=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 26*105=2730, Resulting Numbers: [2730] 2730,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 16:[75, 35, 39], Operations: ['65-26=39'] Exploring Operation: 75+35=110, Resulting Numbers: [39, 110] Generated Node #0,0,0: 16:[39, 110] Operation: 75+35=110 Exploring Operation: 75+39=114, Resulting Numbers: [35, 114] Generated Node #0,0,1: 16:[35, 114] Operation: 75+39=114 Exploring Operation: 75-35=40, Resulting Numbers: [39, 40] Generated Node #0,0,2: 16:[39, 40] Operation: 75-35=40 Exploring Operation: 75-39=36, Resulting Numbers: [35, 36] Generated Node #0,0,3: 16:[35, 36] Operation: 75-39=36 Exploring Operation: 39-35=4, Resulting Numbers: [75, 4] Generated Node #0,0,4: 16:[75, 4] Operation: 39-35=4 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[35, 36], Operations: ['65-26=39', '75-39=36'] Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,16 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 16:[39, 40], Operations: ['65-26=39', '75-35=40'] Exploring Operation: 39*40=1560, Resulting Numbers: [1560] 1560,16 unequal: No Solution Exploring Operation: 39+40=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 40-39=1, Resulting Numbers: [1] 1,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 16:[75, 4], Operations: ['65-26=39', '39-35=4'] Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 75*4=300, Resulting Numbers: [300] 300,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[39, 110], Operations: ['65-26=39', '75+35=110'] Exploring Operation: 110-39=71, Resulting Numbers: [71] 71,16 unequal: No Solution Exploring Operation: 39*110=4290, Resulting Numbers: [4290] 4290,16 unequal: No Solution Exploring Operation: 39+110=149, Resulting Numbers: [149] 149,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[35, 114], Operations: ['65-26=39', '75+39=114'] Exploring Operation: 114-35=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 35*114=3990, Resulting Numbers: [3990] 3990,16 unequal: No Solution Exploring Operation: 35+114=149, Resulting Numbers: [149] 149,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 16:[65, 35, 49], Operations: ['75-26=49'] Exploring Operation: 65-35=30, Resulting Numbers: [49, 30] Generated Node #0,4,0: 16:[49, 30] Operation: 65-35=30 Exploring Operation: 65+35=100, Resulting Numbers: [49, 100] Generated Node #0,4,1: 16:[49, 100] Operation: 65+35=100 Exploring Operation: 65-49=16, Resulting Numbers: [35, 16] Generated Node #0,4,2: 16:[35, 16] Operation: 65-49=16 Exploring Operation: 49-35=14, Resulting Numbers: [65, 14] Generated Node #0,4,3: 16:[65, 14] Operation: 49-35=14 Exploring Operation: 65+49=114, Resulting Numbers: [35, 114] Generated Node #0,4,4: 16:[35, 114] Operation: 65+49=114 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 16:[35, 16], Operations: ['75-26=49', '65-49=16'] Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 16:[49, 30], Operations: ['75-26=49', '65-35=30'] Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 49*30=1470, Resulting Numbers: [1470] 1470,16 unequal: No Solution Exploring Operation: 49+30=79, Resulting Numbers: [79] 79,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 16:[65, 14], Operations: ['75-26=49', '49-35=14'] Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,16 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 16:[49, 100], Operations: ['75-26=49', '65+35=100'] Exploring Operation: 100-49=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 49*100=4900, Resulting Numbers: [4900] 4900,16 unequal: No Solution Exploring Operation: 49+100=149, Resulting Numbers: [149] 149,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 16:[35, 114], Operations: ['75-26=49', '65+49=114'] Exploring Operation: 35*114=3990, Resulting Numbers: [3990] 3990,16 unequal: No Solution Exploring Operation: 114-35=79, Resulting Numbers: [79] 79,16 unequal: No Solution Exploring Operation: 35+114=149, Resulting Numbers: [149] 149,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 66, 36, 51, 38 ]
76
[ "66+36=102", "102/51=2", "38*2=76" ]
Current State: 76:[66, 36, 51, 38], Operations: [] Exploring Operation: 66+36=102, Resulting Numbers: [51, 38, 102] Generated Node #2: [51, 38, 102] from Operation: 66+36=102 Current State: 76:[51, 38, 102], Operations: ['66+36=102'] Exploring Operation: 102/51=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 102/51=2 Current State: 76:[38, 2], Operations: ['66+36=102', '102/51=2'] Exploring Operation: 38*2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[66, 36, 51, 38], Operations: [] Exploring Operation: 51-36=15, Resulting Numbers: [66, 38, 15] Generated Node #0,0: 76:[66, 38, 15] Operation: 51-36=15 Exploring Operation: 66-51=15, Resulting Numbers: [36, 38, 15] Generated Node #0,1: 76:[36, 38, 15] Operation: 66-51=15 Exploring Operation: 66-36=30, Resulting Numbers: [51, 38, 30] Generated Node #0,2: 76:[51, 38, 30] Operation: 66-36=30 Exploring Operation: 51-38=13, Resulting Numbers: [66, 36, 13] Generated Node #0,3: 76:[66, 36, 13] Operation: 51-38=13 Exploring Operation: 36+51=87, Resulting Numbers: [66, 38, 87] Generated Node #0,4: 76:[66, 38, 87] Operation: 36+51=87 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[36, 38, 15], Operations: ['66-51=15'] Exploring Operation: 38-36=2, Resulting Numbers: [15, 2] Generated Node #0,1,0: 76:[15, 2] Operation: 38-36=2 Exploring Operation: 36+15=51, Resulting Numbers: [38, 51] Generated Node #0,1,1: 76:[38, 51] Operation: 36+15=51 Exploring Operation: 36+38=74, Resulting Numbers: [15, 74] Generated Node #0,1,2: 76:[15, 74] Operation: 36+38=74 Exploring Operation: 36-15=21, Resulting Numbers: [38, 21] Generated Node #0,1,3: 76:[38, 21] Operation: 36-15=21 Exploring Operation: 38-15=23, Resulting Numbers: [36, 23] Generated Node #0,1,4: 76:[36, 23] Operation: 38-15=23 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 76:[38, 21], Operations: ['66-51=15', '36-15=21'] Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 38*21=798, Resulting Numbers: [798] 798,76 unequal: No Solution Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,76 unequal: No Solution No 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: 76:[15, 2], Operations: ['66-51=15', '38-36=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,76 unequal: No Solution No 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: 76:[15, 74], Operations: ['66-51=15', '36+38=74'] Exploring Operation: 15*74=1110, Resulting Numbers: [1110] 1110,76 unequal: No Solution Exploring Operation: 15+74=89, Resulting Numbers: [89] 89,76 unequal: No Solution Exploring Operation: 74-15=59, Resulting Numbers: [59] 59,76 unequal: No Solution No 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: 76:[36, 23], Operations: ['66-51=15', '38-15=23'] Exploring Operation: 36*23=828, Resulting Numbers: [828] 828,76 unequal: No Solution Exploring Operation: 36+23=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,76 unequal: No Solution No 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: 76:[38, 51], Operations: ['66-51=15', '36+15=51'] Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,76 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,76 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: 76:[66, 38, 15], Operations: ['51-36=15'] Exploring Operation: 66-15=51, Resulting Numbers: [38, 51] Generated Node #0,0,0: 76:[38, 51] Operation: 66-15=51 Exploring Operation: 66+15=81, Resulting Numbers: [38, 81] Generated Node #0,0,1: 76:[38, 81] Operation: 66+15=81 Exploring Operation: 66-38=28, Resulting Numbers: [15, 28] Generated Node #0,0,2: 76:[15, 28] Operation: 66-38=28 Exploring Operation: 38+15=53, Resulting Numbers: [66, 53] Generated Node #0,0,3: 76:[66, 53] Operation: 38+15=53 Exploring Operation: 38-15=23, Resulting Numbers: [66, 23] Generated Node #0,0,4: 76:[66, 23] Operation: 38-15=23 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 76:[38, 81], Operations: ['51-36=15', '66+15=81'] Exploring Operation: 81-38=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 38*81=3078, Resulting Numbers: [3078] 3078,76 unequal: No Solution Exploring Operation: 38+81=119, Resulting Numbers: [119] 119,76 unequal: No Solution No 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: 76:[38, 51], Operations: ['51-36=15', '66-15=51'] Exploring Operation: 38+51=89, Resulting Numbers: [89] 89,76 unequal: No Solution Exploring Operation: 38*51=1938, Resulting Numbers: [1938] 1938,76 unequal: No Solution Exploring Operation: 51-38=13, Resulting Numbers: [13] 13,76 unequal: No Solution No 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: 76:[15, 28], Operations: ['51-36=15', '66-38=28'] Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 15*28=420, Resulting Numbers: [420] 420,76 unequal: No Solution Exploring Operation: 15+28=43, Resulting Numbers: [43] 43,76 unequal: No Solution No 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: 76:[66, 23], Operations: ['51-36=15', '38-15=23'] Exploring Operation: 66*23=1518, Resulting Numbers: [1518] 1518,76 unequal: No Solution Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 66+23=89, Resulting Numbers: [89] 89,76 unequal: No Solution No 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: 76:[66, 53], Operations: ['51-36=15', '38+15=53'] Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 66*53=3498, Resulting Numbers: [3498] 3498,76 unequal: No Solution Exploring Operation: 66+53=119, Resulting Numbers: [119] 119,76 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: 76:[66, 36, 13], Operations: ['51-38=13'] Exploring Operation: 66+13=79, Resulting Numbers: [36, 79] Generated Node #0,3,0: 76:[36, 79] Operation: 66+13=79 Exploring Operation: 36-13=23, Resulting Numbers: [66, 23] Generated Node #0,3,1: 76:[66, 23] Operation: 36-13=23 Exploring Operation: 36+13=49, Resulting Numbers: [66, 49] Generated Node #0,3,2: 76:[66, 49] Operation: 36+13=49 Exploring Operation: 66-36=30, Resulting Numbers: [13, 30] Generated Node #0,3,3: 76:[13, 30] Operation: 66-36=30 Exploring Operation: 66-13=53, Resulting Numbers: [36, 53] Generated Node #0,3,4: 76:[36, 53] Operation: 66-13=53 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 76:[36, 79], Operations: ['51-38=13', '66+13=79'] Exploring Operation: 36*79=2844, Resulting Numbers: [2844] 2844,76 unequal: No Solution Exploring Operation: 36+79=115, Resulting Numbers: [115] 115,76 unequal: No Solution Exploring Operation: 79-36=43, Resulting Numbers: [43] 43,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 76:[66, 23], Operations: ['51-38=13', '36-13=23'] Exploring Operation: 66+23=89, Resulting Numbers: [89] 89,76 unequal: No Solution Exploring Operation: 66*23=1518, Resulting Numbers: [1518] 1518,76 unequal: No Solution Exploring Operation: 66-23=43, Resulting Numbers: [43] 43,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 76:[13, 30], Operations: ['51-38=13', '66-36=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 76:[36, 53], Operations: ['51-38=13', '66-13=53'] Exploring Operation: 36+53=89, Resulting Numbers: [89] 89,76 unequal: No Solution Exploring Operation: 36*53=1908, Resulting Numbers: [1908] 1908,76 unequal: No Solution Exploring Operation: 53-36=17, Resulting Numbers: [17] 17,76 unequal: No Solution No 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: 76:[66, 49], Operations: ['51-38=13', '36+13=49'] Exploring Operation: 66+49=115, Resulting Numbers: [115] 115,76 unequal: No Solution Exploring Operation: 66*49=3234, Resulting Numbers: [3234] 3234,76 unequal: No Solution Exploring Operation: 66-49=17, Resulting Numbers: [17] 17,76 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: 76:[51, 38, 30], Operations: ['66-36=30'] Exploring Operation: 51-30=21, Resulting Numbers: [38, 21] Generated Node #0,2,0: 76:[38, 21] Operation: 51-30=21 Exploring Operation: 51-38=13, Resulting Numbers: [30, 13] Generated Node #0,2,1: 76:[30, 13] Operation: 51-38=13 Exploring Operation: 51+38=89, Resulting Numbers: [30, 89] Generated Node #0,2,2: 76:[30, 89] Operation: 51+38=89 Exploring Operation: 51+30=81, Resulting Numbers: [38, 81] Generated Node #0,2,3: 76:[38, 81] Operation: 51+30=81 Exploring Operation: 38-30=8, Resulting Numbers: [51, 8] Generated Node #0,2,4: 76:[51, 8] Operation: 38-30=8 Moving to Node #0,2,0 Current State: 76:[38, 21], Operations: ['66-36=30', '51-30=21'] Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 38*21=798, Resulting Numbers: [798] 798,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[38, 81], Operations: ['66-36=30', '51+30=81'] Exploring Operation: 38+81=119, Resulting Numbers: [119] 119,76 unequal: No Solution Exploring Operation: 81-38=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 38*81=3078, Resulting Numbers: [3078] 3078,76 unequal: No Solution Moving to Node #0,2,1 Current State: 76:[30, 13], Operations: ['66-36=30', '51-38=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 30*13=390, Resulting Numbers: [390] 390,76 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[51, 8], Operations: ['66-36=30', '38-30=8'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,76 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,76 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[30, 89], Operations: ['66-36=30', '51+38=89'] Exploring Operation: 30*89=2670, Resulting Numbers: [2670] 2670,76 unequal: No Solution Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 30+89=119, Resulting Numbers: [119] 119,76 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 #0,4 Current State: 76:[66, 38, 87], Operations: ['36+51=87'] Exploring Operation: 38+87=125, Resulting Numbers: [66, 125] Generated Node #0,4,0: 76:[66, 125] Operation: 38+87=125 Exploring Operation: 66-38=28, Resulting Numbers: [87, 28] Generated Node #0,4,1: 76:[87, 28] Operation: 66-38=28 Exploring Operation: 66+38=104, Resulting Numbers: [87, 104] Generated Node #0,4,2: 76:[87, 104] Operation: 66+38=104 Exploring Operation: 87-66=21, Resulting Numbers: [38, 21] Generated Node #0,4,3: 76:[38, 21] Operation: 87-66=21 Exploring Operation: 87-38=49, Resulting Numbers: [66, 49] Generated Node #0,4,4: 76:[66, 49] Operation: 87-38=49 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 76:[38, 21], Operations: ['36+51=87', '87-66=21'] Exploring Operation: 38+21=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 38*21=798, Resulting Numbers: [798] 798,76 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 76:[87, 28], Operations: ['36+51=87', '66-38=28'] Exploring Operation: 87*28=2436, Resulting Numbers: [2436] 2436,76 unequal: No Solution Exploring Operation: 87-28=59, Resulting Numbers: [59] 59,76 unequal: No Solution Exploring Operation: 87+28=115, Resulting Numbers: [115] 115,76 unequal: No Solution No 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: 76:[66, 49], Operations: ['36+51=87', '87-38=49'] Exploring Operation: 66-49=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 66*49=3234, Resulting Numbers: [3234] 3234,76 unequal: No Solution Exploring Operation: 66+49=115, Resulting Numbers: [115] 115,76 unequal: No Solution No 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: 76:[87, 104], Operations: ['36+51=87', '66+38=104'] Exploring Operation: 87*104=9048, Resulting Numbers: [9048] 9048,76 unequal: No Solution Exploring Operation: 87+104=191, Resulting Numbers: [191] 191,76 unequal: No Solution Exploring Operation: 104-87=17, Resulting Numbers: [17] 17,76 unequal: No Solution No 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: 76:[66, 125], Operations: ['36+51=87', '38+87=125'] Exploring Operation: 66*125=8250, Resulting Numbers: [8250] 8250,76 unequal: No Solution Exploring Operation: 66+125=191, Resulting Numbers: [191] 191,76 unequal: No Solution Exploring Operation: 125-66=59, Resulting Numbers: [59] 59,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 7, 4, 51, 37 ]
63
[ "51-37=14", "4*14=56", "7+56=63" ]
Current State: 63:[7, 4, 51, 37], Operations: [] Exploring Operation: 51-37=14, Resulting Numbers: [7, 4, 14] Generated Node #2: [7, 4, 14] from Operation: 51-37=14 Current State: 63:[7, 4, 14], Operations: ['51-37=14'] Exploring Operation: 4*14=56, Resulting Numbers: [7, 56] Generated Node #3: [7, 56] from Operation: 4*14=56 Current State: 63:[7, 56], Operations: ['51-37=14', '4*14=56'] Exploring Operation: 7+56=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[7, 4, 51, 37], Operations: [] Exploring Operation: 51-37=14, Resulting Numbers: [7, 4, 14] Generated Node #0,0: 63:[7, 4, 14] Operation: 51-37=14 Exploring Operation: 4+51=55, Resulting Numbers: [7, 37, 55] Generated Node #0,1: 63:[7, 37, 55] Operation: 4+51=55 Exploring Operation: 7+51=58, Resulting Numbers: [4, 37, 58] Generated Node #0,2: 63:[4, 37, 58] Operation: 7+51=58 Exploring Operation: 37-7=30, Resulting Numbers: [4, 51, 30] Generated Node #0,3: 63:[4, 51, 30] Operation: 37-7=30 Moving to Node #0,0 Current State: 63:[7, 4, 14], Operations: ['51-37=14'] Exploring Operation: 14-4=10, Resulting Numbers: [7, 10] Generated Node #0,0,0: 63:[7, 10] Operation: 14-4=10 Exploring Operation: 7+14=21, Resulting Numbers: [4, 21] Generated Node #0,0,1: 63:[4, 21] Operation: 7+14=21 Exploring Operation: 14-7=7, Resulting Numbers: [4, 7] Generated Node #0,0,2: 63:[4, 7] Operation: 14-7=7 Exploring Operation: 14/7=2, Resulting Numbers: [4, 2] Generated Node #0,0,3: 63:[4, 2] Operation: 14/7=2 Moving to Node #0,3 Current State: 63:[4, 51, 30], Operations: ['37-7=30'] Exploring Operation: 51+30=81, Resulting Numbers: [4, 81] Generated Node #0,3,0: 63:[4, 81] Operation: 51+30=81 Exploring Operation: 4+51=55, Resulting Numbers: [30, 55] Generated Node #0,3,1: 63:[30, 55] Operation: 4+51=55 Exploring Operation: 30-4=26, Resulting Numbers: [51, 26] Generated Node #0,3,2: 63:[51, 26] Operation: 30-4=26 Exploring Operation: 51-30=21, Resulting Numbers: [4, 21] Generated Node #0,3,3: 63:[4, 21] Operation: 51-30=21 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 63:[4, 21], Operations: ['37-7=30', '51-30=21'] Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,63 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 63:[30, 55], Operations: ['37-7=30', '4+51=55'] Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 30*55=1650, Resulting Numbers: [1650] 1650,63 unequal: No Solution Exploring Operation: 30+55=85, Resulting Numbers: [85] 85,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 63:[51, 26], Operations: ['37-7=30', '30-4=26'] Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,63 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,63 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 63:[4, 81], Operations: ['37-7=30', '51+30=81'] Exploring Operation: 4*81=324, Resulting Numbers: [324] 324,63 unequal: No Solution Exploring Operation: 81-4=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 4+81=85, Resulting Numbers: [85] 85,63 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: 63:[4, 37, 58], Operations: ['7+51=58'] Exploring Operation: 4+37=41, Resulting Numbers: [58, 41] Generated Node #0,2,0: 63:[58, 41] Operation: 4+37=41 Exploring Operation: 58-37=21, Resulting Numbers: [4, 21] Generated Node #0,2,1: 63:[4, 21] Operation: 58-37=21 Exploring Operation: 4+58=62, Resulting Numbers: [37, 62] Generated Node #0,2,2: 63:[37, 62] Operation: 4+58=62 Exploring Operation: 37-4=33, Resulting Numbers: [58, 33] Generated Node #0,2,3: 63:[58, 33] Operation: 37-4=33 Moving to Node #0,1 Current State: 63:[7, 37, 55], Operations: ['4+51=55'] Exploring Operation: 7+37=44, Resulting Numbers: [55, 44] Generated Node #0,1,0: 63:[55, 44] Operation: 7+37=44 Exploring Operation: 7+55=62, Resulting Numbers: [37, 62] Generated Node #0,1,1: 63:[37, 62] Operation: 7+55=62 Exploring Operation: 37-7=30, Resulting Numbers: [55, 30] Generated Node #0,1,2: 63:[55, 30] Operation: 37-7=30 Exploring Operation: 55-37=18, Resulting Numbers: [7, 18] Generated Node #0,1,3: 63:[7, 18] Operation: 55-37=18 Moving to Node #0,0,0 Current State: 63:[7, 10], Operations: ['51-37=14', '14-4=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[4, 7], Operations: ['51-37=14', '14-7=7'] Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,63 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,63 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,63 unequal: No Solution Moving to Node #0,0,1 Current State: 63:[4, 21], Operations: ['51-37=14', '7+14=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,63 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,63 unequal: No Solution Moving to Node #0,2,1 Current State: 63:[4, 21], Operations: ['7+51=58', '58-37=21'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,63 unequal: No Solution Moving to Node #0,0,3 Current State: 63:[4, 2], Operations: ['51-37=14', '14/7=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,63 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,63 unequal: No Solution Moving to Node #0,1,3 Current State: 63:[7, 18], Operations: ['4+51=55', '55-37=18'] Exploring Operation: 7+18=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 7*18=126, Resulting Numbers: [126] 126,63 unequal: No Solution Moving to Node #0,2,3 Current State: 63:[58, 33], Operations: ['7+51=58', '37-4=33'] Exploring Operation: 58*33=1914, Resulting Numbers: [1914] 1914,63 unequal: No Solution Exploring Operation: 58-33=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 58+33=91, Resulting Numbers: [91] 91,63 unequal: No Solution Moving to Node #0,2,2 Current State: 63:[37, 62], Operations: ['7+51=58', '4+58=62'] Exploring Operation: 37*62=2294, Resulting Numbers: [2294] 2294,63 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,63 unequal: No Solution Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,63 unequal: No Solution Moving to Node #0,1,1 Current State: 63:[37, 62], Operations: ['4+51=55', '7+55=62'] Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,63 unequal: No Solution Exploring Operation: 37*62=2294, Resulting Numbers: [2294] 2294,63 unequal: No Solution Moving to Node #0,1,2 Current State: 63:[55, 30], Operations: ['4+51=55', '37-7=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,63 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,63 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,63 unequal: No Solution Moving to Node #0,2,0 Current State: 63:[58, 41], Operations: ['7+51=58', '4+37=41'] Exploring Operation: 58*41=2378, Resulting Numbers: [2378] 2378,63 unequal: No Solution Exploring Operation: 58-41=17, Resulting Numbers: [17] 17,63 unequal: No Solution Exploring Operation: 58+41=99, Resulting Numbers: [99] 99,63 unequal: No Solution Moving to Node #0,1,0 Current State: 63:[55, 44], Operations: ['4+51=55', '7+37=44'] Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,63 unequal: No Solution Exploring Operation: 55+44=99, Resulting Numbers: [99] 99,63 unequal: No Solution Exploring Operation: 55*44=2420, Resulting Numbers: [2420] 2420,63 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 25, 60, 16, 88 ]
37
[ "60-25=35", "88-16=72", "72-35=37" ]
Current State: 37:[25, 60, 16, 88], Operations: [] Exploring Operation: 60-25=35, Resulting Numbers: [16, 88, 35] Generated Node #2: [16, 88, 35] from Operation: 60-25=35 Current State: 37:[16, 88, 35], Operations: ['60-25=35'] Exploring Operation: 88-16=72, Resulting Numbers: [35, 72] Generated Node #3: [35, 72] from Operation: 88-16=72 Current State: 37:[35, 72], Operations: ['60-25=35', '88-16=72'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[25, 60, 16, 88], Operations: [] Exploring Operation: 88-25=63, Resulting Numbers: [60, 16, 63] Generated Node #0,0: 37:[60, 16, 63] Operation: 88-25=63 Exploring Operation: 88-60=28, Resulting Numbers: [25, 16, 28] Generated Node #0,1: 37:[25, 16, 28] Operation: 88-60=28 Moving to Node #0,1 Current State: 37:[25, 16, 28], Operations: ['88-60=28'] Exploring Operation: 25+16=41, Resulting Numbers: [28, 41] Generated Node #0,1,0: 37:[28, 41] Operation: 25+16=41 Exploring Operation: 16+28=44, Resulting Numbers: [25, 44] Generated Node #0,1,1: 37:[25, 44] Operation: 16+28=44 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[28, 41], Operations: ['88-60=28', '25+16=41'] Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 28+41=69, Resulting Numbers: [69] 69,37 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:[25, 44], Operations: ['88-60=28', '16+28=44'] Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,37 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,37 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: 37:[60, 16, 63], Operations: ['88-25=63'] Exploring Operation: 63-16=47, Resulting Numbers: [60, 47] Generated Node #0,0,0: 37:[60, 47] Operation: 63-16=47 Exploring Operation: 60-16=44, Resulting Numbers: [63, 44] Generated Node #0,0,1: 37:[63, 44] Operation: 60-16=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[60, 47], Operations: ['88-25=63', '63-16=47'] Exploring Operation: 60-47=13, Resulting Numbers: [13] 13,37 unequal: No Solution Exploring Operation: 60+47=107, Resulting Numbers: [107] 107,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[63, 44], Operations: ['88-25=63', '60-16=44'] Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 63+44=107, Resulting Numbers: [107] 107,37 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
[ 37, 35, 32, 65 ]
74
[ "35+32=67", "67-65=2", "37*2=74" ]
Current State: 74:[37, 35, 32, 65], Operations: [] Exploring Operation: 35+32=67, Resulting Numbers: [37, 65, 67] Generated Node #2: [37, 65, 67] from Operation: 35+32=67 Current State: 74:[37, 65, 67], Operations: ['35+32=67'] Exploring Operation: 67-65=2, Resulting Numbers: [37, 2] Generated Node #3: [37, 2] from Operation: 67-65=2 Current State: 74:[37, 2], Operations: ['35+32=67', '67-65=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[37, 35, 32, 65], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [37, 65, 3] Generated Node #0,0: 74:[37, 65, 3] Operation: 35-32=3 Exploring Operation: 65-32=33, Resulting Numbers: [37, 35, 33] Generated Node #0,1: 74:[37, 35, 33] Operation: 65-32=33 Start Sub Search at level 1: Moving to Node #0,1 Current State: 74:[37, 35, 33], Operations: ['65-32=33'] Exploring Operation: 37-35=2, Resulting Numbers: [33, 2] Generated Node #0,1,0: 74:[33, 2] Operation: 37-35=2 Exploring Operation: 35-33=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 74:[37, 2] Operation: 35-33=2 Moving to Node #0,1,1 Current State: 74:[37, 2], Operations: ['65-32=33', '35-33=2'] Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[37, 35, 32, 65], Operations: [] Exploring Operation: 65-32=33, Resulting Numbers: [37, 35, 33] Generated Node #0,1: 74:[37, 35, 33] Operation: 65-32=33 Moving to Node #0,1 Current State: 74:[37, 35, 33], Operations: ['65-32=33'] Exploring Operation: 35-33=2, Resulting Numbers: [37, 2] Generated Node #0,1,1: 74:[37, 2] Operation: 35-33=2 Moving to Node #0,1,1 Current State: 74:[37, 2], Operations: ['65-32=33', '35-33=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 38, 2, 19, 70 ]
32
[ "38/2=19", "70-19=51", "51-19=32" ]
Current State: 32:[38, 2, 19, 70], Operations: [] Exploring Operation: 38/2=19, Resulting Numbers: [19, 70, 19] Generated Node #2: [19, 70, 19] from Operation: 38/2=19 Current State: 32:[19, 70, 19], Operations: ['38/2=19'] Exploring Operation: 70-19=51, Resulting Numbers: [51] 51,32 equal: Goal Reached Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[38, 2, 19, 70], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [38, 19, 35] Generated Node #0,0: 32:[38, 19, 35] Operation: 70/2=35 Exploring Operation: 70-38=32, Resulting Numbers: [2, 19, 32] Generated Node #0,1: 32:[2, 19, 32] Operation: 70-38=32 Exploring Operation: 38/19=2, Resulting Numbers: [2, 70, 2] Generated Node #0,2: 32:[2, 70, 2] Operation: 38/19=2 Exploring Operation: 70-19=51, Resulting Numbers: [38, 2, 51] Generated Node #0,3: 32:[38, 2, 51] Operation: 70-19=51 Moving to Node #0,1 Current State: 32:[2, 19, 32], Operations: ['70-38=32'] Exploring Operation: 32/2=16, Resulting Numbers: [19, 16] Generated Node #0,1,0: 32:[19, 16] Operation: 32/2=16 Exploring Operation: 32-19=13, Resulting Numbers: [2, 13] Generated Node #0,1,1: 32:[2, 13] Operation: 32-19=13 Exploring Operation: 19-2=17, Resulting Numbers: [32, 17] Generated Node #0,1,2: 32:[32, 17] Operation: 19-2=17 Exploring Operation: 2+19=21, Resulting Numbers: [32, 21] Generated Node #0,1,3: 32:[32, 21] Operation: 2+19=21 Moving to Node #0,0 Current State: 32:[38, 19, 35], Operations: ['70/2=35'] Exploring Operation: 38/19=2, Resulting Numbers: [35, 2] Generated Node #0,0,0: 32:[35, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [35, 19] Generated Node #0,0,1: 32:[35, 19] Operation: 38-19=19 Exploring Operation: 35-19=16, Resulting Numbers: [38, 16] Generated Node #0,0,2: 32:[38, 16] Operation: 35-19=16 Exploring Operation: 38-35=3, Resulting Numbers: [19, 3] Generated Node #0,0,3: 32:[19, 3] Operation: 38-35=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[35, 2], Operations: ['70/2=35', '38/19=2'] Exploring Operation: 35+2=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 35*2=70, Resulting Numbers: [70] 70,32 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 32:[19, 3], Operations: ['70/2=35', '38-35=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,32 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[35, 19], Operations: ['70/2=35', '38-19=19'] Exploring Operation: 35-19=16, Resulting Numbers: [16] 16,32 unequal: No Solution Exploring Operation: 35*19=665, Resulting Numbers: [665] 665,32 unequal: No Solution Exploring Operation: 35+19=54, Resulting Numbers: [54] 54,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[38, 16], Operations: ['70/2=35', '35-19=16'] Exploring Operation: 38+16=54, Resulting Numbers: [54] 54,32 unequal: No Solution Exploring Operation: 38-16=22, Resulting Numbers: [22] 22,32 unequal: No Solution Exploring Operation: 38*16=608, Resulting Numbers: [608] 608,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 32:[38, 2, 51], Operations: ['70-19=51'] Exploring Operation: 51-2=49, Resulting Numbers: [38, 49] Generated Node #0,3,0: 32:[38, 49] Operation: 51-2=49 Exploring Operation: 38/2=19, Resulting Numbers: [51, 19] Generated Node #0,3,1: 32:[51, 19] Operation: 38/2=19 Exploring Operation: 38-2=36, Resulting Numbers: [51, 36] Generated Node #0,3,2: 32:[51, 36] Operation: 38-2=36 Exploring Operation: 51-38=13, Resulting Numbers: [2, 13] Generated Node #0,3,3: 32:[2, 13] Operation: 51-38=13 Moving to Node #0,2 Current State: 32:[2, 70, 2], Operations: ['38/19=2'] Exploring Operation: 70-2=68, Resulting Numbers: [2, 68] Generated Node #0,2,0: 32:[2, 68] Operation: 70-2=68 Exploring Operation: 70/2=35, Resulting Numbers: [2, 35] Generated Node #0,2,1: 32:[2, 35] Operation: 70/2=35 Exploring Operation: 70-2=68, Resulting Numbers: [2, 68] Generated Node #0,2,2: 32:[2, 68] Operation: 70-2=68 Exploring Operation: 70/2=35, Resulting Numbers: [2, 35] Generated Node #0,2,3: 32:[2, 35] Operation: 70/2=35 Moving to Node #0,1,2 Current State: 32:[32, 17], Operations: ['70-38=32', '19-2=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,32 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,32 unequal: No Solution Moving to Node #0,1,1 Current State: 32:[2, 13], Operations: ['70-38=32', '32-19=13'] Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,32 unequal: No Solution Moving to Node #0,1,0 Current State: 32:[19, 16], Operations: ['70-38=32', '32/2=16'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,32 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,32 unequal: No Solution Moving to Node #0,3,3 Current State: 32:[2, 13], Operations: ['70-19=51', '51-38=13'] Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,32 unequal: No Solution Exploring Operation: 2*13=26, Resulting Numbers: [26] 26,32 unequal: No Solution Exploring Operation: 2+13=15, Resulting Numbers: [15] 15,32 unequal: No Solution Moving to Node #0,2,3 Current State: 32:[2, 35], Operations: ['38/19=2', '70/2=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,32 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,32 unequal: No Solution Moving to Node #0,2,1 Current State: 32:[2, 35], Operations: ['38/19=2', '70/2=35'] Exploring Operation: 2*35=70, Resulting Numbers: [70] 70,32 unequal: No Solution Exploring Operation: 2+35=37, Resulting Numbers: [37] 37,32 unequal: No Solution Exploring Operation: 35-2=33, Resulting Numbers: [33] 33,32 unequal: No Solution Moving to Node #0,1,3 Current State: 32:[32, 21], Operations: ['70-38=32', '2+19=21'] Exploring Operation: 32+21=53, Resulting Numbers: [53] 53,32 unequal: No Solution Exploring Operation: 32*21=672, Resulting Numbers: [672] 672,32 unequal: No Solution Exploring Operation: 32-21=11, Resulting Numbers: [11] 11,32 unequal: No Solution Moving to Node #0,3,1 Current State: 32:[51, 19], Operations: ['70-19=51', '38/2=19'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[38, 2, 19, 70], Operations: [] Exploring Operation: 70-19=51, Resulting Numbers: [38, 2, 51] Generated Node #0,3: 32:[38, 2, 51] Operation: 70-19=51 Moving to Node #0,3 Current State: 32:[38, 2, 51], Operations: ['70-19=51'] Exploring Operation: 38/2=19, Resulting Numbers: [51, 19] Generated Node #0,3,1: 32:[51, 19] Operation: 38/2=19 Moving to Node #0,3,1 Current State: 32:[51, 19], Operations: ['70-19=51', '38/2=19'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
0.949653
hs_4
mult_heuristic
[ 4, 84, 54, 26 ]
49
[ "84/4=21", "54-26=28", "21+28=49" ]
Current State: 49:[4, 84, 54, 26], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [54, 26, 21] Generated Node #2: [54, 26, 21] from Operation: 84/4=21 Current State: 49:[54, 26, 21], Operations: ['84/4=21'] Exploring Operation: 54-26=28, Resulting Numbers: [21, 28] Generated Node #3: [21, 28] from Operation: 54-26=28 Current State: 49:[21, 28], Operations: ['84/4=21', '54-26=28'] Exploring Operation: 21+28=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[4, 84, 54, 26], Operations: [] Exploring Operation: 84-26=58, Resulting Numbers: [4, 54, 58] Generated Node #0,0: 49:[4, 54, 58] Operation: 84-26=58 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[4, 54, 58], Operations: ['84-26=58'] Exploring Operation: 58-54=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 49:[4, 4] Operation: 58-54=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[4, 4], Operations: ['84-26=58', '58-54=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,49 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
[ 36, 17, 41, 96 ]
32
[ "41-17=24", "96/24=4", "36-4=32" ]
Current State: 32:[36, 17, 41, 96], Operations: [] Exploring Operation: 41-17=24, Resulting Numbers: [36, 96, 24] Generated Node #2: [36, 96, 24] from Operation: 41-17=24 Current State: 32:[36, 96, 24], Operations: ['41-17=24'] Exploring Operation: 96/24=4, Resulting Numbers: [36, 4] Generated Node #3: [36, 4] from Operation: 96/24=4 Current State: 32:[36, 4], Operations: ['41-17=24', '96/24=4'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[36, 17, 41, 96], Operations: [] Exploring Operation: 96-41=55, Resulting Numbers: [36, 17, 55] Generated Node #0,0: 32:[36, 17, 55] Operation: 96-41=55 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[36, 17, 55], Operations: ['96-41=55'] Exploring Operation: 55-36=19, Resulting Numbers: [17, 19] Generated Node #0,0,0: 32:[17, 19] Operation: 55-36=19 Moving to Node #0,0,0 Current State: 32:[17, 19], Operations: ['96-41=55', '55-36=19'] Exploring Operation: 19-17=2, Resulting Numbers: [2] 2,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 44, 2, 72, 6 ]
86
[ "44+6=50", "72/2=36", "50+36=86" ]
Current State: 86:[44, 2, 72, 6], Operations: [] Exploring Operation: 44+6=50, Resulting Numbers: [2, 72, 50] Generated Node #2: [2, 72, 50] from Operation: 44+6=50 Current State: 86:[2, 72, 50], Operations: ['44+6=50'] Exploring Operation: 72/2=36, Resulting Numbers: [50, 36] Generated Node #3: [50, 36] from Operation: 72/2=36 Current State: 86:[50, 36], Operations: ['44+6=50', '72/2=36'] Exploring Operation: 50+36=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[44, 2, 72, 6], Operations: [] Exploring Operation: 72+6=78, Resulting Numbers: [44, 2, 78] Generated Node #0,0: 86:[44, 2, 78] Operation: 72+6=78 Exploring Operation: 72/6=12, Resulting Numbers: [44, 2, 12] Generated Node #0,1: 86:[44, 2, 12] Operation: 72/6=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[44, 2, 78], Operations: ['72+6=78'] Exploring Operation: 2+78=80, Resulting Numbers: [44, 80] Generated Node #0,0,0: 86:[44, 80] Operation: 2+78=80 Exploring Operation: 78/2=39, Resulting Numbers: [44, 39] Generated Node #0,0,1: 86:[44, 39] Operation: 78/2=39 Moving to Node #0,0,1 Current State: 86:[44, 39], Operations: ['72+6=78', '78/2=39'] Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[44, 80], Operations: ['72+6=78', '2+78=80'] Exploring Operation: 80-44=36, Resulting Numbers: [36] 36,86 unequal: No Solution Exploring Operation: 44+80=124, Resulting Numbers: [124] 124,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[44, 2, 12], Operations: ['72/6=12'] Exploring Operation: 12/2=6, Resulting Numbers: [44, 6] Generated Node #0,1,0: 86:[44, 6] Operation: 12/2=6 Exploring Operation: 12-2=10, Resulting Numbers: [44, 10] Generated Node #0,1,1: 86:[44, 10] Operation: 12-2=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[44, 6], Operations: ['72/6=12', '12/2=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,86 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,86 unequal: No Solution No 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: 86:[44, 10], Operations: ['72/6=12', '12-2=10'] Exploring Operation: 44-10=34, Resulting Numbers: [34] 34,86 unequal: No Solution Exploring Operation: 44+10=54, Resulting Numbers: [54] 54,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 99, 52, 44, 63 ]
35
[ "63-52=11", "99/11=9", "44-9=35" ]
Current State: 35:[99, 52, 44, 63], Operations: [] Exploring Operation: 63-52=11, Resulting Numbers: [99, 44, 11] Generated Node #2: [99, 44, 11] from Operation: 63-52=11 Current State: 35:[99, 44, 11], Operations: ['63-52=11'] Exploring Operation: 99/11=9, Resulting Numbers: [44, 9] Generated Node #3: [44, 9] from Operation: 99/11=9 Current State: 35:[44, 9], Operations: ['63-52=11', '99/11=9'] Exploring Operation: 44-9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[99, 52, 44, 63], Operations: [] Exploring Operation: 99-63=36, Resulting Numbers: [52, 44, 36] Generated Node #0,0: 35:[52, 44, 36] Operation: 99-63=36 Exploring Operation: 99-44=55, Resulting Numbers: [52, 63, 55] Generated Node #0,1: 35:[52, 63, 55] Operation: 99-44=55 Exploring Operation: 99-52=47, Resulting Numbers: [44, 63, 47] Generated Node #0,2: 35:[44, 63, 47] Operation: 99-52=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[52, 44, 36], Operations: ['99-63=36'] Exploring Operation: 44-36=8, Resulting Numbers: [52, 8] Generated Node #0,0,0: 35:[52, 8] Operation: 44-36=8 Exploring Operation: 52-36=16, Resulting Numbers: [44, 16] Generated Node #0,0,1: 35:[44, 16] Operation: 52-36=16 Exploring Operation: 52-44=8, Resulting Numbers: [36, 8] Generated Node #0,0,2: 35:[36, 8] Operation: 52-44=8 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 35:[36, 8], Operations: ['99-63=36', '52-44=8'] Exploring Operation: 36*8=288, Resulting Numbers: [288] 288,35 unequal: No Solution Exploring Operation: 36+8=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 36-8=28, Resulting Numbers: [28] 28,35 unequal: No Solution No 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: 35:[52, 8], Operations: ['99-63=36', '44-36=8'] Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,35 unequal: No Solution Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,35 unequal: No Solution No 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: 35:[44, 16], Operations: ['99-63=36', '52-36=16'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,35 unequal: No Solution Exploring Operation: 44*16=704, Resulting Numbers: [704] 704,35 unequal: No Solution Exploring Operation: 44+16=60, Resulting Numbers: [60] 60,35 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 35:[44, 63, 47], Operations: ['99-52=47'] Exploring Operation: 63-47=16, Resulting Numbers: [44, 16] Generated Node #0,2,0: 35:[44, 16] Operation: 63-47=16 Exploring Operation: 47-44=3, Resulting Numbers: [63, 3] Generated Node #0,2,1: 35:[63, 3] Operation: 47-44=3 Exploring Operation: 63-44=19, Resulting Numbers: [47, 19] Generated Node #0,2,2: 35:[47, 19] Operation: 63-44=19 Moving to Node #0,2,0 Current State: 35:[44, 16], Operations: ['99-52=47', '63-47=16'] Exploring Operation: 44-16=28, Resulting Numbers: [28] 28,35 unequal: No Solution Exploring Operation: 44*16=704, Resulting Numbers: [704] 704,35 unequal: No Solution Exploring Operation: 44+16=60, Resulting Numbers: [60] 60,35 unequal: No Solution Moving to Node #0,2,2 Current State: 35:[47, 19], Operations: ['99-52=47', '63-44=19'] Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,35 unequal: No Solution Exploring Operation: 47*19=893, Resulting Numbers: [893] 893,35 unequal: No Solution Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,35 unequal: No Solution Moving to Node #0,2,1 Current State: 35:[63, 3], Operations: ['99-52=47', '47-44=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,35 unequal: No Solution No 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: 35:[52, 63, 55], Operations: ['99-44=55'] Exploring Operation: 55-52=3, Resulting Numbers: [63, 3] Generated Node #0,1,0: 35:[63, 3] Operation: 55-52=3 Exploring Operation: 63-52=11, Resulting Numbers: [55, 11] Generated Node #0,1,1: 35:[55, 11] Operation: 63-52=11 Exploring Operation: 63-55=8, Resulting Numbers: [52, 8] Generated Node #0,1,2: 35:[52, 8] Operation: 63-55=8 Moving to Node #0,1,2 Current State: 35:[52, 8], Operations: ['99-44=55', '63-55=8'] Exploring Operation: 52*8=416, Resulting Numbers: [416] 416,35 unequal: No Solution Exploring Operation: 52-8=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 52+8=60, Resulting Numbers: [60] 60,35 unequal: No Solution Moving to Node #0,1,1 Current State: 35:[55, 11], Operations: ['99-44=55', '63-52=11'] Exploring Operation: 55+11=66, Resulting Numbers: [66] 66,35 unequal: No Solution Exploring Operation: 55-11=44, Resulting Numbers: [44] 44,35 unequal: No Solution Exploring Operation: 55/11=5, Resulting Numbers: [5] 5,35 unequal: No Solution Moving to Node #0,1,0 Current State: 35:[63, 3], Operations: ['99-44=55', '55-52=3'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,35 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,35 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,35 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
[ 50, 10, 63, 10 ]
30
[ "50+10=60", "63-60=3", "10*3=30" ]
Current State: 30:[50, 10, 63, 10], Operations: [] Exploring Operation: 50+10=60, Resulting Numbers: [63, 60] Generated Node #2: [63, 60] from Operation: 50+10=60 Current State: 30:[63, 60], Operations: ['50+10=60'] Exploring Operation: 63-60=3, Resulting Numbers: [3] 3,30 equal: Goal Reached Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[50, 10, 63, 10], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [10, 10, 13] Generated Node #0,0: 30:[10, 10, 13] Operation: 63-50=13 Exploring Operation: 50/10=5, Resulting Numbers: [10, 63, 5] Generated Node #0,1: 30:[10, 63, 5] Operation: 50/10=5 Exploring Operation: 50/10=5, Resulting Numbers: [63, 10, 5] Generated Node #0,2: 30:[63, 10, 5] Operation: 50/10=5 Exploring Operation: 50-10=40, Resulting Numbers: [63, 10, 40] Generated Node #0,3: 30:[63, 10, 40] Operation: 50-10=40 Moving to Node #0,0 Current State: 30:[10, 10, 13], Operations: ['63-50=13'] Exploring Operation: 10/10=1, Resulting Numbers: [13, 1] Generated Node #0,0,0: 30:[13, 1] Operation: 10/10=1 Exploring Operation: 13-10=3, Resulting Numbers: [10, 3] Generated Node #0,0,1: 30:[10, 3] Operation: 13-10=3 Exploring Operation: 10-10=0, Resulting Numbers: [13, 0] Generated Node #0,0,2: 30:[13, 0] Operation: 10-10=0 Exploring Operation: 13-10=3, Resulting Numbers: [10, 3] Generated Node #0,0,3: 30:[10, 3] Operation: 13-10=3 Moving to Node #0,2 Current State: 30:[63, 10, 5], Operations: ['50/10=5'] Exploring Operation: 10-5=5, Resulting Numbers: [63, 5] Generated Node #0,2,0: 30:[63, 5] Operation: 10-5=5 Exploring Operation: 10+5=15, Resulting Numbers: [63, 15] Generated Node #0,2,1: 30:[63, 15] Operation: 10+5=15 Exploring Operation: 63-10=53, Resulting Numbers: [5, 53] Generated Node #0,2,2: 30:[5, 53] Operation: 63-10=53 Exploring Operation: 63-5=58, Resulting Numbers: [10, 58] Generated Node #0,2,3: 30:[10, 58] Operation: 63-5=58 Moving to Node #0,1 Current State: 30:[10, 63, 5], Operations: ['50/10=5'] Exploring Operation: 10+5=15, Resulting Numbers: [63, 15] Generated Node #0,1,0: 30:[63, 15] Operation: 10+5=15 Exploring Operation: 63-5=58, Resulting Numbers: [10, 58] Generated Node #0,1,1: 30:[10, 58] Operation: 63-5=58 Exploring Operation: 63-10=53, Resulting Numbers: [5, 53] Generated Node #0,1,2: 30:[5, 53] Operation: 63-10=53 Exploring Operation: 10-5=5, Resulting Numbers: [63, 5] Generated Node #0,1,3: 30:[63, 5] Operation: 10-5=5 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[5, 53], Operations: ['50/10=5', '63-10=53'] Exploring Operation: 5+53=58, Resulting Numbers: [58] 58,30 unequal: No Solution Exploring Operation: 5*53=265, Resulting Numbers: [265] 265,30 unequal: No Solution Exploring Operation: 53-5=48, Resulting Numbers: [48] 48,30 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 #0,1,1 Current State: 30:[10, 58], Operations: ['50/10=5', '63-5=58'] Exploring Operation: 58-10=48, Resulting Numbers: [48] 48,30 unequal: No Solution Exploring Operation: 10*58=580, Resulting Numbers: [580] 580,30 unequal: No Solution Exploring Operation: 10+58=68, Resulting Numbers: [68] 68,30 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:[63, 15], Operations: ['50/10=5', '10+5=15'] Exploring Operation: 63+15=78, Resulting Numbers: [78] 78,30 unequal: No Solution Exploring Operation: 63-15=48, Resulting Numbers: [48] 48,30 unequal: No Solution Exploring Operation: 63*15=945, Resulting Numbers: [945] 945,30 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 #0,1,3 Current State: 30:[63, 5], Operations: ['50/10=5', '10-5=5'] Exploring Operation: 63*5=315, Resulting Numbers: [315] 315,30 unequal: No Solution Exploring Operation: 63+5=68, Resulting Numbers: [68] 68,30 unequal: No Solution Exploring Operation: 63-5=58, Resulting Numbers: [58] 58,30 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: 30:[63, 10, 40], Operations: ['50-10=40'] Exploring Operation: 40/10=4, Resulting Numbers: [63, 4] Generated Node #0,3,0: 30:[63, 4] Operation: 40/10=4 Exploring Operation: 40-10=30, Resulting Numbers: [63, 30] Generated Node #0,3,1: 30:[63, 30] Operation: 40-10=30 Exploring Operation: 63-10=53, Resulting Numbers: [40, 53] Generated Node #0,3,2: 30:[40, 53] Operation: 63-10=53 Exploring Operation: 63-40=23, Resulting Numbers: [10, 23] Generated Node #0,3,3: 30:[10, 23] Operation: 63-40=23 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 30:[10, 23], Operations: ['50-10=40', '63-40=23'] Exploring Operation: 10+23=33, Resulting Numbers: [33] 33,30 unequal: No Solution Exploring Operation: 23-10=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 10*23=230, Resulting Numbers: [230] 230,30 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 #0,3,1 Current State: 30:[63, 30], Operations: ['50-10=40', '40-10=30'] Exploring Operation: 63+30=93, Resulting Numbers: [93] 93,30 unequal: No Solution Exploring Operation: 63-30=33, Resulting Numbers: [33] 33,30 unequal: No Solution Exploring Operation: 63*30=1890, Resulting Numbers: [1890] 1890,30 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 #0,3,2 Current State: 30:[40, 53], Operations: ['50-10=40', '63-10=53'] Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 40*53=2120, Resulting Numbers: [2120] 2120,30 unequal: No Solution Exploring Operation: 40+53=93, Resulting Numbers: [93] 93,30 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 #0,3,0 Current State: 30:[63, 4], Operations: ['50-10=40', '40/10=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,30 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,30 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:[10, 3], Operations: ['63-50=13', '13-10=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[50, 10, 63, 10], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [10, 10, 13] Generated Node #0,0: 30:[10, 10, 13] Operation: 63-50=13 Moving to Node #0,0 Current State: 30:[10, 10, 13], Operations: ['63-50=13'] Exploring Operation: 13-10=3, Resulting Numbers: [10, 3] Generated Node #0,0,1: 30:[10, 3] Operation: 13-10=3 Moving to Node #0,0,1 Current State: 30:[10, 3], Operations: ['63-50=13', '13-10=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.957465
hs_4
sum_heuristic
[ 4, 55, 59, 79 ]
39
[ "4+55=59", "79-59=20", "59-20=39" ]
Current State: 39:[4, 55, 59, 79], Operations: [] Exploring Operation: 4+55=59, Resulting Numbers: [59, 79, 59] Generated Node #2: [59, 79, 59] from Operation: 4+55=59 Current State: 39:[59, 79, 59], Operations: ['4+55=59'] Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,39 equal: Goal Reached Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[4, 55, 59, 79], Operations: [] Exploring Operation: 79-55=24, Resulting Numbers: [4, 59, 24] Generated Node #0,0: 39:[4, 59, 24] Operation: 79-55=24 Exploring Operation: 79-59=20, Resulting Numbers: [4, 55, 20] Generated Node #0,1: 39:[4, 55, 20] Operation: 79-59=20 Exploring Operation: 59-55=4, Resulting Numbers: [4, 79, 4] Generated Node #0,2: 39:[4, 79, 4] Operation: 59-55=4 Moving to Node #0,1 Current State: 39:[4, 55, 20], Operations: ['79-59=20'] Exploring Operation: 20/4=5, Resulting Numbers: [55, 5] Generated Node #0,1,0: 39:[55, 5] Operation: 20/4=5 Exploring Operation: 55-20=35, Resulting Numbers: [4, 35] Generated Node #0,1,1: 39:[4, 35] Operation: 55-20=35 Exploring Operation: 55-4=51, Resulting Numbers: [20, 51] Generated Node #0,1,2: 39:[20, 51] Operation: 55-4=51 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[4, 35], Operations: ['79-59=20', '55-20=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[4, 55, 59, 79], Operations: [] Exploring Operation: 79-59=20, Resulting Numbers: [4, 55, 20] Generated Node #0,1: 39:[4, 55, 20] Operation: 79-59=20 Moving to Node #0,1 Current State: 39:[4, 55, 20], Operations: ['79-59=20'] Exploring Operation: 55-20=35, Resulting Numbers: [4, 35] Generated Node #0,1,1: 39:[4, 35] Operation: 55-20=35 Moving to Node #0,1,1 Current State: 39:[4, 35], Operations: ['79-59=20', '55-20=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 87, 5, 13, 85 ]
37
[ "87+13=100", "85+100=185", "185/5=37" ]
Current State: 37:[87, 5, 13, 85], Operations: [] Exploring Operation: 87+13=100, Resulting Numbers: [5, 85, 100] Generated Node #2: [5, 85, 100] from Operation: 87+13=100 Current State: 37:[5, 85, 100], Operations: ['87+13=100'] Exploring Operation: 85+100=185, Resulting Numbers: [5, 185] Generated Node #3: [5, 185] from Operation: 85+100=185 Current State: 37:[5, 185], Operations: ['87+13=100', '85+100=185'] Exploring Operation: 185/5=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[87, 5, 13, 85], Operations: [] Exploring Operation: 85/5=17, Resulting Numbers: [87, 13, 17] Generated Node #0,0: 37:[87, 13, 17] Operation: 85/5=17 Exploring Operation: 87-85=2, Resulting Numbers: [5, 13, 2] Generated Node #0,1: 37:[5, 13, 2] Operation: 87-85=2 Exploring Operation: 87-5=82, Resulting Numbers: [13, 85, 82] Generated Node #0,2: 37:[13, 85, 82] Operation: 87-5=82 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[5, 13, 2], Operations: ['87-85=2'] Exploring Operation: 5+13=18, Resulting Numbers: [2, 18] Generated Node #0,1,0: 37:[2, 18] Operation: 5+13=18 Exploring Operation: 5*2=10, Resulting Numbers: [13, 10] Generated Node #0,1,1: 37:[13, 10] Operation: 5*2=10 Exploring Operation: 13*2=26, Resulting Numbers: [5, 26] Generated Node #0,1,2: 37:[5, 26] Operation: 13*2=26 Moving to Node #0,1,2 Current State: 37:[5, 26], Operations: ['87-85=2', '13*2=26'] Exploring Operation: 5+26=31, Resulting Numbers: [31] 31,37 unequal: No Solution Exploring Operation: 5*26=130, Resulting Numbers: [130] 130,37 unequal: No Solution Exploring Operation: 26-5=21, Resulting Numbers: [21] 21,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[13, 10], Operations: ['87-85=2', '5*2=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,37 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,37 unequal: No Solution Moving to Node #0,1,0 Current State: 37:[2, 18], Operations: ['87-85=2', '5+13=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,37 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[87, 13, 17], Operations: ['85/5=17'] Exploring Operation: 13+17=30, Resulting Numbers: [87, 30] Generated Node #0,0,0: 37:[87, 30] Operation: 13+17=30 Exploring Operation: 87-13=74, Resulting Numbers: [17, 74] Generated Node #0,0,1: 37:[17, 74] Operation: 87-13=74 Exploring Operation: 87-17=70, Resulting Numbers: [13, 70] Generated Node #0,0,2: 37:[13, 70] Operation: 87-17=70 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[87, 30], Operations: ['85/5=17', '13+17=30'] Exploring Operation: 87-30=57, Resulting Numbers: [57] 57,37 unequal: No Solution Exploring Operation: 87*30=2610, Resulting Numbers: [2610] 2610,37 unequal: No Solution Exploring Operation: 87+30=117, Resulting Numbers: [117] 117,37 unequal: No Solution No 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: 37:[17, 74], Operations: ['85/5=17', '87-13=74'] Exploring Operation: 74-17=57, Resulting Numbers: [57] 57,37 unequal: No Solution Exploring Operation: 17*74=1258, Resulting Numbers: [1258] 1258,37 unequal: No Solution Exploring Operation: 17+74=91, Resulting Numbers: [91] 91,37 unequal: No Solution No 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: 37:[13, 70], Operations: ['85/5=17', '87-17=70'] Exploring Operation: 70-13=57, Resulting Numbers: [57] 57,37 unequal: No Solution Exploring Operation: 13*70=910, Resulting Numbers: [910] 910,37 unequal: No Solution Exploring Operation: 13+70=83, Resulting Numbers: [83] 83,37 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: 37:[13, 85, 82], Operations: ['87-5=82'] Exploring Operation: 85-13=72, Resulting Numbers: [82, 72] Generated Node #0,2,0: 37:[82, 72] Operation: 85-13=72 Exploring Operation: 85-82=3, Resulting Numbers: [13, 3] Generated Node #0,2,1: 37:[13, 3] Operation: 85-82=3 Exploring Operation: 82-13=69, Resulting Numbers: [85, 69] Generated Node #0,2,2: 37:[85, 69] Operation: 82-13=69 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 37:[13, 3], Operations: ['87-5=82', '85-82=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,37 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,37 unequal: No Solution No 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: 37:[82, 72], Operations: ['87-5=82', '85-13=72'] Exploring Operation: 82*72=5904, Resulting Numbers: [5904] 5904,37 unequal: No Solution Exploring Operation: 82+72=154, Resulting Numbers: [154] 154,37 unequal: No Solution Exploring Operation: 82-72=10, Resulting Numbers: [10] 10,37 unequal: No Solution No 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: 37:[85, 69], Operations: ['87-5=82', '82-13=69'] Exploring Operation: 85*69=5865, Resulting Numbers: [5865] 5865,37 unequal: No Solution Exploring Operation: 85+69=154, Resulting Numbers: [154] 154,37 unequal: No Solution Exploring Operation: 85-69=16, Resulting Numbers: [16] 16,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 26, 80, 32, 13 ]
78
[ "26*80=2080", "2080/32=65", "13+65=78" ]
Current State: 78:[26, 80, 32, 13], Operations: [] Exploring Operation: 26*80=2080, Resulting Numbers: [32, 13, 2080] Generated Node #2: [32, 13, 2080] from Operation: 26*80=2080 Current State: 78:[32, 13, 2080], Operations: ['26*80=2080'] Exploring Operation: 2080/32=65, Resulting Numbers: [13, 65] Generated Node #3: [13, 65] from Operation: 2080/32=65 Current State: 78:[13, 65], Operations: ['26*80=2080', '2080/32=65'] Exploring Operation: 13+65=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[26, 80, 32, 13], Operations: [] Exploring Operation: 32-26=6, Resulting Numbers: [80, 13, 6] Generated Node #0,0: 78:[80, 13, 6] Operation: 32-26=6 Exploring Operation: 26+13=39, Resulting Numbers: [80, 32, 39] Generated Node #0,1: 78:[80, 32, 39] Operation: 26+13=39 Exploring Operation: 26/13=2, Resulting Numbers: [80, 32, 2] Generated Node #0,2: 78:[80, 32, 2] Operation: 26/13=2 Exploring Operation: 26-13=13, Resulting Numbers: [80, 32, 13] Generated Node #0,3: 78:[80, 32, 13] Operation: 26-13=13 Moving to Node #0,0 Current State: 78:[80, 13, 6], Operations: ['32-26=6'] Exploring Operation: 13-6=7, Resulting Numbers: [80, 7] Generated Node #0,0,0: 78:[80, 7] Operation: 13-6=7 Exploring Operation: 80+6=86, Resulting Numbers: [13, 86] Generated Node #0,0,1: 78:[13, 86] Operation: 80+6=86 Exploring Operation: 13*6=78, Resulting Numbers: [80, 78] Generated Node #0,0,2: 78:[80, 78] Operation: 13*6=78 Exploring Operation: 80-6=74, Resulting Numbers: [13, 74] Generated Node #0,0,3: 78:[13, 74] Operation: 80-6=74 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[80, 78], Operations: ['32-26=6', '13*6=78'] Exploring Operation: 80-78=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 80+78=158, Resulting Numbers: [158] 158,78 unequal: No Solution Exploring Operation: 80*78=6240, Resulting Numbers: [6240] 6240,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[80, 7], Operations: ['32-26=6', '13-6=7'] Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,78 unequal: No Solution Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[13, 74], Operations: ['32-26=6', '80-6=74'] Exploring Operation: 13*74=962, Resulting Numbers: [962] 962,78 unequal: No Solution Exploring Operation: 74-13=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 13+74=87, Resulting Numbers: [87] 87,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[13, 86], Operations: ['32-26=6', '80+6=86'] Exploring Operation: 86-13=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 13+86=99, Resulting Numbers: [99] 99,78 unequal: No Solution Exploring Operation: 13*86=1118, Resulting Numbers: [1118] 1118,78 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: 78:[80, 32, 2], Operations: ['26/13=2'] Exploring Operation: 80/2=40, Resulting Numbers: [32, 40] Generated Node #0,2,0: 78:[32, 40] Operation: 80/2=40 Exploring Operation: 32-2=30, Resulting Numbers: [80, 30] Generated Node #0,2,1: 78:[80, 30] Operation: 32-2=30 Exploring Operation: 32/2=16, Resulting Numbers: [80, 16] Generated Node #0,2,2: 78:[80, 16] Operation: 32/2=16 Exploring Operation: 80-2=78, Resulting Numbers: [32, 78] Generated Node #0,2,3: 78:[32, 78] Operation: 80-2=78 Moving to Node #0,1 Current State: 78:[80, 32, 39], Operations: ['26+13=39'] Exploring Operation: 32+39=71, Resulting Numbers: [80, 71] Generated Node #0,1,0: 78:[80, 71] Operation: 32+39=71 Exploring Operation: 80-32=48, Resulting Numbers: [39, 48] Generated Node #0,1,1: 78:[39, 48] Operation: 80-32=48 Exploring Operation: 39-32=7, Resulting Numbers: [80, 7] Generated Node #0,1,2: 78:[80, 7] Operation: 39-32=7 Exploring Operation: 80-39=41, Resulting Numbers: [32, 41] Generated Node #0,1,3: 78:[32, 41] Operation: 80-39=41 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 78:[80, 7], Operations: ['26+13=39', '39-32=7'] Exploring Operation: 80-7=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 80+7=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 80*7=560, Resulting Numbers: [560] 560,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 78:[32, 41], Operations: ['26+13=39', '80-39=41'] Exploring Operation: 32*41=1312, Resulting Numbers: [1312] 1312,78 unequal: No Solution Exploring Operation: 32+41=73, Resulting Numbers: [73] 73,78 unequal: No Solution Exploring Operation: 41-32=9, Resulting Numbers: [9] 9,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 78:[80, 71], Operations: ['26+13=39', '32+39=71'] Exploring Operation: 80+71=151, Resulting Numbers: [151] 151,78 unequal: No Solution Exploring Operation: 80*71=5680, Resulting Numbers: [5680] 5680,78 unequal: No Solution Exploring Operation: 80-71=9, Resulting Numbers: [9] 9,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 78:[39, 48], Operations: ['26+13=39', '80-32=48'] Exploring Operation: 39+48=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 39*48=1872, Resulting Numbers: [1872] 1872,78 unequal: No Solution Exploring Operation: 48-39=9, Resulting Numbers: [9] 9,78 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: 78:[80, 32, 13], Operations: ['26-13=13'] Exploring Operation: 80-13=67, Resulting Numbers: [32, 67] Generated Node #0,3,0: 78:[32, 67] Operation: 80-13=67 Exploring Operation: 32+13=45, Resulting Numbers: [80, 45] Generated Node #0,3,1: 78:[80, 45] Operation: 32+13=45 Exploring Operation: 32-13=19, Resulting Numbers: [80, 19] Generated Node #0,3,2: 78:[80, 19] Operation: 32-13=19 Exploring Operation: 80-32=48, Resulting Numbers: [13, 48] Generated Node #0,3,3: 78:[13, 48] Operation: 80-32=48 Moving to Node #0,2,2 Current State: 78:[80, 16], Operations: ['26/13=2', '32/2=16'] Exploring Operation: 80-16=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 80/16=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 80*16=1280, Resulting Numbers: [1280] 1280,78 unequal: No Solution Exploring Operation: 80+16=96, Resulting Numbers: [96] 96,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[32, 78], Operations: ['26/13=2', '80-2=78'] Exploring Operation: 32+78=110, Resulting Numbers: [110] 110,78 unequal: No Solution Exploring Operation: 32*78=2496, Resulting Numbers: [2496] 2496,78 unequal: No Solution Exploring Operation: 78-32=46, Resulting Numbers: [46] 46,78 unequal: No Solution Moving to Node #0,2,1 Current State: 78:[80, 30], Operations: ['26/13=2', '32-2=30'] Exploring Operation: 80-30=50, Resulting Numbers: [50] 50,78 unequal: No Solution Exploring Operation: 80+30=110, Resulting Numbers: [110] 110,78 unequal: No Solution Exploring Operation: 80*30=2400, Resulting Numbers: [2400] 2400,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[32, 40], Operations: ['26/13=2', '80/2=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,78 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,78 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,78 unequal: No Solution Moving to Node #0,3,2 Current State: 78:[80, 19], Operations: ['26-13=13', '32-13=19'] Exploring Operation: 80-19=61, Resulting Numbers: [61] 61,78 unequal: No Solution Exploring Operation: 80*19=1520, Resulting Numbers: [1520] 1520,78 unequal: No Solution Exploring Operation: 80+19=99, Resulting Numbers: [99] 99,78 unequal: No Solution Moving to Node #0,3,1 Current State: 78:[80, 45], Operations: ['26-13=13', '32+13=45'] Exploring Operation: 80+45=125, Resulting Numbers: [125] 125,78 unequal: No Solution Exploring Operation: 80-45=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 80*45=3600, Resulting Numbers: [3600] 3600,78 unequal: No Solution Moving to Node #0,3,3 Current State: 78:[13, 48], Operations: ['26-13=13', '80-32=48'] Exploring Operation: 13*48=624, Resulting Numbers: [624] 624,78 unequal: No Solution Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,78 unequal: No Solution Moving to Node #0,3,0 Current State: 78:[32, 67], Operations: ['26-13=13', '80-13=67'] Exploring Operation: 32*67=2144, Resulting Numbers: [2144] 2144,78 unequal: No Solution Exploring Operation: 67-32=35, Resulting Numbers: [35] 35,78 unequal: No Solution Exploring Operation: 32+67=99, Resulting Numbers: [99] 99,78 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 48, 71, 66, 11 ]
32
[ "71-48=23", "66-11=55", "55-23=32" ]
Current State: 32:[48, 71, 66, 11], Operations: [] Exploring Operation: 71-48=23, Resulting Numbers: [66, 11, 23] Generated Node #2: [66, 11, 23] from Operation: 71-48=23 Current State: 32:[66, 11, 23], Operations: ['71-48=23'] Exploring Operation: 66-11=55, Resulting Numbers: [23, 55] Generated Node #3: [23, 55] from Operation: 66-11=55 Current State: 32:[23, 55], Operations: ['71-48=23', '66-11=55'] Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[48, 71, 66, 11], Operations: [] Exploring Operation: 71-66=5, Resulting Numbers: [48, 11, 5] Generated Node #0,0: 32:[48, 11, 5] Operation: 71-66=5 Moving to Node #0,0 Current State: 32:[48, 11, 5], Operations: ['71-66=5'] Exploring Operation: 48-11=37, Resulting Numbers: [5, 37] Generated Node #0,0,0: 32:[5, 37] Operation: 48-11=37 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[5, 37], Operations: ['71-66=5', '48-11=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[48, 71, 66, 11], Operations: [] Exploring Operation: 71-66=5, Resulting Numbers: [48, 11, 5] Generated Node #0,0: 32:[48, 11, 5] Operation: 71-66=5 Moving to Node #0,0 Current State: 32:[48, 11, 5], Operations: ['71-66=5'] Exploring Operation: 48-11=37, Resulting Numbers: [5, 37] Generated Node #0,0,0: 32:[5, 37] Operation: 48-11=37 Moving to Node #0,0,0 Current State: 32:[5, 37], Operations: ['71-66=5', '48-11=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 19, 69, 59, 59 ]
89
[ "19+69=88", "59/59=1", "88+1=89" ]
Current State: 89:[19, 69, 59, 59], Operations: [] Exploring Operation: 19+69=88, Resulting Numbers: [59, 59, 88] Generated Node #2: [59, 59, 88] from Operation: 19+69=88 Current State: 89:[59, 59, 88], Operations: ['19+69=88'] Exploring Operation: 59/59=1, Resulting Numbers: [88, 1] Generated Node #3: [88, 1] from Operation: 59/59=1 Current State: 89:[88, 1], Operations: ['19+69=88', '59/59=1'] Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[19, 69, 59, 59], Operations: [] Exploring Operation: 19+59=78, Resulting Numbers: [69, 59, 78] Generated Node #0,0: 89:[69, 59, 78] Operation: 19+59=78 Exploring Operation: 19+59=78, Resulting Numbers: [69, 59, 78] Generated Node #0,1: 89:[69, 59, 78] Operation: 19+59=78 Exploring Operation: 19+69=88, Resulting Numbers: [59, 59, 88] Generated Node #0,2: 89:[59, 59, 88] Operation: 19+69=88 Moving to Node #0,0 Current State: 89:[69, 59, 78], Operations: ['19+59=78'] Exploring Operation: 69+78=147, Resulting Numbers: [59, 147] Generated Node #0,0,0: 89:[59, 147] Operation: 69+78=147 Exploring Operation: 59+78=137, Resulting Numbers: [69, 137] Generated Node #0,0,1: 89:[69, 137] Operation: 59+78=137 Exploring Operation: 69+59=128, Resulting Numbers: [78, 128] Generated Node #0,0,2: 89:[78, 128] Operation: 69+59=128 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[78, 128], Operations: ['19+59=78', '69+59=128'] Exploring Operation: 128-78=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 78*128=9984, Resulting Numbers: [9984] 9984,89 unequal: No Solution Exploring Operation: 78+128=206, Resulting Numbers: [206] 206,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[69, 137], Operations: ['19+59=78', '59+78=137'] Exploring Operation: 69*137=9453, Resulting Numbers: [9453] 9453,89 unequal: No Solution Exploring Operation: 137-69=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 69+137=206, Resulting Numbers: [206] 206,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[59, 147], Operations: ['19+59=78', '69+78=147'] Exploring Operation: 147-59=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 59*147=8673, Resulting Numbers: [8673] 8673,89 unequal: No Solution Exploring Operation: 59+147=206, Resulting Numbers: [206] 206,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[69, 59, 78], Operations: ['19+59=78'] Exploring Operation: 69+59=128, Resulting Numbers: [78, 128] Generated Node #0,1,0: 89:[78, 128] Operation: 69+59=128 Exploring Operation: 69+78=147, Resulting Numbers: [59, 147] Generated Node #0,1,1: 89:[59, 147] Operation: 69+78=147 Exploring Operation: 59+78=137, Resulting Numbers: [69, 137] Generated Node #0,1,2: 89:[69, 137] Operation: 59+78=137 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[78, 128], Operations: ['19+59=78', '69+59=128'] Exploring Operation: 128-78=50, Resulting Numbers: [50] 50,89 unequal: No Solution Exploring Operation: 78*128=9984, Resulting Numbers: [9984] 9984,89 unequal: No Solution Exploring Operation: 78+128=206, Resulting Numbers: [206] 206,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[69, 137], Operations: ['19+59=78', '59+78=137'] Exploring Operation: 137-69=68, Resulting Numbers: [68] 68,89 unequal: No Solution Exploring Operation: 69+137=206, Resulting Numbers: [206] 206,89 unequal: No Solution Exploring Operation: 69*137=9453, Resulting Numbers: [9453] 9453,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[59, 147], Operations: ['19+59=78', '69+78=147'] Exploring Operation: 59+147=206, Resulting Numbers: [206] 206,89 unequal: No Solution Exploring Operation: 59*147=8673, Resulting Numbers: [8673] 8673,89 unequal: No Solution Exploring Operation: 147-59=88, Resulting Numbers: [88] 88,89 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: 89:[59, 59, 88], Operations: ['19+69=88'] Exploring Operation: 59+88=147, Resulting Numbers: [59, 147] Generated Node #0,2,0: 89:[59, 147] Operation: 59+88=147 Exploring Operation: 59+59=118, Resulting Numbers: [88, 118] Generated Node #0,2,1: 89:[88, 118] Operation: 59+59=118 Exploring Operation: 59+88=147, Resulting Numbers: [59, 147] Generated Node #0,2,2: 89:[59, 147] Operation: 59+88=147 Moving to Node #0,2,1 Current State: 89:[88, 118], Operations: ['19+69=88', '59+59=118'] Exploring Operation: 88*118=10384, Resulting Numbers: [10384] 10384,89 unequal: No Solution Exploring Operation: 118-88=30, Resulting Numbers: [30] 30,89 unequal: No Solution Exploring Operation: 88+118=206, Resulting Numbers: [206] 206,89 unequal: No Solution Moving to Node #0,2,0 Current State: 89:[59, 147], Operations: ['19+69=88', '59+88=147'] Exploring Operation: 147-59=88, Resulting Numbers: [88] 88,89 unequal: No Solution Exploring Operation: 59+147=206, Resulting Numbers: [206] 206,89 unequal: No Solution Exploring Operation: 59*147=8673, Resulting Numbers: [8673] 8673,89 unequal: No Solution Moving to Node #0,2,2 Current State: 89:[59, 147], Operations: ['19+69=88', '59+88=147'] Exploring Operation: 59*147=8673, Resulting Numbers: [8673] 8673,89 unequal: No Solution Exploring Operation: 59+147=206, Resulting Numbers: [206] 206,89 unequal: No Solution Exploring Operation: 147-59=88, Resulting Numbers: [88] 88,89 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 44, 7, 73, 4 ]
75
[ "44-7=37", "4*37=148", "148-73=75" ]
Current State: 75:[44, 7, 73, 4], Operations: [] Exploring Operation: 44-7=37, Resulting Numbers: [73, 4, 37] Generated Node #2: [73, 4, 37] from Operation: 44-7=37 Current State: 75:[73, 4, 37], Operations: ['44-7=37'] Exploring Operation: 4*37=148, Resulting Numbers: [73, 148] Generated Node #3: [73, 148] from Operation: 4*37=148 Current State: 75:[73, 148], Operations: ['44-7=37', '4*37=148'] Exploring Operation: 148-73=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[44, 7, 73, 4], Operations: [] Exploring Operation: 44/4=11, Resulting Numbers: [7, 73, 11] Generated Node #0,0: 75:[7, 73, 11] Operation: 44/4=11 Exploring Operation: 44-7=37, Resulting Numbers: [73, 4, 37] Generated Node #0,1: 75:[73, 4, 37] Operation: 44-7=37 Exploring Operation: 73-44=29, Resulting Numbers: [7, 4, 29] Generated Node #0,2: 75:[7, 4, 29] Operation: 73-44=29 Moving to Node #0,2 Current State: 75:[7, 4, 29], Operations: ['73-44=29'] Exploring Operation: 29-7=22, Resulting Numbers: [4, 22] Generated Node #0,2,0: 75:[4, 22] Operation: 29-7=22 Exploring Operation: 29-4=25, Resulting Numbers: [7, 25] Generated Node #0,2,1: 75:[7, 25] Operation: 29-4=25 Exploring Operation: 7-4=3, Resulting Numbers: [29, 3] Generated Node #0,2,2: 75:[29, 3] Operation: 7-4=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 75:[7, 25], Operations: ['73-44=29', '29-4=25'] Exploring Operation: 25-7=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 7*25=175, Resulting Numbers: [175] 175,75 unequal: No Solution Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 75:[4, 22], Operations: ['73-44=29', '29-7=22'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,75 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,75 unequal: No Solution Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 75:[29, 3], Operations: ['73-44=29', '7-4=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,75 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,75 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 75:[7, 73, 11], Operations: ['44/4=11'] Exploring Operation: 7+11=18, Resulting Numbers: [73, 18] Generated Node #0,0,0: 75:[73, 18] Operation: 7+11=18 Exploring Operation: 11-7=4, Resulting Numbers: [73, 4] Generated Node #0,0,1: 75:[73, 4] Operation: 11-7=4 Exploring Operation: 7*11=77, Resulting Numbers: [73, 77] Generated Node #0,0,2: 75:[73, 77] Operation: 7*11=77 Moving to Node #0,1 Current State: 75:[73, 4, 37], Operations: ['44-7=37'] Exploring Operation: 37-4=33, Resulting Numbers: [73, 33] Generated Node #0,1,0: 75:[73, 33] Operation: 37-4=33 Exploring Operation: 73-37=36, Resulting Numbers: [4, 36] Generated Node #0,1,1: 75:[4, 36] Operation: 73-37=36 Exploring Operation: 73+4=77, Resulting Numbers: [37, 77] Generated Node #0,1,2: 75:[37, 77] Operation: 73+4=77 Moving to Node #0,0,1 Current State: 75:[73, 4], Operations: ['44/4=11', '11-7=4'] Exploring Operation: 73*4=292, Resulting Numbers: [292] 292,75 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,75 unequal: No Solution Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[73, 77], Operations: ['44/4=11', '7*11=77'] Exploring Operation: 73*77=5621, Resulting Numbers: [5621] 5621,75 unequal: No Solution Exploring Operation: 77-73=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 73+77=150, Resulting Numbers: [150] 150,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[73, 18], Operations: ['44/4=11', '7+11=18'] Exploring Operation: 73-18=55, Resulting Numbers: [55] 55,75 unequal: No Solution Exploring Operation: 73+18=91, Resulting Numbers: [91] 91,75 unequal: No Solution Exploring Operation: 73*18=1314, Resulting Numbers: [1314] 1314,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[73, 33], Operations: ['44-7=37', '37-4=33'] Exploring Operation: 73*33=2409, Resulting Numbers: [2409] 2409,75 unequal: No Solution Exploring Operation: 73-33=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 73+33=106, Resulting Numbers: [106] 106,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[4, 36], Operations: ['44-7=37', '73-37=36'] Exploring Operation: 36-4=32, Resulting Numbers: [32] 32,75 unequal: No Solution Exploring Operation: 36/4=9, Resulting Numbers: [9] 9,75 unequal: No Solution Exploring Operation: 4+36=40, Resulting Numbers: [40] 40,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[37, 77], Operations: ['44-7=37', '73+4=77'] Exploring Operation: 77-37=40, Resulting Numbers: [40] 40,75 unequal: No Solution Exploring Operation: 37*77=2849, Resulting Numbers: [2849] 2849,75 unequal: No Solution Exploring Operation: 37+77=114, Resulting Numbers: [114] 114,75 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 19, 84, 13, 42 ]
94
[ "84-19=65", "42-13=29", "65+29=94" ]
Current State: 94:[19, 84, 13, 42], Operations: [] Exploring Operation: 84-19=65, Resulting Numbers: [13, 42, 65] Generated Node #2: [13, 42, 65] from Operation: 84-19=65 Current State: 94:[13, 42, 65], Operations: ['84-19=65'] Exploring Operation: 42-13=29, Resulting Numbers: [65, 29] Generated Node #3: [65, 29] from Operation: 42-13=29 Current State: 94:[65, 29], Operations: ['84-19=65', '42-13=29'] Exploring Operation: 65+29=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[19, 84, 13, 42], Operations: [] Exploring Operation: 19-13=6, Resulting Numbers: [84, 42, 6] Generated Node #0,0: 94:[84, 42, 6] Operation: 19-13=6 Moving to Node #0,0 Current State: 94:[84, 42, 6], Operations: ['19-13=6'] Exploring Operation: 84/42=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 94:[6, 2] Operation: 84/42=2 Moving to Node #0,0,0 Current State: 94:[6, 2], Operations: ['19-13=6', '84/42=2'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,94 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 4, 5, 25, 52 ]
77
[ "5-4=1", "25+52=77", "1*77=77" ]
Current State: 77:[4, 5, 25, 52], Operations: [] Exploring Operation: 5-4=1, Resulting Numbers: [25, 52, 1] Generated Node #2: [25, 52, 1] from Operation: 5-4=1 Current State: 77:[25, 52, 1], Operations: ['5-4=1'] Exploring Operation: 25+52=77, Resulting Numbers: [1, 77] Generated Node #3: [1, 77] from Operation: 25+52=77 Current State: 77:[1, 77], Operations: ['5-4=1', '25+52=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[4, 5, 25, 52], Operations: [] Exploring Operation: 52-25=27, Resulting Numbers: [4, 5, 27] Generated Node #0,0: 77:[4, 5, 27] Operation: 52-25=27 Exploring Operation: 52/4=13, Resulting Numbers: [5, 25, 13] Generated Node #0,1: 77:[5, 25, 13] Operation: 52/4=13 Exploring Operation: 25/5=5, Resulting Numbers: [4, 52, 5] Generated Node #0,2: 77:[4, 52, 5] Operation: 25/5=5 Exploring Operation: 25+52=77, Resulting Numbers: [4, 5, 77] Generated Node #0,3: 77:[4, 5, 77] Operation: 25+52=77 Exploring Operation: 25-4=21, Resulting Numbers: [5, 52, 21] Generated Node #0,4: 77:[5, 52, 21] Operation: 25-4=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[4, 5, 77], Operations: ['25+52=77'] Exploring Operation: 5+77=82, Resulting Numbers: [4, 82] Generated Node #0,3,0: 77:[4, 82] Operation: 5+77=82 Exploring Operation: 4+5=9, Resulting Numbers: [77, 9] Generated Node #0,3,1: 77:[77, 9] Operation: 4+5=9 Exploring Operation: 5-4=1, Resulting Numbers: [77, 1] Generated Node #0,3,2: 77:[77, 1] Operation: 5-4=1 Exploring Operation: 4+77=81, Resulting Numbers: [5, 81] Generated Node #0,3,3: 77:[5, 81] Operation: 4+77=81 Exploring Operation: 77-4=73, Resulting Numbers: [5, 73] Generated Node #0,3,4: 77:[5, 73] Operation: 77-4=73 Moving to Node #0,3,1 Current State: 77:[77, 9], Operations: ['25+52=77', '4+5=9'] Exploring Operation: 77+9=86, Resulting Numbers: [86] 86,77 unequal: No Solution Exploring Operation: 77-9=68, Resulting Numbers: [68] 68,77 unequal: No Solution Exploring Operation: 77*9=693, Resulting Numbers: [693] 693,77 unequal: No Solution Moving to Node #0,3,3 Current State: 77:[5, 81], Operations: ['25+52=77', '4+77=81'] Exploring Operation: 5*81=405, Resulting Numbers: [405] 405,77 unequal: No Solution Exploring Operation: 5+81=86, Resulting Numbers: [86] 86,77 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,77 unequal: No Solution Moving to Node #0,3,2 Current State: 77:[77, 1], Operations: ['25+52=77', '5-4=1'] Exploring Operation: 77+1=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[4, 5, 25, 52], Operations: [] Exploring Operation: 25+52=77, Resulting Numbers: [4, 5, 77] Generated Node #0,3: 77:[4, 5, 77] Operation: 25+52=77 Moving to Node #0,3 Current State: 77:[4, 5, 77], Operations: ['25+52=77'] Exploring Operation: 5-4=1, Resulting Numbers: [77, 1] Generated Node #0,3,2: 77:[77, 1] Operation: 5-4=1 Moving to Node #0,3,2 Current State: 77:[77, 1], Operations: ['25+52=77', '5-4=1'] Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
mult_heuristic
[ 88, 64, 34, 60 ]
90
[ "64-34=30", "60/30=2", "88+2=90" ]
Current State: 90:[88, 64, 34, 60], Operations: [] Exploring Operation: 64-34=30, Resulting Numbers: [88, 60, 30] Generated Node #2: [88, 60, 30] from Operation: 64-34=30 Current State: 90:[88, 60, 30], Operations: ['64-34=30'] Exploring Operation: 60/30=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 60/30=2 Current State: 90:[88, 2], Operations: ['64-34=30', '60/30=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[88, 64, 34, 60], Operations: [] Exploring Operation: 88-60=28, Resulting Numbers: [64, 34, 28] Generated Node #0,0: 90:[64, 34, 28] Operation: 88-60=28 Exploring Operation: 64+34=98, Resulting Numbers: [88, 60, 98] Generated Node #0,1: 90:[88, 60, 98] Operation: 64+34=98 Exploring Operation: 64-60=4, Resulting Numbers: [88, 34, 4] Generated Node #0,2: 90:[88, 34, 4] Operation: 64-60=4 Exploring Operation: 64-34=30, Resulting Numbers: [88, 60, 30] Generated Node #0,3: 90:[88, 60, 30] Operation: 64-34=30 Exploring Operation: 88-64=24, Resulting Numbers: [34, 60, 24] Generated Node #0,4: 90:[34, 60, 24] Operation: 88-64=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[88, 34, 4], Operations: ['64-60=4'] Exploring Operation: 88-34=54, Resulting Numbers: [4, 54] Generated Node #0,2,0: 90:[4, 54] Operation: 88-34=54 Exploring Operation: 88+4=92, Resulting Numbers: [34, 92] Generated Node #0,2,1: 90:[34, 92] Operation: 88+4=92 Exploring Operation: 88/4=22, Resulting Numbers: [34, 22] Generated Node #0,2,2: 90:[34, 22] Operation: 88/4=22 Exploring Operation: 34-4=30, Resulting Numbers: [88, 30] Generated Node #0,2,3: 90:[88, 30] Operation: 34-4=30 Exploring Operation: 34+4=38, Resulting Numbers: [88, 38] Generated Node #0,2,4: 90:[88, 38] Operation: 34+4=38 Moving to Node #0,2,3 Current State: 90:[88, 30], Operations: ['64-60=4', '34-4=30'] Exploring Operation: 88*30=2640, Resulting Numbers: [2640] 2640,90 unequal: No Solution Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 88+30=118, Resulting Numbers: [118] 118,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[34, 92], Operations: ['64-60=4', '88+4=92'] Exploring Operation: 92-34=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 34+92=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 34*92=3128, Resulting Numbers: [3128] 3128,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[34, 22], Operations: ['64-60=4', '88/4=22'] Exploring Operation: 34*22=748, Resulting Numbers: [748] 748,90 unequal: No Solution Exploring Operation: 34+22=56, Resulting Numbers: [56] 56,90 unequal: No Solution Exploring Operation: 34-22=12, Resulting Numbers: [12] 12,90 unequal: No Solution Moving to Node #0,2,4 Current State: 90:[88, 38], Operations: ['64-60=4', '34+4=38'] Exploring Operation: 88+38=126, Resulting Numbers: [126] 126,90 unequal: No Solution Exploring Operation: 88*38=3344, Resulting Numbers: [3344] 3344,90 unequal: No Solution Exploring Operation: 88-38=50, Resulting Numbers: [50] 50,90 unequal: No Solution Moving to Node #0,2,0 Current State: 90:[4, 54], Operations: ['64-60=4', '88-34=54'] Exploring Operation: 4+54=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 4*54=216, Resulting Numbers: [216] 216,90 unequal: No Solution Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,90 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:[88, 60, 30], Operations: ['64-34=30'] Exploring Operation: 60-30=30, Resulting Numbers: [88, 30] Generated Node #0,3,0: 90:[88, 30] Operation: 60-30=30 Exploring Operation: 88-60=28, Resulting Numbers: [30, 28] Generated Node #0,3,1: 90:[30, 28] Operation: 88-60=28 Exploring Operation: 60+30=90, Resulting Numbers: [88, 90] Generated Node #0,3,2: 90:[88, 90] Operation: 60+30=90 Exploring Operation: 60/30=2, Resulting Numbers: [88, 2] Generated Node #0,3,3: 90:[88, 2] Operation: 60/30=2 Exploring Operation: 88-30=58, Resulting Numbers: [60, 58] Generated Node #0,3,4: 90:[60, 58] Operation: 88-30=58 Moving to Node #0,3,0 Current State: 90:[88, 30], Operations: ['64-34=30', '60-30=30'] Exploring Operation: 88-30=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 88+30=118, Resulting Numbers: [118] 118,90 unequal: No Solution Exploring Operation: 88*30=2640, Resulting Numbers: [2640] 2640,90 unequal: No Solution Moving to Node #0,3,2 Current State: 90:[88, 90], Operations: ['64-34=30', '60+30=90'] Exploring Operation: 88+90=178, Resulting Numbers: [178] 178,90 unequal: No Solution Exploring Operation: 90-88=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 88*90=7920, Resulting Numbers: [7920] 7920,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[30, 28], Operations: ['64-34=30', '88-60=28'] Exploring Operation: 30+28=58, Resulting Numbers: [58] 58,90 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 30*28=840, Resulting Numbers: [840] 840,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[88, 2], Operations: ['64-34=30', '60/30=2'] Exploring Operation: 88-2=86, Resulting Numbers: [86] 86,90 unequal: No Solution Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[88, 64, 34, 60], Operations: [] Exploring Operation: 64-34=30, Resulting Numbers: [88, 60, 30] Generated Node #0,3: 90:[88, 60, 30] Operation: 64-34=30 Moving to Node #0,3 Current State: 90:[88, 60, 30], Operations: ['64-34=30'] Exploring Operation: 60/30=2, Resulting Numbers: [88, 2] Generated Node #0,3,3: 90:[88, 2] Operation: 60/30=2 Moving to Node #0,3,3 Current State: 90:[88, 2], Operations: ['64-34=30', '60/30=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_5
mult_heuristic
[ 63, 50, 34, 52 ]
95
[ "63+50=113", "52-34=18", "113-18=95" ]
Current State: 95:[63, 50, 34, 52], Operations: [] Exploring Operation: 63+50=113, Resulting Numbers: [34, 52, 113] Generated Node #2: [34, 52, 113] from Operation: 63+50=113 Current State: 95:[34, 52, 113], Operations: ['63+50=113'] Exploring Operation: 52-34=18, Resulting Numbers: [113, 18] Generated Node #3: [113, 18] from Operation: 52-34=18 Current State: 95:[113, 18], Operations: ['63+50=113', '52-34=18'] Exploring Operation: 113-18=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[63, 50, 34, 52], Operations: [] Exploring Operation: 63-50=13, Resulting Numbers: [34, 52, 13] Generated Node #0,0: 95:[34, 52, 13] Operation: 63-50=13 Exploring Operation: 52-50=2, Resulting Numbers: [63, 34, 2] Generated Node #0,1: 95:[63, 34, 2] Operation: 52-50=2 Exploring Operation: 63-52=11, Resulting Numbers: [50, 34, 11] Generated Node #0,2: 95:[50, 34, 11] Operation: 63-52=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 95:[63, 34, 2], Operations: ['52-50=2'] Exploring Operation: 63+34=97, Resulting Numbers: [2, 97] Generated Node #0,1,0: 95:[2, 97] Operation: 63+34=97 Exploring Operation: 63-34=29, Resulting Numbers: [2, 29] Generated Node #0,1,1: 95:[2, 29] Operation: 63-34=29 Exploring Operation: 34/2=17, Resulting Numbers: [63, 17] Generated Node #0,1,2: 95:[63, 17] Operation: 34/2=17 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 95:[2, 97], Operations: ['52-50=2', '63+34=97'] Exploring Operation: 2*97=194, Resulting Numbers: [194] 194,95 unequal: No Solution Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,95 unequal: No Solution Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Moving to Node #0 Current State: 95:[63, 50, 34, 52], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [63, 34, 2] Generated Node #0,1: 95:[63, 34, 2] Operation: 52-50=2 Moving to Node #0,1 Current State: 95:[63, 34, 2], Operations: ['52-50=2'] Exploring Operation: 63+34=97, Resulting Numbers: [2, 97] Generated Node #0,1,0: 95:[2, 97] Operation: 63+34=97 Moving to Node #0,1,0 Current State: 95:[2, 97], Operations: ['52-50=2', '63+34=97'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,95 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 72, 71, 2, 79 ]
81
[ "72-71=1", "2+79=81", "1*81=81" ]
Current State: 81:[72, 71, 2, 79], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [2, 79, 1] Generated Node #2: [2, 79, 1] from Operation: 72-71=1 Current State: 81:[2, 79, 1], Operations: ['72-71=1'] Exploring Operation: 2+79=81, Resulting Numbers: [1, 81] Generated Node #3: [1, 81] from Operation: 2+79=81 Current State: 81:[1, 81], Operations: ['72-71=1', '2+79=81'] Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[72, 71, 2, 79], Operations: [] Exploring Operation: 79-72=7, Resulting Numbers: [71, 2, 7] Generated Node #0,0: 81:[71, 2, 7] Operation: 79-72=7 Exploring Operation: 72-71=1, Resulting Numbers: [2, 79, 1] Generated Node #0,1: 81:[2, 79, 1] Operation: 72-71=1 Exploring Operation: 79-71=8, Resulting Numbers: [72, 2, 8] Generated Node #0,2: 81:[72, 2, 8] Operation: 79-71=8 Exploring Operation: 72+2=74, Resulting Numbers: [71, 79, 74] Generated Node #0,3: 81:[71, 79, 74] Operation: 72+2=74 Exploring Operation: 71+2=73, Resulting Numbers: [72, 79, 73] Generated Node #0,4: 81:[72, 79, 73] Operation: 71+2=73 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[2, 79, 1], Operations: ['72-71=1'] Exploring Operation: 2+79=81, Resulting Numbers: [1, 81] Generated Node #0,1,0: 81:[1, 81] Operation: 2+79=81 Exploring Operation: 2+1=3, Resulting Numbers: [79, 3] Generated Node #0,1,1: 81:[79, 3] Operation: 2+1=3 Exploring Operation: 79+1=80, Resulting Numbers: [2, 80] Generated Node #0,1,2: 81:[2, 80] Operation: 79+1=80 Exploring Operation: 2*1=2, Resulting Numbers: [79, 2] Generated Node #0,1,3: 81:[79, 2] Operation: 2*1=2 Exploring Operation: 2/1=2, Resulting Numbers: [79, 2] Generated Node #0,1,4: 81:[79, 2] Operation: 2/1=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[1, 81], Operations: ['72-71=1', '2+79=81'] Exploring Operation: 81-1=80, Resulting Numbers: [80] 80,81 unequal: No Solution Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[72, 71, 2, 79], Operations: [] Exploring Operation: 72-71=1, Resulting Numbers: [2, 79, 1] Generated Node #0,1: 81:[2, 79, 1] Operation: 72-71=1 Moving to Node #0,1 Current State: 81:[2, 79, 1], Operations: ['72-71=1'] Exploring Operation: 2+79=81, Resulting Numbers: [1, 81] Generated Node #0,1,0: 81:[1, 81] Operation: 2+79=81 Moving to Node #0,1,0 Current State: 81:[1, 81], Operations: ['72-71=1', '2+79=81'] Exploring Operation: 1*81=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 77, 3, 24, 35 ]
52
[ "77-24=53", "3*35=105", "105-53=52" ]
Current State: 52:[77, 3, 24, 35], Operations: [] Exploring Operation: 77-24=53, Resulting Numbers: [3, 35, 53] Generated Node #2: [3, 35, 53] from Operation: 77-24=53 Current State: 52:[3, 35, 53], Operations: ['77-24=53'] Exploring Operation: 3*35=105, Resulting Numbers: [53, 105] Generated Node #3: [53, 105] from Operation: 3*35=105 Current State: 52:[53, 105], Operations: ['77-24=53', '3*35=105'] Exploring Operation: 105-53=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[77, 3, 24, 35], Operations: [] Exploring Operation: 77-35=42, Resulting Numbers: [3, 24, 42] Generated Node #0,0: 52:[3, 24, 42] Operation: 77-35=42 Exploring Operation: 77-24=53, Resulting Numbers: [3, 35, 53] Generated Node #0,1: 52:[3, 35, 53] Operation: 77-24=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[3, 35, 53], Operations: ['77-24=53'] Exploring Operation: 53-35=18, Resulting Numbers: [3, 18] Generated Node #0,1,0: 52:[3, 18] Operation: 53-35=18 Exploring Operation: 35-3=32, Resulting Numbers: [53, 32] Generated Node #0,1,1: 52:[53, 32] Operation: 35-3=32 Moving to Node #0,1,0 Current State: 52:[3, 18], Operations: ['77-24=53', '53-35=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,52 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[53, 32], Operations: ['77-24=53', '35-3=32'] Exploring Operation: 53+32=85, Resulting Numbers: [85] 85,52 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[3, 24, 42], Operations: ['77-35=42'] Exploring Operation: 42/3=14, Resulting Numbers: [24, 14] Generated Node #0,0,0: 52:[24, 14] Operation: 42/3=14 Exploring Operation: 42-24=18, Resulting Numbers: [3, 18] Generated Node #0,0,1: 52:[3, 18] Operation: 42-24=18 Moving to Node #0,0,0 Current State: 52:[24, 14], Operations: ['77-35=42', '42/3=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,52 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[3, 18], Operations: ['77-35=42', '42-24=18'] Exploring Operation: 3*18=54, Resulting Numbers: [54] 54,52 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,52 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
[ 60, 12, 2, 41 ]
34
[ "60-12=48", "2*41=82", "82-48=34" ]
Current State: 34:[60, 12, 2, 41], Operations: [] Exploring Operation: 60-12=48, Resulting Numbers: [2, 41, 48] Generated Node #2: [2, 41, 48] from Operation: 60-12=48 Current State: 34:[2, 41, 48], Operations: ['60-12=48'] Exploring Operation: 2*41=82, Resulting Numbers: [48, 82] Generated Node #3: [48, 82] from Operation: 2*41=82 Current State: 34:[48, 82], Operations: ['60-12=48', '2*41=82'] Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[60, 12, 2, 41], Operations: [] Exploring Operation: 60/2=30, Resulting Numbers: [12, 41, 30] Generated Node #0,0: 34:[12, 41, 30] Operation: 60/2=30 Exploring Operation: 60/12=5, Resulting Numbers: [2, 41, 5] Generated Node #0,1: 34:[2, 41, 5] Operation: 60/12=5 Exploring Operation: 60-41=19, Resulting Numbers: [12, 2, 19] Generated Node #0,2: 34:[12, 2, 19] Operation: 60-41=19 Moving to Node #0,2 Current State: 34:[12, 2, 19], Operations: ['60-41=19'] Exploring Operation: 12+2=14, Resulting Numbers: [19, 14] Generated Node #0,2,0: 34:[19, 14] Operation: 12+2=14 Exploring Operation: 19-12=7, Resulting Numbers: [2, 7] Generated Node #0,2,1: 34:[2, 7] Operation: 19-12=7 Exploring Operation: 12+19=31, Resulting Numbers: [2, 31] Generated Node #0,2,2: 34:[2, 31] Operation: 12+19=31 Moving to Node #0,1 Current State: 34:[2, 41, 5], Operations: ['60/12=5'] Exploring Operation: 41-2=39, Resulting Numbers: [5, 39] Generated Node #0,1,0: 34:[5, 39] Operation: 41-2=39 Exploring Operation: 5-2=3, Resulting Numbers: [41, 3] Generated Node #0,1,1: 34:[41, 3] Operation: 5-2=3 Exploring Operation: 41-5=36, Resulting Numbers: [2, 36] Generated Node #0,1,2: 34:[2, 36] Operation: 41-5=36 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 34:[2, 36], Operations: ['60/12=5', '41-5=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[60, 12, 2, 41], Operations: [] Exploring Operation: 60/12=5, Resulting Numbers: [2, 41, 5] Generated Node #0,1: 34:[2, 41, 5] Operation: 60/12=5 Moving to Node #0,1 Current State: 34:[2, 41, 5], Operations: ['60/12=5'] Exploring Operation: 41-5=36, Resulting Numbers: [2, 36] Generated Node #0,1,2: 34:[2, 36] Operation: 41-5=36 Moving to Node #0,1,2 Current State: 34:[2, 36], Operations: ['60/12=5', '41-5=36'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 28, 1, 87, 19 ]
41
[ "28-1=27", "87-19=68", "68-27=41" ]
Current State: 41:[28, 1, 87, 19], Operations: [] Exploring Operation: 28-1=27, Resulting Numbers: [87, 19, 27] Generated Node #2: [87, 19, 27] from Operation: 28-1=27 Current State: 41:[87, 19, 27], Operations: ['28-1=27'] Exploring Operation: 87-19=68, Resulting Numbers: [27, 68] Generated Node #3: [27, 68] from Operation: 87-19=68 Current State: 41:[27, 68], Operations: ['28-1=27', '87-19=68'] Exploring Operation: 68-27=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[28, 1, 87, 19], Operations: [] Exploring Operation: 28+1=29, Resulting Numbers: [87, 19, 29] Generated Node #0,0: 41:[87, 19, 29] Operation: 28+1=29 Exploring Operation: 87-28=59, Resulting Numbers: [1, 19, 59] Generated Node #0,1: 41:[1, 19, 59] Operation: 87-28=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[87, 19, 29], Operations: ['28+1=29'] Exploring Operation: 87-29=58, Resulting Numbers: [19, 58] Generated Node #0,0,0: 41:[19, 58] Operation: 87-29=58 Exploring Operation: 87-19=68, Resulting Numbers: [29, 68] Generated Node #0,0,1: 41:[29, 68] Operation: 87-19=68 Moving to Node #0,0,0 Current State: 41:[19, 58], Operations: ['28+1=29', '87-29=58'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 19+58=77, Resulting Numbers: [77] 77,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[29, 68], Operations: ['28+1=29', '87-19=68'] Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 29+68=97, Resulting Numbers: [97] 97,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[1, 19, 59], Operations: ['87-28=59'] Exploring Operation: 59-1=58, Resulting Numbers: [19, 58] Generated Node #0,1,0: 41:[19, 58] Operation: 59-1=58 Exploring Operation: 1+19=20, Resulting Numbers: [59, 20] Generated Node #0,1,1: 41:[59, 20] Operation: 1+19=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[19, 58], Operations: ['87-28=59', '59-1=58'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,41 unequal: No Solution Exploring Operation: 19+58=77, Resulting Numbers: [77] 77,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 41:[59, 20], Operations: ['87-28=59', '1+19=20'] Exploring Operation: 59+20=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 59-20=39, Resulting Numbers: [39] 39,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 15, 69, 2, 14 ]
95
[ "69-14=55", "2*55=110", "110-15=95" ]
Current State: 95:[15, 69, 2, 14], Operations: [] Exploring Operation: 69-14=55, Resulting Numbers: [15, 2, 55] Generated Node #2: [15, 2, 55] from Operation: 69-14=55 Current State: 95:[15, 2, 55], Operations: ['69-14=55'] Exploring Operation: 2*55=110, Resulting Numbers: [15, 110] Generated Node #3: [15, 110] from Operation: 2*55=110 Current State: 95:[15, 110], Operations: ['69-14=55', '2*55=110'] Exploring Operation: 110-15=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[15, 69, 2, 14], Operations: [] Exploring Operation: 69+14=83, Resulting Numbers: [15, 2, 83] Generated Node #0,0: 95:[15, 2, 83] Operation: 69+14=83 Exploring Operation: 15+69=84, Resulting Numbers: [2, 14, 84] Generated Node #0,1: 95:[2, 14, 84] Operation: 15+69=84 Moving to Node #0,0 Current State: 95:[15, 2, 83], Operations: ['69+14=83'] Exploring Operation: 15+83=98, Resulting Numbers: [2, 98] Generated Node #0,0,0: 95:[2, 98] Operation: 15+83=98 Exploring Operation: 15+2=17, Resulting Numbers: [83, 17] Generated Node #0,0,1: 95:[83, 17] Operation: 15+2=17 Moving to Node #0,1 Current State: 95:[2, 14, 84], Operations: ['15+69=84'] Exploring Operation: 84/14=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 95:[2, 6] Operation: 84/14=6 Exploring Operation: 14+84=98, Resulting Numbers: [2, 98] Generated Node #0,1,1: 95:[2, 98] Operation: 14+84=98 Moving to Node #0,1,0 Current State: 95:[2, 6], Operations: ['15+69=84', '84/14=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,95 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[2, 98], Operations: ['69+14=83', '15+83=98'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[2, 98], Operations: ['15+69=84', '14+84=98'] Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,95 unequal: No Solution Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[83, 17], Operations: ['69+14=83', '15+2=17'] Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,95 unequal: No Solution Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,95 unequal: No Solution No solution found.
0
hs_2
mult_heuristic