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
[ 9, 28, 99, 95 ]
16
[ "99-95=4", "28/4=7", "9+7=16" ]
Current State: 16:[9, 28, 99, 95], Operations: [] Exploring Operation: 99-95=4, Resulting Numbers: [9, 28, 4] Generated Node #2: [9, 28, 4] from Operation: 99-95=4 Current State: 16:[9, 28, 4], Operations: ['99-95=4'] Exploring Operation: 28/4=7, Resulting Numbers: [9, 7] Generated Node #3: [9, 7] from Operation: 28/4=7 Current State: 16:[9, 7], Operations: ['99-95=4', '28/4=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[9, 28, 99, 95], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [28, 95, 11] Generated Node #0,0: 16:[28, 95, 11] Operation: 99/9=11 Exploring Operation: 99-28=71, Resulting Numbers: [9, 95, 71] Generated Node #0,1: 16:[9, 95, 71] Operation: 99-28=71 Exploring Operation: 99-95=4, Resulting Numbers: [9, 28, 4] Generated Node #0,2: 16:[9, 28, 4] Operation: 99-95=4 Exploring Operation: 95-28=67, Resulting Numbers: [9, 99, 67] Generated Node #0,3: 16:[9, 99, 67] Operation: 95-28=67 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[9, 28, 4], Operations: ['99-95=4'] Exploring Operation: 28-9=19, Resulting Numbers: [4, 19] Generated Node #0,2,0: 16:[4, 19] Operation: 28-9=19 Exploring Operation: 28-4=24, Resulting Numbers: [9, 24] Generated Node #0,2,1: 16:[9, 24] Operation: 28-4=24 Exploring Operation: 9-4=5, Resulting Numbers: [28, 5] Generated Node #0,2,2: 16:[28, 5] Operation: 9-4=5 Exploring Operation: 28/4=7, Resulting Numbers: [9, 7] Generated Node #0,2,3: 16:[9, 7] Operation: 28/4=7 Moving to Node #0,2,3 Current State: 16:[9, 7], Operations: ['99-95=4', '28/4=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,16 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[9, 28, 99, 95], Operations: [] Exploring Operation: 99-95=4, Resulting Numbers: [9, 28, 4] Generated Node #0,2: 16:[9, 28, 4] Operation: 99-95=4 Moving to Node #0,2 Current State: 16:[9, 28, 4], Operations: ['99-95=4'] Exploring Operation: 28/4=7, Resulting Numbers: [9, 7] Generated Node #0,2,3: 16:[9, 7] Operation: 28/4=7 Moving to Node #0,2,3 Current State: 16:[9, 7], Operations: ['99-95=4', '28/4=7'] Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 37, 26, 91, 9 ]
89
[ "37-26=11", "91+9=100", "100-11=89" ]
Current State: 89:[37, 26, 91, 9], Operations: [] Exploring Operation: 37-26=11, Resulting Numbers: [91, 9, 11] Generated Node #2: [91, 9, 11] from Operation: 37-26=11 Current State: 89:[91, 9, 11], Operations: ['37-26=11'] Exploring Operation: 91+9=100, Resulting Numbers: [11, 100] Generated Node #3: [11, 100] from Operation: 91+9=100 Current State: 89:[11, 100], Operations: ['37-26=11', '91+9=100'] Exploring Operation: 100-11=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[37, 26, 91, 9], Operations: [] Exploring Operation: 37+9=46, Resulting Numbers: [26, 91, 46] Generated Node #0,0: 89:[26, 91, 46] Operation: 37+9=46 Exploring Operation: 26+9=35, Resulting Numbers: [37, 91, 35] Generated Node #0,1: 89:[37, 91, 35] Operation: 26+9=35 Exploring Operation: 91-9=82, Resulting Numbers: [37, 26, 82] Generated Node #0,2: 89:[37, 26, 82] Operation: 91-9=82 Exploring Operation: 37+26=63, Resulting Numbers: [91, 9, 63] Generated Node #0,3: 89:[91, 9, 63] Operation: 37+26=63 Moving to Node #0,0 Current State: 89:[26, 91, 46], Operations: ['37+9=46'] Exploring Operation: 91-26=65, Resulting Numbers: [46, 65] Generated Node #0,0,0: 89:[46, 65] Operation: 91-26=65 Exploring Operation: 46-26=20, Resulting Numbers: [91, 20] Generated Node #0,0,1: 89:[91, 20] Operation: 46-26=20 Exploring Operation: 26+91=117, Resulting Numbers: [46, 117] Generated Node #0,0,2: 89:[46, 117] Operation: 26+91=117 Exploring Operation: 26+46=72, Resulting Numbers: [91, 72] Generated Node #0,0,3: 89:[91, 72] Operation: 26+46=72 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 89:[91, 72], Operations: ['37+9=46', '26+46=72'] Exploring Operation: 91+72=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 91*72=6552, Resulting Numbers: [6552] 6552,89 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,89 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:[46, 65], Operations: ['37+9=46', '91-26=65'] Exploring Operation: 46*65=2990, Resulting Numbers: [2990] 2990,89 unequal: No Solution Exploring Operation: 46+65=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 65-46=19, Resulting Numbers: [19] 19,89 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:[91, 20], Operations: ['37+9=46', '46-26=20'] Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,89 unequal: No Solution Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,89 unequal: No Solution Exploring Operation: 91*20=1820, Resulting Numbers: [1820] 1820,89 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 #0,0,2 Current State: 89:[46, 117], Operations: ['37+9=46', '26+91=117'] Exploring Operation: 46+117=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 46*117=5382, Resulting Numbers: [5382] 5382,89 unequal: No Solution Exploring Operation: 117-46=71, Resulting Numbers: [71] 71,89 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: 89:[91, 9, 63], Operations: ['37+26=63'] Exploring Operation: 91+9=100, Resulting Numbers: [63, 100] Generated Node #0,3,0: 89:[63, 100] Operation: 91+9=100 Exploring Operation: 9+63=72, Resulting Numbers: [91, 72] Generated Node #0,3,1: 89:[91, 72] Operation: 9+63=72 Exploring Operation: 91-9=82, Resulting Numbers: [63, 82] Generated Node #0,3,2: 89:[63, 82] Operation: 91-9=82 Exploring Operation: 63-9=54, Resulting Numbers: [91, 54] Generated Node #0,3,3: 89:[91, 54] Operation: 63-9=54 Moving to Node #0,1 Current State: 89:[37, 91, 35], Operations: ['26+9=35'] Exploring Operation: 91-37=54, Resulting Numbers: [35, 54] Generated Node #0,1,0: 89:[35, 54] Operation: 91-37=54 Exploring Operation: 91-35=56, Resulting Numbers: [37, 56] Generated Node #0,1,1: 89:[37, 56] Operation: 91-35=56 Exploring Operation: 37-35=2, Resulting Numbers: [91, 2] Generated Node #0,1,2: 89:[91, 2] Operation: 37-35=2 Exploring Operation: 37+35=72, Resulting Numbers: [91, 72] Generated Node #0,1,3: 89:[91, 72] Operation: 37+35=72 Moving to Node #0,2 Current State: 89:[37, 26, 82], Operations: ['91-9=82'] Exploring Operation: 26+82=108, Resulting Numbers: [37, 108] Generated Node #0,2,0: 89:[37, 108] Operation: 26+82=108 Exploring Operation: 82-26=56, Resulting Numbers: [37, 56] Generated Node #0,2,1: 89:[37, 56] Operation: 82-26=56 Exploring Operation: 37-26=11, Resulting Numbers: [82, 11] Generated Node #0,2,2: 89:[82, 11] Operation: 37-26=11 Exploring Operation: 37+26=63, Resulting Numbers: [82, 63] Generated Node #0,2,3: 89:[82, 63] Operation: 37+26=63 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 89:[82, 63], Operations: ['91-9=82', '37+26=63'] Exploring Operation: 82-63=19, Resulting Numbers: [19] 19,89 unequal: No Solution Exploring Operation: 82+63=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 82*63=5166, Resulting Numbers: [5166] 5166,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 89:[37, 108], Operations: ['91-9=82', '26+82=108'] Exploring Operation: 37*108=3996, Resulting Numbers: [3996] 3996,89 unequal: No Solution Exploring Operation: 37+108=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 108-37=71, Resulting Numbers: [71] 71,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 89:[37, 56], Operations: ['91-9=82', '82-26=56'] Exploring Operation: 37+56=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,89 unequal: No Solution Exploring Operation: 37*56=2072, Resulting Numbers: [2072] 2072,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 89:[82, 11], Operations: ['91-9=82', '37-26=11'] Exploring Operation: 82*11=902, Resulting Numbers: [902] 902,89 unequal: No Solution Exploring Operation: 82+11=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 82-11=71, Resulting Numbers: [71] 71,89 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: 89:[91, 72], Operations: ['37+26=63', '9+63=72'] Exploring Operation: 91+72=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 91*72=6552, Resulting Numbers: [6552] 6552,89 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,89 unequal: No Solution Moving to Node #0,1,3 Current State: 89:[91, 72], Operations: ['26+9=35', '37+35=72'] Exploring Operation: 91+72=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 91*72=6552, Resulting Numbers: [6552] 6552,89 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,89 unequal: No Solution Moving to Node #0,3,2 Current State: 89:[63, 82], Operations: ['37+26=63', '91-9=82'] Exploring Operation: 82-63=19, Resulting Numbers: [19] 19,89 unequal: No Solution Exploring Operation: 63+82=145, Resulting Numbers: [145] 145,89 unequal: No Solution Exploring Operation: 63*82=5166, Resulting Numbers: [5166] 5166,89 unequal: No Solution Moving to Node #0,3,0 Current State: 89:[63, 100], Operations: ['37+26=63', '91+9=100'] Exploring Operation: 63+100=163, Resulting Numbers: [163] 163,89 unequal: No Solution Exploring Operation: 63*100=6300, Resulting Numbers: [6300] 6300,89 unequal: No Solution Exploring Operation: 100-63=37, Resulting Numbers: [37] 37,89 unequal: No Solution Moving to Node #0,3,3 Current State: 89:[91, 54], Operations: ['37+26=63', '63-9=54'] Exploring Operation: 91*54=4914, Resulting Numbers: [4914] 4914,89 unequal: No Solution Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,89 unequal: No Solution Exploring Operation: 91+54=145, Resulting Numbers: [145] 145,89 unequal: No Solution Moving to Node #0,1,1 Current State: 89:[37, 56], Operations: ['26+9=35', '91-35=56'] Exploring Operation: 37+56=93, Resulting Numbers: [93] 93,89 unequal: No Solution Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,89 unequal: No Solution Exploring Operation: 37*56=2072, Resulting Numbers: [2072] 2072,89 unequal: No Solution Moving to Node #0,1,0 Current State: 89:[35, 54], Operations: ['26+9=35', '91-37=54'] Exploring Operation: 35+54=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[37, 26, 91, 9], Operations: [] Exploring Operation: 26+9=35, Resulting Numbers: [37, 91, 35] Generated Node #0,1: 89:[37, 91, 35] Operation: 26+9=35 Moving to Node #0,1 Current State: 89:[37, 91, 35], Operations: ['26+9=35'] Exploring Operation: 91-37=54, Resulting Numbers: [35, 54] Generated Node #0,1,0: 89:[35, 54] Operation: 91-37=54 Moving to Node #0,1,0 Current State: 89:[35, 54], Operations: ['26+9=35', '91-37=54'] Exploring Operation: 35+54=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
0.94184
hs_4
mult_heuristic
[ 38, 2, 43, 3 ]
51
[ "38-3=35", "2*43=86", "86-35=51" ]
Current State: 51:[38, 2, 43, 3], Operations: [] Exploring Operation: 38-3=35, Resulting Numbers: [2, 43, 35] Generated Node #2: [2, 43, 35] from Operation: 38-3=35 Current State: 51:[2, 43, 35], Operations: ['38-3=35'] Exploring Operation: 2*43=86, Resulting Numbers: [35, 86] Generated Node #3: [35, 86] from Operation: 2*43=86 Current State: 51:[35, 86], Operations: ['38-3=35', '2*43=86'] Exploring Operation: 86-35=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[38, 2, 43, 3], Operations: [] Exploring Operation: 43-38=5, Resulting Numbers: [2, 3, 5] Generated Node #0,0: 51:[2, 3, 5] Operation: 43-38=5 Moving to Node #0,0 Current State: 51:[2, 3, 5], Operations: ['43-38=5'] Exploring Operation: 5-2=3, Resulting Numbers: [3, 3] Generated Node #0,0,0: 51:[3, 3] Operation: 5-2=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[3, 3], Operations: ['43-38=5', '5-2=3'] Exploring Operation: 3/3=1, Resulting Numbers: [1] 1,51 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
[ 40, 38, 30, 42 ]
51
[ "40-38=2", "42/2=21", "30+21=51" ]
Current State: 51:[40, 38, 30, 42], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [30, 42, 2] Generated Node #2: [30, 42, 2] from Operation: 40-38=2 Current State: 51:[30, 42, 2], Operations: ['40-38=2'] Exploring Operation: 42/2=21, Resulting Numbers: [30, 21] Generated Node #3: [30, 21] from Operation: 42/2=21 Current State: 51:[30, 21], Operations: ['40-38=2', '42/2=21'] Exploring Operation: 30+21=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[40, 38, 30, 42], Operations: [] Exploring Operation: 38-30=8, Resulting Numbers: [40, 42, 8] Generated Node #0,0: 51:[40, 42, 8] Operation: 38-30=8 Exploring Operation: 40-38=2, Resulting Numbers: [30, 42, 2] Generated Node #0,1: 51:[30, 42, 2] Operation: 40-38=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 51:[30, 42, 2], Operations: ['40-38=2'] Exploring Operation: 30/2=15, Resulting Numbers: [42, 15] Generated Node #0,1,0: 51:[42, 15] Operation: 30/2=15 Exploring Operation: 42-30=12, Resulting Numbers: [2, 12] Generated Node #0,1,1: 51:[2, 12] Operation: 42-30=12 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[2, 12], Operations: ['40-38=2', '42-30=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,51 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,51 unequal: No Solution No 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: 51:[42, 15], Operations: ['40-38=2', '30/2=15'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,51 unequal: No Solution Exploring Operation: 42+15=57, Resulting Numbers: [57] 57,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[40, 42, 8], Operations: ['38-30=8'] Exploring Operation: 40/8=5, Resulting Numbers: [42, 5] Generated Node #0,0,0: 51:[42, 5] Operation: 40/8=5 Exploring Operation: 42-40=2, Resulting Numbers: [8, 2] Generated Node #0,0,1: 51:[8, 2] Operation: 42-40=2 Moving to Node #0,0,1 Current State: 51:[8, 2], Operations: ['38-30=8', '42-40=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,51 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,51 unequal: No Solution Moving to Node #0,0,0 Current State: 51:[42, 5], Operations: ['38-30=8', '40/8=5'] Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,51 unequal: No Solution Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,51 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
[ 47, 25, 5, 43 ]
16
[ "47-25=22", "43-5=38", "38-22=16" ]
Current State: 16:[47, 25, 5, 43], Operations: [] Exploring Operation: 47-25=22, Resulting Numbers: [5, 43, 22] Generated Node #2: [5, 43, 22] from Operation: 47-25=22 Current State: 16:[5, 43, 22], Operations: ['47-25=22'] Exploring Operation: 43-5=38, Resulting Numbers: [22, 38] Generated Node #3: [22, 38] from Operation: 43-5=38 Current State: 16:[22, 38], Operations: ['47-25=22', '43-5=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[47, 25, 5, 43], Operations: [] Exploring Operation: 47-43=4, Resulting Numbers: [25, 5, 4] Generated Node #0,0: 16:[25, 5, 4] Operation: 47-43=4 Exploring Operation: 47-25=22, Resulting Numbers: [5, 43, 22] Generated Node #0,1: 16:[5, 43, 22] Operation: 47-25=22 Exploring Operation: 43-25=18, Resulting Numbers: [47, 5, 18] Generated Node #0,2: 16:[47, 5, 18] Operation: 43-25=18 Exploring Operation: 47-5=42, Resulting Numbers: [25, 43, 42] Generated Node #0,3: 16:[25, 43, 42] Operation: 47-5=42 Exploring Operation: 25/5=5, Resulting Numbers: [47, 43, 5] Generated Node #0,4: 16:[47, 43, 5] Operation: 25/5=5 Moving to Node #0,0 Current State: 16:[25, 5, 4], Operations: ['47-43=4'] Exploring Operation: 25-4=21, Resulting Numbers: [5, 21] Generated Node #0,0,0: 16:[5, 21] Operation: 25-4=21 Exploring Operation: 25-5=20, Resulting Numbers: [4, 20] Generated Node #0,0,1: 16:[4, 20] Operation: 25-5=20 Exploring Operation: 5-4=1, Resulting Numbers: [25, 1] Generated Node #0,0,2: 16:[25, 1] Operation: 5-4=1 Exploring Operation: 5+4=9, Resulting Numbers: [25, 9] Generated Node #0,0,3: 16:[25, 9] Operation: 5+4=9 Exploring Operation: 25/5=5, Resulting Numbers: [4, 5] Generated Node #0,0,4: 16:[4, 5] Operation: 25/5=5 Moving to Node #0,2 Current State: 16:[47, 5, 18], Operations: ['43-25=18'] Exploring Operation: 47-5=42, Resulting Numbers: [18, 42] Generated Node #0,2,0: 16:[18, 42] Operation: 47-5=42 Exploring Operation: 18-5=13, Resulting Numbers: [47, 13] Generated Node #0,2,1: 16:[47, 13] Operation: 18-5=13 Exploring Operation: 5+18=23, Resulting Numbers: [47, 23] Generated Node #0,2,2: 16:[47, 23] Operation: 5+18=23 Exploring Operation: 47+5=52, Resulting Numbers: [18, 52] Generated Node #0,2,3: 16:[18, 52] Operation: 47+5=52 Exploring Operation: 47-18=29, Resulting Numbers: [5, 29] Generated Node #0,2,4: 16:[5, 29] Operation: 47-18=29 Moving to Node #0,1 Current State: 16:[5, 43, 22], Operations: ['47-25=22'] Exploring Operation: 5+22=27, Resulting Numbers: [43, 27] Generated Node #0,1,0: 16:[43, 27] Operation: 5+22=27 Exploring Operation: 22-5=17, Resulting Numbers: [43, 17] Generated Node #0,1,1: 16:[43, 17] Operation: 22-5=17 Exploring Operation: 5+43=48, Resulting Numbers: [22, 48] Generated Node #0,1,2: 16:[22, 48] Operation: 5+43=48 Exploring Operation: 43-5=38, Resulting Numbers: [22, 38] Generated Node #0,1,3: 16:[22, 38] Operation: 43-5=38 Exploring Operation: 43-22=21, Resulting Numbers: [5, 21] Generated Node #0,1,4: 16:[5, 21] Operation: 43-22=21 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 16:[5, 21], Operations: ['47-25=22', '43-22=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[47, 25, 5, 43], Operations: [] Exploring Operation: 47-25=22, Resulting Numbers: [5, 43, 22] Generated Node #0,1: 16:[5, 43, 22] Operation: 47-25=22 Moving to Node #0,1 Current State: 16:[5, 43, 22], Operations: ['47-25=22'] Exploring Operation: 43-22=21, Resulting Numbers: [5, 21] Generated Node #0,1,4: 16:[5, 21] Operation: 43-22=21 Moving to Node #0,1,4 Current State: 16:[5, 21], Operations: ['47-25=22', '43-22=21'] Exploring Operation: 21-5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_5
mult_heuristic
[ 36, 38, 22, 49 ]
60
[ "38-36=2", "22/2=11", "49+11=60" ]
Current State: 60:[36, 38, 22, 49], Operations: [] Exploring Operation: 38-36=2, Resulting Numbers: [22, 49, 2] Generated Node #2: [22, 49, 2] from Operation: 38-36=2 Current State: 60:[22, 49, 2], Operations: ['38-36=2'] Exploring Operation: 22/2=11, Resulting Numbers: [49, 11] Generated Node #3: [49, 11] from Operation: 22/2=11 Current State: 60:[49, 11], Operations: ['38-36=2', '22/2=11'] Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[36, 38, 22, 49], Operations: [] Exploring Operation: 49-38=11, Resulting Numbers: [36, 22, 11] Generated Node #0,0: 60:[36, 22, 11] Operation: 49-38=11 Exploring Operation: 38-36=2, Resulting Numbers: [22, 49, 2] Generated Node #0,1: 60:[22, 49, 2] Operation: 38-36=2 Exploring Operation: 49-36=13, Resulting Numbers: [38, 22, 13] Generated Node #0,2: 60:[38, 22, 13] Operation: 49-36=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[36, 22, 11], Operations: ['49-38=11'] Exploring Operation: 36-22=14, Resulting Numbers: [11, 14] Generated Node #0,0,0: 60:[11, 14] Operation: 36-22=14 Exploring Operation: 36+22=58, Resulting Numbers: [11, 58] Generated Node #0,0,1: 60:[11, 58] Operation: 36+22=58 Exploring Operation: 22/11=2, Resulting Numbers: [36, 2] Generated Node #0,0,2: 60:[36, 2] Operation: 22/11=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[11, 14], Operations: ['49-38=11', '36-22=14'] Exploring Operation: 14-11=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 11+14=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 11*14=154, Resulting Numbers: [154] 154,60 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 #0,0,1 Current State: 60:[11, 58], Operations: ['49-38=11', '36+22=58'] Exploring Operation: 11*58=638, Resulting Numbers: [638] 638,60 unequal: No Solution Exploring Operation: 58-11=47, Resulting Numbers: [47] 47,60 unequal: No Solution Exploring Operation: 11+58=69, Resulting Numbers: [69] 69,60 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 #0,0,2 Current State: 60:[36, 2], Operations: ['49-38=11', '22/11=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,60 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,60 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,60 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: 60:[38, 22, 13], Operations: ['49-36=13'] Exploring Operation: 38-22=16, Resulting Numbers: [13, 16] Generated Node #0,2,0: 60:[13, 16] Operation: 38-22=16 Exploring Operation: 38+22=60, Resulting Numbers: [13, 60] Generated Node #0,2,1: 60:[13, 60] Operation: 38+22=60 Exploring Operation: 38-13=25, Resulting Numbers: [22, 25] Generated Node #0,2,2: 60:[22, 25] Operation: 38-13=25 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 60:[13, 60], Operations: ['49-36=13', '38+22=60'] Exploring Operation: 13+60=73, Resulting Numbers: [73] 73,60 unequal: No Solution Exploring Operation: 13*60=780, Resulting Numbers: [780] 780,60 unequal: No Solution Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,60 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 #0,2,0 Current State: 60:[13, 16], Operations: ['49-36=13', '38-22=16'] Exploring Operation: 13+16=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 13*16=208, Resulting Numbers: [208] 208,60 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 #0,2,2 Current State: 60:[22, 25], Operations: ['49-36=13', '38-13=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,60 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,60 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,60 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: 60:[22, 49, 2], Operations: ['38-36=2'] Exploring Operation: 22+49=71, Resulting Numbers: [2, 71] Generated Node #0,1,0: 60:[2, 71] Operation: 22+49=71 Exploring Operation: 49-22=27, Resulting Numbers: [2, 27] Generated Node #0,1,1: 60:[2, 27] Operation: 49-22=27 Exploring Operation: 22-2=20, Resulting Numbers: [49, 20] Generated Node #0,1,2: 60:[49, 20] Operation: 22-2=20 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 60:[2, 27], Operations: ['38-36=2', '49-22=27'] Exploring Operation: 2+27=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 27-2=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 2*27=54, Resulting Numbers: [54] 54,60 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 #0,1,0 Current State: 60:[2, 71], Operations: ['38-36=2', '22+49=71'] Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,60 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,60 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 #0,1,2 Current State: 60:[49, 20], Operations: ['38-36=2', '22-2=20'] Exploring Operation: 49+20=69, Resulting Numbers: [69] 69,60 unequal: No Solution Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,60 unequal: No Solution Exploring Operation: 49*20=980, Resulting Numbers: [980] 980,60 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
[ 61, 68, 72, 15 ]
94
[ "68-61=7", "72+15=87", "7+87=94" ]
Current State: 94:[61, 68, 72, 15], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [72, 15, 7] Generated Node #2: [72, 15, 7] from Operation: 68-61=7 Current State: 94:[72, 15, 7], Operations: ['68-61=7'] Exploring Operation: 72+15=87, Resulting Numbers: [7, 87] Generated Node #3: [7, 87] from Operation: 72+15=87 Current State: 94:[7, 87], Operations: ['68-61=7', '72+15=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[61, 68, 72, 15], Operations: [] Exploring Operation: 72+15=87, Resulting Numbers: [61, 68, 87] Generated Node #0,0: 94:[61, 68, 87] Operation: 72+15=87 Exploring Operation: 72-61=11, Resulting Numbers: [68, 15, 11] Generated Node #0,1: 94:[68, 15, 11] Operation: 72-61=11 Exploring Operation: 68-15=53, Resulting Numbers: [61, 72, 53] Generated Node #0,2: 94:[61, 72, 53] Operation: 68-15=53 Exploring Operation: 68-61=7, Resulting Numbers: [72, 15, 7] Generated Node #0,3: 94:[72, 15, 7] Operation: 68-61=7 Exploring Operation: 72-68=4, Resulting Numbers: [61, 15, 4] Generated Node #0,4: 94:[61, 15, 4] Operation: 72-68=4 Start Sub Search at level 1: Moving to Node #0,4 Current State: 94:[61, 15, 4], Operations: ['72-68=4'] Exploring Operation: 61+15=76, Resulting Numbers: [4, 76] Generated Node #0,4,0: 94:[4, 76] Operation: 61+15=76 Exploring Operation: 61-4=57, Resulting Numbers: [15, 57] Generated Node #0,4,1: 94:[15, 57] Operation: 61-4=57 Exploring Operation: 15*4=60, Resulting Numbers: [61, 60] Generated Node #0,4,2: 94:[61, 60] Operation: 15*4=60 Exploring Operation: 15-4=11, Resulting Numbers: [61, 11] Generated Node #0,4,3: 94:[61, 11] Operation: 15-4=11 Exploring Operation: 61-15=46, Resulting Numbers: [4, 46] Generated Node #0,4,4: 94:[4, 46] Operation: 61-15=46 Moving to Node #0,4,4 Current State: 94:[4, 46], Operations: ['72-68=4', '61-15=46'] Exploring Operation: 46-4=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 4+46=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 4*46=184, Resulting Numbers: [184] 184,94 unequal: No Solution Moving to Node #0,4,0 Current State: 94:[4, 76], Operations: ['72-68=4', '61+15=76'] Exploring Operation: 76/4=19, Resulting Numbers: [19] 19,94 unequal: No Solution Exploring Operation: 76-4=72, Resulting Numbers: [72] 72,94 unequal: No Solution Exploring Operation: 4*76=304, Resulting Numbers: [304] 304,94 unequal: No Solution Exploring Operation: 4+76=80, Resulting Numbers: [80] 80,94 unequal: No Solution Moving to Node #0,4,1 Current State: 94:[15, 57], Operations: ['72-68=4', '61-4=57'] Exploring Operation: 15+57=72, Resulting Numbers: [72] 72,94 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,94 unequal: No Solution Exploring Operation: 15*57=855, Resulting Numbers: [855] 855,94 unequal: No Solution Moving to Node #0,4,3 Current State: 94:[61, 11], Operations: ['72-68=4', '15-4=11'] Exploring Operation: 61-11=50, Resulting Numbers: [50] 50,94 unequal: No Solution Exploring Operation: 61+11=72, Resulting Numbers: [72] 72,94 unequal: No Solution Exploring Operation: 61*11=671, Resulting Numbers: [671] 671,94 unequal: No Solution Moving to Node #0,4,2 Current State: 94:[61, 60], Operations: ['72-68=4', '15*4=60'] Exploring Operation: 61*60=3660, Resulting Numbers: [3660] 3660,94 unequal: No Solution Exploring Operation: 61+60=121, Resulting Numbers: [121] 121,94 unequal: No Solution Exploring Operation: 61-60=1, Resulting Numbers: [1] 1,94 unequal: No Solution No 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: 94:[72, 15, 7], Operations: ['68-61=7'] Exploring Operation: 72+15=87, Resulting Numbers: [7, 87] Generated Node #0,3,0: 94:[7, 87] Operation: 72+15=87 Exploring Operation: 72+7=79, Resulting Numbers: [15, 79] Generated Node #0,3,1: 94:[15, 79] Operation: 72+7=79 Exploring Operation: 15-7=8, Resulting Numbers: [72, 8] Generated Node #0,3,2: 94:[72, 8] Operation: 15-7=8 Exploring Operation: 72-7=65, Resulting Numbers: [15, 65] Generated Node #0,3,3: 94:[15, 65] Operation: 72-7=65 Exploring Operation: 72-15=57, Resulting Numbers: [7, 57] Generated Node #0,3,4: 94:[7, 57] Operation: 72-15=57 Moving to Node #0,3,0 Current State: 94:[7, 87], Operations: ['68-61=7', '72+15=87'] Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,94 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,94 unequal: No Solution Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[61, 68, 72, 15], Operations: [] Exploring Operation: 68-61=7, Resulting Numbers: [72, 15, 7] Generated Node #0,3: 94:[72, 15, 7] Operation: 68-61=7 Moving to Node #0,3 Current State: 94:[72, 15, 7], Operations: ['68-61=7'] Exploring Operation: 72+15=87, Resulting Numbers: [7, 87] Generated Node #0,3,0: 94:[7, 87] Operation: 72+15=87 Moving to Node #0,3,0 Current State: 94:[7, 87], Operations: ['68-61=7', '72+15=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 76, 2, 10, 15 ]
81
[ "76-15=61", "2*10=20", "61+20=81" ]
Current State: 81:[76, 2, 10, 15], Operations: [] Exploring Operation: 76-15=61, Resulting Numbers: [2, 10, 61] Generated Node #2: [2, 10, 61] from Operation: 76-15=61 Current State: 81:[2, 10, 61], Operations: ['76-15=61'] Exploring Operation: 2*10=20, Resulting Numbers: [61, 20] Generated Node #3: [61, 20] from Operation: 2*10=20 Current State: 81:[61, 20], Operations: ['76-15=61', '2*10=20'] Exploring Operation: 61+20=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[76, 2, 10, 15], Operations: [] Exploring Operation: 10+15=25, Resulting Numbers: [76, 2, 25] Generated Node #0,0: 81:[76, 2, 25] Operation: 10+15=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[76, 2, 25], Operations: ['10+15=25'] Exploring Operation: 76+2=78, Resulting Numbers: [25, 78] Generated Node #0,0,0: 81:[25, 78] Operation: 76+2=78 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 81:[25, 78], Operations: ['10+15=25', '76+2=78'] Exploring Operation: 25+78=103, Resulting Numbers: [103] 103,81 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 1, 64, 1, 59 ]
69
[ "1+1=2", "64*2=128", "128-59=69" ]
Current State: 69:[1, 64, 1, 59], Operations: [] Exploring Operation: 1+1=2, Resulting Numbers: [64, 59, 2] Generated Node #2: [64, 59, 2] from Operation: 1+1=2 Current State: 69:[64, 59, 2], Operations: ['1+1=2'] Exploring Operation: 64*2=128, Resulting Numbers: [59, 128] Generated Node #3: [59, 128] from Operation: 64*2=128 Current State: 69:[59, 128], Operations: ['1+1=2', '64*2=128'] Exploring Operation: 128-59=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[1, 64, 1, 59], Operations: [] Exploring Operation: 1+1=2, Resulting Numbers: [64, 59, 2] Generated Node #0,0: 69:[64, 59, 2] Operation: 1+1=2 Exploring Operation: 1+64=65, Resulting Numbers: [1, 59, 65] Generated Node #0,1: 69:[1, 59, 65] Operation: 1+64=65 Exploring Operation: 1+59=60, Resulting Numbers: [64, 1, 60] Generated Node #0,2: 69:[64, 1, 60] Operation: 1+59=60 Exploring Operation: 64-59=5, Resulting Numbers: [1, 1, 5] Generated Node #0,3: 69:[1, 1, 5] Operation: 64-59=5 Moving to Node #0,3 Current State: 69:[1, 1, 5], Operations: ['64-59=5'] Exploring Operation: 1+1=2, Resulting Numbers: [5, 2] Generated Node #0,3,0: 69:[5, 2] Operation: 1+1=2 Exploring Operation: 5-1=4, Resulting Numbers: [1, 4] Generated Node #0,3,1: 69:[1, 4] Operation: 5-1=4 Exploring Operation: 1*1=1, Resulting Numbers: [5, 1] Generated Node #0,3,2: 69:[5, 1] Operation: 1*1=1 Exploring Operation: 5-1=4, Resulting Numbers: [1, 4] Generated Node #0,3,3: 69:[1, 4] Operation: 5-1=4 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 69:[5, 2], Operations: ['64-59=5', '1+1=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 69:[1, 4], Operations: ['64-59=5', '5-1=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 69:[1, 4], Operations: ['64-59=5', '5-1=4'] Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 69:[5, 1], Operations: ['64-59=5', '1*1=1'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 69:[1, 59, 65], Operations: ['1+64=65'] Exploring Operation: 1*59=59, Resulting Numbers: [65, 59] Generated Node #0,1,0: 69:[65, 59] Operation: 1*59=59 Exploring Operation: 65-59=6, Resulting Numbers: [1, 6] Generated Node #0,1,1: 69:[1, 6] Operation: 65-59=6 Exploring Operation: 1+65=66, Resulting Numbers: [59, 66] Generated Node #0,1,2: 69:[59, 66] Operation: 1+65=66 Exploring Operation: 1+59=60, Resulting Numbers: [65, 60] Generated Node #0,1,3: 69:[65, 60] Operation: 1+59=60 Moving to Node #0,0 Current State: 69:[64, 59, 2], Operations: ['1+1=2'] Exploring Operation: 64-2=62, Resulting Numbers: [59, 62] Generated Node #0,0,0: 69:[59, 62] Operation: 64-2=62 Exploring Operation: 59+2=61, Resulting Numbers: [64, 61] Generated Node #0,0,1: 69:[64, 61] Operation: 59+2=61 Exploring Operation: 64+2=66, Resulting Numbers: [59, 66] Generated Node #0,0,2: 69:[59, 66] Operation: 64+2=66 Exploring Operation: 64-59=5, Resulting Numbers: [2, 5] Generated Node #0,0,3: 69:[2, 5] Operation: 64-59=5 Moving to Node #0,2 Current State: 69:[64, 1, 60], Operations: ['1+59=60'] Exploring Operation: 64-60=4, Resulting Numbers: [1, 4] Generated Node #0,2,0: 69:[1, 4] Operation: 64-60=4 Exploring Operation: 1+60=61, Resulting Numbers: [64, 61] Generated Node #0,2,1: 69:[64, 61] Operation: 1+60=61 Exploring Operation: 64*1=64, Resulting Numbers: [60, 64] Generated Node #0,2,2: 69:[60, 64] Operation: 64*1=64 Exploring Operation: 64+1=65, Resulting Numbers: [60, 65] Generated Node #0,2,3: 69:[60, 65] Operation: 64+1=65 Moving to Node #0,0,3 Current State: 69:[2, 5], Operations: ['1+1=2', '64-59=5'] Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[1, 4], Operations: ['1+59=60', '64-60=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[1, 6], Operations: ['1+64=65', '65-59=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[65, 60], Operations: ['1+64=65', '1+59=60'] Exploring Operation: 65-60=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 65*60=3900, Resulting Numbers: [3900] 3900,69 unequal: No Solution Exploring Operation: 65+60=125, Resulting Numbers: [125] 125,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[59, 66], Operations: ['1+1=2', '64+2=66'] Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,69 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[60, 65], Operations: ['1+59=60', '64+1=65'] Exploring Operation: 60*65=3900, Resulting Numbers: [3900] 3900,69 unequal: No Solution Exploring Operation: 60+65=125, Resulting Numbers: [125] 125,69 unequal: No Solution Exploring Operation: 65-60=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[64, 61], Operations: ['1+1=2', '59+2=61'] Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,69 unequal: No Solution Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,69 unequal: No Solution Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[59, 66], Operations: ['1+64=65', '1+65=66'] Exploring Operation: 59*66=3894, Resulting Numbers: [3894] 3894,69 unequal: No Solution Exploring Operation: 59+66=125, Resulting Numbers: [125] 125,69 unequal: No Solution Exploring Operation: 66-59=7, Resulting Numbers: [7] 7,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[64, 61], Operations: ['1+59=60', '1+60=61'] Exploring Operation: 64*61=3904, Resulting Numbers: [3904] 3904,69 unequal: No Solution Exploring Operation: 64+61=125, Resulting Numbers: [125] 125,69 unequal: No Solution Exploring Operation: 64-61=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[60, 64], Operations: ['1+59=60', '64*1=64'] Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,69 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,69 unequal: No Solution Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[65, 59], Operations: ['1+64=65', '1*59=59'] Exploring Operation: 65-59=6, Resulting Numbers: [6] 6,69 unequal: No Solution Exploring Operation: 65*59=3835, Resulting Numbers: [3835] 3835,69 unequal: No Solution Exploring Operation: 65+59=124, Resulting Numbers: [124] 124,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[59, 62], Operations: ['1+1=2', '64-2=62'] Exploring Operation: 62-59=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 59+62=121, Resulting Numbers: [121] 121,69 unequal: No Solution Exploring Operation: 59*62=3658, Resulting Numbers: [3658] 3658,69 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 28, 92, 29, 78 ]
43
[ "92-28=64", "29+78=107", "107-64=43" ]
Current State: 43:[28, 92, 29, 78], Operations: [] Exploring Operation: 92-28=64, Resulting Numbers: [29, 78, 64] Generated Node #2: [29, 78, 64] from Operation: 92-28=64 Current State: 43:[29, 78, 64], Operations: ['92-28=64'] Exploring Operation: 29+78=107, Resulting Numbers: [64, 107] Generated Node #3: [64, 107] from Operation: 29+78=107 Current State: 43:[64, 107], Operations: ['92-28=64', '29+78=107'] Exploring Operation: 107-64=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[28, 92, 29, 78], Operations: [] Exploring Operation: 78-28=50, Resulting Numbers: [92, 29, 50] Generated Node #0,0: 43:[92, 29, 50] Operation: 78-28=50 Exploring Operation: 92-29=63, Resulting Numbers: [28, 78, 63] Generated Node #0,1: 43:[28, 78, 63] Operation: 92-29=63 Exploring Operation: 92-78=14, Resulting Numbers: [28, 29, 14] Generated Node #0,2: 43:[28, 29, 14] Operation: 92-78=14 Exploring Operation: 92-28=64, Resulting Numbers: [29, 78, 64] Generated Node #0,3: 43:[29, 78, 64] Operation: 92-28=64 Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[28, 29, 14], Operations: ['92-78=14'] Exploring Operation: 28-14=14, Resulting Numbers: [29, 14] Generated Node #0,2,0: 43:[29, 14] Operation: 28-14=14 Exploring Operation: 28+14=42, Resulting Numbers: [29, 42] Generated Node #0,2,1: 43:[29, 42] Operation: 28+14=42 Exploring Operation: 28+29=57, Resulting Numbers: [14, 57] Generated Node #0,2,2: 43:[14, 57] Operation: 28+29=57 Exploring Operation: 29+14=43, Resulting Numbers: [28, 43] Generated Node #0,2,3: 43:[28, 43] Operation: 29+14=43 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 43:[29, 42], Operations: ['92-78=14', '28+14=42'] Exploring Operation: 29+42=71, Resulting Numbers: [71] 71,43 unequal: No Solution Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,43 unequal: No Solution Exploring Operation: 29*42=1218, Resulting Numbers: [1218] 1218,43 unequal: No Solution No 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: 43:[28, 43], Operations: ['92-78=14', '29+14=43'] Exploring Operation: 28+43=71, Resulting Numbers: [71] 71,43 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 28*43=1204, Resulting Numbers: [1204] 1204,43 unequal: No Solution No 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: 43:[29, 14], Operations: ['92-78=14', '28-14=14'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,43 unequal: No Solution Exploring Operation: 29*14=406, Resulting Numbers: [406] 406,43 unequal: No Solution Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[28, 92, 29, 78], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [28, 29, 14] Generated Node #0,2: 43:[28, 29, 14] Operation: 92-78=14 Moving to Node #0,2 Current State: 43:[28, 29, 14], Operations: ['92-78=14'] Exploring Operation: 28-14=14, Resulting Numbers: [29, 14] Generated Node #0,2,0: 43:[29, 14] Operation: 28-14=14 Moving to Node #0,2,0 Current State: 43:[29, 14], Operations: ['92-78=14', '28-14=14'] Exploring Operation: 29+14=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_4
mult_heuristic
[ 19, 25, 91, 95 ]
34
[ "95/19=5", "25*5=125", "125-91=34" ]
Current State: 34:[19, 25, 91, 95], Operations: [] Exploring Operation: 95/19=5, Resulting Numbers: [25, 91, 5] Generated Node #2: [25, 91, 5] from Operation: 95/19=5 Current State: 34:[25, 91, 5], Operations: ['95/19=5'] Exploring Operation: 25*5=125, Resulting Numbers: [91, 125] Generated Node #3: [91, 125] from Operation: 25*5=125 Current State: 34:[91, 125], Operations: ['95/19=5', '25*5=125'] Exploring Operation: 125-91=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[19, 25, 91, 95], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [19, 25, 4] Generated Node #0,0: 34:[19, 25, 4] Operation: 95-91=4 Exploring Operation: 95/19=5, Resulting Numbers: [25, 91, 5] Generated Node #0,1: 34:[25, 91, 5] Operation: 95/19=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[19, 25, 4], Operations: ['95-91=4'] Exploring Operation: 25-4=21, Resulting Numbers: [19, 21] Generated Node #0,0,0: 34:[19, 21] Operation: 25-4=21 Exploring Operation: 25-19=6, Resulting Numbers: [4, 6] Generated Node #0,0,1: 34:[4, 6] Operation: 25-19=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[19, 21], Operations: ['95-91=4', '25-4=21'] Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 19+21=40, Resulting Numbers: [40] 40,34 unequal: No Solution No 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: 34:[4, 6], Operations: ['95-91=4', '25-19=6'] Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 4+6=10, Resulting Numbers: [10] 10,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[25, 91, 5], Operations: ['95/19=5'] Exploring Operation: 91-25=66, Resulting Numbers: [5, 66] Generated Node #0,1,0: 34:[5, 66] Operation: 91-25=66 Exploring Operation: 25-5=20, Resulting Numbers: [91, 20] Generated Node #0,1,1: 34:[91, 20] Operation: 25-5=20 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[5, 66], Operations: ['95/19=5', '91-25=66'] Exploring Operation: 66-5=61, Resulting Numbers: [61] 61,34 unequal: No Solution Exploring Operation: 5+66=71, Resulting Numbers: [71] 71,34 unequal: No Solution No 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: 34:[91, 20], Operations: ['95/19=5', '25-5=20'] Exploring Operation: 91-20=71, Resulting Numbers: [71] 71,34 unequal: No Solution Exploring Operation: 91+20=111, Resulting Numbers: [111] 111,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 18, 9, 12, 99 ]
35
[ "18*12=216", "99+216=315", "315/9=35" ]
Current State: 35:[18, 9, 12, 99], Operations: [] Exploring Operation: 18*12=216, Resulting Numbers: [9, 99, 216] Generated Node #2: [9, 99, 216] from Operation: 18*12=216 Current State: 35:[9, 99, 216], Operations: ['18*12=216'] Exploring Operation: 99+216=315, Resulting Numbers: [9, 315] Generated Node #3: [9, 315] from Operation: 99+216=315 Current State: 35:[9, 315], Operations: ['18*12=216', '99+216=315'] Exploring Operation: 315/9=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[18, 9, 12, 99], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [18, 12, 11] Generated Node #0,0: 35:[18, 12, 11] Operation: 99/9=11 Moving to Node #0,0 Current State: 35:[18, 12, 11], Operations: ['99/9=11'] Exploring Operation: 18-12=6, Resulting Numbers: [11, 6] Generated Node #0,0,0: 35:[11, 6] Operation: 18-12=6 Moving to Node #0,0,0 Current State: 35:[11, 6], Operations: ['99/9=11', '18-12=6'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,35 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 22, 7, 19, 3 ]
18
[ "22-19=3", "7*3=21", "21-3=18" ]
Current State: 18:[22, 7, 19, 3], Operations: [] Exploring Operation: 22-19=3, Resulting Numbers: [7, 3, 3] Generated Node #2: [7, 3, 3] from Operation: 22-19=3 Current State: 18:[7, 3, 3], Operations: ['22-19=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,18 equal: Goal Reached Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[22, 7, 19, 3], Operations: [] Exploring Operation: 22-3=19, Resulting Numbers: [7, 19, 19] Generated Node #0,0: 18:[7, 19, 19] Operation: 22-3=19 Exploring Operation: 22-7=15, Resulting Numbers: [19, 3, 15] Generated Node #0,1: 18:[19, 3, 15] Operation: 22-7=15 Exploring Operation: 22-19=3, Resulting Numbers: [7, 3, 3] Generated Node #0,2: 18:[7, 3, 3] Operation: 22-19=3 Exploring Operation: 7+3=10, Resulting Numbers: [22, 19, 10] Generated Node #0,3: 18:[22, 19, 10] Operation: 7+3=10 Exploring Operation: 7-3=4, Resulting Numbers: [22, 19, 4] Generated Node #0,4: 18:[22, 19, 4] Operation: 7-3=4 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[7, 3, 3], Operations: ['22-19=3'] Exploring Operation: 7-3=4, Resulting Numbers: [3, 4] Generated Node #0,2,0: 18:[3, 4] Operation: 7-3=4 Exploring Operation: 7+3=10, Resulting Numbers: [3, 10] Generated Node #0,2,1: 18:[3, 10] Operation: 7+3=10 Exploring Operation: 3+3=6, Resulting Numbers: [7, 6] Generated Node #0,2,2: 18:[7, 6] Operation: 3+3=6 Exploring Operation: 7+3=10, Resulting Numbers: [3, 10] Generated Node #0,2,3: 18:[3, 10] Operation: 7+3=10 Exploring Operation: 7-3=4, Resulting Numbers: [3, 4] Generated Node #0,2,4: 18:[3, 4] Operation: 7-3=4 Moving to Node #0,2,0 Current State: 18:[3, 4], Operations: ['22-19=3', '7-3=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[7, 6], Operations: ['22-19=3', '3+3=6'] Exploring Operation: 7*6=42, Resulting Numbers: [42] 42,18 unequal: No Solution Exploring Operation: 7+6=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 7-6=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,2,4 Current State: 18:[3, 4], Operations: ['22-19=3', '7-3=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[3, 10], Operations: ['22-19=3', '7+3=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[3, 10], Operations: ['22-19=3', '7+3=10'] Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[7, 19, 19], Operations: ['22-3=19'] Exploring Operation: 19/19=1, Resulting Numbers: [7, 1] Generated Node #0,0,0: 18:[7, 1] Operation: 19/19=1 Exploring Operation: 19-7=12, Resulting Numbers: [19, 12] Generated Node #0,0,1: 18:[19, 12] Operation: 19-7=12 Exploring Operation: 19-7=12, Resulting Numbers: [19, 12] Generated Node #0,0,2: 18:[19, 12] Operation: 19-7=12 Exploring Operation: 19-19=0, Resulting Numbers: [7, 0] Generated Node #0,0,3: 18:[7, 0] Operation: 19-19=0 Exploring Operation: 7+19=26, Resulting Numbers: [19, 26] Generated Node #0,0,4: 18:[19, 26] Operation: 7+19=26 Moving to Node #0,0,0 Current State: 18:[7, 1], Operations: ['22-3=19', '19/19=1'] Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,18 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[7, 0], Operations: ['22-3=19', '19-19=0'] Exploring Operation: 7+0=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 7*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 7-0=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[19, 12], Operations: ['22-3=19', '19-7=12'] Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[19, 12], Operations: ['22-3=19', '19-7=12'] Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,18 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[19, 26], Operations: ['22-3=19', '7+19=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,18 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[19, 3, 15], Operations: ['22-7=15'] Exploring Operation: 15/3=5, Resulting Numbers: [19, 5] Generated Node #0,1,0: 18:[19, 5] Operation: 15/3=5 Exploring Operation: 15-3=12, Resulting Numbers: [19, 12] Generated Node #0,1,1: 18:[19, 12] Operation: 15-3=12 Exploring Operation: 19-3=16, Resulting Numbers: [15, 16] Generated Node #0,1,2: 18:[15, 16] Operation: 19-3=16 Exploring Operation: 19-15=4, Resulting Numbers: [3, 4] Generated Node #0,1,3: 18:[3, 4] Operation: 19-15=4 Exploring Operation: 3+15=18, Resulting Numbers: [19, 18] Generated Node #0,1,4: 18:[19, 18] Operation: 3+15=18 Moving to Node #0,1,3 Current State: 18:[3, 4], Operations: ['22-7=15', '19-15=4'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,1,4 Current State: 18:[19, 18], Operations: ['22-7=15', '3+15=18'] Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,18 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,18 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[19, 5], Operations: ['22-7=15', '15/3=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,18 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,18 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[19, 12], Operations: ['22-7=15', '15-3=12'] Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,18 unequal: No Solution Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[15, 16], Operations: ['22-7=15', '19-3=16'] Exploring Operation: 15+16=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 16-15=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 15*16=240, Resulting Numbers: [240] 240,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[22, 19, 10], Operations: ['7+3=10'] Exploring Operation: 22+10=32, Resulting Numbers: [19, 32] Generated Node #0,3,0: 18:[19, 32] Operation: 22+10=32 Exploring Operation: 19-10=9, Resulting Numbers: [22, 9] Generated Node #0,3,1: 18:[22, 9] Operation: 19-10=9 Exploring Operation: 22-10=12, Resulting Numbers: [19, 12] Generated Node #0,3,2: 18:[19, 12] Operation: 22-10=12 Exploring Operation: 19+10=29, Resulting Numbers: [22, 29] Generated Node #0,3,3: 18:[22, 29] Operation: 19+10=29 Exploring Operation: 22-19=3, Resulting Numbers: [10, 3] Generated Node #0,3,4: 18:[10, 3] Operation: 22-19=3 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 18:[10, 3], Operations: ['7+3=10', '22-19=3'] Exploring Operation: 10*3=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 10+3=13, Resulting Numbers: [13] 13,18 unequal: No Solution No 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: 18:[22, 9], Operations: ['7+3=10', '19-10=9'] Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,18 unequal: No Solution Exploring Operation: 22*9=198, Resulting Numbers: [198] 198,18 unequal: No Solution Exploring Operation: 22+9=31, Resulting Numbers: [31] 31,18 unequal: No Solution No 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: 18:[19, 12], Operations: ['7+3=10', '22-10=12'] Exploring Operation: 19+12=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 19*12=228, Resulting Numbers: [228] 228,18 unequal: No Solution No 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: 18:[19, 32], Operations: ['7+3=10', '22+10=32'] Exploring Operation: 19*32=608, Resulting Numbers: [608] 608,18 unequal: No Solution Exploring Operation: 19+32=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 32-19=13, Resulting Numbers: [13] 13,18 unequal: No Solution No 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: 18:[22, 29], Operations: ['7+3=10', '19+10=29'] Exploring Operation: 29-22=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 22*29=638, Resulting Numbers: [638] 638,18 unequal: No Solution Exploring Operation: 22+29=51, Resulting Numbers: [51] 51,18 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: 18:[22, 19, 4], Operations: ['7-3=4'] Exploring Operation: 22+4=26, Resulting Numbers: [19, 26] Generated Node #0,4,0: 18:[19, 26] Operation: 22+4=26 Exploring Operation: 19-4=15, Resulting Numbers: [22, 15] Generated Node #0,4,1: 18:[22, 15] Operation: 19-4=15 Exploring Operation: 19+4=23, Resulting Numbers: [22, 23] Generated Node #0,4,2: 18:[22, 23] Operation: 19+4=23 Exploring Operation: 22-19=3, Resulting Numbers: [4, 3] Generated Node #0,4,3: 18:[4, 3] Operation: 22-19=3 Exploring Operation: 22-4=18, Resulting Numbers: [19, 18] Generated Node #0,4,4: 18:[19, 18] Operation: 22-4=18 Moving to Node #0,4,3 Current State: 18:[4, 3], Operations: ['7-3=4', '22-19=3'] Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,18 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,4,4 Current State: 18:[19, 18], Operations: ['7-3=4', '22-4=18'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 19*18=342, Resulting Numbers: [342] 342,18 unequal: No Solution Exploring Operation: 19+18=37, Resulting Numbers: [37] 37,18 unequal: No Solution Moving to Node #0,4,1 Current State: 18:[22, 15], Operations: ['7-3=4', '19-4=15'] Exploring Operation: 22*15=330, Resulting Numbers: [330] 330,18 unequal: No Solution Exploring Operation: 22-15=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 22+15=37, Resulting Numbers: [37] 37,18 unequal: No Solution Moving to Node #0,4,0 Current State: 18:[19, 26], Operations: ['7-3=4', '22+4=26'] Exploring Operation: 19*26=494, Resulting Numbers: [494] 494,18 unequal: No Solution Exploring Operation: 26-19=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,18 unequal: No Solution Moving to Node #0,4,2 Current State: 18:[22, 23], Operations: ['7-3=4', '19+4=23'] Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,18 unequal: No Solution Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,18 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,18 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
[ 90, 32, 80, 40 ]
76
[ "90*32=2880", "2880/80=36", "40+36=76" ]
Current State: 76:[90, 32, 80, 40], Operations: [] Exploring Operation: 90*32=2880, Resulting Numbers: [80, 40, 2880] Generated Node #2: [80, 40, 2880] from Operation: 90*32=2880 Current State: 76:[80, 40, 2880], Operations: ['90*32=2880'] Exploring Operation: 2880/80=36, Resulting Numbers: [40, 36] Generated Node #3: [40, 36] from Operation: 2880/80=36 Current State: 76:[40, 36], Operations: ['90*32=2880', '2880/80=36'] Exploring Operation: 40+36=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[90, 32, 80, 40], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [32, 40, 10] Generated Node #0,0: 76:[32, 40, 10] Operation: 90-80=10 Moving to Node #0,0 Current State: 76:[32, 40, 10], Operations: ['90-80=10'] Exploring Operation: 32-10=22, Resulting Numbers: [40, 22] Generated Node #0,0,0: 76:[40, 22] Operation: 32-10=22 Moving to Node #0,0,0 Current State: 76:[40, 22], Operations: ['90-80=10', '32-10=22'] Exploring Operation: 40-22=18, Resulting Numbers: [18] 18,76 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 4, 28, 17, 31 ]
63
[ "4+17=21", "31-28=3", "21*3=63" ]
Current State: 63:[4, 28, 17, 31], Operations: [] Exploring Operation: 4+17=21, Resulting Numbers: [28, 31, 21] Generated Node #2: [28, 31, 21] from Operation: 4+17=21 Current State: 63:[28, 31, 21], Operations: ['4+17=21'] Exploring Operation: 31-28=3, Resulting Numbers: [21, 3] Generated Node #3: [21, 3] from Operation: 31-28=3 Current State: 63:[21, 3], Operations: ['4+17=21', '31-28=3'] Exploring Operation: 21*3=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[4, 28, 17, 31], Operations: [] Exploring Operation: 31-28=3, Resulting Numbers: [4, 17, 3] Generated Node #0,0: 63:[4, 17, 3] Operation: 31-28=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[4, 17, 3], Operations: ['31-28=3'] Exploring Operation: 4+17=21, Resulting Numbers: [3, 21] Generated Node #0,0,0: 63:[3, 21] Operation: 4+17=21 Moving to Node #0,0,0 Current State: 63:[3, 21], Operations: ['31-28=3', '4+17=21'] Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[4, 28, 17, 31], Operations: [] Exploring Operation: 31-28=3, Resulting Numbers: [4, 17, 3] Generated Node #0,0: 63:[4, 17, 3] Operation: 31-28=3 Moving to Node #0,0 Current State: 63:[4, 17, 3], Operations: ['31-28=3'] Exploring Operation: 4+17=21, Resulting Numbers: [3, 21] Generated Node #0,0,0: 63:[3, 21] Operation: 4+17=21 Moving to Node #0,0,0 Current State: 63:[3, 21], Operations: ['31-28=3', '4+17=21'] Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 50, 79, 27, 87 ]
81
[ "79-50=29", "27*87=2349", "2349/29=81" ]
Current State: 81:[50, 79, 27, 87], Operations: [] Exploring Operation: 79-50=29, Resulting Numbers: [27, 87, 29] Generated Node #2: [27, 87, 29] from Operation: 79-50=29 Current State: 81:[27, 87, 29], Operations: ['79-50=29'] Exploring Operation: 27*87=2349, Resulting Numbers: [29, 2349] Generated Node #3: [29, 2349] from Operation: 27*87=2349 Current State: 81:[29, 2349], Operations: ['79-50=29', '27*87=2349'] Exploring Operation: 2349/29=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[50, 79, 27, 87], Operations: [] Exploring Operation: 50+27=77, Resulting Numbers: [79, 87, 77] Generated Node #0,0: 81:[79, 87, 77] Operation: 50+27=77 Exploring Operation: 79-50=29, Resulting Numbers: [27, 87, 29] Generated Node #0,1: 81:[27, 87, 29] Operation: 79-50=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[27, 87, 29], Operations: ['79-50=29'] Exploring Operation: 87/29=3, Resulting Numbers: [27, 3] Generated Node #0,1,0: 81:[27, 3] Operation: 87/29=3 Exploring Operation: 29-27=2, Resulting Numbers: [87, 2] Generated Node #0,1,1: 81:[87, 2] Operation: 29-27=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[27, 3], Operations: ['79-50=29', '87/29=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[50, 79, 27, 87], Operations: [] Exploring Operation: 79-50=29, Resulting Numbers: [27, 87, 29] Generated Node #0,1: 81:[27, 87, 29] Operation: 79-50=29 Moving to Node #0,1 Current State: 81:[27, 87, 29], Operations: ['79-50=29'] Exploring Operation: 87/29=3, Resulting Numbers: [27, 3] Generated Node #0,1,0: 81:[27, 3] Operation: 87/29=3 Moving to Node #0,1,0 Current State: 81:[27, 3], Operations: ['79-50=29', '87/29=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 56, 20, 2, 45 ]
21
[ "56-45=11", "20/2=10", "11+10=21" ]
Current State: 21:[56, 20, 2, 45], Operations: [] Exploring Operation: 56-45=11, Resulting Numbers: [20, 2, 11] Generated Node #2: [20, 2, 11] from Operation: 56-45=11 Current State: 21:[20, 2, 11], Operations: ['56-45=11'] Exploring Operation: 20/2=10, Resulting Numbers: [11, 10] Generated Node #3: [11, 10] from Operation: 20/2=10 Current State: 21:[11, 10], Operations: ['56-45=11', '20/2=10'] Exploring Operation: 11+10=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[56, 20, 2, 45], Operations: [] Exploring Operation: 56/2=28, Resulting Numbers: [20, 45, 28] Generated Node #0,0: 21:[20, 45, 28] Operation: 56/2=28 Exploring Operation: 56-45=11, Resulting Numbers: [20, 2, 11] Generated Node #0,1: 21:[20, 2, 11] Operation: 56-45=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[20, 2, 11], Operations: ['56-45=11'] Exploring Operation: 2*11=22, Resulting Numbers: [20, 22] Generated Node #0,1,0: 21:[20, 22] Operation: 2*11=22 Exploring Operation: 20-11=9, Resulting Numbers: [2, 9] Generated Node #0,1,1: 21:[2, 9] Operation: 20-11=9 Moving to Node #0,1,0 Current State: 21:[20, 22], Operations: ['56-45=11', '2*11=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,21 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[2, 9], Operations: ['56-45=11', '20-11=9'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[20, 45, 28], Operations: ['56/2=28'] Exploring Operation: 45-20=25, Resulting Numbers: [28, 25] Generated Node #0,0,0: 21:[28, 25] Operation: 45-20=25 Exploring Operation: 45-28=17, Resulting Numbers: [20, 17] Generated Node #0,0,1: 21:[20, 17] Operation: 45-28=17 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[20, 17], Operations: ['56/2=28', '45-28=17'] Exploring Operation: 20+17=37, Resulting Numbers: [37] 37,21 unequal: No Solution Exploring Operation: 20-17=3, Resulting Numbers: [3] 3,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[28, 25], Operations: ['56/2=28', '45-20=25'] Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,21 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 32, 86, 71, 71 ]
53
[ "86-32=54", "71/71=1", "54-1=53" ]
Current State: 53:[32, 86, 71, 71], Operations: [] Exploring Operation: 86-32=54, Resulting Numbers: [71, 71, 54] Generated Node #2: [71, 71, 54] from Operation: 86-32=54 Current State: 53:[71, 71, 54], Operations: ['86-32=54'] Exploring Operation: 71/71=1, Resulting Numbers: [54, 1] Generated Node #3: [54, 1] from Operation: 71/71=1 Current State: 53:[54, 1], Operations: ['86-32=54', '71/71=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[32, 86, 71, 71], Operations: [] Exploring Operation: 86-32=54, Resulting Numbers: [71, 71, 54] Generated Node #0,0: 53:[71, 71, 54] Operation: 86-32=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[71, 71, 54], Operations: ['86-32=54'] Exploring Operation: 71/71=1, Resulting Numbers: [54, 1] Generated Node #0,0,0: 53:[54, 1] Operation: 71/71=1 Moving to Node #0,0,0 Current State: 53:[54, 1], Operations: ['86-32=54', '71/71=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[32, 86, 71, 71], Operations: [] Exploring Operation: 86-32=54, Resulting Numbers: [71, 71, 54] Generated Node #0,0: 53:[71, 71, 54] Operation: 86-32=54 Moving to Node #0,0 Current State: 53:[71, 71, 54], Operations: ['86-32=54'] Exploring Operation: 71/71=1, Resulting Numbers: [54, 1] Generated Node #0,0,0: 53:[54, 1] Operation: 71/71=1 Moving to Node #0,0,0 Current State: 53:[54, 1], Operations: ['86-32=54', '71/71=1'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 9, 19, 19, 95 ]
46
[ "9*95=855", "19+855=874", "874/19=46" ]
Current State: 46:[9, 19, 19, 95], Operations: [] Exploring Operation: 9*95=855, Resulting Numbers: [19, 19, 855] Generated Node #2: [19, 19, 855] from Operation: 9*95=855 Current State: 46:[19, 19, 855], Operations: ['9*95=855'] Exploring Operation: 19+855=874, Resulting Numbers: [874] 874,46 equal: Goal Reached Exploring Operation: 874/19=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[9, 19, 19, 95], Operations: [] Exploring Operation: 95-19=76, Resulting Numbers: [9, 19, 76] Generated Node #0,0: 46:[9, 19, 76] Operation: 95-19=76 Exploring Operation: 95/19=5, Resulting Numbers: [9, 19, 5] Generated Node #0,1: 46:[9, 19, 5] Operation: 95/19=5 Exploring Operation: 95/19=5, Resulting Numbers: [9, 19, 5] Generated Node #0,2: 46:[9, 19, 5] Operation: 95/19=5 Exploring Operation: 95-19=76, Resulting Numbers: [9, 19, 76] Generated Node #0,3: 46:[9, 19, 76] Operation: 95-19=76 Exploring Operation: 95-9=86, Resulting Numbers: [19, 19, 86] Generated Node #0,4: 46:[19, 19, 86] Operation: 95-9=86 Moving to Node #0,1 Current State: 46:[9, 19, 5], Operations: ['95/19=5'] Exploring Operation: 9-5=4, Resulting Numbers: [19, 4] Generated Node #0,1,0: 46:[19, 4] Operation: 9-5=4 Exploring Operation: 19-9=10, Resulting Numbers: [5, 10] Generated Node #0,1,1: 46:[5, 10] Operation: 19-9=10 Exploring Operation: 19+5=24, Resulting Numbers: [9, 24] Generated Node #0,1,2: 46:[9, 24] Operation: 19+5=24 Exploring Operation: 9+19=28, Resulting Numbers: [5, 28] Generated Node #0,1,3: 46:[5, 28] Operation: 9+19=28 Exploring Operation: 9*5=45, Resulting Numbers: [19, 45] Generated Node #0,1,4: 46:[19, 45] Operation: 9*5=45 Moving to Node #0,2 Current State: 46:[9, 19, 5], Operations: ['95/19=5'] Exploring Operation: 19+5=24, Resulting Numbers: [9, 24] Generated Node #0,2,0: 46:[9, 24] Operation: 19+5=24 Exploring Operation: 19-9=10, Resulting Numbers: [5, 10] Generated Node #0,2,1: 46:[5, 10] Operation: 19-9=10 Exploring Operation: 9+19=28, Resulting Numbers: [5, 28] Generated Node #0,2,2: 46:[5, 28] Operation: 9+19=28 Exploring Operation: 9*5=45, Resulting Numbers: [19, 45] Generated Node #0,2,3: 46:[19, 45] Operation: 9*5=45 Exploring Operation: 9-5=4, Resulting Numbers: [19, 4] Generated Node #0,2,4: 46:[19, 4] Operation: 9-5=4 Moving to Node #0,0 Current State: 46:[9, 19, 76], Operations: ['95-19=76'] Exploring Operation: 76-9=67, Resulting Numbers: [19, 67] Generated Node #0,0,0: 46:[19, 67] Operation: 76-9=67 Exploring Operation: 76-19=57, Resulting Numbers: [9, 57] Generated Node #0,0,1: 46:[9, 57] Operation: 76-19=57 Exploring Operation: 76/19=4, Resulting Numbers: [9, 4] Generated Node #0,0,2: 46:[9, 4] Operation: 76/19=4 Exploring Operation: 9+19=28, Resulting Numbers: [76, 28] Generated Node #0,0,3: 46:[76, 28] Operation: 9+19=28 Exploring Operation: 19-9=10, Resulting Numbers: [76, 10] Generated Node #0,0,4: 46:[76, 10] Operation: 19-9=10 Moving to Node #0,3 Current State: 46:[9, 19, 76], Operations: ['95-19=76'] Exploring Operation: 76-19=57, Resulting Numbers: [9, 57] Generated Node #0,3,0: 46:[9, 57] Operation: 76-19=57 Exploring Operation: 76-9=67, Resulting Numbers: [19, 67] Generated Node #0,3,1: 46:[19, 67] Operation: 76-9=67 Exploring Operation: 9+19=28, Resulting Numbers: [76, 28] Generated Node #0,3,2: 46:[76, 28] Operation: 9+19=28 Exploring Operation: 19-9=10, Resulting Numbers: [76, 10] Generated Node #0,3,3: 46:[76, 10] Operation: 19-9=10 Exploring Operation: 76/19=4, Resulting Numbers: [9, 4] Generated Node #0,3,4: 46:[9, 4] Operation: 76/19=4 Moving to Node #0,4 Current State: 46:[19, 19, 86], Operations: ['95-9=86'] Exploring Operation: 86-19=67, Resulting Numbers: [19, 67] Generated Node #0,4,0: 46:[19, 67] Operation: 86-19=67 Exploring Operation: 19/19=1, Resulting Numbers: [86, 1] Generated Node #0,4,1: 46:[86, 1] Operation: 19/19=1 Exploring Operation: 19+19=38, Resulting Numbers: [86, 38] Generated Node #0,4,2: 46:[86, 38] Operation: 19+19=38 Exploring Operation: 19-19=0, Resulting Numbers: [86, 0] Generated Node #0,4,3: 46:[86, 0] Operation: 19-19=0 Exploring Operation: 86-19=67, Resulting Numbers: [19, 67] Generated Node #0,4,4: 46:[19, 67] Operation: 86-19=67 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 46:[19, 67], Operations: ['95-9=86', '86-19=67'] Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,46 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 #0,4,4 Current State: 46:[19, 67], Operations: ['95-9=86', '86-19=67'] Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,46 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,46 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 #0,4,1 Current State: 46:[86, 1], Operations: ['95-9=86', '19/19=1'] Exploring Operation: 86/1=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 86*1=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 86-1=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 86+1=87, Resulting Numbers: [87] 87,46 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 #0,4,3 Current State: 46:[86, 0], Operations: ['95-9=86', '19-19=0'] Exploring Operation: 86+0=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 86-0=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 86*0=0, Resulting Numbers: [0] 0,46 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 #0,4,2 Current State: 46:[86, 38], Operations: ['95-9=86', '19+19=38'] Exploring Operation: 86+38=124, Resulting Numbers: [124] 124,46 unequal: No Solution Exploring Operation: 86-38=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 86*38=3268, Resulting Numbers: [3268] 3268,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 46:[19, 45], Operations: ['95/19=5', '9*5=45'] Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,46 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,46 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[19, 45], Operations: ['95/19=5', '9*5=45'] Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,46 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,46 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,46 unequal: No Solution Moving to Node #0,2,4 Current State: 46:[19, 4], Operations: ['95/19=5', '9-5=4'] Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,46 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[19, 4], Operations: ['95/19=5', '9-5=4'] Exploring Operation: 19+4=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 19*4=76, Resulting Numbers: [76] 76,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[9, 24], Operations: ['95/19=5', '19+5=24'] Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,46 unequal: No Solution Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,46 unequal: No Solution Moving to Node #0,1,3 Current State: 46:[5, 28], Operations: ['95/19=5', '9+19=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,46 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[5, 28], Operations: ['95/19=5', '9+19=28'] Exploring Operation: 5+28=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 5*28=140, Resulting Numbers: [140] 140,46 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[9, 24], Operations: ['95/19=5', '19+5=24'] Exploring Operation: 9+24=33, Resulting Numbers: [33] 33,46 unequal: No Solution Exploring Operation: 24-9=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 9*24=216, Resulting Numbers: [216] 216,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[9, 4], Operations: ['95-19=76', '76/19=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,46 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,46 unequal: No Solution Moving to Node #0,3,4 Current State: 46:[9, 4], Operations: ['95-19=76', '76/19=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[5, 10], Operations: ['95/19=5', '19-9=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[5, 10], Operations: ['95/19=5', '19-9=10'] Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,46 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[9, 57], Operations: ['95-19=76', '76-19=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 9*57=513, Resulting Numbers: [513] 513,46 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[9, 57], Operations: ['95-19=76', '76-19=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 9*57=513, Resulting Numbers: [513] 513,46 unequal: No Solution Exploring Operation: 57-9=48, Resulting Numbers: [48] 48,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[19, 67], Operations: ['95-19=76', '76-9=67'] Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,46 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[19, 67], Operations: ['95-19=76', '76-9=67'] Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,46 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[76, 28], Operations: ['95-19=76', '9+19=28'] Exploring Operation: 76*28=2128, Resulting Numbers: [2128] 2128,46 unequal: No Solution Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 76+28=104, Resulting Numbers: [104] 104,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[76, 28], Operations: ['95-19=76', '9+19=28'] Exploring Operation: 76-28=48, Resulting Numbers: [48] 48,46 unequal: No Solution Exploring Operation: 76+28=104, Resulting Numbers: [104] 104,46 unequal: No Solution Exploring Operation: 76*28=2128, Resulting Numbers: [2128] 2128,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[76, 10], Operations: ['95-19=76', '19-9=10'] Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,46 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[76, 10], Operations: ['95-19=76', '19-9=10'] Exploring Operation: 76-10=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 76*10=760, Resulting Numbers: [760] 760,46 unequal: No Solution Exploring Operation: 76+10=86, Resulting Numbers: [86] 86,46 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 25, 79, 70, 2 ]
69
[ "25+79=104", "70/2=35", "104-35=69" ]
Current State: 69:[25, 79, 70, 2], Operations: [] Exploring Operation: 25+79=104, Resulting Numbers: [70, 2, 104] Generated Node #2: [70, 2, 104] from Operation: 25+79=104 Current State: 69:[70, 2, 104], Operations: ['25+79=104'] Exploring Operation: 70/2=35, Resulting Numbers: [104, 35] Generated Node #3: [104, 35] from Operation: 70/2=35 Current State: 69:[104, 35], Operations: ['25+79=104', '70/2=35'] Exploring Operation: 104-35=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[25, 79, 70, 2], Operations: [] Exploring Operation: 79-70=9, Resulting Numbers: [25, 2, 9] Generated Node #0,0: 69:[25, 2, 9] Operation: 79-70=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[25, 2, 9], Operations: ['79-70=9'] Exploring Operation: 25-2=23, Resulting Numbers: [9, 23] Generated Node #0,0,0: 69:[9, 23] Operation: 25-2=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[9, 23], Operations: ['79-70=9', '25-2=23'] Exploring Operation: 9+23=32, Resulting Numbers: [32] 32,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 88, 68, 43, 8 ]
31
[ "88-68=20", "43+8=51", "51-20=31" ]
Current State: 31:[88, 68, 43, 8], Operations: [] Exploring Operation: 88-68=20, Resulting Numbers: [43, 8, 20] Generated Node #2: [43, 8, 20] from Operation: 88-68=20 Current State: 31:[43, 8, 20], Operations: ['88-68=20'] Exploring Operation: 43+8=51, Resulting Numbers: [20, 51] Generated Node #3: [20, 51] from Operation: 43+8=51 Current State: 31:[20, 51], Operations: ['88-68=20', '43+8=51'] Exploring Operation: 51-20=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[88, 68, 43, 8], Operations: [] Exploring Operation: 88-68=20, Resulting Numbers: [43, 8, 20] Generated Node #0,0: 31:[43, 8, 20] Operation: 88-68=20 Moving to Node #0,0 Current State: 31:[43, 8, 20], Operations: ['88-68=20'] Exploring Operation: 43-8=35, Resulting Numbers: [20, 35] Generated Node #0,0,0: 31:[20, 35] Operation: 43-8=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 31:[20, 35], Operations: ['88-68=20', '43-8=35'] Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,31 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
[ 29, 56, 4, 55 ]
78
[ "56-29=27", "55-4=51", "27+51=78" ]
Current State: 78:[29, 56, 4, 55], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [4, 55, 27] Generated Node #2: [4, 55, 27] from Operation: 56-29=27 Current State: 78:[4, 55, 27], Operations: ['56-29=27'] Exploring Operation: 55-4=51, Resulting Numbers: [27, 51] Generated Node #3: [27, 51] from Operation: 55-4=51 Current State: 78:[27, 51], Operations: ['56-29=27', '55-4=51'] Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[29, 56, 4, 55], Operations: [] Exploring Operation: 29+56=85, Resulting Numbers: [4, 55, 85] Generated Node #0,0: 78:[4, 55, 85] Operation: 29+56=85 Exploring Operation: 56-29=27, Resulting Numbers: [4, 55, 27] Generated Node #0,1: 78:[4, 55, 27] Operation: 56-29=27 Exploring Operation: 56-55=1, Resulting Numbers: [29, 4, 1] Generated Node #0,2: 78:[29, 4, 1] Operation: 56-55=1 Exploring Operation: 56/4=14, Resulting Numbers: [29, 55, 14] Generated Node #0,3: 78:[29, 55, 14] Operation: 56/4=14 Exploring Operation: 55-29=26, Resulting Numbers: [56, 4, 26] Generated Node #0,4: 78:[56, 4, 26] Operation: 55-29=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[29, 4, 1], Operations: ['56-55=1'] Exploring Operation: 29-4=25, Resulting Numbers: [1, 25] Generated Node #0,2,0: 78:[1, 25] Operation: 29-4=25 Exploring Operation: 29-1=28, Resulting Numbers: [4, 28] Generated Node #0,2,1: 78:[4, 28] Operation: 29-1=28 Exploring Operation: 29/1=29, Resulting Numbers: [4, 29] Generated Node #0,2,2: 78:[4, 29] Operation: 29/1=29 Exploring Operation: 29*1=29, Resulting Numbers: [4, 29] Generated Node #0,2,3: 78:[4, 29] Operation: 29*1=29 Exploring Operation: 4-1=3, Resulting Numbers: [29, 3] Generated Node #0,2,4: 78:[29, 3] Operation: 4-1=3 Moving to Node #0,2,0 Current State: 78:[1, 25], Operations: ['56-55=1', '29-4=25'] Exploring Operation: 1+25=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 1*25=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,78 unequal: No Solution Moving to Node #0,2,4 Current State: 78:[29, 3], Operations: ['56-55=1', '4-1=3'] Exploring Operation: 29*3=87, Resulting Numbers: [87] 87,78 unequal: No Solution Exploring Operation: 29-3=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 29+3=32, Resulting Numbers: [32] 32,78 unequal: No Solution Moving to Node #0,2,1 Current State: 78:[4, 28], Operations: ['56-55=1', '29-1=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,78 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[4, 29], Operations: ['56-55=1', '29/1=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[4, 29], Operations: ['56-55=1', '29*1=29'] Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,78 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,78 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,78 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 Current State: 78:[4, 55, 27], Operations: ['56-29=27'] Exploring Operation: 4+55=59, Resulting Numbers: [27, 59] Generated Node #0,1,0: 78:[27, 59] Operation: 4+55=59 Exploring Operation: 55-4=51, Resulting Numbers: [27, 51] Generated Node #0,1,1: 78:[27, 51] Operation: 55-4=51 Exploring Operation: 27-4=23, Resulting Numbers: [55, 23] Generated Node #0,1,2: 78:[55, 23] Operation: 27-4=23 Exploring Operation: 55-27=28, Resulting Numbers: [4, 28] Generated Node #0,1,3: 78:[4, 28] Operation: 55-27=28 Exploring Operation: 55+27=82, Resulting Numbers: [4, 82] Generated Node #0,1,4: 78:[4, 82] Operation: 55+27=82 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 78:[4, 28], Operations: ['56-29=27', '55-27=28'] Exploring Operation: 4*28=112, Resulting Numbers: [112] 112,78 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,78 unequal: No Solution Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,78 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,78 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 78:[4, 82], Operations: ['56-29=27', '55+27=82'] Exploring Operation: 4*82=328, Resulting Numbers: [328] 328,78 unequal: No Solution Exploring Operation: 4+82=86, Resulting Numbers: [86] 86,78 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[29, 56, 4, 55], Operations: [] Exploring Operation: 56-29=27, Resulting Numbers: [4, 55, 27] Generated Node #0,1: 78:[4, 55, 27] Operation: 56-29=27 Moving to Node #0,1 Current State: 78:[4, 55, 27], Operations: ['56-29=27'] Exploring Operation: 55+27=82, Resulting Numbers: [4, 82] Generated Node #0,1,4: 78:[4, 82] Operation: 55+27=82 Moving to Node #0,1,4 Current State: 78:[4, 82], Operations: ['56-29=27', '55+27=82'] Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.962674
hs_5
mult_heuristic
[ 93, 1, 8, 83 ]
90
[ "93-83=10", "1+8=9", "10*9=90" ]
Current State: 90:[93, 1, 8, 83], Operations: [] Exploring Operation: 93-83=10, Resulting Numbers: [1, 8, 10] Generated Node #2: [1, 8, 10] from Operation: 93-83=10 Current State: 90:[1, 8, 10], Operations: ['93-83=10'] Exploring Operation: 1+8=9, Resulting Numbers: [10, 9] Generated Node #3: [10, 9] from Operation: 1+8=9 Current State: 90:[10, 9], Operations: ['93-83=10', '1+8=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[93, 1, 8, 83], Operations: [] Exploring Operation: 8+83=91, Resulting Numbers: [93, 1, 91] Generated Node #0,0: 90:[93, 1, 91] Operation: 8+83=91 Exploring Operation: 93-83=10, Resulting Numbers: [1, 8, 10] Generated Node #0,1: 90:[1, 8, 10] Operation: 93-83=10 Moving to Node #0,1 Current State: 90:[1, 8, 10], Operations: ['93-83=10'] Exploring Operation: 1*8=8, Resulting Numbers: [10, 8] Generated Node #0,1,0: 90:[10, 8] Operation: 1*8=8 Exploring Operation: 1+8=9, Resulting Numbers: [10, 9] Generated Node #0,1,1: 90:[10, 9] Operation: 1+8=9 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[10, 9], Operations: ['93-83=10', '1+8=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[93, 1, 8, 83], Operations: [] Exploring Operation: 93-83=10, Resulting Numbers: [1, 8, 10] Generated Node #0,1: 90:[1, 8, 10] Operation: 93-83=10 Moving to Node #0,1 Current State: 90:[1, 8, 10], Operations: ['93-83=10'] Exploring Operation: 1+8=9, Resulting Numbers: [10, 9] Generated Node #0,1,1: 90:[10, 9] Operation: 1+8=9 Moving to Node #0,1,1 Current State: 90:[10, 9], Operations: ['93-83=10', '1+8=9'] Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 1, 51, 31, 78 ]
99
[ "1+51=52", "78-31=47", "52+47=99" ]
Current State: 99:[1, 51, 31, 78], Operations: [] Exploring Operation: 1+51=52, Resulting Numbers: [31, 78, 52] Generated Node #2: [31, 78, 52] from Operation: 1+51=52 Current State: 99:[31, 78, 52], Operations: ['1+51=52'] Exploring Operation: 78-31=47, Resulting Numbers: [52, 47] Generated Node #3: [52, 47] from Operation: 78-31=47 Current State: 99:[52, 47], Operations: ['1+51=52', '78-31=47'] Exploring Operation: 52+47=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[1, 51, 31, 78], Operations: [] Exploring Operation: 31+78=109, Resulting Numbers: [1, 51, 109] Generated Node #0,0: 99:[1, 51, 109] Operation: 31+78=109 Exploring Operation: 78-31=47, Resulting Numbers: [1, 51, 47] Generated Node #0,1: 99:[1, 51, 47] Operation: 78-31=47 Exploring Operation: 51+78=129, Resulting Numbers: [1, 31, 129] Generated Node #0,2: 99:[1, 31, 129] Operation: 51+78=129 Exploring Operation: 51-31=20, Resulting Numbers: [1, 78, 20] Generated Node #0,3: 99:[1, 78, 20] Operation: 51-31=20 Exploring Operation: 78-51=27, Resulting Numbers: [1, 31, 27] Generated Node #0,4: 99:[1, 31, 27] Operation: 78-51=27 Start Sub Search at level 1: Moving to Node #0,4 Current State: 99:[1, 31, 27], Operations: ['78-51=27'] Exploring Operation: 1+27=28, Resulting Numbers: [31, 28] Generated Node #0,4,0: 99:[31, 28] Operation: 1+27=28 Exploring Operation: 31-27=4, Resulting Numbers: [1, 4] Generated Node #0,4,1: 99:[1, 4] Operation: 31-27=4 Exploring Operation: 31/1=31, Resulting Numbers: [27, 31] Generated Node #0,4,2: 99:[27, 31] Operation: 31/1=31 Exploring Operation: 1*31=31, Resulting Numbers: [27, 31] Generated Node #0,4,3: 99:[27, 31] Operation: 1*31=31 Exploring Operation: 1+31=32, Resulting Numbers: [27, 32] Generated Node #0,4,4: 99:[27, 32] Operation: 1+31=32 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 99:[1, 4], Operations: ['78-51=27', '31-27=4'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,99 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,99 unequal: No Solution No 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: 99:[31, 28], Operations: ['78-51=27', '1+27=28'] Exploring Operation: 31*28=868, Resulting Numbers: [868] 868,99 unequal: No Solution Exploring Operation: 31+28=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 31-28=3, Resulting Numbers: [3] 3,99 unequal: No Solution No 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: 99:[27, 32], Operations: ['78-51=27', '1+31=32'] Exploring Operation: 27*32=864, Resulting Numbers: [864] 864,99 unequal: No Solution Exploring Operation: 27+32=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,99 unequal: No Solution No 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: 99:[27, 31], Operations: ['78-51=27', '31/1=31'] Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,99 unequal: No Solution Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,99 unequal: No Solution No 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: 99:[27, 31], Operations: ['78-51=27', '1*31=31'] Exploring Operation: 31-27=4, Resulting Numbers: [4] 4,99 unequal: No Solution Exploring Operation: 27+31=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 27*31=837, Resulting Numbers: [837] 837,99 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: 99:[1, 51, 109], Operations: ['31+78=109'] Exploring Operation: 1*51=51, Resulting Numbers: [109, 51] Generated Node #0,0,0: 99:[109, 51] Operation: 1*51=51 Exploring Operation: 109-1=108, Resulting Numbers: [51, 108] Generated Node #0,0,1: 99:[51, 108] Operation: 109-1=108 Exploring Operation: 51/1=51, Resulting Numbers: [109, 51] Generated Node #0,0,2: 99:[109, 51] Operation: 51/1=51 Exploring Operation: 109-51=58, Resulting Numbers: [1, 58] Generated Node #0,0,3: 99:[1, 58] Operation: 109-51=58 Exploring Operation: 51-1=50, Resulting Numbers: [109, 50] Generated Node #0,0,4: 99:[109, 50] Operation: 51-1=50 Moving to Node #0,0,1 Current State: 99:[51, 108], Operations: ['31+78=109', '109-1=108'] Exploring Operation: 51+108=159, Resulting Numbers: [159] 159,99 unequal: No Solution Exploring Operation: 108-51=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 51*108=5508, Resulting Numbers: [5508] 5508,99 unequal: No Solution Moving to Node #0,0,4 Current State: 99:[109, 50], Operations: ['31+78=109', '51-1=50'] Exploring Operation: 109*50=5450, Resulting Numbers: [5450] 5450,99 unequal: No Solution Exploring Operation: 109+50=159, Resulting Numbers: [159] 159,99 unequal: No Solution Exploring Operation: 109-50=59, Resulting Numbers: [59] 59,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[1, 58], Operations: ['31+78=109', '109-51=58'] Exploring Operation: 1*58=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 1+58=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 58-1=57, Resulting Numbers: [57] 57,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[109, 51], Operations: ['31+78=109', '1*51=51'] Exploring Operation: 109-51=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 109+51=160, Resulting Numbers: [160] 160,99 unequal: No Solution Exploring Operation: 109*51=5559, Resulting Numbers: [5559] 5559,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[109, 51], Operations: ['31+78=109', '51/1=51'] Exploring Operation: 109-51=58, Resulting Numbers: [58] 58,99 unequal: No Solution Exploring Operation: 109+51=160, Resulting Numbers: [160] 160,99 unequal: No Solution Exploring Operation: 109*51=5559, Resulting Numbers: [5559] 5559,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[1, 78, 20], Operations: ['51-31=20'] Exploring Operation: 1+78=79, Resulting Numbers: [20, 79] Generated Node #0,3,0: 99:[20, 79] Operation: 1+78=79 Exploring Operation: 78-20=58, Resulting Numbers: [1, 58] Generated Node #0,3,1: 99:[1, 58] Operation: 78-20=58 Exploring Operation: 78+20=98, Resulting Numbers: [1, 98] Generated Node #0,3,2: 99:[1, 98] Operation: 78+20=98 Exploring Operation: 20-1=19, Resulting Numbers: [78, 19] Generated Node #0,3,3: 99:[78, 19] Operation: 20-1=19 Exploring Operation: 1*78=78, Resulting Numbers: [20, 78] Generated Node #0,3,4: 99:[20, 78] Operation: 1*78=78 Moving to Node #0,3,2 Current State: 99:[1, 98], Operations: ['51-31=20', '78+20=98'] Exploring Operation: 98-1=97, Resulting Numbers: [97] 97,99 unequal: No Solution Exploring Operation: 1*98=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 98/1=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 1+98=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[1, 51, 31, 78], Operations: [] Exploring Operation: 51-31=20, Resulting Numbers: [1, 78, 20] Generated Node #0,3: 99:[1, 78, 20] Operation: 51-31=20 Moving to Node #0,3 Current State: 99:[1, 78, 20], Operations: ['51-31=20'] Exploring Operation: 78+20=98, Resulting Numbers: [1, 98] Generated Node #0,3,2: 99:[1, 98] Operation: 78+20=98 Moving to Node #0,3,2 Current State: 99:[1, 98], Operations: ['51-31=20', '78+20=98'] Exploring Operation: 1+98=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
sum_heuristic
[ 78, 18, 16, 37 ]
81
[ "78-18=60", "37-16=21", "60+21=81" ]
Current State: 81:[78, 18, 16, 37], Operations: [] Exploring Operation: 78-18=60, Resulting Numbers: [16, 37, 60] Generated Node #2: [16, 37, 60] from Operation: 78-18=60 Current State: 81:[16, 37, 60], Operations: ['78-18=60'] Exploring Operation: 37-16=21, Resulting Numbers: [60, 21] Generated Node #3: [60, 21] from Operation: 37-16=21 Current State: 81:[60, 21], Operations: ['78-18=60', '37-16=21'] Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[78, 18, 16, 37], Operations: [] Exploring Operation: 18-16=2, Resulting Numbers: [78, 37, 2] Generated Node #0,0: 81:[78, 37, 2] Operation: 18-16=2 Exploring Operation: 37-18=19, Resulting Numbers: [78, 16, 19] Generated Node #0,1: 81:[78, 16, 19] Operation: 37-18=19 Exploring Operation: 37-16=21, Resulting Numbers: [78, 18, 21] Generated Node #0,2: 81:[78, 18, 21] Operation: 37-16=21 Exploring Operation: 18+16=34, Resulting Numbers: [78, 37, 34] Generated Node #0,3: 81:[78, 37, 34] Operation: 18+16=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[78, 37, 2], Operations: ['18-16=2'] Exploring Operation: 78+2=80, Resulting Numbers: [37, 80] Generated Node #0,0,0: 81:[37, 80] Operation: 78+2=80 Exploring Operation: 37*2=74, Resulting Numbers: [78, 74] Generated Node #0,0,1: 81:[78, 74] Operation: 37*2=74 Exploring Operation: 37-2=35, Resulting Numbers: [78, 35] Generated Node #0,0,2: 81:[78, 35] Operation: 37-2=35 Exploring Operation: 78-37=41, Resulting Numbers: [2, 41] Generated Node #0,0,3: 81:[2, 41] Operation: 78-37=41 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 81:[78, 74], Operations: ['18-16=2', '37*2=74'] Exploring Operation: 78*74=5772, Resulting Numbers: [5772] 5772,81 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 78+74=152, Resulting Numbers: [152] 152,81 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 #0,0,0 Current State: 81:[37, 80], Operations: ['18-16=2', '78+2=80'] Exploring Operation: 37+80=117, Resulting Numbers: [117] 117,81 unequal: No Solution Exploring Operation: 80-37=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 37*80=2960, Resulting Numbers: [2960] 2960,81 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 #0,0,2 Current State: 81:[78, 35], Operations: ['18-16=2', '37-2=35'] Exploring Operation: 78*35=2730, Resulting Numbers: [2730] 2730,81 unequal: No Solution Exploring Operation: 78-35=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 78+35=113, Resulting Numbers: [113] 113,81 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 #0,0,3 Current State: 81:[2, 41], Operations: ['18-16=2', '78-37=41'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,81 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,81 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,81 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 #0,1 Current State: 81:[78, 16, 19], Operations: ['37-18=19'] Exploring Operation: 78+16=94, Resulting Numbers: [19, 94] Generated Node #0,1,0: 81:[19, 94] Operation: 78+16=94 Exploring Operation: 19-16=3, Resulting Numbers: [78, 3] Generated Node #0,1,1: 81:[78, 3] Operation: 19-16=3 Exploring Operation: 16+19=35, Resulting Numbers: [78, 35] Generated Node #0,1,2: 81:[78, 35] Operation: 16+19=35 Exploring Operation: 78+19=97, Resulting Numbers: [16, 97] Generated Node #0,1,3: 81:[16, 97] Operation: 78+19=97 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 81:[78, 3], Operations: ['37-18=19', '19-16=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[78, 18, 16, 37], Operations: [] Exploring Operation: 37-18=19, Resulting Numbers: [78, 16, 19] Generated Node #0,1: 81:[78, 16, 19] Operation: 37-18=19 Moving to Node #0,1 Current State: 81:[78, 16, 19], Operations: ['37-18=19'] Exploring Operation: 19-16=3, Resulting Numbers: [78, 3] Generated Node #0,1,1: 81:[78, 3] Operation: 19-16=3 Moving to Node #0,1,1 Current State: 81:[78, 3], Operations: ['37-18=19', '19-16=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 2, 70, 79, 86 ]
68
[ "79-70=9", "2*9=18", "86-18=68" ]
Current State: 68:[2, 70, 79, 86], Operations: [] Exploring Operation: 79-70=9, Resulting Numbers: [2, 86, 9] Generated Node #2: [2, 86, 9] from Operation: 79-70=9 Current State: 68:[2, 86, 9], Operations: ['79-70=9'] Exploring Operation: 2*9=18, Resulting Numbers: [86, 18] Generated Node #3: [86, 18] from Operation: 2*9=18 Current State: 68:[86, 18], Operations: ['79-70=9', '2*9=18'] Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[2, 70, 79, 86], Operations: [] Exploring Operation: 86-70=16, Resulting Numbers: [2, 79, 16] Generated Node #0,0: 68:[2, 79, 16] Operation: 86-70=16 Exploring Operation: 86-79=7, Resulting Numbers: [2, 70, 7] Generated Node #0,1: 68:[2, 70, 7] Operation: 86-79=7 Exploring Operation: 79-70=9, Resulting Numbers: [2, 86, 9] Generated Node #0,2: 68:[2, 86, 9] Operation: 79-70=9 Exploring Operation: 86/2=43, Resulting Numbers: [70, 79, 43] Generated Node #0,3: 68:[70, 79, 43] Operation: 86/2=43 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[2, 70, 7], Operations: ['86-79=7'] Exploring Operation: 2*7=14, Resulting Numbers: [70, 14] Generated Node #0,1,0: 68:[70, 14] Operation: 2*7=14 Exploring Operation: 70/2=35, Resulting Numbers: [7, 35] Generated Node #0,1,1: 68:[7, 35] Operation: 70/2=35 Exploring Operation: 7-2=5, Resulting Numbers: [70, 5] Generated Node #0,1,2: 68:[70, 5] Operation: 7-2=5 Exploring Operation: 70-2=68, Resulting Numbers: [7, 68] Generated Node #0,1,3: 68:[7, 68] Operation: 70-2=68 Moving to Node #0,1,2 Current State: 68:[70, 5], Operations: ['86-79=7', '7-2=5'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,68 unequal: No Solution Exploring Operation: 70+5=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,68 unequal: No Solution Exploring Operation: 70*5=350, Resulting Numbers: [350] 350,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[7, 68], Operations: ['86-79=7', '70-2=68'] Exploring Operation: 7+68=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 68-7=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 7*68=476, Resulting Numbers: [476] 476,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[7, 35], Operations: ['86-79=7', '70/2=35'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,68 unequal: No Solution Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,68 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[70, 14], Operations: ['86-79=7', '2*7=14'] Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 70*14=980, Resulting Numbers: [980] 980,68 unequal: No Solution Exploring Operation: 70+14=84, Resulting Numbers: [84] 84,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[2, 79, 16], Operations: ['86-70=16'] Exploring Operation: 79-2=77, Resulting Numbers: [16, 77] Generated Node #0,0,0: 68:[16, 77] Operation: 79-2=77 Exploring Operation: 2+16=18, Resulting Numbers: [79, 18] Generated Node #0,0,1: 68:[79, 18] Operation: 2+16=18 Exploring Operation: 2*16=32, Resulting Numbers: [79, 32] Generated Node #0,0,2: 68:[79, 32] Operation: 2*16=32 Exploring Operation: 79-16=63, Resulting Numbers: [2, 63] Generated Node #0,0,3: 68:[2, 63] Operation: 79-16=63 Moving to Node #0,0,3 Current State: 68:[2, 63], Operations: ['86-70=16', '79-16=63'] Exploring Operation: 2+63=65, Resulting Numbers: [65] 65,68 unequal: No Solution Exploring Operation: 2*63=126, Resulting Numbers: [126] 126,68 unequal: No Solution Exploring Operation: 63-2=61, Resulting Numbers: [61] 61,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[16, 77], Operations: ['86-70=16', '79-2=77'] Exploring Operation: 16+77=93, Resulting Numbers: [93] 93,68 unequal: No Solution Exploring Operation: 77-16=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 16*77=1232, Resulting Numbers: [1232] 1232,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[79, 18], Operations: ['86-70=16', '2+16=18'] Exploring Operation: 79-18=61, Resulting Numbers: [61] 61,68 unequal: No Solution Exploring Operation: 79+18=97, Resulting Numbers: [97] 97,68 unequal: No Solution Exploring Operation: 79*18=1422, Resulting Numbers: [1422] 1422,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[79, 32], Operations: ['86-70=16', '2*16=32'] Exploring Operation: 79-32=47, Resulting Numbers: [47] 47,68 unequal: No Solution Exploring Operation: 79+32=111, Resulting Numbers: [111] 111,68 unequal: No Solution Exploring Operation: 79*32=2528, Resulting Numbers: [2528] 2528,68 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:[70, 79, 43], Operations: ['86/2=43'] Exploring Operation: 79-43=36, Resulting Numbers: [70, 36] Generated Node #0,3,0: 68:[70, 36] Operation: 79-43=36 Exploring Operation: 70-43=27, Resulting Numbers: [79, 27] Generated Node #0,3,1: 68:[79, 27] Operation: 70-43=27 Exploring Operation: 70+43=113, Resulting Numbers: [79, 113] Generated Node #0,3,2: 68:[79, 113] Operation: 70+43=113 Exploring Operation: 79-70=9, Resulting Numbers: [43, 9] Generated Node #0,3,3: 68:[43, 9] Operation: 79-70=9 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 68:[70, 36], Operations: ['86/2=43', '79-43=36'] Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,68 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,68 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 #0,3,3 Current State: 68:[43, 9], Operations: ['86/2=43', '79-70=9'] Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 43+9=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 43*9=387, Resulting Numbers: [387] 387,68 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 #0,3,1 Current State: 68:[79, 27], Operations: ['86/2=43', '70-43=27'] Exploring Operation: 79+27=106, Resulting Numbers: [106] 106,68 unequal: No Solution Exploring Operation: 79-27=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 79*27=2133, Resulting Numbers: [2133] 2133,68 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 #0,3,2 Current State: 68:[79, 113], Operations: ['86/2=43', '70+43=113'] Exploring Operation: 113-79=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 79*113=8927, Resulting Numbers: [8927] 8927,68 unequal: No Solution Exploring Operation: 79+113=192, Resulting Numbers: [192] 192,68 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 #0,2 Current State: 68:[2, 86, 9], Operations: ['79-70=9'] Exploring Operation: 86/2=43, Resulting Numbers: [9, 43] Generated Node #0,2,0: 68:[9, 43] Operation: 86/2=43 Exploring Operation: 86-9=77, Resulting Numbers: [2, 77] Generated Node #0,2,1: 68:[2, 77] Operation: 86-9=77 Exploring Operation: 2*9=18, Resulting Numbers: [86, 18] Generated Node #0,2,2: 68:[86, 18] Operation: 2*9=18 Exploring Operation: 86-2=84, Resulting Numbers: [9, 84] Generated Node #0,2,3: 68:[9, 84] Operation: 86-2=84 Moving to Node #0,2,1 Current State: 68:[2, 77], Operations: ['79-70=9', '86-9=77'] Exploring Operation: 2+77=79, Resulting Numbers: [79] 79,68 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,68 unequal: No Solution Exploring Operation: 2*77=154, Resulting Numbers: [154] 154,68 unequal: No Solution Moving to Node #0,2,0 Current State: 68:[9, 43], Operations: ['79-70=9', '86/2=43'] Exploring Operation: 9+43=52, Resulting Numbers: [52] 52,68 unequal: No Solution Exploring Operation: 43-9=34, Resulting Numbers: [34] 34,68 unequal: No Solution Exploring Operation: 9*43=387, Resulting Numbers: [387] 387,68 unequal: No Solution Moving to Node #0,2,2 Current State: 68:[86, 18], Operations: ['79-70=9', '2*9=18'] Exploring Operation: 86+18=104, Resulting Numbers: [104] 104,68 unequal: No Solution Exploring Operation: 86*18=1548, Resulting Numbers: [1548] 1548,68 unequal: No Solution Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[2, 70, 79, 86], Operations: [] Exploring Operation: 79-70=9, Resulting Numbers: [2, 86, 9] Generated Node #0,2: 68:[2, 86, 9] Operation: 79-70=9 Moving to Node #0,2 Current State: 68:[2, 86, 9], Operations: ['79-70=9'] Exploring Operation: 2*9=18, Resulting Numbers: [86, 18] Generated Node #0,2,2: 68:[86, 18] Operation: 2*9=18 Moving to Node #0,2,2 Current State: 68:[86, 18], Operations: ['79-70=9', '2*9=18'] Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.9375
hs_4
sum_heuristic
[ 13, 95, 5, 89 ]
71
[ "13*5=65", "95-89=6", "65+6=71" ]
Current State: 71:[13, 95, 5, 89], Operations: [] Exploring Operation: 13*5=65, Resulting Numbers: [95, 89, 65] Generated Node #2: [95, 89, 65] from Operation: 13*5=65 Current State: 71:[95, 89, 65], Operations: ['13*5=65'] Exploring Operation: 95-89=6, Resulting Numbers: [65, 6] Generated Node #3: [65, 6] from Operation: 95-89=6 Current State: 71:[65, 6], Operations: ['13*5=65', '95-89=6'] Exploring Operation: 65+6=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[13, 95, 5, 89], Operations: [] Exploring Operation: 13*5=65, Resulting Numbers: [95, 89, 65] Generated Node #0,0: 71:[95, 89, 65] Operation: 13*5=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[95, 89, 65], Operations: ['13*5=65'] Exploring Operation: 95-65=30, Resulting Numbers: [89, 30] Generated Node #0,0,0: 71:[89, 30] Operation: 95-65=30 Moving to Node #0,0,0 Current State: 71:[89, 30], Operations: ['13*5=65', '95-65=30'] Exploring Operation: 89-30=59, Resulting Numbers: [59] 59,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 79, 2, 6, 9 ]
23
[ "79-2=77", "6*9=54", "77-54=23" ]
Current State: 23:[79, 2, 6, 9], Operations: [] Exploring Operation: 79-2=77, Resulting Numbers: [6, 9, 77] Generated Node #2: [6, 9, 77] from Operation: 79-2=77 Current State: 23:[6, 9, 77], Operations: ['79-2=77'] Exploring Operation: 6*9=54, Resulting Numbers: [77, 54] Generated Node #3: [77, 54] from Operation: 6*9=54 Current State: 23:[77, 54], Operations: ['79-2=77', '6*9=54'] Exploring Operation: 77-54=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[79, 2, 6, 9], Operations: [] Exploring Operation: 79-6=73, Resulting Numbers: [2, 9, 73] Generated Node #0,0: 23:[2, 9, 73] Operation: 79-6=73 Exploring Operation: 79-9=70, Resulting Numbers: [2, 6, 70] Generated Node #0,1: 23:[2, 6, 70] Operation: 79-9=70 Exploring Operation: 2*6=12, Resulting Numbers: [79, 9, 12] Generated Node #0,2: 23:[79, 9, 12] Operation: 2*6=12 Exploring Operation: 79-2=77, Resulting Numbers: [6, 9, 77] Generated Node #0,3: 23:[6, 9, 77] Operation: 79-2=77 Exploring Operation: 2*9=18, Resulting Numbers: [79, 6, 18] Generated Node #0,4: 23:[79, 6, 18] Operation: 2*9=18 Start Sub Search at level 1: Moving to Node #0,4 Current State: 23:[79, 6, 18], Operations: ['2*9=18'] Exploring Operation: 6+18=24, Resulting Numbers: [79, 24] Generated Node #0,4,0: 23:[79, 24] Operation: 6+18=24 Exploring Operation: 18-6=12, Resulting Numbers: [79, 12] Generated Node #0,4,1: 23:[79, 12] Operation: 18-6=12 Exploring Operation: 79-6=73, Resulting Numbers: [18, 73] Generated Node #0,4,2: 23:[18, 73] Operation: 79-6=73 Exploring Operation: 79-18=61, Resulting Numbers: [6, 61] Generated Node #0,4,3: 23:[6, 61] Operation: 79-18=61 Exploring Operation: 79+6=85, Resulting Numbers: [18, 85] Generated Node #0,4,4: 23:[18, 85] Operation: 79+6=85 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 23:[18, 73], Operations: ['2*9=18', '79-6=73'] Exploring Operation: 18*73=1314, Resulting Numbers: [1314] 1314,23 unequal: No Solution Exploring Operation: 73-18=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 18+73=91, Resulting Numbers: [91] 91,23 unequal: No Solution No 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: 23:[6, 61], Operations: ['2*9=18', '79-18=61'] Exploring Operation: 61-6=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 6*61=366, Resulting Numbers: [366] 366,23 unequal: No Solution Exploring Operation: 6+61=67, Resulting Numbers: [67] 67,23 unequal: No Solution No 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: 23:[79, 24], Operations: ['2*9=18', '6+18=24'] Exploring Operation: 79+24=103, Resulting Numbers: [103] 103,23 unequal: No Solution Exploring Operation: 79-24=55, Resulting Numbers: [55] 55,23 unequal: No Solution Exploring Operation: 79*24=1896, Resulting Numbers: [1896] 1896,23 unequal: No Solution No 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: 23:[79, 12], Operations: ['2*9=18', '18-6=12'] Exploring Operation: 79*12=948, Resulting Numbers: [948] 948,23 unequal: No Solution Exploring Operation: 79+12=91, Resulting Numbers: [91] 91,23 unequal: No Solution Exploring Operation: 79-12=67, Resulting Numbers: [67] 67,23 unequal: No Solution No 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: 23:[18, 85], Operations: ['2*9=18', '79+6=85'] Exploring Operation: 18+85=103, Resulting Numbers: [103] 103,23 unequal: No Solution Exploring Operation: 18*85=1530, Resulting Numbers: [1530] 1530,23 unequal: No Solution Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,23 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: 23:[79, 9, 12], Operations: ['2*6=12'] Exploring Operation: 12-9=3, Resulting Numbers: [79, 3] Generated Node #0,2,0: 23:[79, 3] Operation: 12-9=3 Exploring Operation: 79+9=88, Resulting Numbers: [12, 88] Generated Node #0,2,1: 23:[12, 88] Operation: 79+9=88 Exploring Operation: 79-9=70, Resulting Numbers: [12, 70] Generated Node #0,2,2: 23:[12, 70] Operation: 79-9=70 Exploring Operation: 9+12=21, Resulting Numbers: [79, 21] Generated Node #0,2,3: 23:[79, 21] Operation: 9+12=21 Exploring Operation: 79-12=67, Resulting Numbers: [9, 67] Generated Node #0,2,4: 23:[9, 67] Operation: 79-12=67 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[12, 70], Operations: ['2*6=12', '79-9=70'] Exploring Operation: 12*70=840, Resulting Numbers: [840] 840,23 unequal: No Solution Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,23 unequal: No Solution Exploring Operation: 12+70=82, Resulting Numbers: [82] 82,23 unequal: No Solution No 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: 23:[79, 21], Operations: ['2*6=12', '9+12=21'] Exploring Operation: 79+21=100, Resulting Numbers: [100] 100,23 unequal: No Solution Exploring Operation: 79*21=1659, Resulting Numbers: [1659] 1659,23 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,23 unequal: No Solution No 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: 23:[9, 67], Operations: ['2*6=12', '79-12=67'] Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,23 unequal: No Solution Exploring Operation: 9+67=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 9*67=603, Resulting Numbers: [603] 603,23 unequal: No Solution No 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: 23:[79, 3], Operations: ['2*6=12', '12-9=3'] Exploring Operation: 79+3=82, Resulting Numbers: [82] 82,23 unequal: No Solution Exploring Operation: 79*3=237, Resulting Numbers: [237] 237,23 unequal: No Solution Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,23 unequal: No Solution No 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: 23:[12, 88], Operations: ['2*6=12', '79+9=88'] Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,23 unequal: No Solution Exploring Operation: 12+88=100, Resulting Numbers: [100] 100,23 unequal: No Solution Exploring Operation: 12*88=1056, Resulting Numbers: [1056] 1056,23 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: 23:[2, 9, 73], Operations: ['79-6=73'] Exploring Operation: 9-2=7, Resulting Numbers: [73, 7] Generated Node #0,0,0: 23:[73, 7] Operation: 9-2=7 Exploring Operation: 2*9=18, Resulting Numbers: [73, 18] Generated Node #0,0,1: 23:[73, 18] Operation: 2*9=18 Exploring Operation: 2+9=11, Resulting Numbers: [73, 11] Generated Node #0,0,2: 23:[73, 11] Operation: 2+9=11 Exploring Operation: 73-9=64, Resulting Numbers: [2, 64] Generated Node #0,0,3: 23:[2, 64] Operation: 73-9=64 Exploring Operation: 73-2=71, Resulting Numbers: [9, 71] Generated Node #0,0,4: 23:[9, 71] Operation: 73-2=71 Moving to Node #0,0,1 Current State: 23:[73, 18], Operations: ['79-6=73', '2*9=18'] Exploring Operation: 73*18=1314, Resulting Numbers: [1314] 1314,23 unequal: No Solution Exploring Operation: 73+18=91, Resulting Numbers: [91] 91,23 unequal: No Solution Exploring Operation: 73-18=55, Resulting Numbers: [55] 55,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[2, 64], Operations: ['79-6=73', '73-9=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,23 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[73, 11], Operations: ['79-6=73', '2+9=11'] Exploring Operation: 73*11=803, Resulting Numbers: [803] 803,23 unequal: No Solution Exploring Operation: 73-11=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 73+11=84, Resulting Numbers: [84] 84,23 unequal: No Solution Moving to Node #0,0,4 Current State: 23:[9, 71], Operations: ['79-6=73', '73-2=71'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,23 unequal: No Solution Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,23 unequal: No Solution Moving to Node #0,0,0 Current State: 23:[73, 7], Operations: ['79-6=73', '9-2=7'] Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 73*7=511, Resulting Numbers: [511] 511,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[2, 6, 70], Operations: ['79-9=70'] Exploring Operation: 2+6=8, Resulting Numbers: [70, 8] Generated Node #0,1,0: 23:[70, 8] Operation: 2+6=8 Exploring Operation: 70-6=64, Resulting Numbers: [2, 64] Generated Node #0,1,1: 23:[2, 64] Operation: 70-6=64 Exploring Operation: 70/2=35, Resulting Numbers: [6, 35] Generated Node #0,1,2: 23:[6, 35] Operation: 70/2=35 Exploring Operation: 70-2=68, Resulting Numbers: [6, 68] Generated Node #0,1,3: 23:[6, 68] Operation: 70-2=68 Exploring Operation: 2*6=12, Resulting Numbers: [70, 12] Generated Node #0,1,4: 23:[70, 12] Operation: 2*6=12 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 23:[6, 35], Operations: ['79-9=70', '70/2=35'] Exploring Operation: 6*35=210, Resulting Numbers: [210] 210,23 unequal: No Solution Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,23 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,23 unequal: No Solution No 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: 23:[70, 12], Operations: ['79-9=70', '2*6=12'] Exploring Operation: 70-12=58, Resulting Numbers: [58] 58,23 unequal: No Solution Exploring Operation: 70+12=82, Resulting Numbers: [82] 82,23 unequal: No Solution Exploring Operation: 70*12=840, Resulting Numbers: [840] 840,23 unequal: No Solution No 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: 23:[70, 8], Operations: ['79-9=70', '2+6=8'] Exploring Operation: 70-8=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 70*8=560, Resulting Numbers: [560] 560,23 unequal: No Solution Exploring Operation: 70+8=78, Resulting Numbers: [78] 78,23 unequal: No Solution No 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: 23:[2, 64], Operations: ['79-9=70', '70-6=64'] Exploring Operation: 64-2=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 2+64=66, Resulting Numbers: [66] 66,23 unequal: No Solution Exploring Operation: 64/2=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 2*64=128, Resulting Numbers: [128] 128,23 unequal: No Solution No 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: 23:[6, 68], Operations: ['79-9=70', '70-2=68'] Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,23 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,23 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: 23:[6, 9, 77], Operations: ['79-2=77'] Exploring Operation: 77-9=68, Resulting Numbers: [6, 68] Generated Node #0,3,0: 23:[6, 68] Operation: 77-9=68 Exploring Operation: 9-6=3, Resulting Numbers: [77, 3] Generated Node #0,3,1: 23:[77, 3] Operation: 9-6=3 Exploring Operation: 6+77=83, Resulting Numbers: [9, 83] Generated Node #0,3,2: 23:[9, 83] Operation: 6+77=83 Exploring Operation: 6+9=15, Resulting Numbers: [77, 15] Generated Node #0,3,3: 23:[77, 15] Operation: 6+9=15 Exploring Operation: 77-6=71, Resulting Numbers: [9, 71] Generated Node #0,3,4: 23:[9, 71] Operation: 77-6=71 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 23:[6, 68], Operations: ['79-2=77', '77-9=68'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 6+68=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 6*68=408, Resulting Numbers: [408] 408,23 unequal: No Solution No 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: 23:[77, 15], Operations: ['79-2=77', '6+9=15'] Exploring Operation: 77-15=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 77*15=1155, Resulting Numbers: [1155] 1155,23 unequal: No Solution Exploring Operation: 77+15=92, Resulting Numbers: [92] 92,23 unequal: No Solution No 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: 23:[9, 71], Operations: ['79-2=77', '77-6=71'] Exploring Operation: 71-9=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 9*71=639, Resulting Numbers: [639] 639,23 unequal: No Solution Exploring Operation: 9+71=80, Resulting Numbers: [80] 80,23 unequal: No Solution No 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: 23:[77, 3], Operations: ['79-2=77', '9-6=3'] Exploring Operation: 77+3=80, Resulting Numbers: [80] 80,23 unequal: No Solution Exploring Operation: 77-3=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 77*3=231, Resulting Numbers: [231] 231,23 unequal: No Solution No 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: 23:[9, 83], Operations: ['79-2=77', '6+77=83'] Exploring Operation: 9*83=747, Resulting Numbers: [747] 747,23 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 9+83=92, Resulting Numbers: [92] 92,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 10, 26, 39, 82 ]
97
[ "10*39=390", "390/26=15", "82+15=97" ]
Current State: 97:[10, 26, 39, 82], Operations: [] Exploring Operation: 10*39=390, Resulting Numbers: [26, 82, 390] Generated Node #2: [26, 82, 390] from Operation: 10*39=390 Current State: 97:[26, 82, 390], Operations: ['10*39=390'] Exploring Operation: 390/26=15, Resulting Numbers: [82, 15] Generated Node #3: [82, 15] from Operation: 390/26=15 Current State: 97:[82, 15], Operations: ['10*39=390', '390/26=15'] Exploring Operation: 82+15=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[10, 26, 39, 82], Operations: [] Exploring Operation: 26+39=65, Resulting Numbers: [10, 82, 65] Generated Node #0,0: 97:[10, 82, 65] Operation: 26+39=65 Exploring Operation: 10+39=49, Resulting Numbers: [26, 82, 49] Generated Node #0,1: 97:[26, 82, 49] Operation: 10+39=49 Exploring Operation: 10+26=36, Resulting Numbers: [39, 82, 36] Generated Node #0,2: 97:[39, 82, 36] Operation: 10+26=36 Exploring Operation: 10+82=92, Resulting Numbers: [26, 39, 92] Generated Node #0,3: 97:[26, 39, 92] Operation: 10+82=92 Moving to Node #0,0 Current State: 97:[10, 82, 65], Operations: ['26+39=65'] Exploring Operation: 10+65=75, Resulting Numbers: [82, 75] Generated Node #0,0,0: 97:[82, 75] Operation: 10+65=75 Exploring Operation: 10+82=92, Resulting Numbers: [65, 92] Generated Node #0,0,1: 97:[65, 92] Operation: 10+82=92 Exploring Operation: 82-10=72, Resulting Numbers: [65, 72] Generated Node #0,0,2: 97:[65, 72] Operation: 82-10=72 Exploring Operation: 65-10=55, Resulting Numbers: [82, 55] Generated Node #0,0,3: 97:[82, 55] Operation: 65-10=55 Moving to Node #0,2 Current State: 97:[39, 82, 36], Operations: ['10+26=36'] Exploring Operation: 39+82=121, Resulting Numbers: [36, 121] Generated Node #0,2,0: 97:[36, 121] Operation: 39+82=121 Exploring Operation: 39+36=75, Resulting Numbers: [82, 75] Generated Node #0,2,1: 97:[82, 75] Operation: 39+36=75 Exploring Operation: 39-36=3, Resulting Numbers: [82, 3] Generated Node #0,2,2: 97:[82, 3] Operation: 39-36=3 Exploring Operation: 82+36=118, Resulting Numbers: [39, 118] Generated Node #0,2,3: 97:[39, 118] Operation: 82+36=118 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 97:[82, 75], Operations: ['10+26=36', '39+36=75'] Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 97:[39, 118], Operations: ['10+26=36', '82+36=118'] Exploring Operation: 39+118=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 118-39=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 39*118=4602, Resulting Numbers: [4602] 4602,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 97:[36, 121], Operations: ['10+26=36', '39+82=121'] Exploring Operation: 36+121=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 36*121=4356, Resulting Numbers: [4356] 4356,97 unequal: No Solution Exploring Operation: 121-36=85, Resulting Numbers: [85] 85,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 97:[82, 3], Operations: ['10+26=36', '39-36=3'] Exploring Operation: 82*3=246, Resulting Numbers: [246] 246,97 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 82+3=85, Resulting Numbers: [85] 85,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 97:[26, 82, 49], Operations: ['10+39=49'] Exploring Operation: 26+49=75, Resulting Numbers: [82, 75] Generated Node #0,1,0: 97:[82, 75] Operation: 26+49=75 Exploring Operation: 49-26=23, Resulting Numbers: [82, 23] Generated Node #0,1,1: 97:[82, 23] Operation: 49-26=23 Exploring Operation: 26+82=108, Resulting Numbers: [49, 108] Generated Node #0,1,2: 97:[49, 108] Operation: 26+82=108 Exploring Operation: 82-26=56, Resulting Numbers: [49, 56] Generated Node #0,1,3: 97:[49, 56] Operation: 82-26=56 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[82, 75], Operations: ['10+39=49', '26+49=75'] Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,97 unequal: No Solution Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 97:[49, 108], Operations: ['10+39=49', '26+82=108'] Exploring Operation: 108-49=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 49*108=5292, Resulting Numbers: [5292] 5292,97 unequal: No Solution Exploring Operation: 49+108=157, Resulting Numbers: [157] 157,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 97:[82, 23], Operations: ['10+39=49', '49-26=23'] Exploring Operation: 82+23=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 82-23=59, Resulting Numbers: [59] 59,97 unequal: No Solution Exploring Operation: 82*23=1886, Resulting Numbers: [1886] 1886,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 97:[49, 56], Operations: ['10+39=49', '82-26=56'] Exploring Operation: 49+56=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 56-49=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 49*56=2744, Resulting Numbers: [2744] 2744,97 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: 97:[26, 39, 92], Operations: ['10+82=92'] Exploring Operation: 26+39=65, Resulting Numbers: [92, 65] Generated Node #0,3,0: 97:[92, 65] Operation: 26+39=65 Exploring Operation: 39-26=13, Resulting Numbers: [92, 13] Generated Node #0,3,1: 97:[92, 13] Operation: 39-26=13 Exploring Operation: 26+92=118, Resulting Numbers: [39, 118] Generated Node #0,3,2: 97:[39, 118] Operation: 26+92=118 Exploring Operation: 92-26=66, Resulting Numbers: [39, 66] Generated Node #0,3,3: 97:[39, 66] Operation: 92-26=66 Moving to Node #0,0,0 Current State: 97:[82, 75], Operations: ['26+39=65', '10+65=75'] Exploring Operation: 82*75=6150, Resulting Numbers: [6150] 6150,97 unequal: No Solution Exploring Operation: 82-75=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 82+75=157, Resulting Numbers: [157] 157,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[65, 92], Operations: ['26+39=65', '10+82=92'] Exploring Operation: 65+92=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 65*92=5980, Resulting Numbers: [5980] 5980,97 unequal: No Solution Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[92, 65], Operations: ['10+82=92', '26+39=65'] Exploring Operation: 92-65=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 92+65=157, Resulting Numbers: [157] 157,97 unequal: No Solution Exploring Operation: 92*65=5980, Resulting Numbers: [5980] 5980,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[65, 72], Operations: ['26+39=65', '82-10=72'] Exploring Operation: 65+72=137, Resulting Numbers: [137] 137,97 unequal: No Solution Exploring Operation: 72-65=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 65*72=4680, Resulting Numbers: [4680] 4680,97 unequal: No Solution Moving to Node #0,0,3 Current State: 97:[82, 55], Operations: ['26+39=65', '65-10=55'] Exploring Operation: 82+55=137, Resulting Numbers: [137] 137,97 unequal: No Solution Exploring Operation: 82-55=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 82*55=4510, Resulting Numbers: [4510] 4510,97 unequal: No Solution Moving to Node #0,3,2 Current State: 97:[39, 118], Operations: ['10+82=92', '26+92=118'] Exploring Operation: 39*118=4602, Resulting Numbers: [4602] 4602,97 unequal: No Solution Exploring Operation: 118-39=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 39+118=157, Resulting Numbers: [157] 157,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[92, 13], Operations: ['10+82=92', '39-26=13'] Exploring Operation: 92+13=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,97 unequal: No Solution Exploring Operation: 92*13=1196, Resulting Numbers: [1196] 1196,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[39, 66], Operations: ['10+82=92', '92-26=66'] Exploring Operation: 66-39=27, Resulting Numbers: [27] 27,97 unequal: No Solution Exploring Operation: 39+66=105, Resulting Numbers: [105] 105,97 unequal: No Solution Exploring Operation: 39*66=2574, Resulting Numbers: [2574] 2574,97 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 33, 23, 28, 36 ]
31
[ "33+36=69", "69/23=3", "28+3=31" ]
Current State: 31:[33, 23, 28, 36], Operations: [] Exploring Operation: 33+36=69, Resulting Numbers: [23, 28, 69] Generated Node #2: [23, 28, 69] from Operation: 33+36=69 Current State: 31:[23, 28, 69], Operations: ['33+36=69'] Exploring Operation: 69/23=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 69/23=3 Current State: 31:[28, 3], Operations: ['33+36=69', '69/23=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[33, 23, 28, 36], Operations: [] Exploring Operation: 36-23=13, Resulting Numbers: [33, 28, 13] Generated Node #0,0: 31:[33, 28, 13] Operation: 36-23=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[33, 28, 13], Operations: ['36-23=13'] Exploring Operation: 28+13=41, Resulting Numbers: [33, 41] Generated Node #0,0,0: 31:[33, 41] Operation: 28+13=41 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[33, 41], Operations: ['36-23=13', '28+13=41'] Exploring Operation: 41-33=8, Resulting Numbers: [8] 8,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 12, 67, 66, 36 ]
85
[ "67-12=55", "66-36=30", "55+30=85" ]
Current State: 85:[12, 67, 66, 36], Operations: [] Exploring Operation: 67-12=55, Resulting Numbers: [66, 36, 55] Generated Node #2: [66, 36, 55] from Operation: 67-12=55 Current State: 85:[66, 36, 55], Operations: ['67-12=55'] Exploring Operation: 66-36=30, Resulting Numbers: [55, 30] Generated Node #3: [55, 30] from Operation: 66-36=30 Current State: 85:[55, 30], Operations: ['67-12=55', '66-36=30'] Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[12, 67, 66, 36], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [12, 67, 30] Generated Node #0,0: 85:[12, 67, 30] Operation: 66-36=30 Exploring Operation: 67-36=31, Resulting Numbers: [12, 66, 31] Generated Node #0,1: 85:[12, 66, 31] Operation: 67-36=31 Exploring Operation: 36/12=3, Resulting Numbers: [67, 66, 3] Generated Node #0,2: 85:[67, 66, 3] Operation: 36/12=3 Exploring Operation: 67-66=1, Resulting Numbers: [12, 36, 1] Generated Node #0,3: 85:[12, 36, 1] Operation: 67-66=1 Moving to Node #0,3 Current State: 85:[12, 36, 1], Operations: ['67-66=1'] Exploring Operation: 36/12=3, Resulting Numbers: [1, 3] Generated Node #0,3,0: 85:[1, 3] Operation: 36/12=3 Exploring Operation: 12+1=13, Resulting Numbers: [36, 13] Generated Node #0,3,1: 85:[36, 13] Operation: 12+1=13 Exploring Operation: 36-1=35, Resulting Numbers: [12, 35] Generated Node #0,3,2: 85:[12, 35] Operation: 36-1=35 Exploring Operation: 36-12=24, Resulting Numbers: [1, 24] Generated Node #0,3,3: 85:[1, 24] Operation: 36-12=24 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[1, 3], Operations: ['67-66=1', '36/12=3'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 85:[1, 24], Operations: ['67-66=1', '36-12=24'] Exploring Operation: 1+24=25, Resulting Numbers: [25] 25,85 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 1*24=24, Resulting Numbers: [24] 24,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 85:[36, 13], Operations: ['67-66=1', '12+1=13'] Exploring Operation: 36-13=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 36+13=49, Resulting Numbers: [49] 49,85 unequal: No Solution Exploring Operation: 36*13=468, Resulting Numbers: [468] 468,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[12, 35], Operations: ['67-66=1', '36-1=35'] Exploring Operation: 12*35=420, Resulting Numbers: [420] 420,85 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,85 unequal: No Solution Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,85 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: 85:[12, 67, 30], Operations: ['66-36=30'] Exploring Operation: 30-12=18, Resulting Numbers: [67, 18] Generated Node #0,0,0: 85:[67, 18] Operation: 30-12=18 Exploring Operation: 67-30=37, Resulting Numbers: [12, 37] Generated Node #0,0,1: 85:[12, 37] Operation: 67-30=37 Exploring Operation: 12+67=79, Resulting Numbers: [30, 79] Generated Node #0,0,2: 85:[30, 79] Operation: 12+67=79 Exploring Operation: 67+30=97, Resulting Numbers: [12, 97] Generated Node #0,0,3: 85:[12, 97] Operation: 67+30=97 Moving to Node #0,1 Current State: 85:[12, 66, 31], Operations: ['67-36=31'] Exploring Operation: 12+66=78, Resulting Numbers: [31, 78] Generated Node #0,1,0: 85:[31, 78] Operation: 12+66=78 Exploring Operation: 66-31=35, Resulting Numbers: [12, 35] Generated Node #0,1,1: 85:[12, 35] Operation: 66-31=35 Exploring Operation: 66+31=97, Resulting Numbers: [12, 97] Generated Node #0,1,2: 85:[12, 97] Operation: 66+31=97 Exploring Operation: 31-12=19, Resulting Numbers: [66, 19] Generated Node #0,1,3: 85:[66, 19] Operation: 31-12=19 Moving to Node #0,2 Current State: 85:[67, 66, 3], Operations: ['36/12=3'] Exploring Operation: 67+3=70, Resulting Numbers: [66, 70] Generated Node #0,2,0: 85:[66, 70] Operation: 67+3=70 Exploring Operation: 67-66=1, Resulting Numbers: [3, 1] Generated Node #0,2,1: 85:[3, 1] Operation: 67-66=1 Exploring Operation: 66+3=69, Resulting Numbers: [67, 69] Generated Node #0,2,2: 85:[67, 69] Operation: 66+3=69 Exploring Operation: 66/3=22, Resulting Numbers: [67, 22] Generated Node #0,2,3: 85:[67, 22] Operation: 66/3=22 Moving to Node #0,2,1 Current State: 85:[3, 1], Operations: ['36/12=3', '67-66=1'] Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,85 unequal: No Solution Exploring Operation: 3+1=4, Resulting Numbers: [4] 4,85 unequal: No Solution Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,85 unequal: No Solution Moving to Node #0,0,3 Current State: 85:[12, 97], Operations: ['66-36=30', '67+30=97'] Exploring Operation: 97-12=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[12, 67, 66, 36], Operations: [] Exploring Operation: 66-36=30, Resulting Numbers: [12, 67, 30] Generated Node #0,0: 85:[12, 67, 30] Operation: 66-36=30 Moving to Node #0,0 Current State: 85:[12, 67, 30], Operations: ['66-36=30'] Exploring Operation: 67+30=97, Resulting Numbers: [12, 97] Generated Node #0,0,3: 85:[12, 97] Operation: 67+30=97 Moving to Node #0,0,3 Current State: 85:[12, 97], Operations: ['66-36=30', '67+30=97'] Exploring Operation: 97-12=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
0.962674
hs_4
mult_heuristic
[ 12, 13, 8, 80 ]
88
[ "13-12=1", "8+80=88", "1*88=88" ]
Current State: 88:[12, 13, 8, 80], Operations: [] Exploring Operation: 13-12=1, Resulting Numbers: [8, 80, 1] Generated Node #2: [8, 80, 1] from Operation: 13-12=1 Current State: 88:[8, 80, 1], Operations: ['13-12=1'] Exploring Operation: 8+80=88, Resulting Numbers: [1, 88] Generated Node #3: [1, 88] from Operation: 8+80=88 Current State: 88:[1, 88], Operations: ['13-12=1', '8+80=88'] Exploring Operation: 1*88=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[12, 13, 8, 80], Operations: [] Exploring Operation: 8+80=88, Resulting Numbers: [12, 13, 88] Generated Node #0,0: 88:[12, 13, 88] Operation: 8+80=88 Exploring Operation: 80/8=10, Resulting Numbers: [12, 13, 10] Generated Node #0,1: 88:[12, 13, 10] Operation: 80/8=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[12, 13, 88], Operations: ['8+80=88'] Exploring Operation: 13-12=1, Resulting Numbers: [88, 1] Generated Node #0,0,0: 88:[88, 1] Operation: 13-12=1 Exploring Operation: 12+13=25, Resulting Numbers: [88, 25] Generated Node #0,0,1: 88:[88, 25] Operation: 12+13=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[88, 1], Operations: ['8+80=88', '13-12=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[12, 13, 8, 80], Operations: [] Exploring Operation: 8+80=88, Resulting Numbers: [12, 13, 88] Generated Node #0,0: 88:[12, 13, 88] Operation: 8+80=88 Moving to Node #0,0 Current State: 88:[12, 13, 88], Operations: ['8+80=88'] Exploring Operation: 13-12=1, Resulting Numbers: [88, 1] Generated Node #0,0,0: 88:[88, 1] Operation: 13-12=1 Moving to Node #0,0,0 Current State: 88:[88, 1], Operations: ['8+80=88', '13-12=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 51, 35, 22, 53 ]
47
[ "51-35=16", "53-22=31", "16+31=47" ]
Current State: 47:[51, 35, 22, 53], Operations: [] Exploring Operation: 51-35=16, Resulting Numbers: [22, 53, 16] Generated Node #2: [22, 53, 16] from Operation: 51-35=16 Current State: 47:[22, 53, 16], Operations: ['51-35=16'] Exploring Operation: 53-22=31, Resulting Numbers: [16, 31] Generated Node #3: [16, 31] from Operation: 53-22=31 Current State: 47:[16, 31], Operations: ['51-35=16', '53-22=31'] Exploring Operation: 16+31=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[51, 35, 22, 53], Operations: [] Exploring Operation: 35+22=57, Resulting Numbers: [51, 53, 57] Generated Node #0,0: 47:[51, 53, 57] Operation: 35+22=57 Exploring Operation: 51+22=73, Resulting Numbers: [35, 53, 73] Generated Node #0,1: 47:[35, 53, 73] Operation: 51+22=73 Exploring Operation: 53-22=31, Resulting Numbers: [51, 35, 31] Generated Node #0,2: 47:[51, 35, 31] Operation: 53-22=31 Exploring Operation: 51-22=29, Resulting Numbers: [35, 53, 29] Generated Node #0,3: 47:[35, 53, 29] Operation: 51-22=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[51, 53, 57], Operations: ['35+22=57'] Exploring Operation: 53-51=2, Resulting Numbers: [57, 2] Generated Node #0,0,0: 47:[57, 2] Operation: 53-51=2 Exploring Operation: 57-51=6, Resulting Numbers: [53, 6] Generated Node #0,0,1: 47:[53, 6] Operation: 57-51=6 Exploring Operation: 57-53=4, Resulting Numbers: [51, 4] Generated Node #0,0,2: 47:[51, 4] Operation: 57-53=4 Exploring Operation: 51+53=104, Resulting Numbers: [57, 104] Generated Node #0,0,3: 47:[57, 104] Operation: 51+53=104 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[53, 6], Operations: ['35+22=57', '57-51=6'] Exploring Operation: 53+6=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[51, 35, 22, 53], Operations: [] Exploring Operation: 35+22=57, Resulting Numbers: [51, 53, 57] Generated Node #0,0: 47:[51, 53, 57] Operation: 35+22=57 Moving to Node #0,0 Current State: 47:[51, 53, 57], Operations: ['35+22=57'] Exploring Operation: 57-51=6, Resulting Numbers: [53, 6] Generated Node #0,0,1: 47:[53, 6] Operation: 57-51=6 Moving to Node #0,0,1 Current State: 47:[53, 6], Operations: ['35+22=57', '57-51=6'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 26, 50, 94, 37 ]
19
[ "26+50=76", "94-37=57", "76-57=19" ]
Current State: 19:[26, 50, 94, 37], Operations: [] Exploring Operation: 26+50=76, Resulting Numbers: [94, 37, 76] Generated Node #2: [94, 37, 76] from Operation: 26+50=76 Current State: 19:[94, 37, 76], Operations: ['26+50=76'] Exploring Operation: 94-37=57, Resulting Numbers: [76, 57] Generated Node #3: [76, 57] from Operation: 94-37=57 Current State: 19:[76, 57], Operations: ['26+50=76', '94-37=57'] Exploring Operation: 76-57=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[26, 50, 94, 37], Operations: [] Exploring Operation: 94-37=57, Resulting Numbers: [26, 50, 57] Generated Node #0,0: 19:[26, 50, 57] Operation: 94-37=57 Exploring Operation: 50-37=13, Resulting Numbers: [26, 94, 13] Generated Node #0,1: 19:[26, 94, 13] Operation: 50-37=13 Exploring Operation: 50-26=24, Resulting Numbers: [94, 37, 24] Generated Node #0,2: 19:[94, 37, 24] Operation: 50-26=24 Exploring Operation: 94-50=44, Resulting Numbers: [26, 37, 44] Generated Node #0,3: 19:[26, 37, 44] Operation: 94-50=44 Start Sub Search at level 1: Moving to Node #0,3 Current State: 19:[26, 37, 44], Operations: ['94-50=44'] Exploring Operation: 26+37=63, Resulting Numbers: [44, 63] Generated Node #0,3,0: 19:[44, 63] Operation: 26+37=63 Exploring Operation: 44-37=7, Resulting Numbers: [26, 7] Generated Node #0,3,1: 19:[26, 7] Operation: 44-37=7 Exploring Operation: 44-26=18, Resulting Numbers: [37, 18] Generated Node #0,3,2: 19:[37, 18] Operation: 44-26=18 Exploring Operation: 37-26=11, Resulting Numbers: [44, 11] Generated Node #0,3,3: 19:[44, 11] Operation: 37-26=11 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 19:[26, 7], Operations: ['94-50=44', '44-37=7'] Exploring Operation: 26*7=182, Resulting Numbers: [182] 182,19 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[26, 50, 94, 37], Operations: [] Exploring Operation: 94-50=44, Resulting Numbers: [26, 37, 44] Generated Node #0,3: 19:[26, 37, 44] Operation: 94-50=44 Moving to Node #0,3 Current State: 19:[26, 37, 44], Operations: ['94-50=44'] Exploring Operation: 44-37=7, Resulting Numbers: [26, 7] Generated Node #0,3,1: 19:[26, 7] Operation: 44-37=7 Moving to Node #0,3,1 Current State: 19:[26, 7], Operations: ['94-50=44', '44-37=7'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 97, 47, 95, 32 ]
13
[ "97-47=50", "95-32=63", "63-50=13" ]
Current State: 13:[97, 47, 95, 32], Operations: [] Exploring Operation: 97-47=50, Resulting Numbers: [95, 32, 50] Generated Node #2: [95, 32, 50] from Operation: 97-47=50 Current State: 13:[95, 32, 50], Operations: ['97-47=50'] Exploring Operation: 95-32=63, Resulting Numbers: [50, 63] Generated Node #3: [50, 63] from Operation: 95-32=63 Current State: 13:[50, 63], Operations: ['97-47=50', '95-32=63'] Exploring Operation: 63-50=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[97, 47, 95, 32], Operations: [] Exploring Operation: 95-47=48, Resulting Numbers: [97, 32, 48] Generated Node #0,0: 13:[97, 32, 48] Operation: 95-47=48 Exploring Operation: 97-47=50, Resulting Numbers: [95, 32, 50] Generated Node #0,1: 13:[95, 32, 50] Operation: 97-47=50 Exploring Operation: 97-95=2, Resulting Numbers: [47, 32, 2] Generated Node #0,2: 13:[47, 32, 2] Operation: 97-95=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[47, 32, 2], Operations: ['97-95=2'] Exploring Operation: 47-2=45, Resulting Numbers: [32, 45] Generated Node #0,2,0: 13:[32, 45] Operation: 47-2=45 Exploring Operation: 32/2=16, Resulting Numbers: [47, 16] Generated Node #0,2,1: 13:[47, 16] Operation: 32/2=16 Exploring Operation: 47-32=15, Resulting Numbers: [2, 15] Generated Node #0,2,2: 13:[2, 15] Operation: 47-32=15 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 13:[2, 15], Operations: ['97-95=2', '47-32=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[97, 47, 95, 32], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [47, 32, 2] Generated Node #0,2: 13:[47, 32, 2] Operation: 97-95=2 Moving to Node #0,2 Current State: 13:[47, 32, 2], Operations: ['97-95=2'] Exploring Operation: 47-32=15, Resulting Numbers: [2, 15] Generated Node #0,2,2: 13:[2, 15] Operation: 47-32=15 Moving to Node #0,2,2 Current State: 13:[2, 15], Operations: ['97-95=2', '47-32=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 45, 9, 14, 36 ]
76
[ "45+9=54", "36-14=22", "54+22=76" ]
Current State: 76:[45, 9, 14, 36], Operations: [] Exploring Operation: 45+9=54, Resulting Numbers: [14, 36, 54] Generated Node #2: [14, 36, 54] from Operation: 45+9=54 Current State: 76:[14, 36, 54], Operations: ['45+9=54'] Exploring Operation: 36-14=22, Resulting Numbers: [54, 22] Generated Node #3: [54, 22] from Operation: 36-14=22 Current State: 76:[54, 22], Operations: ['45+9=54', '36-14=22'] Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[45, 9, 14, 36], Operations: [] Exploring Operation: 9+14=23, Resulting Numbers: [45, 36, 23] Generated Node #0,0: 76:[45, 36, 23] Operation: 9+14=23 Exploring Operation: 36/9=4, Resulting Numbers: [45, 14, 4] Generated Node #0,1: 76:[45, 14, 4] Operation: 36/9=4 Exploring Operation: 45-9=36, Resulting Numbers: [14, 36, 36] Generated Node #0,2: 76:[14, 36, 36] Operation: 45-9=36 Exploring Operation: 14-9=5, Resulting Numbers: [45, 36, 5] Generated Node #0,3: 76:[45, 36, 5] Operation: 14-9=5 Exploring Operation: 45/9=5, Resulting Numbers: [14, 36, 5] Generated Node #0,4: 76:[14, 36, 5] Operation: 45/9=5 Start Sub Search at level 1: Moving to Node #0,4 Current State: 76:[14, 36, 5], Operations: ['45/9=5'] Exploring Operation: 36+5=41, Resulting Numbers: [14, 41] Generated Node #0,4,0: 76:[14, 41] Operation: 36+5=41 Exploring Operation: 14*5=70, Resulting Numbers: [36, 70] Generated Node #0,4,1: 76:[36, 70] Operation: 14*5=70 Exploring Operation: 14+5=19, Resulting Numbers: [36, 19] Generated Node #0,4,2: 76:[36, 19] Operation: 14+5=19 Exploring Operation: 14-5=9, Resulting Numbers: [36, 9] Generated Node #0,4,3: 76:[36, 9] Operation: 14-5=9 Exploring Operation: 36-14=22, Resulting Numbers: [5, 22] Generated Node #0,4,4: 76:[5, 22] Operation: 36-14=22 Moving to Node #0,4,2 Current State: 76:[36, 19], Operations: ['45/9=5', '14+5=19'] Exploring Operation: 36-19=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 36*19=684, Resulting Numbers: [684] 684,76 unequal: No Solution Exploring Operation: 36+19=55, Resulting Numbers: [55] 55,76 unequal: No Solution Moving to Node #0,4,4 Current State: 76:[5, 22], Operations: ['45/9=5', '36-14=22'] Exploring Operation: 5*22=110, Resulting Numbers: [110] 110,76 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,76 unequal: No Solution Exploring Operation: 5+22=27, Resulting Numbers: [27] 27,76 unequal: No Solution Moving to Node #0,4,3 Current State: 76:[36, 9], Operations: ['45/9=5', '14-5=9'] Exploring Operation: 36*9=324, Resulting Numbers: [324] 324,76 unequal: No Solution Exploring Operation: 36+9=45, Resulting Numbers: [45] 45,76 unequal: No Solution Exploring Operation: 36-9=27, Resulting Numbers: [27] 27,76 unequal: No Solution Exploring Operation: 36/9=4, Resulting Numbers: [4] 4,76 unequal: No Solution Moving to Node #0,4,0 Current State: 76:[14, 41], Operations: ['45/9=5', '36+5=41'] Exploring Operation: 14*41=574, Resulting Numbers: [574] 574,76 unequal: No Solution Exploring Operation: 14+41=55, Resulting Numbers: [55] 55,76 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,76 unequal: No Solution Moving to Node #0,4,1 Current State: 76:[36, 70], Operations: ['45/9=5', '14*5=70'] Exploring Operation: 36+70=106, Resulting Numbers: [106] 106,76 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,76 unequal: No Solution Exploring Operation: 36*70=2520, Resulting Numbers: [2520] 2520,76 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[14, 36, 36], Operations: ['45-9=36'] Exploring Operation: 36/36=1, Resulting Numbers: [14, 1] Generated Node #0,2,0: 76:[14, 1] Operation: 36/36=1 Exploring Operation: 36-14=22, Resulting Numbers: [36, 22] Generated Node #0,2,1: 76:[36, 22] Operation: 36-14=22 Exploring Operation: 36-14=22, Resulting Numbers: [36, 22] Generated Node #0,2,2: 76:[36, 22] Operation: 36-14=22 Exploring Operation: 36+36=72, Resulting Numbers: [14, 72] Generated Node #0,2,3: 76:[14, 72] Operation: 36+36=72 Exploring Operation: 36-36=0, Resulting Numbers: [14, 0] Generated Node #0,2,4: 76:[14, 0] Operation: 36-36=0 Moving to Node #0,2,1 Current State: 76:[36, 22], Operations: ['45-9=36', '36-14=22'] Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,76 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,76 unequal: No Solution Moving to Node #0,2,2 Current State: 76:[36, 22], Operations: ['45-9=36', '36-14=22'] Exploring Operation: 36+22=58, Resulting Numbers: [58] 58,76 unequal: No Solution Exploring Operation: 36*22=792, Resulting Numbers: [792] 792,76 unequal: No Solution Exploring Operation: 36-22=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,2,0 Current State: 76:[14, 1], Operations: ['45-9=36', '36/36=1'] Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,76 unequal: No Solution Exploring Operation: 14+1=15, Resulting Numbers: [15] 15,76 unequal: No Solution Exploring Operation: 14*1=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,2,4 Current State: 76:[14, 0], Operations: ['45-9=36', '36-36=0'] Exploring Operation: 14*0=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 14-0=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 14+0=14, Resulting Numbers: [14] 14,76 unequal: No Solution Moving to Node #0,2,3 Current State: 76:[14, 72], Operations: ['45-9=36', '36+36=72'] Exploring Operation: 14+72=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,76 unequal: No Solution Exploring Operation: 14*72=1008, Resulting Numbers: [1008] 1008,76 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 #0,3 Current State: 76:[45, 36, 5], Operations: ['14-9=5'] Exploring Operation: 45+36=81, Resulting Numbers: [5, 81] Generated Node #0,3,0: 76:[5, 81] Operation: 45+36=81 Exploring Operation: 45-5=40, Resulting Numbers: [36, 40] Generated Node #0,3,1: 76:[36, 40] Operation: 45-5=40 Exploring Operation: 45-36=9, Resulting Numbers: [5, 9] Generated Node #0,3,2: 76:[5, 9] Operation: 45-36=9 Exploring Operation: 36+5=41, Resulting Numbers: [45, 41] Generated Node #0,3,3: 76:[45, 41] Operation: 36+5=41 Exploring Operation: 45/5=9, Resulting Numbers: [36, 9] Generated Node #0,3,4: 76:[36, 9] Operation: 45/5=9 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 76:[36, 40], Operations: ['14-9=5', '45-5=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[45, 9, 14, 36], Operations: [] Exploring Operation: 14-9=5, Resulting Numbers: [45, 36, 5] Generated Node #0,3: 76:[45, 36, 5] Operation: 14-9=5 Moving to Node #0,3 Current State: 76:[45, 36, 5], Operations: ['14-9=5'] Exploring Operation: 45-5=40, Resulting Numbers: [36, 40] Generated Node #0,3,1: 76:[36, 40] Operation: 45-5=40 Moving to Node #0,3,1 Current State: 76:[36, 40], Operations: ['14-9=5', '45-5=40'] Exploring Operation: 36+40=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 31, 16, 1, 89 ]
43
[ "31+16=47", "1+89=90", "90-47=43" ]
Current State: 43:[31, 16, 1, 89], Operations: [] Exploring Operation: 31+16=47, Resulting Numbers: [1, 89, 47] Generated Node #2: [1, 89, 47] from Operation: 31+16=47 Current State: 43:[1, 89, 47], Operations: ['31+16=47'] Exploring Operation: 1+89=90, Resulting Numbers: [47, 90] Generated Node #3: [47, 90] from Operation: 1+89=90 Current State: 43:[47, 90], Operations: ['31+16=47', '1+89=90'] Exploring Operation: 90-47=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[31, 16, 1, 89], Operations: [] Exploring Operation: 89-31=58, Resulting Numbers: [16, 1, 58] Generated Node #0,0: 43:[16, 1, 58] Operation: 89-31=58 Exploring Operation: 31+1=32, Resulting Numbers: [16, 89, 32] Generated Node #0,1: 43:[16, 89, 32] Operation: 31+1=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[16, 1, 58], Operations: ['89-31=58'] Exploring Operation: 58-1=57, Resulting Numbers: [16, 57] Generated Node #0,0,0: 43:[16, 57] Operation: 58-1=57 Exploring Operation: 16+1=17, Resulting Numbers: [58, 17] Generated Node #0,0,1: 43:[58, 17] Operation: 16+1=17 Moving to Node #0,0,0 Current State: 43:[16, 57], Operations: ['89-31=58', '58-1=57'] Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[58, 17], Operations: ['89-31=58', '16+1=17'] Exploring Operation: 58-17=41, Resulting Numbers: [41] 41,43 unequal: No Solution Exploring Operation: 58+17=75, Resulting Numbers: [75] 75,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 43:[16, 89, 32], Operations: ['31+1=32'] Exploring Operation: 89-16=73, Resulting Numbers: [32, 73] Generated Node #0,1,0: 43:[32, 73] Operation: 89-16=73 Exploring Operation: 89-32=57, Resulting Numbers: [16, 57] Generated Node #0,1,1: 43:[16, 57] Operation: 89-32=57 Moving to Node #0,1,0 Current State: 43:[32, 73], Operations: ['31+1=32', '89-16=73'] Exploring Operation: 32+73=105, Resulting Numbers: [105] 105,43 unequal: No Solution Exploring Operation: 73-32=41, Resulting Numbers: [41] 41,43 unequal: No Solution Moving to Node #0,1,1 Current State: 43:[16, 57], Operations: ['31+1=32', '89-32=57'] Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,43 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 14, 21, 48, 6 ]
27
[ "14+21=35", "48/6=8", "35-8=27" ]
Current State: 27:[14, 21, 48, 6], Operations: [] Exploring Operation: 14+21=35, Resulting Numbers: [48, 6, 35] Generated Node #2: [48, 6, 35] from Operation: 14+21=35 Current State: 27:[48, 6, 35], Operations: ['14+21=35'] Exploring Operation: 48/6=8, Resulting Numbers: [35, 8] Generated Node #3: [35, 8] from Operation: 48/6=8 Current State: 27:[35, 8], Operations: ['14+21=35', '48/6=8'] Exploring Operation: 35-8=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[14, 21, 48, 6], Operations: [] Exploring Operation: 48/6=8, Resulting Numbers: [14, 21, 8] Generated Node #0,0: 27:[14, 21, 8] Operation: 48/6=8 Exploring Operation: 48-21=27, Resulting Numbers: [14, 6, 27] Generated Node #0,1: 27:[14, 6, 27] Operation: 48-21=27 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[14, 6, 27], Operations: ['48-21=27'] Exploring Operation: 14+6=20, Resulting Numbers: [27, 20] Generated Node #0,1,0: 27:[27, 20] Operation: 14+6=20 Exploring Operation: 14-6=8, Resulting Numbers: [27, 8] Generated Node #0,1,1: 27:[27, 8] Operation: 14-6=8 Moving to Node #0,1,1 Current State: 27:[27, 8], Operations: ['48-21=27', '14-6=8'] Exploring Operation: 27+8=35, Resulting Numbers: [35] 35,27 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[27, 20], Operations: ['48-21=27', '14+6=20'] Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,27 unequal: No Solution Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[14, 21, 8], Operations: ['48/6=8'] Exploring Operation: 21+8=29, Resulting Numbers: [14, 29] Generated Node #0,0,0: 27:[14, 29] Operation: 21+8=29 Exploring Operation: 21-14=7, Resulting Numbers: [8, 7] Generated Node #0,0,1: 27:[8, 7] Operation: 21-14=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 27:[8, 7], Operations: ['48/6=8', '21-14=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,27 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[14, 29], Operations: ['48/6=8', '21+8=29'] Exploring Operation: 29-14=15, Resulting Numbers: [15] 15,27 unequal: No Solution Exploring Operation: 14+29=43, Resulting Numbers: [43] 43,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 88, 65, 96, 49 ]
70
[ "88-65=23", "96-49=47", "23+47=70" ]
Current State: 70:[88, 65, 96, 49], Operations: [] Exploring Operation: 88-65=23, Resulting Numbers: [96, 49, 23] Generated Node #2: [96, 49, 23] from Operation: 88-65=23 Current State: 70:[96, 49, 23], Operations: ['88-65=23'] Exploring Operation: 96-49=47, Resulting Numbers: [23, 47] Generated Node #3: [23, 47] from Operation: 96-49=47 Current State: 70:[23, 47], Operations: ['88-65=23', '96-49=47'] Exploring Operation: 23+47=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[88, 65, 96, 49], Operations: [] Exploring Operation: 96-88=8, Resulting Numbers: [65, 49, 8] Generated Node #0,0: 70:[65, 49, 8] Operation: 96-88=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[65, 49, 8], Operations: ['96-88=8'] Exploring Operation: 65-49=16, Resulting Numbers: [8, 16] Generated Node #0,0,0: 70:[8, 16] Operation: 65-49=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[8, 16], Operations: ['96-88=8', '65-49=16'] Exploring Operation: 16/8=2, Resulting Numbers: [2] 2,70 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
[ 82, 21, 46, 89 ]
32
[ "82+21=103", "46+89=135", "135-103=32" ]
Current State: 32:[82, 21, 46, 89], Operations: [] Exploring Operation: 82+21=103, Resulting Numbers: [46, 89, 103] Generated Node #2: [46, 89, 103] from Operation: 82+21=103 Current State: 32:[46, 89, 103], Operations: ['82+21=103'] Exploring Operation: 46+89=135, Resulting Numbers: [103, 135] Generated Node #3: [103, 135] from Operation: 46+89=135 Current State: 32:[103, 135], Operations: ['82+21=103', '46+89=135'] Exploring Operation: 135-103=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[82, 21, 46, 89], Operations: [] Exploring Operation: 89-82=7, Resulting Numbers: [21, 46, 7] Generated Node #0,0: 32:[21, 46, 7] Operation: 89-82=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 32:[21, 46, 7], Operations: ['89-82=7'] Exploring Operation: 46-21=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 32:[7, 25] Operation: 46-21=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 32:[7, 25], Operations: ['89-82=7', '46-21=25'] Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[82, 21, 46, 89], Operations: [] Exploring Operation: 89-82=7, Resulting Numbers: [21, 46, 7] Generated Node #0,0: 32:[21, 46, 7] Operation: 89-82=7 Moving to Node #0,0 Current State: 32:[21, 46, 7], Operations: ['89-82=7'] Exploring Operation: 46-21=25, Resulting Numbers: [7, 25] Generated Node #0,0,0: 32:[7, 25] Operation: 46-21=25 Moving to Node #0,0,0 Current State: 32:[7, 25], Operations: ['89-82=7', '46-21=25'] Exploring Operation: 7+25=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 11, 12, 48, 26 ]
22
[ "12-11=1", "48-26=22", "1*22=22" ]
Current State: 22:[11, 12, 48, 26], Operations: [] Exploring Operation: 12-11=1, Resulting Numbers: [48, 26, 1] Generated Node #2: [48, 26, 1] from Operation: 12-11=1 Current State: 22:[48, 26, 1], Operations: ['12-11=1'] Exploring Operation: 48-26=22, Resulting Numbers: [1, 22] Generated Node #3: [1, 22] from Operation: 48-26=22 Current State: 22:[1, 22], Operations: ['12-11=1', '48-26=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[11, 12, 48, 26], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [11, 12, 22] Generated Node #0,0: 22:[11, 12, 22] Operation: 48-26=22 Exploring Operation: 48-12=36, Resulting Numbers: [11, 26, 36] Generated Node #0,1: 22:[11, 26, 36] Operation: 48-12=36 Exploring Operation: 48/12=4, Resulting Numbers: [11, 26, 4] Generated Node #0,2: 22:[11, 26, 4] Operation: 48/12=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[11, 12, 22], Operations: ['48-26=22'] Exploring Operation: 11+12=23, Resulting Numbers: [22, 23] Generated Node #0,0,0: 22:[22, 23] Operation: 11+12=23 Exploring Operation: 22-11=11, Resulting Numbers: [12, 11] Generated Node #0,0,1: 22:[12, 11] Operation: 22-11=11 Exploring Operation: 12-11=1, Resulting Numbers: [22, 1] Generated Node #0,0,2: 22:[22, 1] Operation: 12-11=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 22:[22, 23], Operations: ['48-26=22', '11+12=23'] Exploring Operation: 22+23=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,22 unequal: No Solution Exploring Operation: 22*23=506, Resulting Numbers: [506] 506,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 22:[12, 11], Operations: ['48-26=22', '22-11=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,22 unequal: No Solution Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,22 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 22:[22, 1], Operations: ['48-26=22', '12-11=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[11, 12, 48, 26], Operations: [] Exploring Operation: 48-26=22, Resulting Numbers: [11, 12, 22] Generated Node #0,0: 22:[11, 12, 22] Operation: 48-26=22 Moving to Node #0,0 Current State: 22:[11, 12, 22], Operations: ['48-26=22'] Exploring Operation: 12-11=1, Resulting Numbers: [22, 1] Generated Node #0,0,2: 22:[22, 1] Operation: 12-11=1 Moving to Node #0,0,2 Current State: 22:[22, 1], Operations: ['48-26=22', '12-11=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 91, 14, 81, 59 ]
83
[ "91+14=105", "81-59=22", "105-22=83" ]
Current State: 83:[91, 14, 81, 59], Operations: [] Exploring Operation: 91+14=105, Resulting Numbers: [81, 59, 105] Generated Node #2: [81, 59, 105] from Operation: 91+14=105 Current State: 83:[81, 59, 105], Operations: ['91+14=105'] Exploring Operation: 81-59=22, Resulting Numbers: [105, 22] Generated Node #3: [105, 22] from Operation: 81-59=22 Current State: 83:[105, 22], Operations: ['91+14=105', '81-59=22'] Exploring Operation: 105-22=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[91, 14, 81, 59], Operations: [] Exploring Operation: 14+59=73, Resulting Numbers: [91, 81, 73] Generated Node #0,0: 83:[91, 81, 73] Operation: 14+59=73 Exploring Operation: 91-14=77, Resulting Numbers: [81, 59, 77] Generated Node #0,1: 83:[81, 59, 77] Operation: 91-14=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[91, 81, 73], Operations: ['14+59=73'] Exploring Operation: 91-73=18, Resulting Numbers: [81, 18] Generated Node #0,0,0: 83:[81, 18] Operation: 91-73=18 Exploring Operation: 81+73=154, Resulting Numbers: [91, 154] Generated Node #0,0,1: 83:[91, 154] Operation: 81+73=154 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[81, 18], Operations: ['14+59=73', '91-73=18'] Exploring Operation: 81-18=63, Resulting Numbers: [63] 63,83 unequal: No Solution Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,83 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:[91, 154], Operations: ['14+59=73', '81+73=154'] Exploring Operation: 154-91=63, Resulting Numbers: [63] 63,83 unequal: No Solution Exploring Operation: 91+154=245, Resulting Numbers: [245] 245,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[81, 59, 77], Operations: ['91-14=77'] Exploring Operation: 59+77=136, Resulting Numbers: [81, 136] Generated Node #0,1,0: 83:[81, 136] Operation: 59+77=136 Exploring Operation: 81+59=140, Resulting Numbers: [77, 140] Generated Node #0,1,1: 83:[77, 140] Operation: 81+59=140 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[81, 136], Operations: ['91-14=77', '59+77=136'] Exploring Operation: 136-81=55, Resulting Numbers: [55] 55,83 unequal: No Solution Exploring Operation: 81+136=217, Resulting Numbers: [217] 217,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[77, 140], Operations: ['91-14=77', '81+59=140'] Exploring Operation: 77+140=217, Resulting Numbers: [217] 217,83 unequal: No Solution Exploring Operation: 140-77=63, Resulting Numbers: [63] 63,83 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
[ 88, 76, 73, 11 ]
96
[ "88-76=12", "73+11=84", "12+84=96" ]
Current State: 96:[88, 76, 73, 11], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [73, 11, 12] Generated Node #2: [73, 11, 12] from Operation: 88-76=12 Current State: 96:[73, 11, 12], Operations: ['88-76=12'] Exploring Operation: 73+11=84, Resulting Numbers: [12, 84] Generated Node #3: [12, 84] from Operation: 73+11=84 Current State: 96:[12, 84], Operations: ['88-76=12', '73+11=84'] Exploring Operation: 12+84=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[88, 76, 73, 11], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [88, 11, 3] Generated Node #0,0: 96:[88, 11, 3] Operation: 76-73=3 Moving to Node #0,0 Current State: 96:[88, 11, 3], Operations: ['76-73=3'] Exploring Operation: 88/11=8, Resulting Numbers: [3, 8] Generated Node #0,0,0: 96:[3, 8] Operation: 88/11=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[3, 8], Operations: ['76-73=3', '88/11=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,96 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
[ 91, 85, 80, 17 ]
69
[ "91-85=6", "80-17=63", "6+63=69" ]
Current State: 69:[91, 85, 80, 17], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [80, 17, 6] Generated Node #2: [80, 17, 6] from Operation: 91-85=6 Current State: 69:[80, 17, 6], Operations: ['91-85=6'] Exploring Operation: 80-17=63, Resulting Numbers: [6, 63] Generated Node #3: [6, 63] from Operation: 80-17=63 Current State: 69:[6, 63], Operations: ['91-85=6', '80-17=63'] Exploring Operation: 6+63=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[91, 85, 80, 17], Operations: [] Exploring Operation: 85-17=68, Resulting Numbers: [91, 80, 68] Generated Node #0,0: 69:[91, 80, 68] Operation: 85-17=68 Exploring Operation: 91-17=74, Resulting Numbers: [85, 80, 74] Generated Node #0,1: 69:[85, 80, 74] Operation: 91-17=74 Exploring Operation: 91-85=6, Resulting Numbers: [80, 17, 6] Generated Node #0,2: 69:[80, 17, 6] Operation: 91-85=6 Exploring Operation: 91-80=11, Resulting Numbers: [85, 17, 11] Generated Node #0,3: 69:[85, 17, 11] Operation: 91-80=11 Exploring Operation: 85-80=5, Resulting Numbers: [91, 17, 5] Generated Node #0,4: 69:[91, 17, 5] Operation: 85-80=5 Moving to Node #0,2 Current State: 69:[80, 17, 6], Operations: ['91-85=6'] Exploring Operation: 17-6=11, Resulting Numbers: [80, 11] Generated Node #0,2,0: 69:[80, 11] Operation: 17-6=11 Exploring Operation: 80-17=63, Resulting Numbers: [6, 63] Generated Node #0,2,1: 69:[6, 63] Operation: 80-17=63 Exploring Operation: 80-6=74, Resulting Numbers: [17, 74] Generated Node #0,2,2: 69:[17, 74] Operation: 80-6=74 Exploring Operation: 80+6=86, Resulting Numbers: [17, 86] Generated Node #0,2,3: 69:[17, 86] Operation: 80+6=86 Exploring Operation: 17+6=23, Resulting Numbers: [80, 23] Generated Node #0,2,4: 69:[80, 23] Operation: 17+6=23 Moving to Node #0,4 Current State: 69:[91, 17, 5], Operations: ['85-80=5'] Exploring Operation: 17-5=12, Resulting Numbers: [91, 12] Generated Node #0,4,0: 69:[91, 12] Operation: 17-5=12 Exploring Operation: 91-5=86, Resulting Numbers: [17, 86] Generated Node #0,4,1: 69:[17, 86] Operation: 91-5=86 Exploring Operation: 91-17=74, Resulting Numbers: [5, 74] Generated Node #0,4,2: 69:[5, 74] Operation: 91-17=74 Exploring Operation: 17+5=22, Resulting Numbers: [91, 22] Generated Node #0,4,3: 69:[91, 22] Operation: 17+5=22 Exploring Operation: 91+5=96, Resulting Numbers: [17, 96] Generated Node #0,4,4: 69:[17, 96] Operation: 91+5=96 Moving to Node #0,3 Current State: 69:[85, 17, 11], Operations: ['91-80=11'] Exploring Operation: 85-17=68, Resulting Numbers: [11, 68] Generated Node #0,3,0: 69:[11, 68] Operation: 85-17=68 Exploring Operation: 85-11=74, Resulting Numbers: [17, 74] Generated Node #0,3,1: 69:[17, 74] Operation: 85-11=74 Exploring Operation: 17+11=28, Resulting Numbers: [85, 28] Generated Node #0,3,2: 69:[85, 28] Operation: 17+11=28 Exploring Operation: 85/17=5, Resulting Numbers: [11, 5] Generated Node #0,3,3: 69:[11, 5] Operation: 85/17=5 Exploring Operation: 17-11=6, Resulting Numbers: [85, 6] Generated Node #0,3,4: 69:[85, 6] Operation: 17-11=6 Moving to Node #0,1 Current State: 69:[85, 80, 74], Operations: ['91-17=74'] Exploring Operation: 80-74=6, Resulting Numbers: [85, 6] Generated Node #0,1,0: 69:[85, 6] Operation: 80-74=6 Exploring Operation: 85+74=159, Resulting Numbers: [80, 159] Generated Node #0,1,1: 69:[80, 159] Operation: 85+74=159 Exploring Operation: 85+80=165, Resulting Numbers: [74, 165] Generated Node #0,1,2: 69:[74, 165] Operation: 85+80=165 Exploring Operation: 85-74=11, Resulting Numbers: [80, 11] Generated Node #0,1,3: 69:[80, 11] Operation: 85-74=11 Exploring Operation: 85-80=5, Resulting Numbers: [74, 5] Generated Node #0,1,4: 69:[74, 5] Operation: 85-80=5 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 69:[74, 5], Operations: ['91-17=74', '85-80=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[91, 85, 80, 17], Operations: [] Exploring Operation: 91-17=74, Resulting Numbers: [85, 80, 74] Generated Node #0,1: 69:[85, 80, 74] Operation: 91-17=74 Moving to Node #0,1 Current State: 69:[85, 80, 74], Operations: ['91-17=74'] Exploring Operation: 85-80=5, Resulting Numbers: [74, 5] Generated Node #0,1,4: 69:[74, 5] Operation: 85-80=5 Moving to Node #0,1,4 Current State: 69:[74, 5], Operations: ['91-17=74', '85-80=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_5
sum_heuristic
[ 33, 28, 82, 93 ]
25
[ "93-82=11", "33/11=3", "28-3=25" ]
Current State: 25:[33, 28, 82, 93], Operations: [] Exploring Operation: 93-82=11, Resulting Numbers: [33, 28, 11] Generated Node #2: [33, 28, 11] from Operation: 93-82=11 Current State: 25:[33, 28, 11], Operations: ['93-82=11'] Exploring Operation: 33/11=3, Resulting Numbers: [28, 3] Generated Node #3: [28, 3] from Operation: 33/11=3 Current State: 25:[28, 3], Operations: ['93-82=11', '33/11=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[33, 28, 82, 93], Operations: [] Exploring Operation: 93-82=11, Resulting Numbers: [33, 28, 11] Generated Node #0,0: 25:[33, 28, 11] Operation: 93-82=11 Moving to Node #0,0 Current State: 25:[33, 28, 11], Operations: ['93-82=11'] Exploring Operation: 33/11=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 25:[28, 3] Operation: 33/11=3 Moving to Node #0,0,0 Current State: 25:[28, 3], Operations: ['93-82=11', '33/11=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[33, 28, 82, 93], Operations: [] Exploring Operation: 93-82=11, Resulting Numbers: [33, 28, 11] Generated Node #0,0: 25:[33, 28, 11] Operation: 93-82=11 Moving to Node #0,0 Current State: 25:[33, 28, 11], Operations: ['93-82=11'] Exploring Operation: 33/11=3, Resulting Numbers: [28, 3] Generated Node #0,0,0: 25:[28, 3] Operation: 33/11=3 Moving to Node #0,0,0 Current State: 25:[28, 3], Operations: ['93-82=11', '33/11=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 65, 95, 64, 22 ]
55
[ "65+95=160", "22*160=3520", "3520/64=55" ]
Current State: 55:[65, 95, 64, 22], Operations: [] Exploring Operation: 65+95=160, Resulting Numbers: [64, 22, 160] Generated Node #2: [64, 22, 160] from Operation: 65+95=160 Current State: 55:[64, 22, 160], Operations: ['65+95=160'] Exploring Operation: 22*160=3520, Resulting Numbers: [64, 3520] Generated Node #3: [64, 3520] from Operation: 22*160=3520 Current State: 55:[64, 3520], Operations: ['65+95=160', '22*160=3520'] Exploring Operation: 3520/64=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[65, 95, 64, 22], Operations: [] Exploring Operation: 95-22=73, Resulting Numbers: [65, 64, 73] Generated Node #0,0: 55:[65, 64, 73] Operation: 95-22=73 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[65, 64, 73], Operations: ['95-22=73'] Exploring Operation: 73-65=8, Resulting Numbers: [64, 8] Generated Node #0,0,0: 55:[64, 8] Operation: 73-65=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[64, 8], Operations: ['95-22=73', '73-65=8'] Exploring Operation: 64-8=56, Resulting Numbers: [56] 56,55 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
[ 8, 95, 8, 90 ]
95
[ "8-8=0", "90*0=0", "95+0=95" ]
Current State: 95:[8, 95, 8, 90], Operations: [] Exploring Operation: 8-8=0, Resulting Numbers: [95, 90, 0] Generated Node #2: [95, 90, 0] from Operation: 8-8=0 Current State: 95:[95, 90, 0], Operations: ['8-8=0'] Exploring Operation: 90*0=0, Resulting Numbers: [95, 0] Generated Node #3: [95, 0] from Operation: 90*0=0 Current State: 95:[95, 0], Operations: ['8-8=0', '90*0=0'] Exploring Operation: 95+0=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[8, 95, 8, 90], Operations: [] Exploring Operation: 8+90=98, Resulting Numbers: [8, 95, 98] Generated Node #0,0: 95:[8, 95, 98] Operation: 8+90=98 Exploring Operation: 8+90=98, Resulting Numbers: [95, 8, 98] Generated Node #0,1: 95:[95, 8, 98] Operation: 8+90=98 Exploring Operation: 95-90=5, Resulting Numbers: [8, 8, 5] Generated Node #0,2: 95:[8, 8, 5] Operation: 95-90=5 Moving to Node #0,0 Current State: 95:[8, 95, 98], Operations: ['8+90=98'] Exploring Operation: 98-8=90, Resulting Numbers: [95, 90] Generated Node #0,0,0: 95:[95, 90] Operation: 98-8=90 Exploring Operation: 8+95=103, Resulting Numbers: [98, 103] Generated Node #0,0,1: 95:[98, 103] Operation: 8+95=103 Exploring Operation: 98-95=3, Resulting Numbers: [8, 3] Generated Node #0,0,2: 95:[8, 3] Operation: 98-95=3 Moving to Node #0,1 Current State: 95:[95, 8, 98], Operations: ['8+90=98'] Exploring Operation: 98-8=90, Resulting Numbers: [95, 90] Generated Node #0,1,0: 95:[95, 90] Operation: 98-8=90 Exploring Operation: 98-95=3, Resulting Numbers: [8, 3] Generated Node #0,1,1: 95:[8, 3] Operation: 98-95=3 Exploring Operation: 95+8=103, Resulting Numbers: [98, 103] Generated Node #0,1,2: 95:[98, 103] Operation: 95+8=103 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[95, 90], Operations: ['8+90=98', '98-8=90'] Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,95 unequal: No Solution Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[8, 3], Operations: ['8+90=98', '98-95=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 95:[98, 103], Operations: ['8+90=98', '95+8=103'] Exploring Operation: 103-98=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 98*103=10094, Resulting Numbers: [10094] 10094,95 unequal: No Solution Exploring Operation: 98+103=201, Resulting Numbers: [201] 201,95 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: 95:[8, 8, 5], Operations: ['95-90=5'] Exploring Operation: 8+8=16, Resulting Numbers: [5, 16] Generated Node #0,2,0: 95:[5, 16] Operation: 8+8=16 Exploring Operation: 8-8=0, Resulting Numbers: [5, 0] Generated Node #0,2,1: 95:[5, 0] Operation: 8-8=0 Exploring Operation: 8/8=1, Resulting Numbers: [5, 1] Generated Node #0,2,2: 95:[5, 1] Operation: 8/8=1 Moving to Node #0,2,0 Current State: 95:[5, 16], Operations: ['95-90=5', '8+8=16'] Exploring Operation: 5+16=21, Resulting Numbers: [21] 21,95 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,95 unequal: No Solution Exploring Operation: 5*16=80, Resulting Numbers: [80] 80,95 unequal: No Solution Moving to Node #0,2,2 Current State: 95:[5, 1], Operations: ['95-90=5', '8/8=1'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,95 unequal: No Solution Moving to Node #0,2,1 Current State: 95:[5, 0], Operations: ['95-90=5', '8-8=0'] Exploring Operation: 5*0=0, Resulting Numbers: [0] 0,95 unequal: No Solution Exploring Operation: 5+0=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 5-0=5, Resulting Numbers: [5] 5,95 unequal: No Solution Moving to Node #0,0,0 Current State: 95:[95, 90], Operations: ['8+90=98', '98-8=90'] Exploring Operation: 95*90=8550, Resulting Numbers: [8550] 8550,95 unequal: No Solution Exploring Operation: 95+90=185, Resulting Numbers: [185] 185,95 unequal: No Solution Exploring Operation: 95-90=5, Resulting Numbers: [5] 5,95 unequal: No Solution Moving to Node #0,0,2 Current State: 95:[8, 3], Operations: ['8+90=98', '98-95=3'] Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,95 unequal: No Solution Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,95 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[98, 103], Operations: ['8+90=98', '8+95=103'] Exploring Operation: 98*103=10094, Resulting Numbers: [10094] 10094,95 unequal: No Solution Exploring Operation: 98+103=201, Resulting Numbers: [201] 201,95 unequal: No Solution Exploring Operation: 103-98=5, Resulting Numbers: [5] 5,95 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 39, 92, 46, 87 ]
24
[ "87-39=48", "92/46=2", "48/2=24" ]
Current State: 24:[39, 92, 46, 87], Operations: [] Exploring Operation: 87-39=48, Resulting Numbers: [92, 46, 48] Generated Node #2: [92, 46, 48] from Operation: 87-39=48 Current State: 24:[92, 46, 48], Operations: ['87-39=48'] Exploring Operation: 92/46=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 92/46=2 Current State: 24:[48, 2], Operations: ['87-39=48', '92/46=2'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[39, 92, 46, 87], Operations: [] Exploring Operation: 92-46=46, Resulting Numbers: [39, 87, 46] Generated Node #0,0: 24:[39, 87, 46] Operation: 92-46=46 Exploring Operation: 92/46=2, Resulting Numbers: [39, 87, 2] Generated Node #0,1: 24:[39, 87, 2] Operation: 92/46=2 Exploring Operation: 92-87=5, Resulting Numbers: [39, 46, 5] Generated Node #0,2: 24:[39, 46, 5] Operation: 92-87=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[39, 46, 5], Operations: ['92-87=5'] Exploring Operation: 46-5=41, Resulting Numbers: [39, 41] Generated Node #0,2,0: 24:[39, 41] Operation: 46-5=41 Exploring Operation: 46-39=7, Resulting Numbers: [5, 7] Generated Node #0,2,1: 24:[5, 7] Operation: 46-39=7 Exploring Operation: 39-5=34, Resulting Numbers: [46, 34] Generated Node #0,2,2: 24:[46, 34] Operation: 39-5=34 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 24:[5, 7], Operations: ['92-87=5', '46-39=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 5+7=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,24 unequal: No Solution No 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: 24:[39, 41], Operations: ['92-87=5', '46-5=41'] Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 39+41=80, Resulting Numbers: [80] 80,24 unequal: No Solution Exploring Operation: 39*41=1599, Resulting Numbers: [1599] 1599,24 unequal: No Solution No 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: 24:[46, 34], Operations: ['92-87=5', '39-5=34'] Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 46*34=1564, Resulting Numbers: [1564] 1564,24 unequal: No Solution Exploring Operation: 46+34=80, Resulting Numbers: [80] 80,24 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: 24:[39, 87, 2], Operations: ['92/46=2'] Exploring Operation: 39-2=37, Resulting Numbers: [87, 37] Generated Node #0,1,0: 24:[87, 37] Operation: 39-2=37 Exploring Operation: 87-2=85, Resulting Numbers: [39, 85] Generated Node #0,1,1: 24:[39, 85] Operation: 87-2=85 Exploring Operation: 87-39=48, Resulting Numbers: [2, 48] Generated Node #0,1,2: 24:[2, 48] Operation: 87-39=48 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 24:[2, 48], Operations: ['92/46=2', '87-39=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,24 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[39, 92, 46, 87], Operations: [] Exploring Operation: 92/46=2, Resulting Numbers: [39, 87, 2] Generated Node #0,1: 24:[39, 87, 2] Operation: 92/46=2 Moving to Node #0,1 Current State: 24:[39, 87, 2], Operations: ['92/46=2'] Exploring Operation: 87-39=48, Resulting Numbers: [2, 48] Generated Node #0,1,2: 24:[2, 48] Operation: 87-39=48 Moving to Node #0,1,2 Current State: 24:[2, 48], Operations: ['92/46=2', '87-39=48'] Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 96, 23, 32, 2 ]
85
[ "96+23=119", "32+2=34", "119-34=85" ]
Current State: 85:[96, 23, 32, 2], Operations: [] Exploring Operation: 96+23=119, Resulting Numbers: [32, 2, 119] Generated Node #2: [32, 2, 119] from Operation: 96+23=119 Current State: 85:[32, 2, 119], Operations: ['96+23=119'] Exploring Operation: 32+2=34, Resulting Numbers: [119, 34] Generated Node #3: [119, 34] from Operation: 32+2=34 Current State: 85:[119, 34], Operations: ['96+23=119', '32+2=34'] Exploring Operation: 119-34=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[96, 23, 32, 2], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [96, 23, 16] Generated Node #0,0: 85:[96, 23, 16] Operation: 32/2=16 Exploring Operation: 96/32=3, Resulting Numbers: [23, 2, 3] Generated Node #0,1: 85:[23, 2, 3] Operation: 96/32=3 Exploring Operation: 32-23=9, Resulting Numbers: [96, 2, 9] Generated Node #0,2: 85:[96, 2, 9] Operation: 32-23=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[23, 2, 3], Operations: ['96/32=3'] Exploring Operation: 23-3=20, Resulting Numbers: [2, 20] Generated Node #0,1,0: 85:[2, 20] Operation: 23-3=20 Exploring Operation: 23-2=21, Resulting Numbers: [3, 21] Generated Node #0,1,1: 85:[3, 21] Operation: 23-2=21 Exploring Operation: 2+3=5, Resulting Numbers: [23, 5] Generated Node #0,1,2: 85:[23, 5] Operation: 2+3=5 Moving to Node #0,1,0 Current State: 85:[2, 20], Operations: ['96/32=3', '23-3=20'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[3, 21], Operations: ['96/32=3', '23-2=21'] Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,85 unequal: No Solution Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,85 unequal: No Solution Moving to Node #0,1,2 Current State: 85:[23, 5], Operations: ['96/32=3', '2+3=5'] Exploring Operation: 23+5=28, Resulting Numbers: [28] 28,85 unequal: No Solution Exploring Operation: 23-5=18, Resulting Numbers: [18] 18,85 unequal: No Solution Exploring Operation: 23*5=115, Resulting Numbers: [115] 115,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[96, 23, 16], Operations: ['32/2=16'] Exploring Operation: 96-16=80, Resulting Numbers: [23, 80] Generated Node #0,0,0: 85:[23, 80] Operation: 96-16=80 Exploring Operation: 96/16=6, Resulting Numbers: [23, 6] Generated Node #0,0,1: 85:[23, 6] Operation: 96/16=6 Exploring Operation: 96-23=73, Resulting Numbers: [16, 73] Generated Node #0,0,2: 85:[16, 73] Operation: 96-23=73 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 85:[23, 6], Operations: ['32/2=16', '96/16=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,85 unequal: No Solution Exploring Operation: 23*6=138, Resulting Numbers: [138] 138,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[23, 80], Operations: ['32/2=16', '96-16=80'] Exploring Operation: 23+80=103, Resulting Numbers: [103] 103,85 unequal: No Solution Exploring Operation: 80-23=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 23*80=1840, Resulting Numbers: [1840] 1840,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 85:[16, 73], Operations: ['32/2=16', '96-23=73'] Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,85 unequal: No Solution Exploring Operation: 16*73=1168, Resulting Numbers: [1168] 1168,85 unequal: No Solution Exploring Operation: 16+73=89, Resulting Numbers: [89] 89,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 85:[96, 2, 9], Operations: ['32-23=9'] Exploring Operation: 96-2=94, Resulting Numbers: [9, 94] Generated Node #0,2,0: 85:[9, 94] Operation: 96-2=94 Exploring Operation: 96-9=87, Resulting Numbers: [2, 87] Generated Node #0,2,1: 85:[2, 87] Operation: 96-9=87 Exploring Operation: 2*9=18, Resulting Numbers: [96, 18] Generated Node #0,2,2: 85:[96, 18] Operation: 2*9=18 Moving to Node #0,2,1 Current State: 85:[2, 87], Operations: ['32-23=9', '96-9=87'] Exploring Operation: 2+87=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 2*87=174, Resulting Numbers: [174] 174,85 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[96, 23, 32, 2], Operations: [] Exploring Operation: 32-23=9, Resulting Numbers: [96, 2, 9] Generated Node #0,2: 85:[96, 2, 9] Operation: 32-23=9 Moving to Node #0,2 Current State: 85:[96, 2, 9], Operations: ['32-23=9'] Exploring Operation: 96-9=87, Resulting Numbers: [2, 87] Generated Node #0,2,1: 85:[2, 87] Operation: 96-9=87 Moving to Node #0,2,1 Current State: 85:[2, 87], Operations: ['32-23=9', '96-9=87'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.967882
hs_3
sum_heuristic
[ 31, 65, 69, 56 ]
100
[ "56-31=25", "69-65=4", "25*4=100" ]
Current State: 100:[31, 65, 69, 56], Operations: [] Exploring Operation: 56-31=25, Resulting Numbers: [65, 69, 25] Generated Node #2: [65, 69, 25] from Operation: 56-31=25 Current State: 100:[65, 69, 25], Operations: ['56-31=25'] Exploring Operation: 69-65=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 69-65=4 Current State: 100:[25, 4], Operations: ['56-31=25', '69-65=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[31, 65, 69, 56], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [31, 56, 4] Generated Node #0,0: 100:[31, 56, 4] Operation: 69-65=4 Exploring Operation: 69-56=13, Resulting Numbers: [31, 65, 13] Generated Node #0,1: 100:[31, 65, 13] Operation: 69-56=13 Exploring Operation: 31+69=100, Resulting Numbers: [65, 56, 100] Generated Node #0,2: 100:[65, 56, 100] Operation: 31+69=100 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[31, 56, 4], Operations: ['69-65=4'] Exploring Operation: 56-4=52, Resulting Numbers: [31, 52] Generated Node #0,0,0: 100:[31, 52] Operation: 56-4=52 Exploring Operation: 56-31=25, Resulting Numbers: [4, 25] Generated Node #0,0,1: 100:[4, 25] Operation: 56-31=25 Exploring Operation: 31-4=27, Resulting Numbers: [56, 27] Generated Node #0,0,2: 100:[56, 27] Operation: 31-4=27 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 100:[4, 25], Operations: ['69-65=4', '56-31=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[31, 65, 69, 56], Operations: [] Exploring Operation: 69-65=4, Resulting Numbers: [31, 56, 4] Generated Node #0,0: 100:[31, 56, 4] Operation: 69-65=4 Moving to Node #0,0 Current State: 100:[31, 56, 4], Operations: ['69-65=4'] Exploring Operation: 56-31=25, Resulting Numbers: [4, 25] Generated Node #0,0,1: 100:[4, 25] Operation: 56-31=25 Moving to Node #0,0,1 Current State: 100:[4, 25], Operations: ['69-65=4', '56-31=25'] Exploring Operation: 4*25=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 25, 21, 44, 37 ]
11
[ "25-21=4", "44-37=7", "4+7=11" ]
Current State: 11:[25, 21, 44, 37], Operations: [] Exploring Operation: 25-21=4, Resulting Numbers: [44, 37, 4] Generated Node #2: [44, 37, 4] from Operation: 25-21=4 Current State: 11:[44, 37, 4], Operations: ['25-21=4'] Exploring Operation: 44-37=7, Resulting Numbers: [4, 7] Generated Node #3: [4, 7] from Operation: 44-37=7 Current State: 11:[4, 7], Operations: ['25-21=4', '44-37=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[25, 21, 44, 37], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [25, 21, 7] Generated Node #0,0: 11:[25, 21, 7] Operation: 44-37=7 Moving to Node #0,0 Current State: 11:[25, 21, 7], Operations: ['44-37=7'] Exploring Operation: 25-21=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 11:[7, 4] Operation: 25-21=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 11:[7, 4], Operations: ['44-37=7', '25-21=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[25, 21, 44, 37], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [25, 21, 7] Generated Node #0,0: 11:[25, 21, 7] Operation: 44-37=7 Moving to Node #0,0 Current State: 11:[25, 21, 7], Operations: ['44-37=7'] Exploring Operation: 25-21=4, Resulting Numbers: [7, 4] Generated Node #0,0,0: 11:[7, 4] Operation: 25-21=4 Moving to Node #0,0,0 Current State: 11:[7, 4], Operations: ['44-37=7', '25-21=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 59, 2, 7, 65 ]
57
[ "65-7=58", "2*58=116", "116-59=57" ]
Current State: 57:[59, 2, 7, 65], Operations: [] Exploring Operation: 65-7=58, Resulting Numbers: [59, 2, 58] Generated Node #2: [59, 2, 58] from Operation: 65-7=58 Current State: 57:[59, 2, 58], Operations: ['65-7=58'] Exploring Operation: 2*58=116, Resulting Numbers: [59, 116] Generated Node #3: [59, 116] from Operation: 2*58=116 Current State: 57:[59, 116], Operations: ['65-7=58', '2*58=116'] Exploring Operation: 116-59=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[59, 2, 7, 65], Operations: [] Exploring Operation: 7-2=5, Resulting Numbers: [59, 65, 5] Generated Node #0,0: 57:[59, 65, 5] Operation: 7-2=5 Exploring Operation: 59-2=57, Resulting Numbers: [7, 65, 57] Generated Node #0,1: 57:[7, 65, 57] Operation: 59-2=57 Exploring Operation: 65-7=58, Resulting Numbers: [59, 2, 58] Generated Node #0,2: 57:[59, 2, 58] Operation: 65-7=58 Exploring Operation: 65-59=6, Resulting Numbers: [2, 7, 6] Generated Node #0,3: 57:[2, 7, 6] Operation: 65-59=6 Start Sub Search at level 1: Moving to Node #0,2 Current State: 57:[59, 2, 58], Operations: ['65-7=58'] Exploring Operation: 59-2=57, Resulting Numbers: [58, 57] Generated Node #0,2,0: 57:[58, 57] Operation: 59-2=57 Exploring Operation: 59-58=1, Resulting Numbers: [2, 1] Generated Node #0,2,1: 57:[2, 1] Operation: 59-58=1 Exploring Operation: 59+2=61, Resulting Numbers: [58, 61] Generated Node #0,2,2: 57:[58, 61] Operation: 59+2=61 Exploring Operation: 58-2=56, Resulting Numbers: [59, 56] Generated Node #0,2,3: 57:[59, 56] Operation: 58-2=56 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 57:[58, 57], Operations: ['65-7=58', '59-2=57'] Exploring Operation: 58*57=3306, Resulting Numbers: [3306] 3306,57 unequal: No Solution Exploring Operation: 58+57=115, Resulting Numbers: [115] 115,57 unequal: No Solution Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 57:[2, 1], Operations: ['65-7=58', '59-58=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 57:[59, 56], Operations: ['65-7=58', '58-2=56'] Exploring Operation: 59*56=3304, Resulting Numbers: [3304] 3304,57 unequal: No Solution Exploring Operation: 59-56=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 59+56=115, Resulting Numbers: [115] 115,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 57:[58, 61], Operations: ['65-7=58', '59+2=61'] Exploring Operation: 58+61=119, Resulting Numbers: [119] 119,57 unequal: No Solution Exploring Operation: 61-58=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 58*61=3538, Resulting Numbers: [3538] 3538,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 57:[2, 7, 6], Operations: ['65-59=6'] Exploring Operation: 7-2=5, Resulting Numbers: [6, 5] Generated Node #0,3,0: 57:[6, 5] Operation: 7-2=5 Exploring Operation: 6/2=3, Resulting Numbers: [7, 3] Generated Node #0,3,1: 57:[7, 3] Operation: 6/2=3 Exploring Operation: 6-2=4, Resulting Numbers: [7, 4] Generated Node #0,3,2: 57:[7, 4] Operation: 6-2=4 Exploring Operation: 7-6=1, Resulting Numbers: [2, 1] Generated Node #0,3,3: 57:[2, 1] Operation: 7-6=1 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 57:[2, 1], Operations: ['65-59=6', '7-6=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,57 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 57:[7, 3], Operations: ['65-59=6', '6/2=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,57 unequal: No Solution Exploring Operation: 7-3=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 57:[6, 5], Operations: ['65-59=6', '7-2=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,57 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 57:[7, 4], Operations: ['65-59=6', '6-2=4'] Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,57 unequal: No Solution Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[59, 65, 5], Operations: ['7-2=5'] Exploring Operation: 59-5=54, Resulting Numbers: [65, 54] Generated Node #0,0,0: 57:[65, 54] Operation: 59-5=54 Exploring Operation: 65/5=13, Resulting Numbers: [59, 13] Generated Node #0,0,1: 57:[59, 13] Operation: 65/5=13 Exploring Operation: 65-5=60, Resulting Numbers: [59, 60] Generated Node #0,0,2: 57:[59, 60] Operation: 65-5=60 Exploring Operation: 65-59=6, Resulting Numbers: [5, 6] Generated Node #0,0,3: 57:[5, 6] Operation: 65-59=6 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 57:[59, 60], Operations: ['7-2=5', '65-5=60'] Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,57 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 57:[5, 6], Operations: ['7-2=5', '65-59=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 57:[59, 13], Operations: ['7-2=5', '65/5=13'] Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,57 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,57 unequal: No Solution Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[65, 54], Operations: ['7-2=5', '59-5=54'] Exploring Operation: 65-54=11, Resulting Numbers: [11] 11,57 unequal: No Solution Exploring Operation: 65*54=3510, Resulting Numbers: [3510] 3510,57 unequal: No Solution Exploring Operation: 65+54=119, Resulting Numbers: [119] 119,57 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[7, 65, 57], Operations: ['59-2=57'] Exploring Operation: 7+65=72, Resulting Numbers: [57, 72] Generated Node #0,1,0: 57:[57, 72] Operation: 7+65=72 Exploring Operation: 65-7=58, Resulting Numbers: [57, 58] Generated Node #0,1,1: 57:[57, 58] Operation: 65-7=58 Exploring Operation: 7+57=64, Resulting Numbers: [65, 64] Generated Node #0,1,2: 57:[65, 64] Operation: 7+57=64 Exploring Operation: 65-57=8, Resulting Numbers: [7, 8] Generated Node #0,1,3: 57:[7, 8] Operation: 65-57=8 Moving to Node #0,1,1 Current State: 57:[57, 58], Operations: ['59-2=57', '65-7=58'] Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 57*58=3306, Resulting Numbers: [3306] 3306,57 unequal: No Solution Exploring Operation: 57+58=115, Resulting Numbers: [115] 115,57 unequal: No Solution Moving to Node #0,1,3 Current State: 57:[7, 8], Operations: ['59-2=57', '65-57=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 7*8=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 8-7=1, Resulting Numbers: [1] 1,57 unequal: No Solution Moving to Node #0,1,2 Current State: 57:[65, 64], Operations: ['59-2=57', '7+57=64'] Exploring Operation: 65-64=1, Resulting Numbers: [1] 1,57 unequal: No Solution Exploring Operation: 65+64=129, Resulting Numbers: [129] 129,57 unequal: No Solution Exploring Operation: 65*64=4160, Resulting Numbers: [4160] 4160,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[57, 72], Operations: ['59-2=57', '7+65=72'] Exploring Operation: 72-57=15, Resulting Numbers: [15] 15,57 unequal: No Solution Exploring Operation: 57+72=129, Resulting Numbers: [129] 129,57 unequal: No Solution Exploring Operation: 57*72=4104, Resulting Numbers: [4104] 4104,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 24, 69, 95, 38 ]
88
[ "69-24=45", "95+38=133", "133-45=88" ]
Current State: 88:[24, 69, 95, 38], Operations: [] Exploring Operation: 69-24=45, Resulting Numbers: [95, 38, 45] Generated Node #2: [95, 38, 45] from Operation: 69-24=45 Current State: 88:[95, 38, 45], Operations: ['69-24=45'] Exploring Operation: 95+38=133, Resulting Numbers: [45, 133] Generated Node #3: [45, 133] from Operation: 95+38=133 Current State: 88:[45, 133], Operations: ['69-24=45', '95+38=133'] Exploring Operation: 133-45=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[24, 69, 95, 38], Operations: [] Exploring Operation: 95-69=26, Resulting Numbers: [24, 38, 26] Generated Node #0,0: 88:[24, 38, 26] Operation: 95-69=26 Moving to Node #0,0 Current State: 88:[24, 38, 26], Operations: ['95-69=26'] Exploring Operation: 38-26=12, Resulting Numbers: [24, 12] Generated Node #0,0,0: 88:[24, 12] Operation: 38-26=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[24, 12], Operations: ['95-69=26', '38-26=12'] Exploring Operation: 24/12=2, Resulting Numbers: [2] 2,88 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
[ 64, 10, 28, 25 ]
77
[ "64+10=74", "28-25=3", "74+3=77" ]
Current State: 77:[64, 10, 28, 25], Operations: [] Exploring Operation: 64+10=74, Resulting Numbers: [28, 25, 74] Generated Node #2: [28, 25, 74] from Operation: 64+10=74 Current State: 77:[28, 25, 74], Operations: ['64+10=74'] Exploring Operation: 28-25=3, Resulting Numbers: [74, 3] Generated Node #3: [74, 3] from Operation: 28-25=3 Current State: 77:[74, 3], Operations: ['64+10=74', '28-25=3'] Exploring Operation: 74+3=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[64, 10, 28, 25], Operations: [] Exploring Operation: 28-25=3, Resulting Numbers: [64, 10, 3] Generated Node #0,0: 77:[64, 10, 3] Operation: 28-25=3 Exploring Operation: 64+25=89, Resulting Numbers: [10, 28, 89] Generated Node #0,1: 77:[10, 28, 89] Operation: 64+25=89 Exploring Operation: 64+28=92, Resulting Numbers: [10, 25, 92] Generated Node #0,2: 77:[10, 25, 92] Operation: 64+28=92 Exploring Operation: 28-10=18, Resulting Numbers: [64, 25, 18] Generated Node #0,3: 77:[64, 25, 18] Operation: 28-10=18 Exploring Operation: 64+10=74, Resulting Numbers: [28, 25, 74] Generated Node #0,4: 77:[28, 25, 74] Operation: 64+10=74 Moving to Node #0,0 Current State: 77:[64, 10, 3], Operations: ['28-25=3'] Exploring Operation: 64+3=67, Resulting Numbers: [10, 67] Generated Node #0,0,0: 77:[10, 67] Operation: 64+3=67 Exploring Operation: 64-3=61, Resulting Numbers: [10, 61] Generated Node #0,0,1: 77:[10, 61] Operation: 64-3=61 Exploring Operation: 64+10=74, Resulting Numbers: [3, 74] Generated Node #0,0,2: 77:[3, 74] Operation: 64+10=74 Exploring Operation: 10-3=7, Resulting Numbers: [64, 7] Generated Node #0,0,3: 77:[64, 7] Operation: 10-3=7 Exploring Operation: 10+3=13, Resulting Numbers: [64, 13] Generated Node #0,0,4: 77:[64, 13] Operation: 10+3=13 Moving to Node #0,2 Current State: 77:[10, 25, 92], Operations: ['64+28=92'] Exploring Operation: 10+25=35, Resulting Numbers: [92, 35] Generated Node #0,2,0: 77:[92, 35] Operation: 10+25=35 Exploring Operation: 92-10=82, Resulting Numbers: [25, 82] Generated Node #0,2,1: 77:[25, 82] Operation: 92-10=82 Exploring Operation: 25-10=15, Resulting Numbers: [92, 15] Generated Node #0,2,2: 77:[92, 15] Operation: 25-10=15 Exploring Operation: 92-25=67, Resulting Numbers: [10, 67] Generated Node #0,2,3: 77:[10, 67] Operation: 92-25=67 Exploring Operation: 10+92=102, Resulting Numbers: [25, 102] Generated Node #0,2,4: 77:[25, 102] Operation: 10+92=102 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 77:[10, 67], Operations: ['64+28=92', '92-25=67'] Exploring Operation: 67-10=57, Resulting Numbers: [57] 57,77 unequal: No Solution Exploring Operation: 10+67=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[64, 10, 28, 25], Operations: [] Exploring Operation: 64+28=92, Resulting Numbers: [10, 25, 92] Generated Node #0,2: 77:[10, 25, 92] Operation: 64+28=92 Moving to Node #0,2 Current State: 77:[10, 25, 92], Operations: ['64+28=92'] Exploring Operation: 92-25=67, Resulting Numbers: [10, 67] Generated Node #0,2,3: 77:[10, 67] Operation: 92-25=67 Moving to Node #0,2,3 Current State: 77:[10, 67], Operations: ['64+28=92', '92-25=67'] Exploring Operation: 10+67=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 25, 22, 20, 14 ]
31
[ "25-22=3", "20+14=34", "34-3=31" ]
Current State: 31:[25, 22, 20, 14], Operations: [] Exploring Operation: 25-22=3, Resulting Numbers: [20, 14, 3] Generated Node #2: [20, 14, 3] from Operation: 25-22=3 Current State: 31:[20, 14, 3], Operations: ['25-22=3'] Exploring Operation: 20+14=34, Resulting Numbers: [3, 34] Generated Node #3: [3, 34] from Operation: 20+14=34 Current State: 31:[3, 34], Operations: ['25-22=3', '20+14=34'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[25, 22, 20, 14], Operations: [] Exploring Operation: 22+14=36, Resulting Numbers: [25, 20, 36] Generated Node #0,0: 31:[25, 20, 36] Operation: 22+14=36 Exploring Operation: 20+14=34, Resulting Numbers: [25, 22, 34] Generated Node #0,1: 31:[25, 22, 34] Operation: 20+14=34 Exploring Operation: 25+14=39, Resulting Numbers: [22, 20, 39] Generated Node #0,2: 31:[22, 20, 39] Operation: 25+14=39 Moving to Node #0,1 Current State: 31:[25, 22, 34], Operations: ['20+14=34'] Exploring Operation: 25-22=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 31:[34, 3] Operation: 25-22=3 Exploring Operation: 25+22=47, Resulting Numbers: [34, 47] Generated Node #0,1,1: 31:[34, 47] Operation: 25+22=47 Exploring Operation: 34-22=12, Resulting Numbers: [25, 12] Generated Node #0,1,2: 31:[25, 12] Operation: 34-22=12 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[34, 47], Operations: ['20+14=34', '25+22=47'] Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,31 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,31 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,31 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 #0,1,2 Current State: 31:[25, 12], Operations: ['20+14=34', '34-22=12'] Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,31 unequal: No Solution Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,31 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 #0,1,0 Current State: 31:[34, 3], Operations: ['20+14=34', '25-22=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[25, 22, 20, 14], Operations: [] Exploring Operation: 20+14=34, Resulting Numbers: [25, 22, 34] Generated Node #0,1: 31:[25, 22, 34] Operation: 20+14=34 Moving to Node #0,1 Current State: 31:[25, 22, 34], Operations: ['20+14=34'] Exploring Operation: 25-22=3, Resulting Numbers: [34, 3] Generated Node #0,1,0: 31:[34, 3] Operation: 25-22=3 Moving to Node #0,1,0 Current State: 31:[34, 3], Operations: ['20+14=34', '25-22=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 29, 20, 89, 33 ]
84
[ "33-29=4", "20/4=5", "89-5=84" ]
Current State: 84:[29, 20, 89, 33], Operations: [] Exploring Operation: 33-29=4, Resulting Numbers: [20, 89, 4] Generated Node #2: [20, 89, 4] from Operation: 33-29=4 Current State: 84:[20, 89, 4], Operations: ['33-29=4'] Exploring Operation: 20/4=5, Resulting Numbers: [89, 5] Generated Node #3: [89, 5] from Operation: 20/4=5 Current State: 84:[89, 5], Operations: ['33-29=4', '20/4=5'] Exploring Operation: 89-5=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[29, 20, 89, 33], Operations: [] Exploring Operation: 33-29=4, Resulting Numbers: [20, 89, 4] Generated Node #0,0: 84:[20, 89, 4] Operation: 33-29=4 Moving to Node #0,0 Current State: 84:[20, 89, 4], Operations: ['33-29=4'] Exploring Operation: 89-4=85, Resulting Numbers: [20, 85] Generated Node #0,0,0: 84:[20, 85] Operation: 89-4=85 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[20, 85], Operations: ['33-29=4', '89-4=85'] Exploring Operation: 85-20=65, Resulting Numbers: [65] 65,84 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
[ 89, 94, 85, 70 ]
87
[ "94-89=5", "85/5=17", "70+17=87" ]
Current State: 87:[89, 94, 85, 70], Operations: [] Exploring Operation: 94-89=5, Resulting Numbers: [85, 70, 5] Generated Node #2: [85, 70, 5] from Operation: 94-89=5 Current State: 87:[85, 70, 5], Operations: ['94-89=5'] Exploring Operation: 85/5=17, Resulting Numbers: [70, 17] Generated Node #3: [70, 17] from Operation: 85/5=17 Current State: 87:[70, 17], Operations: ['94-89=5', '85/5=17'] Exploring Operation: 70+17=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[89, 94, 85, 70], Operations: [] Exploring Operation: 89-70=19, Resulting Numbers: [94, 85, 19] Generated Node #0,0: 87:[94, 85, 19] Operation: 89-70=19 Exploring Operation: 94-70=24, Resulting Numbers: [89, 85, 24] Generated Node #0,1: 87:[89, 85, 24] Operation: 94-70=24 Exploring Operation: 85-70=15, Resulting Numbers: [89, 94, 15] Generated Node #0,2: 87:[89, 94, 15] Operation: 85-70=15 Exploring Operation: 94-89=5, Resulting Numbers: [85, 70, 5] Generated Node #0,3: 87:[85, 70, 5] Operation: 94-89=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[89, 85, 24], Operations: ['94-70=24'] Exploring Operation: 89-85=4, Resulting Numbers: [24, 4] Generated Node #0,1,0: 87:[24, 4] Operation: 89-85=4 Exploring Operation: 89-24=65, Resulting Numbers: [85, 65] Generated Node #0,1,1: 87:[85, 65] Operation: 89-24=65 Exploring Operation: 89+24=113, Resulting Numbers: [85, 113] Generated Node #0,1,2: 87:[85, 113] Operation: 89+24=113 Exploring Operation: 85+24=109, Resulting Numbers: [89, 109] Generated Node #0,1,3: 87:[89, 109] Operation: 85+24=109 Moving to Node #0,1,0 Current State: 87:[24, 4], Operations: ['94-70=24', '89-85=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,87 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 24+4=28, Resulting Numbers: [28] 28,87 unequal: No Solution Moving to Node #0,1,3 Current State: 87:[89, 109], Operations: ['94-70=24', '85+24=109'] Exploring Operation: 89*109=9701, Resulting Numbers: [9701] 9701,87 unequal: No Solution Exploring Operation: 89+109=198, Resulting Numbers: [198] 198,87 unequal: No Solution Exploring Operation: 109-89=20, Resulting Numbers: [20] 20,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[85, 65], Operations: ['94-70=24', '89-24=65'] Exploring Operation: 85*65=5525, Resulting Numbers: [5525] 5525,87 unequal: No Solution Exploring Operation: 85+65=150, Resulting Numbers: [150] 150,87 unequal: No Solution Exploring Operation: 85-65=20, Resulting Numbers: [20] 20,87 unequal: No Solution Moving to Node #0,1,2 Current State: 87:[85, 113], Operations: ['94-70=24', '89+24=113'] Exploring Operation: 85*113=9605, Resulting Numbers: [9605] 9605,87 unequal: No Solution Exploring Operation: 85+113=198, Resulting Numbers: [198] 198,87 unequal: No Solution Exploring Operation: 113-85=28, Resulting Numbers: [28] 28,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[94, 85, 19], Operations: ['89-70=19'] Exploring Operation: 94-85=9, Resulting Numbers: [19, 9] Generated Node #0,0,0: 87:[19, 9] Operation: 94-85=9 Exploring Operation: 94+19=113, Resulting Numbers: [85, 113] Generated Node #0,0,1: 87:[85, 113] Operation: 94+19=113 Exploring Operation: 94-19=75, Resulting Numbers: [85, 75] Generated Node #0,0,2: 87:[85, 75] Operation: 94-19=75 Exploring Operation: 85+19=104, Resulting Numbers: [94, 104] Generated Node #0,0,3: 87:[94, 104] Operation: 85+19=104 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[85, 75], Operations: ['89-70=19', '94-19=75'] Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 85+75=160, Resulting Numbers: [160] 160,87 unequal: No Solution Exploring Operation: 85*75=6375, Resulting Numbers: [6375] 6375,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[19, 9], Operations: ['89-70=19', '94-85=9'] Exploring Operation: 19+9=28, Resulting Numbers: [28] 28,87 unequal: No Solution Exploring Operation: 19*9=171, Resulting Numbers: [171] 171,87 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[94, 104], Operations: ['89-70=19', '85+19=104'] Exploring Operation: 94*104=9776, Resulting Numbers: [9776] 9776,87 unequal: No Solution Exploring Operation: 94+104=198, Resulting Numbers: [198] 198,87 unequal: No Solution Exploring Operation: 104-94=10, Resulting Numbers: [10] 10,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[85, 113], Operations: ['89-70=19', '94+19=113'] Exploring Operation: 85+113=198, Resulting Numbers: [198] 198,87 unequal: No Solution Exploring Operation: 85*113=9605, Resulting Numbers: [9605] 9605,87 unequal: No Solution Exploring Operation: 113-85=28, Resulting Numbers: [28] 28,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[89, 94, 15], Operations: ['85-70=15'] Exploring Operation: 89-15=74, Resulting Numbers: [94, 74] Generated Node #0,2,0: 87:[94, 74] Operation: 89-15=74 Exploring Operation: 89+15=104, Resulting Numbers: [94, 104] Generated Node #0,2,1: 87:[94, 104] Operation: 89+15=104 Exploring Operation: 94-89=5, Resulting Numbers: [15, 5] Generated Node #0,2,2: 87:[15, 5] Operation: 94-89=5 Exploring Operation: 94-15=79, Resulting Numbers: [89, 79] Generated Node #0,2,3: 87:[89, 79] Operation: 94-15=79 Moving to Node #0,2,3 Current State: 87:[89, 79], Operations: ['85-70=15', '94-15=79'] Exploring Operation: 89-79=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 89*79=7031, Resulting Numbers: [7031] 7031,87 unequal: No Solution Exploring Operation: 89+79=168, Resulting Numbers: [168] 168,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[15, 5], Operations: ['85-70=15', '94-89=5'] Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 15*5=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 15+5=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,87 unequal: No Solution Moving to Node #0,2,0 Current State: 87:[94, 74], Operations: ['85-70=15', '89-15=74'] Exploring Operation: 94+74=168, Resulting Numbers: [168] 168,87 unequal: No Solution Exploring Operation: 94*74=6956, Resulting Numbers: [6956] 6956,87 unequal: No Solution Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[94, 104], Operations: ['85-70=15', '89+15=104'] Exploring Operation: 104-94=10, Resulting Numbers: [10] 10,87 unequal: No Solution Exploring Operation: 94*104=9776, Resulting Numbers: [9776] 9776,87 unequal: No Solution Exploring Operation: 94+104=198, Resulting Numbers: [198] 198,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 87:[85, 70, 5], Operations: ['94-89=5'] Exploring Operation: 85+5=90, Resulting Numbers: [70, 90] Generated Node #0,3,0: 87:[70, 90] Operation: 85+5=90 Exploring Operation: 85-70=15, Resulting Numbers: [5, 15] Generated Node #0,3,1: 87:[5, 15] Operation: 85-70=15 Exploring Operation: 70/5=14, Resulting Numbers: [85, 14] Generated Node #0,3,2: 87:[85, 14] Operation: 70/5=14 Exploring Operation: 70+5=75, Resulting Numbers: [85, 75] Generated Node #0,3,3: 87:[85, 75] Operation: 70+5=75 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 87:[85, 14], Operations: ['94-89=5', '70/5=14'] Exploring Operation: 85-14=71, Resulting Numbers: [71] 71,87 unequal: No Solution Exploring Operation: 85+14=99, Resulting Numbers: [99] 99,87 unequal: No Solution Exploring Operation: 85*14=1190, Resulting Numbers: [1190] 1190,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 87:[5, 15], Operations: ['94-89=5', '85-70=15'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,87 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,87 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 87:[85, 75], Operations: ['94-89=5', '70+5=75'] Exploring Operation: 85*75=6375, Resulting Numbers: [6375] 6375,87 unequal: No Solution Exploring Operation: 85+75=160, Resulting Numbers: [160] 160,87 unequal: No Solution Exploring Operation: 85-75=10, Resulting Numbers: [10] 10,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 87:[70, 90], Operations: ['94-89=5', '85+5=90'] Exploring Operation: 90-70=20, Resulting Numbers: [20] 20,87 unequal: No Solution Exploring Operation: 70*90=6300, Resulting Numbers: [6300] 6300,87 unequal: No Solution Exploring Operation: 70+90=160, Resulting Numbers: [160] 160,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 32, 2, 33, 18 ]
37
[ "33-32=1", "2*18=36", "1+36=37" ]
Current State: 37:[32, 2, 33, 18], Operations: [] Exploring Operation: 33-32=1, Resulting Numbers: [2, 18, 1] Generated Node #2: [2, 18, 1] from Operation: 33-32=1 Current State: 37:[2, 18, 1], Operations: ['33-32=1'] Exploring Operation: 2*18=36, Resulting Numbers: [1, 36] Generated Node #3: [1, 36] from Operation: 2*18=36 Current State: 37:[1, 36], Operations: ['33-32=1', '2*18=36'] Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[32, 2, 33, 18], Operations: [] Exploring Operation: 2+18=20, Resulting Numbers: [32, 33, 20] Generated Node #0,0: 37:[32, 33, 20] Operation: 2+18=20 Exploring Operation: 2+33=35, Resulting Numbers: [32, 18, 35] Generated Node #0,1: 37:[32, 18, 35] Operation: 2+33=35 Exploring Operation: 2*18=36, Resulting Numbers: [32, 33, 36] Generated Node #0,2: 37:[32, 33, 36] Operation: 2*18=36 Exploring Operation: 32+2=34, Resulting Numbers: [33, 18, 34] Generated Node #0,3: 37:[33, 18, 34] Operation: 32+2=34 Moving to Node #0,2 Current State: 37:[32, 33, 36], Operations: ['2*18=36'] Exploring Operation: 32+36=68, Resulting Numbers: [33, 68] Generated Node #0,2,0: 37:[33, 68] Operation: 32+36=68 Exploring Operation: 32+33=65, Resulting Numbers: [36, 65] Generated Node #0,2,1: 37:[36, 65] Operation: 32+33=65 Exploring Operation: 33-32=1, Resulting Numbers: [36, 1] Generated Node #0,2,2: 37:[36, 1] Operation: 33-32=1 Exploring Operation: 36-32=4, Resulting Numbers: [33, 4] Generated Node #0,2,3: 37:[33, 4] Operation: 36-32=4 Moving to Node #0,1 Current State: 37:[32, 18, 35], Operations: ['2+33=35'] Exploring Operation: 32+18=50, Resulting Numbers: [35, 50] Generated Node #0,1,0: 37:[35, 50] Operation: 32+18=50 Exploring Operation: 32-18=14, Resulting Numbers: [35, 14] Generated Node #0,1,1: 37:[35, 14] Operation: 32-18=14 Exploring Operation: 18+35=53, Resulting Numbers: [32, 53] Generated Node #0,1,2: 37:[32, 53] Operation: 18+35=53 Exploring Operation: 35-18=17, Resulting Numbers: [32, 17] Generated Node #0,1,3: 37:[32, 17] Operation: 35-18=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 37:[35, 50], Operations: ['2+33=35', '32+18=50'] Exploring Operation: 50-35=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 35*50=1750, Resulting Numbers: [1750] 1750,37 unequal: No Solution Exploring Operation: 35+50=85, Resulting Numbers: [85] 85,37 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 #0,1,2 Current State: 37:[32, 53], Operations: ['2+33=35', '18+35=53'] Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,37 unequal: No Solution Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,37 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,37 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:[35, 14], Operations: ['2+33=35', '32-18=14'] Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,37 unequal: No Solution Exploring Operation: 35+14=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 35*14=490, Resulting Numbers: [490] 490,37 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 #0,1,3 Current State: 37:[32, 17], Operations: ['2+33=35', '35-18=17'] Exploring Operation: 32-17=15, Resulting Numbers: [15] 15,37 unequal: No Solution Exploring Operation: 32+17=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 32*17=544, Resulting Numbers: [544] 544,37 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:[32, 33, 20], Operations: ['2+18=20'] Exploring Operation: 33-20=13, Resulting Numbers: [32, 13] Generated Node #0,0,0: 37:[32, 13] Operation: 33-20=13 Exploring Operation: 32-20=12, Resulting Numbers: [33, 12] Generated Node #0,0,1: 37:[33, 12] Operation: 32-20=12 Exploring Operation: 33+20=53, Resulting Numbers: [32, 53] Generated Node #0,0,2: 37:[32, 53] Operation: 33+20=53 Exploring Operation: 32+20=52, Resulting Numbers: [33, 52] Generated Node #0,0,3: 37:[33, 52] Operation: 32+20=52 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[33, 52], Operations: ['2+18=20', '32+20=52'] Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,37 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,37 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 #0,0,2 Current State: 37:[32, 53], Operations: ['2+18=20', '33+20=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,37 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,37 unequal: No Solution Exploring Operation: 32*53=1696, Resulting Numbers: [1696] 1696,37 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 #0,0,0 Current State: 37:[32, 13], Operations: ['2+18=20', '33-20=13'] Exploring Operation: 32+13=45, Resulting Numbers: [45] 45,37 unequal: No Solution Exploring Operation: 32*13=416, Resulting Numbers: [416] 416,37 unequal: No Solution Exploring Operation: 32-13=19, Resulting Numbers: [19] 19,37 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:[33, 12], Operations: ['2+18=20', '32-20=12'] Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,37 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,37 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,37 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: 37:[33, 18, 34], Operations: ['32+2=34'] Exploring Operation: 33+18=51, Resulting Numbers: [34, 51] Generated Node #0,3,0: 37:[34, 51] Operation: 33+18=51 Exploring Operation: 18+34=52, Resulting Numbers: [33, 52] Generated Node #0,3,1: 37:[33, 52] Operation: 18+34=52 Exploring Operation: 34-18=16, Resulting Numbers: [33, 16] Generated Node #0,3,2: 37:[33, 16] Operation: 34-18=16 Exploring Operation: 33-18=15, Resulting Numbers: [34, 15] Generated Node #0,3,3: 37:[34, 15] Operation: 33-18=15 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[34, 51], Operations: ['32+2=34', '33+18=51'] Exploring Operation: 34+51=85, Resulting Numbers: [85] 85,37 unequal: No Solution Exploring Operation: 34*51=1734, Resulting Numbers: [1734] 1734,37 unequal: No Solution Exploring Operation: 51-34=17, Resulting Numbers: [17] 17,37 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 #0,3,1 Current State: 37:[33, 52], Operations: ['32+2=34', '18+34=52'] Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,37 unequal: No Solution Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,37 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 #0,3,2 Current State: 37:[33, 16], Operations: ['32+2=34', '34-18=16'] Exploring Operation: 33-16=17, Resulting Numbers: [17] 17,37 unequal: No Solution Exploring Operation: 33*16=528, Resulting Numbers: [528] 528,37 unequal: No Solution Exploring Operation: 33+16=49, Resulting Numbers: [49] 49,37 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 #0,3,3 Current State: 37:[34, 15], Operations: ['32+2=34', '33-18=15'] Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,37 unequal: No Solution Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,37 unequal: No Solution Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 37:[36, 65], Operations: ['2*18=36', '32+33=65'] Exploring Operation: 36+65=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 65-36=29, Resulting Numbers: [29] 29,37 unequal: No Solution Exploring Operation: 36*65=2340, Resulting Numbers: [2340] 2340,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[33, 68], Operations: ['2*18=36', '32+36=68'] Exploring Operation: 33+68=101, Resulting Numbers: [101] 101,37 unequal: No Solution Exploring Operation: 68-33=35, Resulting Numbers: [35] 35,37 unequal: No Solution Exploring Operation: 33*68=2244, Resulting Numbers: [2244] 2244,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[33, 4], Operations: ['2*18=36', '36-32=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[32, 2, 33, 18], Operations: [] Exploring Operation: 2*18=36, Resulting Numbers: [32, 33, 36] Generated Node #0,2: 37:[32, 33, 36] Operation: 2*18=36 Moving to Node #0,2 Current State: 37:[32, 33, 36], Operations: ['2*18=36'] Exploring Operation: 36-32=4, Resulting Numbers: [33, 4] Generated Node #0,2,3: 37:[33, 4] Operation: 36-32=4 Moving to Node #0,2,3 Current State: 37:[33, 4], Operations: ['2*18=36', '36-32=4'] Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.94184
hs_4
mult_heuristic
[ 3, 98, 62, 31 ]
77
[ "98-62=36", "3*36=108", "108-31=77" ]
Current State: 77:[3, 98, 62, 31], Operations: [] Exploring Operation: 98-62=36, Resulting Numbers: [3, 31, 36] Generated Node #2: [3, 31, 36] from Operation: 98-62=36 Current State: 77:[3, 31, 36], Operations: ['98-62=36'] Exploring Operation: 3*36=108, Resulting Numbers: [31, 108] Generated Node #3: [31, 108] from Operation: 3*36=108 Current State: 77:[31, 108], Operations: ['98-62=36', '3*36=108'] Exploring Operation: 108-31=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[3, 98, 62, 31], Operations: [] Exploring Operation: 62/31=2, Resulting Numbers: [3, 98, 2] Generated Node #0,0: 77:[3, 98, 2] Operation: 62/31=2 Exploring Operation: 98-31=67, Resulting Numbers: [3, 62, 67] Generated Node #0,1: 77:[3, 62, 67] Operation: 98-31=67 Moving to Node #0,1 Current State: 77:[3, 62, 67], Operations: ['98-31=67'] Exploring Operation: 67-62=5, Resulting Numbers: [3, 5] Generated Node #0,1,0: 77:[3, 5] Operation: 67-62=5 Exploring Operation: 3+62=65, Resulting Numbers: [67, 65] Generated Node #0,1,1: 77:[67, 65] Operation: 3+62=65 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 77:[3, 5], Operations: ['98-31=67', '67-62=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 77:[67, 65], Operations: ['98-31=67', '3+62=65'] Exploring Operation: 67-65=2, Resulting Numbers: [2] 2,77 unequal: No Solution Exploring Operation: 67+65=132, Resulting Numbers: [132] 132,77 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: 77:[3, 98, 2], Operations: ['62/31=2'] Exploring Operation: 98-3=95, Resulting Numbers: [2, 95] Generated Node #0,0,0: 77:[2, 95] Operation: 98-3=95 Exploring Operation: 3*2=6, Resulting Numbers: [98, 6] Generated Node #0,0,1: 77:[98, 6] Operation: 3*2=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 77:[98, 6], Operations: ['62/31=2', '3*2=6'] Exploring Operation: 98+6=104, Resulting Numbers: [104] 104,77 unequal: No Solution Exploring Operation: 98-6=92, Resulting Numbers: [92] 92,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[2, 95], Operations: ['62/31=2', '98-3=95'] Exploring Operation: 2+95=97, Resulting Numbers: [97] 97,77 unequal: No Solution Exploring Operation: 95-2=93, Resulting Numbers: [93] 93,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 59, 51, 83, 3 ]
37
[ "83-51=32", "3*32=96", "96-59=37" ]
Current State: 37:[59, 51, 83, 3], Operations: [] Exploring Operation: 83-51=32, Resulting Numbers: [59, 3, 32] Generated Node #2: [59, 3, 32] from Operation: 83-51=32 Current State: 37:[59, 3, 32], Operations: ['83-51=32'] Exploring Operation: 3*32=96, Resulting Numbers: [59, 96] Generated Node #3: [59, 96] from Operation: 3*32=96 Current State: 37:[59, 96], Operations: ['83-51=32', '3*32=96'] Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[59, 51, 83, 3], Operations: [] Exploring Operation: 83-59=24, Resulting Numbers: [51, 3, 24] Generated Node #0,0: 37:[51, 3, 24] Operation: 83-59=24 Exploring Operation: 83-51=32, Resulting Numbers: [59, 3, 32] Generated Node #0,1: 37:[59, 3, 32] Operation: 83-51=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[51, 3, 24], Operations: ['83-59=24'] Exploring Operation: 51-3=48, Resulting Numbers: [24, 48] Generated Node #0,0,0: 37:[24, 48] Operation: 51-3=48 Exploring Operation: 3+24=27, Resulting Numbers: [51, 27] Generated Node #0,0,1: 37:[51, 27] Operation: 3+24=27 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[24, 48], Operations: ['83-59=24', '51-3=48'] Exploring Operation: 24+48=72, Resulting Numbers: [72] 72,37 unequal: No Solution Exploring Operation: 48-24=24, Resulting Numbers: [24] 24,37 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:[51, 27], Operations: ['83-59=24', '3+24=27'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,37 unequal: No Solution Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,37 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 #0,1 Current State: 37:[59, 3, 32], Operations: ['83-51=32'] Exploring Operation: 59-3=56, Resulting Numbers: [32, 56] Generated Node #0,1,0: 37:[32, 56] Operation: 59-3=56 Exploring Operation: 3+32=35, Resulting Numbers: [59, 35] Generated Node #0,1,1: 37:[59, 35] Operation: 3+32=35 Moving to Node #0,1,0 Current State: 37:[32, 56], Operations: ['83-51=32', '59-3=56'] Exploring Operation: 56-32=24, Resulting Numbers: [24] 24,37 unequal: No Solution Exploring Operation: 32+56=88, Resulting Numbers: [88] 88,37 unequal: No Solution Moving to Node #0,1,1 Current State: 37:[59, 35], Operations: ['83-51=32', '3+32=35'] Exploring Operation: 59+35=94, Resulting Numbers: [94] 94,37 unequal: No Solution Exploring Operation: 59-35=24, Resulting Numbers: [24] 24,37 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
[ 84, 60, 65, 79 ]
12
[ "84*65=5460", "5460/60=91", "91-79=12" ]
Current State: 12:[84, 60, 65, 79], Operations: [] Exploring Operation: 84*65=5460, Resulting Numbers: [60, 79, 5460] Generated Node #2: [60, 79, 5460] from Operation: 84*65=5460 Current State: 12:[60, 79, 5460], Operations: ['84*65=5460'] Exploring Operation: 5460/60=91, Resulting Numbers: [79, 91] Generated Node #3: [79, 91] from Operation: 5460/60=91 Current State: 12:[79, 91], Operations: ['84*65=5460', '5460/60=91'] Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[84, 60, 65, 79], Operations: [] Exploring Operation: 84-79=5, Resulting Numbers: [60, 65, 5] Generated Node #0,0: 12:[60, 65, 5] Operation: 84-79=5 Exploring Operation: 84-65=19, Resulting Numbers: [60, 79, 19] Generated Node #0,1: 12:[60, 79, 19] Operation: 84-65=19 Exploring Operation: 79-65=14, Resulting Numbers: [84, 60, 14] Generated Node #0,2: 12:[84, 60, 14] Operation: 79-65=14 Exploring Operation: 84-60=24, Resulting Numbers: [65, 79, 24] Generated Node #0,3: 12:[65, 79, 24] Operation: 84-60=24 Moving to Node #0,0 Current State: 12:[60, 65, 5], Operations: ['84-79=5'] Exploring Operation: 60-5=55, Resulting Numbers: [65, 55] Generated Node #0,0,0: 12:[65, 55] Operation: 60-5=55 Exploring Operation: 65-60=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 12:[5, 5] Operation: 65-60=5 Exploring Operation: 65/5=13, Resulting Numbers: [60, 13] Generated Node #0,0,2: 12:[60, 13] Operation: 65/5=13 Exploring Operation: 60/5=12, Resulting Numbers: [65, 12] Generated Node #0,0,3: 12:[65, 12] Operation: 60/5=12 Moving to Node #0,2 Current State: 12:[84, 60, 14], Operations: ['79-65=14'] Exploring Operation: 84-14=70, Resulting Numbers: [60, 70] Generated Node #0,2,0: 12:[60, 70] Operation: 84-14=70 Exploring Operation: 84-60=24, Resulting Numbers: [14, 24] Generated Node #0,2,1: 12:[14, 24] Operation: 84-60=24 Exploring Operation: 60-14=46, Resulting Numbers: [84, 46] Generated Node #0,2,2: 12:[84, 46] Operation: 60-14=46 Exploring Operation: 84/14=6, Resulting Numbers: [60, 6] Generated Node #0,2,3: 12:[60, 6] Operation: 84/14=6 Moving to Node #0,1 Current State: 12:[60, 79, 19], Operations: ['84-65=19'] Exploring Operation: 79-19=60, Resulting Numbers: [60, 60] Generated Node #0,1,0: 12:[60, 60] Operation: 79-19=60 Exploring Operation: 60-19=41, Resulting Numbers: [79, 41] Generated Node #0,1,1: 12:[79, 41] Operation: 60-19=41 Exploring Operation: 60+79=139, Resulting Numbers: [19, 139] Generated Node #0,1,2: 12:[19, 139] Operation: 60+79=139 Exploring Operation: 79-60=19, Resulting Numbers: [19, 19] Generated Node #0,1,3: 12:[19, 19] Operation: 79-60=19 Moving to Node #0,3 Current State: 12:[65, 79, 24], Operations: ['84-60=24'] Exploring Operation: 65+79=144, Resulting Numbers: [24, 144] Generated Node #0,3,0: 12:[24, 144] Operation: 65+79=144 Exploring Operation: 79-24=55, Resulting Numbers: [65, 55] Generated Node #0,3,1: 12:[65, 55] Operation: 79-24=55 Exploring Operation: 79-65=14, Resulting Numbers: [24, 14] Generated Node #0,3,2: 12:[24, 14] Operation: 79-65=14 Exploring Operation: 65-24=41, Resulting Numbers: [79, 41] Generated Node #0,3,3: 12:[79, 41] Operation: 65-24=41 Moving to Node #0,0,1 Current State: 12:[5, 5], Operations: ['84-79=5', '65-60=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[24, 14], Operations: ['84-60=24', '79-65=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[14, 24], Operations: ['79-65=14', '84-60=24'] Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 14+24=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 14*24=336, Resulting Numbers: [336] 336,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[19, 19], Operations: ['84-65=19', '79-60=19'] Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,12 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[60, 6], Operations: ['79-65=14', '84/14=6'] Exploring Operation: 60/6=10, Resulting Numbers: [10] 10,12 unequal: No Solution Exploring Operation: 60+6=66, Resulting Numbers: [66] 66,12 unequal: No Solution Exploring Operation: 60*6=360, Resulting Numbers: [360] 360,12 unequal: No Solution Exploring Operation: 60-6=54, Resulting Numbers: [54] 54,12 unequal: No Solution Moving to Node #0,0,2 Current State: 12:[60, 13], Operations: ['84-79=5', '65/5=13'] Exploring Operation: 60+13=73, Resulting Numbers: [73] 73,12 unequal: No Solution Exploring Operation: 60*13=780, Resulting Numbers: [780] 780,12 unequal: No Solution Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,12 unequal: No Solution Moving to Node #0,0,3 Current State: 12:[65, 12], Operations: ['84-79=5', '60/5=12'] Exploring Operation: 65*12=780, Resulting Numbers: [780] 780,12 unequal: No Solution Exploring Operation: 65+12=77, Resulting Numbers: [77] 77,12 unequal: No Solution Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[65, 55], Operations: ['84-60=24', '79-24=55'] Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,12 unequal: No Solution Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[79, 41], Operations: ['84-65=19', '60-19=41'] Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,12 unequal: No Solution Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[60, 60], Operations: ['84-65=19', '79-19=60'] Exploring Operation: 60*60=3600, Resulting Numbers: [3600] 3600,12 unequal: No Solution Exploring Operation: 60/60=1, Resulting Numbers: [1] 1,12 unequal: No Solution Exploring Operation: 60-60=0, Resulting Numbers: [0] 0,12 unequal: No Solution Exploring Operation: 60+60=120, Resulting Numbers: [120] 120,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[79, 41], Operations: ['84-60=24', '65-24=41'] Exploring Operation: 79+41=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 79-41=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 79*41=3239, Resulting Numbers: [3239] 3239,12 unequal: No Solution Moving to Node #0,0,0 Current State: 12:[65, 55], Operations: ['84-79=5', '60-5=55'] Exploring Operation: 65*55=3575, Resulting Numbers: [3575] 3575,12 unequal: No Solution Exploring Operation: 65+55=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 65-55=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[60, 70], Operations: ['79-65=14', '84-14=70'] Exploring Operation: 60*70=4200, Resulting Numbers: [4200] 4200,12 unequal: No Solution Exploring Operation: 60+70=130, Resulting Numbers: [130] 130,12 unequal: No Solution Exploring Operation: 70-60=10, Resulting Numbers: [10] 10,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[84, 46], Operations: ['79-65=14', '60-14=46'] Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,12 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,12 unequal: No Solution Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,12 unequal: No Solution Moving to Node #0,1,2 Current State: 12:[19, 139], Operations: ['84-65=19', '60+79=139'] Exploring Operation: 19*139=2641, Resulting Numbers: [2641] 2641,12 unequal: No Solution Exploring Operation: 19+139=158, Resulting Numbers: [158] 158,12 unequal: No Solution Exploring Operation: 139-19=120, Resulting Numbers: [120] 120,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[24, 144], Operations: ['84-60=24', '65+79=144'] Exploring Operation: 144-24=120, Resulting Numbers: [120] 120,12 unequal: No Solution Exploring Operation: 144/24=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 24+144=168, Resulting Numbers: [168] 168,12 unequal: No Solution Exploring Operation: 24*144=3456, Resulting Numbers: [3456] 3456,12 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 65, 20, 40, 45 ]
40
[ "65-20=45", "40+45=85", "85-45=40" ]
Current State: 40:[65, 20, 40, 45], Operations: [] Exploring Operation: 65-20=45, Resulting Numbers: [40, 45, 45] Generated Node #2: [40, 45, 45] from Operation: 65-20=45 Current State: 40:[40, 45, 45], Operations: ['65-20=45'] Exploring Operation: 40+45=85, Resulting Numbers: [85] 85,40 equal: Goal Reached Exploring Operation: 85-45=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[65, 20, 40, 45], Operations: [] Exploring Operation: 65-45=20, Resulting Numbers: [20, 40, 20] Generated Node #0,0: 40:[20, 40, 20] Operation: 65-45=20 Exploring Operation: 65-20=45, Resulting Numbers: [40, 45, 45] Generated Node #0,1: 40:[40, 45, 45] Operation: 65-20=45 Exploring Operation: 65-40=25, Resulting Numbers: [20, 45, 25] Generated Node #0,2: 40:[20, 45, 25] Operation: 65-40=25 Exploring Operation: 45-40=5, Resulting Numbers: [65, 20, 5] Generated Node #0,3: 40:[65, 20, 5] Operation: 45-40=5 Exploring Operation: 40-20=20, Resulting Numbers: [65, 45, 20] Generated Node #0,4: 40:[65, 45, 20] Operation: 40-20=20 Moving to Node #0,0 Current State: 40:[20, 40, 20], Operations: ['65-45=20'] Exploring Operation: 40/20=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 40:[20, 2] Operation: 40/20=2 Exploring Operation: 40-20=20, Resulting Numbers: [20, 20] Generated Node #0,0,1: 40:[20, 20] Operation: 40-20=20 Exploring Operation: 40-20=20, Resulting Numbers: [20, 20] Generated Node #0,0,2: 40:[20, 20] Operation: 40-20=20 Exploring Operation: 20+20=40, Resulting Numbers: [40, 40] Generated Node #0,0,3: 40:[40, 40] Operation: 20+20=40 Exploring Operation: 40/20=2, Resulting Numbers: [20, 2] Generated Node #0,0,4: 40:[20, 2] Operation: 40/20=2 Moving to Node #0,2 Current State: 40:[20, 45, 25], Operations: ['65-40=25'] Exploring Operation: 45-20=25, Resulting Numbers: [25, 25] Generated Node #0,2,0: 40:[25, 25] Operation: 45-20=25 Exploring Operation: 20+45=65, Resulting Numbers: [25, 65] Generated Node #0,2,1: 40:[25, 65] Operation: 20+45=65 Exploring Operation: 25-20=5, Resulting Numbers: [45, 5] Generated Node #0,2,2: 40:[45, 5] Operation: 25-20=5 Exploring Operation: 20+25=45, Resulting Numbers: [45, 45] Generated Node #0,2,3: 40:[45, 45] Operation: 20+25=45 Exploring Operation: 45-25=20, Resulting Numbers: [20, 20] Generated Node #0,2,4: 40:[20, 20] Operation: 45-25=20 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 40:[20, 20], Operations: ['65-40=25', '45-25=20'] Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,40 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[65, 20, 40, 45], Operations: [] Exploring Operation: 65-40=25, Resulting Numbers: [20, 45, 25] Generated Node #0,2: 40:[20, 45, 25] Operation: 65-40=25 Moving to Node #0,2 Current State: 40:[20, 45, 25], Operations: ['65-40=25'] Exploring Operation: 45-25=20, Resulting Numbers: [20, 20] Generated Node #0,2,4: 40:[20, 20] Operation: 45-25=20 Moving to Node #0,2,4 Current State: 40:[20, 20], Operations: ['65-40=25', '45-25=20'] Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 65, 43, 51, 4 ]
99
[ "65-51=14", "4*14=56", "43+56=99" ]
Current State: 99:[65, 43, 51, 4], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [43, 4, 14] Generated Node #2: [43, 4, 14] from Operation: 65-51=14 Current State: 99:[43, 4, 14], Operations: ['65-51=14'] Exploring Operation: 4*14=56, Resulting Numbers: [43, 56] Generated Node #3: [43, 56] from Operation: 4*14=56 Current State: 99:[43, 56], Operations: ['65-51=14', '4*14=56'] Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[65, 43, 51, 4], Operations: [] Exploring Operation: 65-51=14, Resulting Numbers: [43, 4, 14] Generated Node #0,0: 99:[43, 4, 14] Operation: 65-51=14 Exploring Operation: 65+51=116, Resulting Numbers: [43, 4, 116] Generated Node #0,1: 99:[43, 4, 116] Operation: 65+51=116 Exploring Operation: 65-43=22, Resulting Numbers: [51, 4, 22] Generated Node #0,2: 99:[51, 4, 22] Operation: 65-43=22 Exploring Operation: 65+43=108, Resulting Numbers: [51, 4, 108] Generated Node #0,3: 99:[51, 4, 108] Operation: 65+43=108 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[43, 4, 14], Operations: ['65-51=14'] Exploring Operation: 14-4=10, Resulting Numbers: [43, 10] Generated Node #0,0,0: 99:[43, 10] Operation: 14-4=10 Exploring Operation: 43-14=29, Resulting Numbers: [4, 29] Generated Node #0,0,1: 99:[4, 29] Operation: 43-14=29 Exploring Operation: 43-4=39, Resulting Numbers: [14, 39] Generated Node #0,0,2: 99:[14, 39] Operation: 43-4=39 Exploring Operation: 43+4=47, Resulting Numbers: [14, 47] Generated Node #0,0,3: 99:[14, 47] Operation: 43+4=47 Moving to Node #0,0,1 Current State: 99:[4, 29], Operations: ['65-51=14', '43-14=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,99 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,99 unequal: No Solution Moving to Node #0,0,2 Current State: 99:[14, 39], Operations: ['65-51=14', '43-4=39'] Exploring Operation: 39-14=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 14+39=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 14*39=546, Resulting Numbers: [546] 546,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[43, 10], Operations: ['65-51=14', '14-4=10'] Exploring Operation: 43+10=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 43*10=430, Resulting Numbers: [430] 430,99 unequal: No Solution Exploring Operation: 43-10=33, Resulting Numbers: [33] 33,99 unequal: No Solution Moving to Node #0,0,3 Current State: 99:[14, 47], Operations: ['65-51=14', '43+4=47'] Exploring Operation: 14+47=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 47-14=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 14*47=658, Resulting Numbers: [658] 658,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[43, 4, 116], Operations: ['65+51=116'] Exploring Operation: 116/4=29, Resulting Numbers: [43, 29] Generated Node #0,1,0: 99:[43, 29] Operation: 116/4=29 Exploring Operation: 116-4=112, Resulting Numbers: [43, 112] Generated Node #0,1,1: 99:[43, 112] Operation: 116-4=112 Exploring Operation: 116-43=73, Resulting Numbers: [4, 73] Generated Node #0,1,2: 99:[4, 73] Operation: 116-43=73 Exploring Operation: 43-4=39, Resulting Numbers: [116, 39] Generated Node #0,1,3: 99:[116, 39] Operation: 43-4=39 Moving to Node #0,1,0 Current State: 99:[43, 29], Operations: ['65+51=116', '116/4=29'] Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,99 unequal: No Solution Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,99 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[116, 39], Operations: ['65+51=116', '43-4=39'] Exploring Operation: 116-39=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 116*39=4524, Resulting Numbers: [4524] 4524,99 unequal: No Solution Exploring Operation: 116+39=155, Resulting Numbers: [155] 155,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[43, 112], Operations: ['65+51=116', '116-4=112'] Exploring Operation: 43*112=4816, Resulting Numbers: [4816] 4816,99 unequal: No Solution Exploring Operation: 43+112=155, Resulting Numbers: [155] 155,99 unequal: No Solution Exploring Operation: 112-43=69, Resulting Numbers: [69] 69,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[4, 73], Operations: ['65+51=116', '116-43=73'] Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,99 unequal: No Solution Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,99 unequal: No Solution Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[51, 4, 108], Operations: ['65+43=108'] Exploring Operation: 51-4=47, Resulting Numbers: [108, 47] Generated Node #0,3,0: 99:[108, 47] Operation: 51-4=47 Exploring Operation: 108/4=27, Resulting Numbers: [51, 27] Generated Node #0,3,1: 99:[51, 27] Operation: 108/4=27 Exploring Operation: 108-51=57, Resulting Numbers: [4, 57] Generated Node #0,3,2: 99:[4, 57] Operation: 108-51=57 Exploring Operation: 108-4=104, Resulting Numbers: [51, 104] Generated Node #0,3,3: 99:[51, 104] Operation: 108-4=104 Moving to Node #0,3,0 Current State: 99:[108, 47], Operations: ['65+43=108', '51-4=47'] Exploring Operation: 108+47=155, Resulting Numbers: [155] 155,99 unequal: No Solution Exploring Operation: 108-47=61, Resulting Numbers: [61] 61,99 unequal: No Solution Exploring Operation: 108*47=5076, Resulting Numbers: [5076] 5076,99 unequal: No Solution Moving to Node #0,3,3 Current State: 99:[51, 104], Operations: ['65+43=108', '108-4=104'] Exploring Operation: 104-51=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 51+104=155, Resulting Numbers: [155] 155,99 unequal: No Solution Exploring Operation: 51*104=5304, Resulting Numbers: [5304] 5304,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[51, 27], Operations: ['65+43=108', '108/4=27'] Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,99 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,99 unequal: No Solution Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[4, 57], Operations: ['65+43=108', '108-51=57'] Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,99 unequal: No Solution Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,99 unequal: No Solution Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[51, 4, 22], Operations: ['65-43=22'] Exploring Operation: 51-4=47, Resulting Numbers: [22, 47] Generated Node #0,2,0: 99:[22, 47] Operation: 51-4=47 Exploring Operation: 51-22=29, Resulting Numbers: [4, 29] Generated Node #0,2,1: 99:[4, 29] Operation: 51-22=29 Exploring Operation: 4+22=26, Resulting Numbers: [51, 26] Generated Node #0,2,2: 99:[51, 26] Operation: 4+22=26 Exploring Operation: 22-4=18, Resulting Numbers: [51, 18] Generated Node #0,2,3: 99:[51, 18] Operation: 22-4=18 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[4, 29], Operations: ['65-43=22', '51-22=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,99 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,99 unequal: No Solution No 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: 99:[22, 47], Operations: ['65-43=22', '51-4=47'] Exploring Operation: 22+47=69, Resulting Numbers: [69] 69,99 unequal: No Solution Exploring Operation: 22*47=1034, Resulting Numbers: [1034] 1034,99 unequal: No Solution Exploring Operation: 47-22=25, Resulting Numbers: [25] 25,99 unequal: No Solution No 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: 99:[51, 26], Operations: ['65-43=22', '4+22=26'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,99 unequal: No Solution Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,99 unequal: No Solution Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,99 unequal: No Solution No 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: 99:[51, 18], Operations: ['65-43=22', '22-4=18'] Exploring Operation: 51*18=918, Resulting Numbers: [918] 918,99 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 51+18=69, Resulting Numbers: [69] 69,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 6, 38, 49, 86 ]
69
[ "38-6=32", "86-49=37", "32+37=69" ]
Current State: 69:[6, 38, 49, 86], Operations: [] Exploring Operation: 38-6=32, Resulting Numbers: [49, 86, 32] Generated Node #2: [49, 86, 32] from Operation: 38-6=32 Current State: 69:[49, 86, 32], Operations: ['38-6=32'] Exploring Operation: 86-49=37, Resulting Numbers: [32, 37] Generated Node #3: [32, 37] from Operation: 86-49=37 Current State: 69:[32, 37], Operations: ['38-6=32', '86-49=37'] Exploring Operation: 32+37=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[6, 38, 49, 86], Operations: [] Exploring Operation: 49-38=11, Resulting Numbers: [6, 86, 11] Generated Node #0,0: 69:[6, 86, 11] Operation: 49-38=11 Moving to Node #0,0 Current State: 69:[6, 86, 11], Operations: ['49-38=11'] Exploring Operation: 86-11=75, Resulting Numbers: [6, 75] Generated Node #0,0,0: 69:[6, 75] Operation: 86-11=75 Moving to Node #0,0,0 Current State: 69:[6, 75], Operations: ['49-38=11', '86-11=75'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[6, 38, 49, 86], Operations: [] Exploring Operation: 49-38=11, Resulting Numbers: [6, 86, 11] Generated Node #0,0: 69:[6, 86, 11] Operation: 49-38=11 Moving to Node #0,0 Current State: 69:[6, 86, 11], Operations: ['49-38=11'] Exploring Operation: 86-11=75, Resulting Numbers: [6, 75] Generated Node #0,0,0: 69:[6, 75] Operation: 86-11=75 Moving to Node #0,0,0 Current State: 69:[6, 75], Operations: ['49-38=11', '86-11=75'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 41, 71, 35, 82 ]
53
[ "82/41=2", "71+35=106", "106/2=53" ]
Current State: 53:[41, 71, 35, 82], Operations: [] Exploring Operation: 82/41=2, Resulting Numbers: [71, 35, 2] Generated Node #2: [71, 35, 2] from Operation: 82/41=2 Current State: 53:[71, 35, 2], Operations: ['82/41=2'] Exploring Operation: 71+35=106, Resulting Numbers: [2, 106] Generated Node #3: [2, 106] from Operation: 71+35=106 Current State: 53:[2, 106], Operations: ['82/41=2', '71+35=106'] Exploring Operation: 106/2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[41, 71, 35, 82], Operations: [] Exploring Operation: 82-35=47, Resulting Numbers: [41, 71, 47] Generated Node #0,0: 53:[41, 71, 47] Operation: 82-35=47 Exploring Operation: 71-41=30, Resulting Numbers: [35, 82, 30] Generated Node #0,1: 53:[35, 82, 30] Operation: 71-41=30 Exploring Operation: 71-35=36, Resulting Numbers: [41, 82, 36] Generated Node #0,2: 53:[41, 82, 36] Operation: 71-35=36 Exploring Operation: 82-41=41, Resulting Numbers: [71, 35, 41] Generated Node #0,3: 53:[71, 35, 41] Operation: 82-41=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[41, 71, 47], Operations: ['82-35=47'] Exploring Operation: 71-47=24, Resulting Numbers: [41, 24] Generated Node #0,0,0: 53:[41, 24] Operation: 71-47=24 Exploring Operation: 41+47=88, Resulting Numbers: [71, 88] Generated Node #0,0,1: 53:[71, 88] Operation: 41+47=88 Exploring Operation: 71-41=30, Resulting Numbers: [47, 30] Generated Node #0,0,2: 53:[47, 30] Operation: 71-41=30 Exploring Operation: 41+71=112, Resulting Numbers: [47, 112] Generated Node #0,0,3: 53:[47, 112] Operation: 41+71=112 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 53:[47, 30], Operations: ['82-35=47', '71-41=30'] Exploring Operation: 47+30=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 47*30=1410, Resulting Numbers: [1410] 1410,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 53:[41, 24], Operations: ['82-35=47', '71-47=24'] Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,53 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 53:[71, 88], Operations: ['82-35=47', '41+47=88'] Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 71+88=159, Resulting Numbers: [159] 159,53 unequal: No Solution Exploring Operation: 71*88=6248, Resulting Numbers: [6248] 6248,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 53:[47, 112], Operations: ['82-35=47', '41+71=112'] Exploring Operation: 112-47=65, Resulting Numbers: [65] 65,53 unequal: No Solution Exploring Operation: 47+112=159, Resulting Numbers: [159] 159,53 unequal: No Solution Exploring Operation: 47*112=5264, Resulting Numbers: [5264] 5264,53 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: 53:[71, 35, 41], Operations: ['82-41=41'] Exploring Operation: 71+35=106, Resulting Numbers: [41, 106] Generated Node #0,3,0: 53:[41, 106] Operation: 71+35=106 Exploring Operation: 71-35=36, Resulting Numbers: [41, 36] Generated Node #0,3,1: 53:[41, 36] Operation: 71-35=36 Exploring Operation: 71-41=30, Resulting Numbers: [35, 30] Generated Node #0,3,2: 53:[35, 30] Operation: 71-41=30 Exploring Operation: 35+41=76, Resulting Numbers: [71, 76] Generated Node #0,3,3: 53:[71, 76] Operation: 35+41=76 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[41, 36], Operations: ['82-41=41', '71-35=36'] Exploring Operation: 41+36=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 41*36=1476, Resulting Numbers: [1476] 1476,53 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[35, 30], Operations: ['82-41=41', '71-41=30'] Exploring Operation: 35-30=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 35+30=65, Resulting Numbers: [65] 65,53 unequal: No Solution Exploring Operation: 35*30=1050, Resulting Numbers: [1050] 1050,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[71, 76], Operations: ['82-41=41', '35+41=76'] Exploring Operation: 71+76=147, Resulting Numbers: [147] 147,53 unequal: No Solution Exploring Operation: 76-71=5, Resulting Numbers: [5] 5,53 unequal: No Solution Exploring Operation: 71*76=5396, Resulting Numbers: [5396] 5396,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[41, 106], Operations: ['82-41=41', '71+35=106'] Exploring Operation: 41+106=147, Resulting Numbers: [147] 147,53 unequal: No Solution Exploring Operation: 106-41=65, Resulting Numbers: [65] 65,53 unequal: No Solution Exploring Operation: 41*106=4346, Resulting Numbers: [4346] 4346,53 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: 53:[41, 82, 36], Operations: ['71-35=36'] Exploring Operation: 82-36=46, Resulting Numbers: [41, 46] Generated Node #0,2,0: 53:[41, 46] Operation: 82-36=46 Exploring Operation: 41+36=77, Resulting Numbers: [82, 77] Generated Node #0,2,1: 53:[82, 77] Operation: 41+36=77 Exploring Operation: 82/41=2, Resulting Numbers: [36, 2] Generated Node #0,2,2: 53:[36, 2] Operation: 82/41=2 Exploring Operation: 82-41=41, Resulting Numbers: [36, 41] Generated Node #0,2,3: 53:[36, 41] Operation: 82-41=41 Moving to Node #0,2,0 Current State: 53:[41, 46], Operations: ['71-35=36', '82-36=46'] Exploring Operation: 41+46=87, Resulting Numbers: [87] 87,53 unequal: No Solution Exploring Operation: 41*46=1886, Resulting Numbers: [1886] 1886,53 unequal: No Solution Exploring Operation: 46-41=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[36, 41], Operations: ['71-35=36', '82-41=41'] Exploring Operation: 36+41=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 36*41=1476, Resulting Numbers: [1476] 1476,53 unequal: No Solution Exploring Operation: 41-36=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[82, 77], Operations: ['71-35=36', '41+36=77'] Exploring Operation: 82*77=6314, Resulting Numbers: [6314] 6314,53 unequal: No Solution Exploring Operation: 82+77=159, Resulting Numbers: [159] 159,53 unequal: No Solution Exploring Operation: 82-77=5, Resulting Numbers: [5] 5,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[36, 2], Operations: ['71-35=36', '82/41=2'] Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,53 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,53 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[35, 82, 30], Operations: ['71-41=30'] Exploring Operation: 82-30=52, Resulting Numbers: [35, 52] Generated Node #0,1,0: 53:[35, 52] Operation: 82-30=52 Exploring Operation: 82-35=47, Resulting Numbers: [30, 47] Generated Node #0,1,1: 53:[30, 47] Operation: 82-35=47 Exploring Operation: 35-30=5, Resulting Numbers: [82, 5] Generated Node #0,1,2: 53:[82, 5] Operation: 35-30=5 Exploring Operation: 35+30=65, Resulting Numbers: [82, 65] Generated Node #0,1,3: 53:[82, 65] Operation: 35+30=65 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 53:[35, 52], Operations: ['71-41=30', '82-30=52'] Exploring Operation: 35*52=1820, Resulting Numbers: [1820] 1820,53 unequal: No Solution Exploring Operation: 52-35=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 35+52=87, Resulting Numbers: [87] 87,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 53:[30, 47], Operations: ['71-41=30', '82-35=47'] Exploring Operation: 30*47=1410, Resulting Numbers: [1410] 1410,53 unequal: No Solution Exploring Operation: 30+47=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 47-30=17, Resulting Numbers: [17] 17,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 53:[82, 65], Operations: ['71-41=30', '35+30=65'] Exploring Operation: 82*65=5330, Resulting Numbers: [5330] 5330,53 unequal: No Solution Exploring Operation: 82+65=147, Resulting Numbers: [147] 147,53 unequal: No Solution Exploring Operation: 82-65=17, Resulting Numbers: [17] 17,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 53:[82, 5], Operations: ['71-41=30', '35-30=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,53 unequal: No Solution Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,53 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 81, 38, 90, 95 ]
66
[ "81+38=119", "90+95=185", "185-119=66" ]
Current State: 66:[81, 38, 90, 95], Operations: [] Exploring Operation: 81+38=119, Resulting Numbers: [90, 95, 119] Generated Node #2: [90, 95, 119] from Operation: 81+38=119 Current State: 66:[90, 95, 119], Operations: ['81+38=119'] Exploring Operation: 90+95=185, Resulting Numbers: [119, 185] Generated Node #3: [119, 185] from Operation: 90+95=185 Current State: 66:[119, 185], Operations: ['81+38=119', '90+95=185'] Exploring Operation: 185-119=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[81, 38, 90, 95], Operations: [] Exploring Operation: 95-90=5, Resulting Numbers: [81, 38, 5] Generated Node #0,0: 66:[81, 38, 5] Operation: 95-90=5 Exploring Operation: 95-81=14, Resulting Numbers: [38, 90, 14] Generated Node #0,1: 66:[38, 90, 14] Operation: 95-81=14 Exploring Operation: 90-81=9, Resulting Numbers: [38, 95, 9] Generated Node #0,2: 66:[38, 95, 9] Operation: 90-81=9 Moving to Node #0,0 Current State: 66:[81, 38, 5], Operations: ['95-90=5'] Exploring Operation: 81-38=43, Resulting Numbers: [5, 43] Generated Node #0,0,0: 66:[5, 43] Operation: 81-38=43 Exploring Operation: 81-5=76, Resulting Numbers: [38, 76] Generated Node #0,0,1: 66:[38, 76] Operation: 81-5=76 Exploring Operation: 38-5=33, Resulting Numbers: [81, 33] Generated Node #0,0,2: 66:[81, 33] Operation: 38-5=33 Moving to Node #0,1 Current State: 66:[38, 90, 14], Operations: ['95-81=14'] Exploring Operation: 90-14=76, Resulting Numbers: [38, 76] Generated Node #0,1,0: 66:[38, 76] Operation: 90-14=76 Exploring Operation: 38-14=24, Resulting Numbers: [90, 24] Generated Node #0,1,1: 66:[90, 24] Operation: 38-14=24 Exploring Operation: 90-38=52, Resulting Numbers: [14, 52] Generated Node #0,1,2: 66:[14, 52] Operation: 90-38=52 Moving to Node #0,2 Current State: 66:[38, 95, 9], Operations: ['90-81=9'] Exploring Operation: 38-9=29, Resulting Numbers: [95, 29] Generated Node #0,2,0: 66:[95, 29] Operation: 38-9=29 Exploring Operation: 95-9=86, Resulting Numbers: [38, 86] Generated Node #0,2,1: 66:[38, 86] Operation: 95-9=86 Exploring Operation: 95-38=57, Resulting Numbers: [9, 57] Generated Node #0,2,2: 66:[9, 57] Operation: 95-38=57 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[9, 57], Operations: ['90-81=9', '95-38=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[81, 38, 90, 95], Operations: [] Exploring Operation: 90-81=9, Resulting Numbers: [38, 95, 9] Generated Node #0,2: 66:[38, 95, 9] Operation: 90-81=9 Moving to Node #0,2 Current State: 66:[38, 95, 9], Operations: ['90-81=9'] Exploring Operation: 95-38=57, Resulting Numbers: [9, 57] Generated Node #0,2,2: 66:[9, 57] Operation: 95-38=57 Moving to Node #0,2,2 Current State: 66:[9, 57], Operations: ['90-81=9', '95-38=57'] Exploring Operation: 9+57=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
sum_heuristic
[ 36, 16, 93, 12 ]
41
[ "16*93=1488", "1488-12=1476", "1476/36=41" ]
Current State: 41:[36, 16, 93, 12], Operations: [] Exploring Operation: 16*93=1488, Resulting Numbers: [36, 12, 1488] Generated Node #2: [36, 12, 1488] from Operation: 16*93=1488 Current State: 41:[36, 12, 1488], Operations: ['16*93=1488'] Exploring Operation: 1488-12=1476, Resulting Numbers: [36, 1476] Generated Node #3: [36, 1476] from Operation: 1488-12=1476 Current State: 41:[36, 1476], Operations: ['16*93=1488', '1488-12=1476'] Exploring Operation: 1476/36=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[36, 16, 93, 12], Operations: [] Exploring Operation: 93-36=57, Resulting Numbers: [16, 12, 57] Generated Node #0,0: 41:[16, 12, 57] Operation: 93-36=57 Moving to Node #0,0 Current State: 41:[16, 12, 57], Operations: ['93-36=57'] Exploring Operation: 16+12=28, Resulting Numbers: [57, 28] Generated Node #0,0,0: 41:[57, 28] Operation: 16+12=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 41:[57, 28], Operations: ['93-36=57', '16+12=28'] Exploring Operation: 57-28=29, Resulting Numbers: [29] 29,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 6, 72, 82, 83 ]
65
[ "72-6=66", "83-82=1", "66-1=65" ]
Current State: 65:[6, 72, 82, 83], Operations: [] Exploring Operation: 72-6=66, Resulting Numbers: [82, 83, 66] Generated Node #2: [82, 83, 66] from Operation: 72-6=66 Current State: 65:[82, 83, 66], Operations: ['72-6=66'] Exploring Operation: 83-82=1, Resulting Numbers: [66, 1] Generated Node #3: [66, 1] from Operation: 83-82=1 Current State: 65:[66, 1], Operations: ['72-6=66', '83-82=1'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[6, 72, 82, 83], Operations: [] Exploring Operation: 72-6=66, Resulting Numbers: [82, 83, 66] Generated Node #0,0: 65:[82, 83, 66] Operation: 72-6=66 Exploring Operation: 83-82=1, Resulting Numbers: [6, 72, 1] Generated Node #0,1: 65:[6, 72, 1] Operation: 83-82=1 Exploring Operation: 82-72=10, Resulting Numbers: [6, 83, 10] Generated Node #0,2: 65:[6, 83, 10] Operation: 82-72=10 Exploring Operation: 83-72=11, Resulting Numbers: [6, 82, 11] Generated Node #0,3: 65:[6, 82, 11] Operation: 83-72=11 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[6, 72, 1], Operations: ['83-82=1'] Exploring Operation: 72-6=66, Resulting Numbers: [1, 66] Generated Node #0,1,0: 65:[1, 66] Operation: 72-6=66 Exploring Operation: 6-1=5, Resulting Numbers: [72, 5] Generated Node #0,1,1: 65:[72, 5] Operation: 6-1=5 Exploring Operation: 72-1=71, Resulting Numbers: [6, 71] Generated Node #0,1,2: 65:[6, 71] Operation: 72-1=71 Exploring Operation: 72/6=12, Resulting Numbers: [1, 12] Generated Node #0,1,3: 65:[1, 12] Operation: 72/6=12 Moving to Node #0,1,0 Current State: 65:[1, 66], Operations: ['83-82=1', '72-6=66'] Exploring Operation: 66/1=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 1+66=67, Resulting Numbers: [67] 67,65 unequal: No Solution Exploring Operation: 1*66=66, Resulting Numbers: [66] 66,65 unequal: No Solution Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[6, 72, 82, 83], Operations: [] Exploring Operation: 83-82=1, Resulting Numbers: [6, 72, 1] Generated Node #0,1: 65:[6, 72, 1] Operation: 83-82=1 Moving to Node #0,1 Current State: 65:[6, 72, 1], Operations: ['83-82=1'] Exploring Operation: 72-6=66, Resulting Numbers: [1, 66] Generated Node #0,1,0: 65:[1, 66] Operation: 72-6=66 Moving to Node #0,1,0 Current State: 65:[1, 66], Operations: ['83-82=1', '72-6=66'] Exploring Operation: 66-1=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 58, 77, 78, 19 ]
76
[ "58+77=135", "78-19=59", "135-59=76" ]
Current State: 76:[58, 77, 78, 19], Operations: [] Exploring Operation: 58+77=135, Resulting Numbers: [78, 19, 135] Generated Node #2: [78, 19, 135] from Operation: 58+77=135 Current State: 76:[78, 19, 135], Operations: ['58+77=135'] Exploring Operation: 78-19=59, Resulting Numbers: [135, 59] Generated Node #3: [135, 59] from Operation: 78-19=59 Current State: 76:[135, 59], Operations: ['58+77=135', '78-19=59'] Exploring Operation: 135-59=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[58, 77, 78, 19], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [77, 19, 20] Generated Node #0,0: 76:[77, 19, 20] Operation: 78-58=20 Exploring Operation: 58+19=77, Resulting Numbers: [77, 78, 77] Generated Node #0,1: 76:[77, 78, 77] Operation: 58+19=77 Exploring Operation: 58-19=39, Resulting Numbers: [77, 78, 39] Generated Node #0,2: 76:[77, 78, 39] Operation: 58-19=39 Exploring Operation: 77-58=19, Resulting Numbers: [78, 19, 19] Generated Node #0,3: 76:[78, 19, 19] Operation: 77-58=19 Moving to Node #0,0 Current State: 76:[77, 19, 20], Operations: ['78-58=20'] Exploring Operation: 19+20=39, Resulting Numbers: [77, 39] Generated Node #0,0,0: 76:[77, 39] Operation: 19+20=39 Exploring Operation: 77-20=57, Resulting Numbers: [19, 57] Generated Node #0,0,1: 76:[19, 57] Operation: 77-20=57 Exploring Operation: 77-19=58, Resulting Numbers: [20, 58] Generated Node #0,0,2: 76:[20, 58] Operation: 77-19=58 Exploring Operation: 20-19=1, Resulting Numbers: [77, 1] Generated Node #0,0,3: 76:[77, 1] Operation: 20-19=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 76:[77, 39], Operations: ['78-58=20', '19+20=39'] Exploring Operation: 77-39=38, Resulting Numbers: [38] 38,76 unequal: No Solution Exploring Operation: 77+39=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 77*39=3003, Resulting Numbers: [3003] 3003,76 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 #0,0,3 Current State: 76:[77, 1], Operations: ['78-58=20', '20-19=1'] Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 77+1=78, Resulting Numbers: [78] 78,76 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[58, 77, 78, 19], Operations: [] Exploring Operation: 78-58=20, Resulting Numbers: [77, 19, 20] Generated Node #0,0: 76:[77, 19, 20] Operation: 78-58=20 Moving to Node #0,0 Current State: 76:[77, 19, 20], Operations: ['78-58=20'] Exploring Operation: 20-19=1, Resulting Numbers: [77, 1] Generated Node #0,0,3: 76:[77, 1] Operation: 20-19=1 Moving to Node #0,0,3 Current State: 76:[77, 1], Operations: ['78-58=20', '20-19=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 90, 86, 2, 4 ]
14
[ "90-86=4", "4*4=16", "16-2=14" ]
Current State: 14:[90, 86, 2, 4], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [2, 4, 4] Generated Node #2: [2, 4, 4] from Operation: 90-86=4 Current State: 14:[2, 4, 4], Operations: ['90-86=4'] Exploring Operation: 4*4=16, Resulting Numbers: [2, 16] Generated Node #3: [2, 16] from Operation: 4*4=16 Current State: 14:[2, 16], Operations: ['90-86=4', '4*4=16'] Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[90, 86, 2, 4], Operations: [] Exploring Operation: 86-4=82, Resulting Numbers: [90, 2, 82] Generated Node #0,0: 14:[90, 2, 82] Operation: 86-4=82 Exploring Operation: 90/2=45, Resulting Numbers: [86, 4, 45] Generated Node #0,1: 14:[86, 4, 45] Operation: 90/2=45 Exploring Operation: 90-4=86, Resulting Numbers: [86, 2, 86] Generated Node #0,2: 14:[86, 2, 86] Operation: 90-4=86 Exploring Operation: 86/2=43, Resulting Numbers: [90, 4, 43] Generated Node #0,3: 14:[90, 4, 43] Operation: 86/2=43 Exploring Operation: 90-86=4, Resulting Numbers: [2, 4, 4] Generated Node #0,4: 14:[2, 4, 4] Operation: 90-86=4 Moving to Node #0,4 Current State: 14:[2, 4, 4], Operations: ['90-86=4'] Exploring Operation: 4/4=1, Resulting Numbers: [2, 1] Generated Node #0,4,0: 14:[2, 1] Operation: 4/4=1 Exploring Operation: 4+4=8, Resulting Numbers: [2, 8] Generated Node #0,4,1: 14:[2, 8] Operation: 4+4=8 Exploring Operation: 4-2=2, Resulting Numbers: [4, 2] Generated Node #0,4,2: 14:[4, 2] Operation: 4-2=2 Exploring Operation: 4-2=2, Resulting Numbers: [4, 2] Generated Node #0,4,3: 14:[4, 2] Operation: 4-2=2 Exploring Operation: 4/2=2, Resulting Numbers: [4, 2] Generated Node #0,4,4: 14:[4, 2] Operation: 4/2=2 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 14:[2, 1], Operations: ['90-86=4', '4/4=1'] Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,14 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 14:[2, 8], Operations: ['90-86=4', '4+4=8'] Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,14 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 14:[4, 2], Operations: ['90-86=4', '4-2=2'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 14:[4, 2], Operations: ['90-86=4', '4-2=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 14:[4, 2], Operations: ['90-86=4', '4/2=2'] Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,14 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 14:[86, 4, 45], Operations: ['90/2=45'] Exploring Operation: 86+4=90, Resulting Numbers: [45, 90] Generated Node #0,1,0: 14:[45, 90] Operation: 86+4=90 Exploring Operation: 45-4=41, Resulting Numbers: [86, 41] Generated Node #0,1,1: 14:[86, 41] Operation: 45-4=41 Exploring Operation: 4+45=49, Resulting Numbers: [86, 49] Generated Node #0,1,2: 14:[86, 49] Operation: 4+45=49 Exploring Operation: 86-4=82, Resulting Numbers: [45, 82] Generated Node #0,1,3: 14:[45, 82] Operation: 86-4=82 Exploring Operation: 86-45=41, Resulting Numbers: [4, 41] Generated Node #0,1,4: 14:[4, 41] Operation: 86-45=41 Moving to Node #0,3 Current State: 14:[90, 4, 43], Operations: ['86/2=43'] Exploring Operation: 4+43=47, Resulting Numbers: [90, 47] Generated Node #0,3,0: 14:[90, 47] Operation: 4+43=47 Exploring Operation: 43-4=39, Resulting Numbers: [90, 39] Generated Node #0,3,1: 14:[90, 39] Operation: 43-4=39 Exploring Operation: 90-4=86, Resulting Numbers: [43, 86] Generated Node #0,3,2: 14:[43, 86] Operation: 90-4=86 Exploring Operation: 90-43=47, Resulting Numbers: [4, 47] Generated Node #0,3,3: 14:[4, 47] Operation: 90-43=47 Exploring Operation: 90+4=94, Resulting Numbers: [43, 94] Generated Node #0,3,4: 14:[43, 94] Operation: 90+4=94 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 14:[4, 47], Operations: ['86/2=43', '90-43=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,14 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 14:[90, 39], Operations: ['86/2=43', '43-4=39'] Exploring Operation: 90+39=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 90*39=3510, Resulting Numbers: [3510] 3510,14 unequal: No Solution Exploring Operation: 90-39=51, Resulting Numbers: [51] 51,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 14:[43, 86], Operations: ['86/2=43', '90-4=86'] Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 43+86=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 43*86=3698, Resulting Numbers: [3698] 3698,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 14:[90, 47], Operations: ['86/2=43', '4+43=47'] Exploring Operation: 90*47=4230, Resulting Numbers: [4230] 4230,14 unequal: No Solution Exploring Operation: 90-47=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 90+47=137, Resulting Numbers: [137] 137,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 14:[43, 94], Operations: ['86/2=43', '90+4=94'] Exploring Operation: 43*94=4042, Resulting Numbers: [4042] 4042,14 unequal: No Solution Exploring Operation: 43+94=137, Resulting Numbers: [137] 137,14 unequal: No Solution Exploring Operation: 94-43=51, Resulting Numbers: [51] 51,14 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: 14:[90, 2, 82], Operations: ['86-4=82'] Exploring Operation: 90-82=8, Resulting Numbers: [2, 8] Generated Node #0,0,0: 14:[2, 8] Operation: 90-82=8 Exploring Operation: 90/2=45, Resulting Numbers: [82, 45] Generated Node #0,0,1: 14:[82, 45] Operation: 90/2=45 Exploring Operation: 90-2=88, Resulting Numbers: [82, 88] Generated Node #0,0,2: 14:[82, 88] Operation: 90-2=88 Exploring Operation: 82/2=41, Resulting Numbers: [90, 41] Generated Node #0,0,3: 14:[90, 41] Operation: 82/2=41 Exploring Operation: 82-2=80, Resulting Numbers: [90, 80] Generated Node #0,0,4: 14:[90, 80] Operation: 82-2=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[2, 8], Operations: ['86-4=82', '90-82=8'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,14 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,14 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[82, 45], Operations: ['86-4=82', '90/2=45'] Exploring Operation: 82+45=127, Resulting Numbers: [127] 127,14 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 82*45=3690, Resulting Numbers: [3690] 3690,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 14:[90, 41], Operations: ['86-4=82', '82/2=41'] Exploring Operation: 90+41=131, Resulting Numbers: [131] 131,14 unequal: No Solution Exploring Operation: 90*41=3690, Resulting Numbers: [3690] 3690,14 unequal: No Solution Exploring Operation: 90-41=49, Resulting Numbers: [49] 49,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 14:[82, 88], Operations: ['86-4=82', '90-2=88'] Exploring Operation: 82*88=7216, Resulting Numbers: [7216] 7216,14 unequal: No Solution Exploring Operation: 88-82=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 82+88=170, Resulting Numbers: [170] 170,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 14:[90, 80], Operations: ['86-4=82', '82-2=80'] Exploring Operation: 90*80=7200, Resulting Numbers: [7200] 7200,14 unequal: No Solution Exploring Operation: 90+80=170, Resulting Numbers: [170] 170,14 unequal: No Solution Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 14:[86, 2, 86], Operations: ['90-4=86'] Exploring Operation: 86/2=43, Resulting Numbers: [86, 43] Generated Node #0,2,0: 14:[86, 43] Operation: 86/2=43 Exploring Operation: 86-2=84, Resulting Numbers: [86, 84] Generated Node #0,2,1: 14:[86, 84] Operation: 86-2=84 Exploring Operation: 86/2=43, Resulting Numbers: [86, 43] Generated Node #0,2,2: 14:[86, 43] Operation: 86/2=43 Exploring Operation: 86-86=0, Resulting Numbers: [2, 0] Generated Node #0,2,3: 14:[2, 0] Operation: 86-86=0 Exploring Operation: 86/86=1, Resulting Numbers: [2, 1] Generated Node #0,2,4: 14:[2, 1] Operation: 86/86=1 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 14:[2, 1], Operations: ['90-4=86', '86/86=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,14 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 14:[2, 0], Operations: ['90-4=86', '86-86=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[86, 43], Operations: ['90-4=86', '86/2=43'] Exploring Operation: 86*43=3698, Resulting Numbers: [3698] 3698,14 unequal: No Solution Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 86+43=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 14:[86, 43], Operations: ['90-4=86', '86/2=43'] Exploring Operation: 86-43=43, Resulting Numbers: [43] 43,14 unequal: No Solution Exploring Operation: 86+43=129, Resulting Numbers: [129] 129,14 unequal: No Solution Exploring Operation: 86*43=3698, Resulting Numbers: [3698] 3698,14 unequal: No Solution Exploring Operation: 86/43=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 14:[86, 84], Operations: ['90-4=86', '86-2=84'] Exploring Operation: 86*84=7224, Resulting Numbers: [7224] 7224,14 unequal: No Solution Exploring Operation: 86+84=170, Resulting Numbers: [170] 170,14 unequal: No Solution Exploring Operation: 86-84=2, Resulting Numbers: [2] 2,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,4 Current State: 14:[4, 41], Operations: ['90/2=45', '86-45=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,14 unequal: No Solution Moving to Node #0,1,3 Current State: 14:[45, 82], Operations: ['90/2=45', '86-4=82'] Exploring Operation: 45+82=127, Resulting Numbers: [127] 127,14 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 45*82=3690, Resulting Numbers: [3690] 3690,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[86, 41], Operations: ['90/2=45', '45-4=41'] Exploring Operation: 86+41=127, Resulting Numbers: [127] 127,14 unequal: No Solution Exploring Operation: 86-41=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 86*41=3526, Resulting Numbers: [3526] 3526,14 unequal: No Solution Moving to Node #0,1,0 Current State: 14:[45, 90], Operations: ['90/2=45', '86+4=90'] Exploring Operation: 45+90=135, Resulting Numbers: [135] 135,14 unequal: No Solution Exploring Operation: 90-45=45, Resulting Numbers: [45] 45,14 unequal: No Solution Exploring Operation: 45*90=4050, Resulting Numbers: [4050] 4050,14 unequal: No Solution Exploring Operation: 90/45=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[86, 49], Operations: ['90/2=45', '4+45=49'] Exploring Operation: 86*49=4214, Resulting Numbers: [4214] 4214,14 unequal: No Solution Exploring Operation: 86+49=135, Resulting Numbers: [135] 135,14 unequal: No Solution Exploring Operation: 86-49=37, Resulting Numbers: [37] 37,14 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 61, 20, 32, 14 ]
99
[ "61+20=81", "32-14=18", "81+18=99" ]
Current State: 99:[61, 20, 32, 14], Operations: [] Exploring Operation: 61+20=81, Resulting Numbers: [32, 14, 81] Generated Node #2: [32, 14, 81] from Operation: 61+20=81 Current State: 99:[32, 14, 81], Operations: ['61+20=81'] Exploring Operation: 32-14=18, Resulting Numbers: [81, 18] Generated Node #3: [81, 18] from Operation: 32-14=18 Current State: 99:[81, 18], Operations: ['61+20=81', '32-14=18'] Exploring Operation: 81+18=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[61, 20, 32, 14], Operations: [] Exploring Operation: 61+20=81, Resulting Numbers: [32, 14, 81] Generated Node #0,0: 99:[32, 14, 81] Operation: 61+20=81 Exploring Operation: 61-32=29, Resulting Numbers: [20, 14, 29] Generated Node #0,1: 99:[20, 14, 29] Operation: 61-32=29 Exploring Operation: 61+32=93, Resulting Numbers: [20, 14, 93] Generated Node #0,2: 99:[20, 14, 93] Operation: 61+32=93 Exploring Operation: 61-20=41, Resulting Numbers: [32, 14, 41] Generated Node #0,3: 99:[32, 14, 41] Operation: 61-20=41 Moving to Node #0,3 Current State: 99:[32, 14, 41], Operations: ['61-20=41'] Exploring Operation: 32+14=46, Resulting Numbers: [41, 46] Generated Node #0,3,0: 99:[41, 46] Operation: 32+14=46 Exploring Operation: 41-32=9, Resulting Numbers: [14, 9] Generated Node #0,3,1: 99:[14, 9] Operation: 41-32=9 Exploring Operation: 41-14=27, Resulting Numbers: [32, 27] Generated Node #0,3,2: 99:[32, 27] Operation: 41-14=27 Exploring Operation: 32-14=18, Resulting Numbers: [41, 18] Generated Node #0,3,3: 99:[41, 18] Operation: 32-14=18 Moving to Node #0,1 Current State: 99:[20, 14, 29], Operations: ['61-32=29'] Exploring Operation: 20+14=34, Resulting Numbers: [29, 34] Generated Node #0,1,0: 99:[29, 34] Operation: 20+14=34 Exploring Operation: 29-20=9, Resulting Numbers: [14, 9] Generated Node #0,1,1: 99:[14, 9] Operation: 29-20=9 Exploring Operation: 29-14=15, Resulting Numbers: [20, 15] Generated Node #0,1,2: 99:[20, 15] Operation: 29-14=15 Exploring Operation: 20-14=6, Resulting Numbers: [29, 6] Generated Node #0,1,3: 99:[29, 6] Operation: 20-14=6 Moving to Node #0,2 Current State: 99:[20, 14, 93], Operations: ['61+32=93'] Exploring Operation: 14+93=107, Resulting Numbers: [20, 107] Generated Node #0,2,0: 99:[20, 107] Operation: 14+93=107 Exploring Operation: 20+14=34, Resulting Numbers: [93, 34] Generated Node #0,2,1: 99:[93, 34] Operation: 20+14=34 Exploring Operation: 20-14=6, Resulting Numbers: [93, 6] Generated Node #0,2,2: 99:[93, 6] Operation: 20-14=6 Exploring Operation: 20+93=113, Resulting Numbers: [14, 113] Generated Node #0,2,3: 99:[14, 113] Operation: 20+93=113 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 99:[93, 34], Operations: ['61+32=93', '20+14=34'] Exploring Operation: 93*34=3162, Resulting Numbers: [3162] 3162,99 unequal: No Solution Exploring Operation: 93-34=59, Resulting Numbers: [59] 59,99 unequal: No Solution Exploring Operation: 93+34=127, Resulting Numbers: [127] 127,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 99:[93, 6], Operations: ['61+32=93', '20-14=6'] Exploring Operation: 93-6=87, Resulting Numbers: [87] 87,99 unequal: No Solution Exploring Operation: 93*6=558, Resulting Numbers: [558] 558,99 unequal: No Solution Exploring Operation: 93+6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[61, 20, 32, 14], Operations: [] Exploring Operation: 61+32=93, Resulting Numbers: [20, 14, 93] Generated Node #0,2: 99:[20, 14, 93] Operation: 61+32=93 Moving to Node #0,2 Current State: 99:[20, 14, 93], Operations: ['61+32=93'] Exploring Operation: 20-14=6, Resulting Numbers: [93, 6] Generated Node #0,2,2: 99:[93, 6] Operation: 20-14=6 Moving to Node #0,2,2 Current State: 99:[93, 6], Operations: ['61+32=93', '20-14=6'] Exploring Operation: 93+6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_4
sum_heuristic
[ 80, 79, 10, 7 ]
77
[ "80-79=1", "10+1=11", "7*11=77" ]
Current State: 77:[80, 79, 10, 7], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [10, 7, 1] Generated Node #2: [10, 7, 1] from Operation: 80-79=1 Current State: 77:[10, 7, 1], Operations: ['80-79=1'] Exploring Operation: 10+1=11, Resulting Numbers: [7, 11] Generated Node #3: [7, 11] from Operation: 10+1=11 Current State: 77:[7, 11], Operations: ['80-79=1', '10+1=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[80, 79, 10, 7], Operations: [] Exploring Operation: 80-7=73, Resulting Numbers: [79, 10, 73] Generated Node #0,0: 77:[79, 10, 73] Operation: 80-7=73 Exploring Operation: 80-79=1, Resulting Numbers: [10, 7, 1] Generated Node #0,1: 77:[10, 7, 1] Operation: 80-79=1 Exploring Operation: 80/10=8, Resulting Numbers: [79, 7, 8] Generated Node #0,2: 77:[79, 7, 8] Operation: 80/10=8 Moving to Node #0,2 Current State: 77:[79, 7, 8], Operations: ['80/10=8'] Exploring Operation: 79-7=72, Resulting Numbers: [8, 72] Generated Node #0,2,0: 77:[8, 72] Operation: 79-7=72 Exploring Operation: 79-8=71, Resulting Numbers: [7, 71] Generated Node #0,2,1: 77:[7, 71] Operation: 79-8=71 Exploring Operation: 7+8=15, Resulting Numbers: [79, 15] Generated Node #0,2,2: 77:[79, 15] Operation: 7+8=15 Moving to Node #0,0 Current State: 77:[79, 10, 73], Operations: ['80-7=73'] Exploring Operation: 79-10=69, Resulting Numbers: [73, 69] Generated Node #0,0,0: 77:[73, 69] Operation: 79-10=69 Exploring Operation: 10+73=83, Resulting Numbers: [79, 83] Generated Node #0,0,1: 77:[79, 83] Operation: 10+73=83 Exploring Operation: 79-73=6, Resulting Numbers: [10, 6] Generated Node #0,0,2: 77:[10, 6] Operation: 79-73=6 Moving to Node #0,1 Current State: 77:[10, 7, 1], Operations: ['80-79=1'] Exploring Operation: 10*1=10, Resulting Numbers: [7, 10] Generated Node #0,1,0: 77:[7, 10] Operation: 10*1=10 Exploring Operation: 10+1=11, Resulting Numbers: [7, 11] Generated Node #0,1,1: 77:[7, 11] Operation: 10+1=11 Exploring Operation: 10/1=10, Resulting Numbers: [7, 10] Generated Node #0,1,2: 77:[7, 10] Operation: 10/1=10 Moving to Node #0,1,1 Current State: 77:[7, 11], Operations: ['80-79=1', '10+1=11'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,77 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,77 unequal: No Solution Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[80, 79, 10, 7], Operations: [] Exploring Operation: 80-79=1, Resulting Numbers: [10, 7, 1] Generated Node #0,1: 77:[10, 7, 1] Operation: 80-79=1 Moving to Node #0,1 Current State: 77:[10, 7, 1], Operations: ['80-79=1'] Exploring Operation: 10+1=11, Resulting Numbers: [7, 11] Generated Node #0,1,1: 77:[7, 11] Operation: 10+1=11 Moving to Node #0,1,1 Current State: 77:[7, 11], Operations: ['80-79=1', '10+1=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
0.983507
hs_3
sum_heuristic
[ 19, 4, 18, 11 ]
17
[ "4+18=22", "22/11=2", "19-2=17" ]
Current State: 17:[19, 4, 18, 11], Operations: [] Exploring Operation: 4+18=22, Resulting Numbers: [19, 11, 22] Generated Node #2: [19, 11, 22] from Operation: 4+18=22 Current State: 17:[19, 11, 22], Operations: ['4+18=22'] Exploring Operation: 22/11=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 22/11=2 Current State: 17:[19, 2], Operations: ['4+18=22', '22/11=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[19, 4, 18, 11], Operations: [] Exploring Operation: 19-4=15, Resulting Numbers: [18, 11, 15] Generated Node #0,0: 17:[18, 11, 15] Operation: 19-4=15 Exploring Operation: 4+11=15, Resulting Numbers: [19, 18, 15] Generated Node #0,1: 17:[19, 18, 15] Operation: 4+11=15 Exploring Operation: 19+4=23, Resulting Numbers: [18, 11, 23] Generated Node #0,2: 17:[18, 11, 23] Operation: 19+4=23 Exploring Operation: 18-4=14, Resulting Numbers: [19, 11, 14] Generated Node #0,3: 17:[19, 11, 14] Operation: 18-4=14 Moving to Node #0,1 Current State: 17:[19, 18, 15], Operations: ['4+11=15'] Exploring Operation: 19-15=4, Resulting Numbers: [18, 4] Generated Node #0,1,0: 17:[18, 4] Operation: 19-15=4 Exploring Operation: 18-15=3, Resulting Numbers: [19, 3] Generated Node #0,1,1: 17:[19, 3] Operation: 18-15=3 Exploring Operation: 19-18=1, Resulting Numbers: [15, 1] Generated Node #0,1,2: 17:[15, 1] Operation: 19-18=1 Exploring Operation: 19+15=34, Resulting Numbers: [18, 34] Generated Node #0,1,3: 17:[18, 34] Operation: 19+15=34 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 17:[18, 4], Operations: ['4+11=15', '19-15=4'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 17:[19, 3], Operations: ['4+11=15', '18-15=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,17 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 17:[15, 1], Operations: ['4+11=15', '19-18=1'] Exploring Operation: 15*1=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 15+1=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 15/1=15, Resulting Numbers: [15] 15,17 unequal: No Solution Exploring Operation: 15-1=14, Resulting Numbers: [14] 14,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 17:[18, 34], Operations: ['4+11=15', '19+15=34'] Exploring Operation: 18*34=612, Resulting Numbers: [612] 612,17 unequal: No Solution Exploring Operation: 34-18=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 18+34=52, Resulting Numbers: [52] 52,17 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: 17:[18, 11, 15], Operations: ['19-4=15'] Exploring Operation: 18-11=7, Resulting Numbers: [15, 7] Generated Node #0,0,0: 17:[15, 7] Operation: 18-11=7 Exploring Operation: 15-11=4, Resulting Numbers: [18, 4] Generated Node #0,0,1: 17:[18, 4] Operation: 15-11=4 Exploring Operation: 18+11=29, Resulting Numbers: [15, 29] Generated Node #0,0,2: 17:[15, 29] Operation: 18+11=29 Exploring Operation: 11+15=26, Resulting Numbers: [18, 26] Generated Node #0,0,3: 17:[18, 26] Operation: 11+15=26 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 17:[18, 26], Operations: ['19-4=15', '11+15=26'] Exploring Operation: 26-18=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 18+26=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 18*26=468, Resulting Numbers: [468] 468,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 17:[15, 7], Operations: ['19-4=15', '18-11=7'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,17 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 17:[18, 4], Operations: ['19-4=15', '15-11=4'] Exploring Operation: 18+4=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 18*4=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 17:[15, 29], Operations: ['19-4=15', '18+11=29'] Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,17 unequal: No Solution Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,17 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:[19, 11, 14], Operations: ['18-4=14'] Exploring Operation: 14-11=3, Resulting Numbers: [19, 3] Generated Node #0,3,0: 17:[19, 3] Operation: 14-11=3 Exploring Operation: 19-11=8, Resulting Numbers: [14, 8] Generated Node #0,3,1: 17:[14, 8] Operation: 19-11=8 Exploring Operation: 19+11=30, Resulting Numbers: [14, 30] Generated Node #0,3,2: 17:[14, 30] Operation: 19+11=30 Exploring Operation: 11+14=25, Resulting Numbers: [19, 25] Generated Node #0,3,3: 17:[19, 25] Operation: 11+14=25 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 17:[19, 25], Operations: ['18-4=14', '11+14=25'] Exploring Operation: 19*25=475, Resulting Numbers: [475] 475,17 unequal: No Solution Exploring Operation: 19+25=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 25-19=6, Resulting Numbers: [6] 6,17 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 #0,3,1 Current State: 17:[14, 8], Operations: ['18-4=14', '19-11=8'] Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,17 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:[19, 3], Operations: ['18-4=14', '14-11=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,17 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,17 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:[14, 30], Operations: ['18-4=14', '19+11=30'] Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,17 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,17 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: 17:[18, 11, 23], Operations: ['19+4=23'] Exploring Operation: 18+11=29, Resulting Numbers: [23, 29] Generated Node #0,2,0: 17:[23, 29] Operation: 18+11=29 Exploring Operation: 23-18=5, Resulting Numbers: [11, 5] Generated Node #0,2,1: 17:[11, 5] Operation: 23-18=5 Exploring Operation: 18-11=7, Resulting Numbers: [23, 7] Generated Node #0,2,2: 17:[23, 7] Operation: 18-11=7 Exploring Operation: 23-11=12, Resulting Numbers: [18, 12] Generated Node #0,2,3: 17:[18, 12] Operation: 23-11=12 Moving to Node #0,2,3 Current State: 17:[18, 12], Operations: ['19+4=23', '23-11=12'] Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,17 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[23, 7], Operations: ['19+4=23', '18-11=7'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,17 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[11, 5], Operations: ['19+4=23', '23-18=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,17 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,17 unequal: No Solution Moving to Node #0,2,0 Current State: 17:[23, 29], Operations: ['19+4=23', '18+11=29'] Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,17 unequal: No Solution Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,17 unequal: No Solution Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,17 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 34, 27, 16, 44 ]
18
[ "44-27=17", "34/17=2", "16+2=18" ]
Current State: 18:[34, 27, 16, 44], Operations: [] Exploring Operation: 44-27=17, Resulting Numbers: [34, 16, 17] Generated Node #2: [34, 16, 17] from Operation: 44-27=17 Current State: 18:[34, 16, 17], Operations: ['44-27=17'] Exploring Operation: 34/17=2, Resulting Numbers: [16, 2] Generated Node #3: [16, 2] from Operation: 34/17=2 Current State: 18:[16, 2], Operations: ['44-27=17', '34/17=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[34, 27, 16, 44], Operations: [] Exploring Operation: 34-27=7, Resulting Numbers: [16, 44, 7] Generated Node #0,0: 18:[16, 44, 7] Operation: 34-27=7 Exploring Operation: 44-34=10, Resulting Numbers: [27, 16, 10] Generated Node #0,1: 18:[27, 16, 10] Operation: 44-34=10 Exploring Operation: 44-27=17, Resulting Numbers: [34, 16, 17] Generated Node #0,2: 18:[34, 16, 17] Operation: 44-27=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[27, 16, 10], Operations: ['44-34=10'] Exploring Operation: 27-16=11, Resulting Numbers: [10, 11] Generated Node #0,1,0: 18:[10, 11] Operation: 27-16=11 Exploring Operation: 27-10=17, Resulting Numbers: [16, 17] Generated Node #0,1,1: 18:[16, 17] Operation: 27-10=17 Exploring Operation: 16-10=6, Resulting Numbers: [27, 6] Generated Node #0,1,2: 18:[27, 6] Operation: 16-10=6 Moving to Node #0,1,0 Current State: 18:[10, 11], Operations: ['44-34=10', '27-16=11'] Exploring Operation: 10*11=110, Resulting Numbers: [110] 110,18 unequal: No Solution Exploring Operation: 10+11=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 11-10=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[16, 17], Operations: ['44-34=10', '27-10=17'] Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,18 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[27, 6], Operations: ['44-34=10', '16-10=6'] Exploring Operation: 27*6=162, Resulting Numbers: [162] 162,18 unequal: No Solution Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[34, 16, 17], Operations: ['44-27=17'] Exploring Operation: 34-16=18, Resulting Numbers: [17, 18] Generated Node #0,2,0: 18:[17, 18] Operation: 34-16=18 Exploring Operation: 34-17=17, Resulting Numbers: [16, 17] Generated Node #0,2,1: 18:[16, 17] Operation: 34-17=17 Exploring Operation: 34/17=2, Resulting Numbers: [16, 2] Generated Node #0,2,2: 18:[16, 2] Operation: 34/17=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 18:[17, 18], Operations: ['44-27=17', '34-16=18'] Exploring Operation: 17*18=306, Resulting Numbers: [306] 306,18 unequal: No Solution Exploring Operation: 18-17=1, Resulting Numbers: [1] 1,18 unequal: No Solution Exploring Operation: 17+18=35, Resulting Numbers: [35] 35,18 unequal: No Solution No 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: 18:[16, 2], Operations: ['44-27=17', '34/17=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[34, 27, 16, 44], Operations: [] Exploring Operation: 44-27=17, Resulting Numbers: [34, 16, 17] Generated Node #0,2: 18:[34, 16, 17] Operation: 44-27=17 Moving to Node #0,2 Current State: 18:[34, 16, 17], Operations: ['44-27=17'] Exploring Operation: 34/17=2, Resulting Numbers: [16, 2] Generated Node #0,2,2: 18:[16, 2] Operation: 34/17=2 Moving to Node #0,2,2 Current State: 18:[16, 2], Operations: ['44-27=17', '34/17=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 42, 43, 55, 50 ]
90
[ "42+43=85", "55-50=5", "85+5=90" ]
Current State: 90:[42, 43, 55, 50], Operations: [] Exploring Operation: 42+43=85, Resulting Numbers: [55, 50, 85] Generated Node #2: [55, 50, 85] from Operation: 42+43=85 Current State: 90:[55, 50, 85], Operations: ['42+43=85'] Exploring Operation: 55-50=5, Resulting Numbers: [85, 5] Generated Node #3: [85, 5] from Operation: 55-50=5 Current State: 90:[85, 5], Operations: ['42+43=85', '55-50=5'] Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[42, 43, 55, 50], Operations: [] Exploring Operation: 50-42=8, Resulting Numbers: [43, 55, 8] Generated Node #0,0: 90:[43, 55, 8] Operation: 50-42=8 Exploring Operation: 42+55=97, Resulting Numbers: [43, 50, 97] Generated Node #0,1: 90:[43, 50, 97] Operation: 42+55=97 Exploring Operation: 55-43=12, Resulting Numbers: [42, 50, 12] Generated Node #0,2: 90:[42, 50, 12] Operation: 55-43=12 Exploring Operation: 55-42=13, Resulting Numbers: [43, 50, 13] Generated Node #0,3: 90:[43, 50, 13] Operation: 55-42=13 Exploring Operation: 55-50=5, Resulting Numbers: [42, 43, 5] Generated Node #0,4: 90:[42, 43, 5] Operation: 55-50=5 Moving to Node #0,4 Current State: 90:[42, 43, 5], Operations: ['55-50=5'] Exploring Operation: 42-5=37, Resulting Numbers: [43, 37] Generated Node #0,4,0: 90:[43, 37] Operation: 42-5=37 Exploring Operation: 43-42=1, Resulting Numbers: [5, 1] Generated Node #0,4,1: 90:[5, 1] Operation: 43-42=1 Exploring Operation: 42+43=85, Resulting Numbers: [5, 85] Generated Node #0,4,2: 90:[5, 85] Operation: 42+43=85 Exploring Operation: 42+5=47, Resulting Numbers: [43, 47] Generated Node #0,4,3: 90:[43, 47] Operation: 42+5=47 Exploring Operation: 43+5=48, Resulting Numbers: [42, 48] Generated Node #0,4,4: 90:[42, 48] Operation: 43+5=48 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 90:[5, 1], Operations: ['55-50=5', '43-42=1'] Exploring Operation: 5+1=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,90 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 5*1=5, Resulting Numbers: [5] 5,90 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 #0,4,3 Current State: 90:[43, 47], Operations: ['55-50=5', '42+5=47'] Exploring Operation: 43+47=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[42, 43, 55, 50], Operations: [] Exploring Operation: 55-50=5, Resulting Numbers: [42, 43, 5] Generated Node #0,4: 90:[42, 43, 5] Operation: 55-50=5 Moving to Node #0,4 Current State: 90:[42, 43, 5], Operations: ['55-50=5'] Exploring Operation: 42+5=47, Resulting Numbers: [43, 47] Generated Node #0,4,3: 90:[43, 47] Operation: 42+5=47 Moving to Node #0,4,3 Current State: 90:[43, 47], Operations: ['55-50=5', '42+5=47'] Exploring Operation: 43+47=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
mult_heuristic
[ 96, 62, 6, 26 ]
65
[ "6+26=32", "96/32=3", "62+3=65" ]
Current State: 65:[96, 62, 6, 26], Operations: [] Exploring Operation: 6+26=32, Resulting Numbers: [96, 62, 32] Generated Node #2: [96, 62, 32] from Operation: 6+26=32 Current State: 65:[96, 62, 32], Operations: ['6+26=32'] Exploring Operation: 96/32=3, Resulting Numbers: [62, 3] Generated Node #3: [62, 3] from Operation: 96/32=3 Current State: 65:[62, 3], Operations: ['6+26=32', '96/32=3'] Exploring Operation: 62+3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[96, 62, 6, 26], Operations: [] Exploring Operation: 96-26=70, Resulting Numbers: [62, 6, 70] Generated Node #0,0: 65:[62, 6, 70] Operation: 96-26=70 Exploring Operation: 96/6=16, Resulting Numbers: [62, 26, 16] Generated Node #0,1: 65:[62, 26, 16] Operation: 96/6=16 Moving to Node #0,0 Current State: 65:[62, 6, 70], Operations: ['96-26=70'] Exploring Operation: 70-6=64, Resulting Numbers: [62, 64] Generated Node #0,0,0: 65:[62, 64] Operation: 70-6=64 Exploring Operation: 70-62=8, Resulting Numbers: [6, 8] Generated Node #0,0,1: 65:[6, 8] Operation: 70-62=8 Moving to Node #0,1 Current State: 65:[62, 26, 16], Operations: ['96/6=16'] Exploring Operation: 26-16=10, Resulting Numbers: [62, 10] Generated Node #0,1,0: 65:[62, 10] Operation: 26-16=10 Exploring Operation: 62+26=88, Resulting Numbers: [16, 88] Generated Node #0,1,1: 65:[16, 88] Operation: 62+26=88 Moving to Node #0,0,0 Current State: 65:[62, 64], Operations: ['96-26=70', '70-6=64'] Exploring Operation: 64-62=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 62+64=126, Resulting Numbers: [126] 126,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[6, 8], Operations: ['96-26=70', '70-62=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,65 unequal: No Solution Moving to Node #0,1,0 Current State: 65:[62, 10], Operations: ['96/6=16', '26-16=10'] Exploring Operation: 62-10=52, Resulting Numbers: [52] 52,65 unequal: No Solution Exploring Operation: 62+10=72, Resulting Numbers: [72] 72,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[16, 88], Operations: ['96/6=16', '62+26=88'] Exploring Operation: 16+88=104, Resulting Numbers: [104] 104,65 unequal: No Solution Exploring Operation: 88-16=72, Resulting Numbers: [72] 72,65 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 79, 48, 10, 10 ]
51
[ "79-48=31", "10+10=20", "31+20=51" ]
Current State: 51:[79, 48, 10, 10], Operations: [] Exploring Operation: 79-48=31, Resulting Numbers: [10, 10, 31] Generated Node #2: [10, 10, 31] from Operation: 79-48=31 Current State: 51:[10, 10, 31], Operations: ['79-48=31'] Exploring Operation: 10+10=20, Resulting Numbers: [31, 20] Generated Node #3: [31, 20] from Operation: 10+10=20 Current State: 51:[31, 20], Operations: ['79-48=31', '10+10=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[79, 48, 10, 10], Operations: [] Exploring Operation: 79-10=69, Resulting Numbers: [48, 10, 69] Generated Node #0,0: 51:[48, 10, 69] Operation: 79-10=69 Exploring Operation: 10/10=1, Resulting Numbers: [79, 48, 1] Generated Node #0,1: 51:[79, 48, 1] Operation: 10/10=1 Exploring Operation: 79-10=69, Resulting Numbers: [48, 10, 69] Generated Node #0,2: 51:[48, 10, 69] Operation: 79-10=69 Exploring Operation: 79-48=31, Resulting Numbers: [10, 10, 31] Generated Node #0,3: 51:[10, 10, 31] Operation: 79-48=31 Moving to Node #0,0 Current State: 51:[48, 10, 69], Operations: ['79-10=69'] Exploring Operation: 48+10=58, Resulting Numbers: [69, 58] Generated Node #0,0,0: 51:[69, 58] Operation: 48+10=58 Exploring Operation: 69-10=59, Resulting Numbers: [48, 59] Generated Node #0,0,1: 51:[48, 59] Operation: 69-10=59 Exploring Operation: 69-48=21, Resulting Numbers: [10, 21] Generated Node #0,0,2: 51:[10, 21] Operation: 69-48=21 Exploring Operation: 48-10=38, Resulting Numbers: [69, 38] Generated Node #0,0,3: 51:[69, 38] Operation: 48-10=38 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[48, 59], Operations: ['79-10=69', '69-10=59'] Exploring Operation: 48*59=2832, Resulting Numbers: [2832] 2832,51 unequal: No Solution Exploring Operation: 59-48=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 48+59=107, Resulting Numbers: [107] 107,51 unequal: No Solution No 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: 51:[10, 21], Operations: ['79-10=69', '69-48=21'] Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,51 unequal: No Solution Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,51 unequal: No Solution No 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: 51:[69, 58], Operations: ['79-10=69', '48+10=58'] Exploring Operation: 69-58=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 69*58=4002, Resulting Numbers: [4002] 4002,51 unequal: No Solution Exploring Operation: 69+58=127, Resulting Numbers: [127] 127,51 unequal: No Solution No 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: 51:[69, 38], Operations: ['79-10=69', '48-10=38'] Exploring Operation: 69*38=2622, Resulting Numbers: [2622] 2622,51 unequal: No Solution Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 69+38=107, Resulting Numbers: [107] 107,51 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: 51:[10, 10, 31], Operations: ['79-48=31'] Exploring Operation: 10/10=1, Resulting Numbers: [31, 1] Generated Node #0,3,0: 51:[31, 1] Operation: 10/10=1 Exploring Operation: 10+10=20, Resulting Numbers: [31, 20] Generated Node #0,3,1: 51:[31, 20] Operation: 10+10=20 Exploring Operation: 31-10=21, Resulting Numbers: [10, 21] Generated Node #0,3,2: 51:[10, 21] Operation: 31-10=21 Exploring Operation: 31-10=21, Resulting Numbers: [10, 21] Generated Node #0,3,3: 51:[10, 21] Operation: 31-10=21 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 51:[10, 21], Operations: ['79-48=31', '31-10=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,51 unequal: No Solution No 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: 51:[10, 21], Operations: ['79-48=31', '31-10=21'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,51 unequal: No Solution Exploring Operation: 10*21=210, Resulting Numbers: [210] 210,51 unequal: No Solution Exploring Operation: 10+21=31, Resulting Numbers: [31] 31,51 unequal: No Solution No 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: 51:[31, 1], Operations: ['79-48=31', '10/10=1'] Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,51 unequal: No Solution Exploring Operation: 31+1=32, Resulting Numbers: [32] 32,51 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,51 unequal: No Solution Exploring Operation: 31*1=31, Resulting Numbers: [31] 31,51 unequal: No Solution No 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: 51:[31, 20], Operations: ['79-48=31', '10+10=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[79, 48, 10, 10], Operations: [] Exploring Operation: 79-48=31, Resulting Numbers: [10, 10, 31] Generated Node #0,3: 51:[10, 10, 31] Operation: 79-48=31 Moving to Node #0,3 Current State: 51:[10, 10, 31], Operations: ['79-48=31'] Exploring Operation: 10+10=20, Resulting Numbers: [31, 20] Generated Node #0,3,1: 51:[31, 20] Operation: 10+10=20 Moving to Node #0,3,1 Current State: 51:[31, 20], Operations: ['79-48=31', '10+10=20'] Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_4
mult_heuristic
[ 41, 45, 44, 93 ]
52
[ "93-41=52", "45-44=1", "52*1=52" ]
Current State: 52:[41, 45, 44, 93], Operations: [] Exploring Operation: 93-41=52, Resulting Numbers: [45, 44, 52] Generated Node #2: [45, 44, 52] from Operation: 93-41=52 Current State: 52:[45, 44, 52], Operations: ['93-41=52'] Exploring Operation: 45-44=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 45-44=1 Current State: 52:[52, 1], Operations: ['93-41=52', '45-44=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[41, 45, 44, 93], Operations: [] Exploring Operation: 45-41=4, Resulting Numbers: [44, 93, 4] Generated Node #0,0: 52:[44, 93, 4] Operation: 45-41=4 Exploring Operation: 93-45=48, Resulting Numbers: [41, 44, 48] Generated Node #0,1: 52:[41, 44, 48] Operation: 93-45=48 Exploring Operation: 93-41=52, Resulting Numbers: [45, 44, 52] Generated Node #0,2: 52:[45, 44, 52] Operation: 93-41=52 Exploring Operation: 93-44=49, Resulting Numbers: [41, 45, 49] Generated Node #0,3: 52:[41, 45, 49] Operation: 93-44=49 Moving to Node #0,2 Current State: 52:[45, 44, 52], Operations: ['93-41=52'] Exploring Operation: 52-44=8, Resulting Numbers: [45, 8] Generated Node #0,2,0: 52:[45, 8] Operation: 52-44=8 Exploring Operation: 52-45=7, Resulting Numbers: [44, 7] Generated Node #0,2,1: 52:[44, 7] Operation: 52-45=7 Exploring Operation: 45+44=89, Resulting Numbers: [52, 89] Generated Node #0,2,2: 52:[52, 89] Operation: 45+44=89 Exploring Operation: 45-44=1, Resulting Numbers: [52, 1] Generated Node #0,2,3: 52:[52, 1] Operation: 45-44=1 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 52:[52, 1], Operations: ['93-41=52', '45-44=1'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[41, 45, 44, 93], Operations: [] Exploring Operation: 93-41=52, Resulting Numbers: [45, 44, 52] Generated Node #0,2: 52:[45, 44, 52] Operation: 93-41=52 Moving to Node #0,2 Current State: 52:[45, 44, 52], Operations: ['93-41=52'] Exploring Operation: 45-44=1, Resulting Numbers: [52, 1] Generated Node #0,2,3: 52:[52, 1] Operation: 45-44=1 Moving to Node #0,2,3 Current State: 52:[52, 1], Operations: ['93-41=52', '45-44=1'] Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 78, 53, 13, 31 ]
69
[ "78-53=25", "13+31=44", "25+44=69" ]
Current State: 69:[78, 53, 13, 31], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [13, 31, 25] Generated Node #2: [13, 31, 25] from Operation: 78-53=25 Current State: 69:[13, 31, 25], Operations: ['78-53=25'] Exploring Operation: 13+31=44, Resulting Numbers: [25, 44] Generated Node #3: [25, 44] from Operation: 13+31=44 Current State: 69:[25, 44], Operations: ['78-53=25', '13+31=44'] Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[78, 53, 13, 31], Operations: [] Exploring Operation: 78-53=25, Resulting Numbers: [13, 31, 25] Generated Node #0,0: 69:[13, 31, 25] Operation: 78-53=25 Moving to Node #0,0 Current State: 69:[13, 31, 25], Operations: ['78-53=25'] Exploring Operation: 31-13=18, Resulting Numbers: [25, 18] Generated Node #0,0,0: 69:[25, 18] Operation: 31-13=18 Moving to Node #0,0,0 Current State: 69:[25, 18], Operations: ['78-53=25', '31-13=18'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,69 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 25, 98, 21, 42 ]
60
[ "25+98=123", "21+42=63", "123-63=60" ]
Current State: 60:[25, 98, 21, 42], Operations: [] Exploring Operation: 25+98=123, Resulting Numbers: [21, 42, 123] Generated Node #2: [21, 42, 123] from Operation: 25+98=123 Current State: 60:[21, 42, 123], Operations: ['25+98=123'] Exploring Operation: 21+42=63, Resulting Numbers: [123, 63] Generated Node #3: [123, 63] from Operation: 21+42=63 Current State: 60:[123, 63], Operations: ['25+98=123', '21+42=63'] Exploring Operation: 123-63=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[25, 98, 21, 42], Operations: [] Exploring Operation: 98-42=56, Resulting Numbers: [25, 21, 56] Generated Node #0,0: 60:[25, 21, 56] Operation: 98-42=56 Exploring Operation: 98-25=73, Resulting Numbers: [21, 42, 73] Generated Node #0,1: 60:[21, 42, 73] Operation: 98-25=73 Exploring Operation: 98-21=77, Resulting Numbers: [25, 42, 77] Generated Node #0,2: 60:[25, 42, 77] Operation: 98-21=77 Moving to Node #0,0 Current State: 60:[25, 21, 56], Operations: ['98-42=56'] Exploring Operation: 56-25=31, Resulting Numbers: [21, 31] Generated Node #0,0,0: 60:[21, 31] Operation: 56-25=31 Exploring Operation: 56-21=35, Resulting Numbers: [25, 35] Generated Node #0,0,1: 60:[25, 35] Operation: 56-21=35 Exploring Operation: 25-21=4, Resulting Numbers: [56, 4] Generated Node #0,0,2: 60:[56, 4] Operation: 25-21=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[21, 31], Operations: ['98-42=56', '56-25=31'] Exploring Operation: 21*31=651, Resulting Numbers: [651] 651,60 unequal: No Solution Exploring Operation: 21+31=52, Resulting Numbers: [52] 52,60 unequal: No Solution Exploring Operation: 31-21=10, Resulting Numbers: [10] 10,60 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 #0,0,2 Current State: 60:[56, 4], Operations: ['98-42=56', '25-21=4'] Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[25, 98, 21, 42], Operations: [] Exploring Operation: 98-42=56, Resulting Numbers: [25, 21, 56] Generated Node #0,0: 60:[25, 21, 56] Operation: 98-42=56 Moving to Node #0,0 Current State: 60:[25, 21, 56], Operations: ['98-42=56'] Exploring Operation: 25-21=4, Resulting Numbers: [56, 4] Generated Node #0,0,2: 60:[56, 4] Operation: 25-21=4 Moving to Node #0,0,2 Current State: 60:[56, 4], Operations: ['98-42=56', '25-21=4'] Exploring Operation: 56+4=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
sum_heuristic
[ 4, 36, 14, 39 ]
41
[ "4+14=18", "36/18=2", "39+2=41" ]
Current State: 41:[4, 36, 14, 39], Operations: [] Exploring Operation: 4+14=18, Resulting Numbers: [36, 39, 18] Generated Node #2: [36, 39, 18] from Operation: 4+14=18 Current State: 41:[36, 39, 18], Operations: ['4+14=18'] Exploring Operation: 36/18=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 36/18=2 Current State: 41:[39, 2], Operations: ['4+14=18', '36/18=2'] Exploring Operation: 39+2=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[4, 36, 14, 39], Operations: [] Exploring Operation: 4+36=40, Resulting Numbers: [14, 39, 40] Generated Node #0,0: 41:[14, 39, 40] Operation: 4+36=40 Exploring Operation: 4*14=56, Resulting Numbers: [36, 39, 56] Generated Node #0,1: 41:[36, 39, 56] Operation: 4*14=56 Exploring Operation: 4+39=43, Resulting Numbers: [36, 14, 43] Generated Node #0,2: 41:[36, 14, 43] Operation: 4+39=43 Exploring Operation: 4+14=18, Resulting Numbers: [36, 39, 18] Generated Node #0,3: 41:[36, 39, 18] Operation: 4+14=18 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[36, 39, 56], Operations: ['4*14=56'] Exploring Operation: 56-36=20, Resulting Numbers: [39, 20] Generated Node #0,1,0: 41:[39, 20] Operation: 56-36=20 Exploring Operation: 56-39=17, Resulting Numbers: [36, 17] Generated Node #0,1,1: 41:[36, 17] Operation: 56-39=17 Exploring Operation: 36+39=75, Resulting Numbers: [56, 75] Generated Node #0,1,2: 41:[56, 75] Operation: 36+39=75 Exploring Operation: 39-36=3, Resulting Numbers: [56, 3] Generated Node #0,1,3: 41:[56, 3] Operation: 39-36=3 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 41:[39, 20], Operations: ['4*14=56', '56-36=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,41 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,41 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:[36, 17], Operations: ['4*14=56', '56-39=17'] Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,41 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 41:[56, 75], Operations: ['4*14=56', '36+39=75'] Exploring Operation: 56*75=4200, Resulting Numbers: [4200] 4200,41 unequal: No Solution Exploring Operation: 75-56=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 56+75=131, Resulting Numbers: [131] 131,41 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 #0,1,3 Current State: 41:[56, 3], Operations: ['4*14=56', '39-36=3'] Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,41 unequal: No Solution Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,41 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[14, 39, 40], Operations: ['4+36=40'] Exploring Operation: 14+40=54, Resulting Numbers: [39, 54] Generated Node #0,0,0: 41:[39, 54] Operation: 14+40=54 Exploring Operation: 40-14=26, Resulting Numbers: [39, 26] Generated Node #0,0,1: 41:[39, 26] Operation: 40-14=26 Exploring Operation: 14+39=53, Resulting Numbers: [40, 53] Generated Node #0,0,2: 41:[40, 53] Operation: 14+39=53 Exploring Operation: 39-14=25, Resulting Numbers: [40, 25] Generated Node #0,0,3: 41:[40, 25] Operation: 39-14=25 Moving to Node #0,0,2 Current State: 41:[40, 53], Operations: ['4+36=40', '14+39=53'] Exploring Operation: 53-40=13, Resulting Numbers: [13] 13,41 unequal: No Solution Exploring Operation: 40*53=2120, Resulting Numbers: [2120] 2120,41 unequal: No Solution Exploring Operation: 40+53=93, Resulting Numbers: [93] 93,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[39, 54], Operations: ['4+36=40', '14+40=54'] Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 39*54=2106, Resulting Numbers: [2106] 2106,41 unequal: No Solution Exploring Operation: 39+54=93, Resulting Numbers: [93] 93,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[40, 25], Operations: ['4+36=40', '39-14=25'] Exploring Operation: 40+25=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 40*25=1000, Resulting Numbers: [1000] 1000,41 unequal: No Solution Exploring Operation: 40-25=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[39, 26], Operations: ['4+36=40', '40-14=26'] Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 39*26=1014, Resulting Numbers: [1014] 1014,41 unequal: No Solution Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[36, 39, 18], Operations: ['4+14=18'] Exploring Operation: 39-18=21, Resulting Numbers: [36, 21] Generated Node #0,3,0: 41:[36, 21] Operation: 39-18=21 Exploring Operation: 36+18=54, Resulting Numbers: [39, 54] Generated Node #0,3,1: 41:[39, 54] Operation: 36+18=54 Exploring Operation: 39+18=57, Resulting Numbers: [36, 57] Generated Node #0,3,2: 41:[36, 57] Operation: 39+18=57 Exploring Operation: 36-18=18, Resulting Numbers: [39, 18] Generated Node #0,3,3: 41:[39, 18] Operation: 36-18=18 Moving to Node #0,3,1 Current State: 41:[39, 54], Operations: ['4+14=18', '36+18=54'] Exploring Operation: 39+54=93, Resulting Numbers: [93] 93,41 unequal: No Solution Exploring Operation: 39*54=2106, Resulting Numbers: [2106] 2106,41 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[36, 57], Operations: ['4+14=18', '39+18=57'] Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 36*57=2052, Resulting Numbers: [2052] 2052,41 unequal: No Solution Exploring Operation: 36+57=93, Resulting Numbers: [93] 93,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[39, 18], Operations: ['4+14=18', '36-18=18'] Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,41 unequal: No Solution Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[36, 21], Operations: ['4+14=18', '39-18=21'] Exploring Operation: 36*21=756, Resulting Numbers: [756] 756,41 unequal: No Solution Exploring Operation: 36-21=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 36+21=57, Resulting Numbers: [57] 57,41 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 #0,2 Current State: 41:[36, 14, 43], Operations: ['4+39=43'] Exploring Operation: 36-14=22, Resulting Numbers: [43, 22] Generated Node #0,2,0: 41:[43, 22] Operation: 36-14=22 Exploring Operation: 43-14=29, Resulting Numbers: [36, 29] Generated Node #0,2,1: 41:[36, 29] Operation: 43-14=29 Exploring Operation: 36+14=50, Resulting Numbers: [43, 50] Generated Node #0,2,2: 41:[43, 50] Operation: 36+14=50 Exploring Operation: 14+43=57, Resulting Numbers: [36, 57] Generated Node #0,2,3: 41:[36, 57] Operation: 14+43=57 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 41:[43, 50], Operations: ['4+39=43', '36+14=50'] Exploring Operation: 43+50=93, Resulting Numbers: [93] 93,41 unequal: No Solution Exploring Operation: 43*50=2150, Resulting Numbers: [2150] 2150,41 unequal: No Solution Exploring Operation: 50-43=7, Resulting Numbers: [7] 7,41 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 #0,2,1 Current State: 41:[36, 29], Operations: ['4+39=43', '43-14=29'] Exploring Operation: 36*29=1044, Resulting Numbers: [1044] 1044,41 unequal: No Solution Exploring Operation: 36+29=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 36-29=7, Resulting Numbers: [7] 7,41 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 #0,2,0 Current State: 41:[43, 22], Operations: ['4+39=43', '36-14=22'] Exploring Operation: 43-22=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 43+22=65, Resulting Numbers: [65] 65,41 unequal: No Solution Exploring Operation: 43*22=946, Resulting Numbers: [946] 946,41 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 #0,2,3 Current State: 41:[36, 57], Operations: ['4+39=43', '14+43=57'] Exploring Operation: 36*57=2052, Resulting Numbers: [2052] 2052,41 unequal: No Solution Exploring Operation: 57-36=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 36+57=93, Resulting Numbers: [93] 93,41 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_4
sum_heuristic
[ 31, 90, 7, 86 ]
30
[ "31*90=2790", "7+86=93", "2790/93=30" ]
Current State: 30:[31, 90, 7, 86], Operations: [] Exploring Operation: 31*90=2790, Resulting Numbers: [7, 86, 2790] Generated Node #2: [7, 86, 2790] from Operation: 31*90=2790 Current State: 30:[7, 86, 2790], Operations: ['31*90=2790'] Exploring Operation: 7+86=93, Resulting Numbers: [2790, 93] Generated Node #3: [2790, 93] from Operation: 7+86=93 Current State: 30:[2790, 93], Operations: ['31*90=2790', '7+86=93'] Exploring Operation: 2790/93=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[31, 90, 7, 86], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [31, 7, 4] Generated Node #0,0: 30:[31, 7, 4] Operation: 90-86=4 Exploring Operation: 90-31=59, Resulting Numbers: [7, 86, 59] Generated Node #0,1: 30:[7, 86, 59] Operation: 90-31=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[31, 7, 4], Operations: ['90-86=4'] Exploring Operation: 7+4=11, Resulting Numbers: [31, 11] Generated Node #0,0,0: 30:[31, 11] Operation: 7+4=11 Exploring Operation: 7-4=3, Resulting Numbers: [31, 3] Generated Node #0,0,1: 30:[31, 3] Operation: 7-4=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[31, 3], Operations: ['90-86=4', '7-4=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,30 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,30 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 #0,0,0 Current State: 30:[31, 11], Operations: ['90-86=4', '7+4=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,30 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,30 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 #0,1 Current State: 30:[7, 86, 59], Operations: ['90-31=59'] Exploring Operation: 86-7=79, Resulting Numbers: [59, 79] Generated Node #0,1,0: 30:[59, 79] Operation: 86-7=79 Exploring Operation: 86-59=27, Resulting Numbers: [7, 27] Generated Node #0,1,1: 30:[7, 27] Operation: 86-59=27 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[7, 27], Operations: ['90-31=59', '86-59=27'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 7+27=34, Resulting Numbers: [34] 34,30 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 #0,1,0 Current State: 30:[59, 79], Operations: ['90-31=59', '86-7=79'] Exploring Operation: 59+79=138, Resulting Numbers: [138] 138,30 unequal: No Solution Exploring Operation: 79-59=20, Resulting Numbers: [20] 20,30 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 No solution found.
0
hs_2
mult_heuristic
[ 58, 36, 50, 7 ]
79
[ "58-36=22", "50+7=57", "22+57=79" ]
Current State: 79:[58, 36, 50, 7], Operations: [] Exploring Operation: 58-36=22, Resulting Numbers: [50, 7, 22] Generated Node #2: [50, 7, 22] from Operation: 58-36=22 Current State: 79:[50, 7, 22], Operations: ['58-36=22'] Exploring Operation: 50+7=57, Resulting Numbers: [22, 57] Generated Node #3: [22, 57] from Operation: 50+7=57 Current State: 79:[22, 57], Operations: ['58-36=22', '50+7=57'] Exploring Operation: 22+57=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[58, 36, 50, 7], Operations: [] Exploring Operation: 36+7=43, Resulting Numbers: [58, 50, 43] Generated Node #0,0: 79:[58, 50, 43] Operation: 36+7=43 Exploring Operation: 58-7=51, Resulting Numbers: [36, 50, 51] Generated Node #0,1: 79:[36, 50, 51] Operation: 58-7=51 Exploring Operation: 50+7=57, Resulting Numbers: [58, 36, 57] Generated Node #0,2: 79:[58, 36, 57] Operation: 50+7=57 Exploring Operation: 58+7=65, Resulting Numbers: [36, 50, 65] Generated Node #0,3: 79:[36, 50, 65] Operation: 58+7=65 Moving to Node #0,0 Current State: 79:[58, 50, 43], Operations: ['36+7=43'] Exploring Operation: 50+43=93, Resulting Numbers: [58, 93] Generated Node #0,0,0: 79:[58, 93] Operation: 50+43=93 Exploring Operation: 58+50=108, Resulting Numbers: [43, 108] Generated Node #0,0,1: 79:[43, 108] Operation: 58+50=108 Exploring Operation: 58-43=15, Resulting Numbers: [50, 15] Generated Node #0,0,2: 79:[50, 15] Operation: 58-43=15 Exploring Operation: 58+43=101, Resulting Numbers: [50, 101] Generated Node #0,0,3: 79:[50, 101] Operation: 58+43=101 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[58, 93], Operations: ['36+7=43', '50+43=93'] Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 58*93=5394, Resulting Numbers: [5394] 5394,79 unequal: No Solution Exploring Operation: 58+93=151, Resulting Numbers: [151] 151,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 79:[50, 101], Operations: ['36+7=43', '58+43=101'] Exploring Operation: 101-50=51, Resulting Numbers: [51] 51,79 unequal: No Solution Exploring Operation: 50+101=151, Resulting Numbers: [151] 151,79 unequal: No Solution Exploring Operation: 50*101=5050, Resulting Numbers: [5050] 5050,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 79:[43, 108], Operations: ['36+7=43', '58+50=108'] Exploring Operation: 43*108=4644, Resulting Numbers: [4644] 4644,79 unequal: No Solution Exploring Operation: 108-43=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 43+108=151, Resulting Numbers: [151] 151,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 79:[50, 15], Operations: ['36+7=43', '58-43=15'] Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,79 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:[36, 50, 65], Operations: ['58+7=65'] Exploring Operation: 50-36=14, Resulting Numbers: [65, 14] Generated Node #0,3,0: 79:[65, 14] Operation: 50-36=14 Exploring Operation: 65-36=29, Resulting Numbers: [50, 29] Generated Node #0,3,1: 79:[50, 29] Operation: 65-36=29 Exploring Operation: 36+65=101, Resulting Numbers: [50, 101] Generated Node #0,3,2: 79:[50, 101] Operation: 36+65=101 Exploring Operation: 36+50=86, Resulting Numbers: [65, 86] Generated Node #0,3,3: 79:[65, 86] Operation: 36+50=86 Moving to Node #0,2 Current State: 79:[58, 36, 57], Operations: ['50+7=57'] Exploring Operation: 58+36=94, Resulting Numbers: [57, 94] Generated Node #0,2,0: 79:[57, 94] Operation: 58+36=94 Exploring Operation: 58+57=115, Resulting Numbers: [36, 115] Generated Node #0,2,1: 79:[36, 115] Operation: 58+57=115 Exploring Operation: 58-36=22, Resulting Numbers: [57, 22] Generated Node #0,2,2: 79:[57, 22] Operation: 58-36=22 Exploring Operation: 36+57=93, Resulting Numbers: [58, 93] Generated Node #0,2,3: 79:[58, 93] Operation: 36+57=93 Moving to Node #0,1 Current State: 79:[36, 50, 51], Operations: ['58-7=51'] Exploring Operation: 36+50=86, Resulting Numbers: [51, 86] Generated Node #0,1,0: 79:[51, 86] Operation: 36+50=86 Exploring Operation: 50-36=14, Resulting Numbers: [51, 14] Generated Node #0,1,1: 79:[51, 14] Operation: 50-36=14 Exploring Operation: 36+51=87, Resulting Numbers: [50, 87] Generated Node #0,1,2: 79:[50, 87] Operation: 36+51=87 Exploring Operation: 50+51=101, Resulting Numbers: [36, 101] Generated Node #0,1,3: 79:[36, 101] Operation: 50+51=101 Moving to Node #0,3,3 Current State: 79:[65, 86], Operations: ['58+7=65', '36+50=86'] Exploring Operation: 65*86=5590, Resulting Numbers: [5590] 5590,79 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,79 unequal: No Solution Exploring Operation: 65+86=151, Resulting Numbers: [151] 151,79 unequal: No Solution Moving to Node #0,2,3 Current State: 79:[58, 93], Operations: ['50+7=57', '36+57=93'] Exploring Operation: 58+93=151, Resulting Numbers: [151] 151,79 unequal: No Solution Exploring Operation: 58*93=5394, Resulting Numbers: [5394] 5394,79 unequal: No Solution Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,79 unequal: No Solution Moving to Node #0,1,0 Current State: 79:[51, 86], Operations: ['58-7=51', '36+50=86'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,79 unequal: No Solution Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[57, 94], Operations: ['50+7=57', '58+36=94'] Exploring Operation: 57+94=151, Resulting Numbers: [151] 151,79 unequal: No Solution Exploring Operation: 57*94=5358, Resulting Numbers: [5358] 5358,79 unequal: No Solution Exploring Operation: 94-57=37, Resulting Numbers: [37] 37,79 unequal: No Solution Moving to Node #0,1,2 Current State: 79:[50, 87], Operations: ['58-7=51', '36+51=87'] Exploring Operation: 50+87=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 50*87=4350, Resulting Numbers: [4350] 4350,79 unequal: No Solution Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,79 unequal: No Solution Moving to Node #0,3,2 Current State: 79:[50, 101], Operations: ['58+7=65', '36+65=101'] Exploring Operation: 50+101=151, Resulting Numbers: [151] 151,79 unequal: No Solution Exploring Operation: 50*101=5050, Resulting Numbers: [5050] 5050,79 unequal: No Solution Exploring Operation: 101-50=51, Resulting Numbers: [51] 51,79 unequal: No Solution Moving to Node #0,1,3 Current State: 79:[36, 101], Operations: ['58-7=51', '50+51=101'] Exploring Operation: 36+101=137, Resulting Numbers: [137] 137,79 unequal: No Solution Exploring Operation: 101-36=65, Resulting Numbers: [65] 65,79 unequal: No Solution Exploring Operation: 36*101=3636, Resulting Numbers: [3636] 3636,79 unequal: No Solution Moving to Node #0,3,0 Current State: 79:[65, 14], Operations: ['58+7=65', '50-36=14'] Exploring Operation: 65*14=910, Resulting Numbers: [910] 910,79 unequal: No Solution Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[58, 36, 50, 7], Operations: [] Exploring Operation: 58+7=65, Resulting Numbers: [36, 50, 65] Generated Node #0,3: 79:[36, 50, 65] Operation: 58+7=65 Moving to Node #0,3 Current State: 79:[36, 50, 65], Operations: ['58+7=65'] Exploring Operation: 50-36=14, Resulting Numbers: [65, 14] Generated Node #0,3,0: 79:[65, 14] Operation: 50-36=14 Moving to Node #0,3,0 Current State: 79:[65, 14], Operations: ['58+7=65', '50-36=14'] Exploring Operation: 65+14=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
0.948785
hs_4
mult_heuristic
[ 56, 40, 83, 63 ]
28
[ "83-63=20", "56*20=1120", "1120/40=28" ]
Current State: 28:[56, 40, 83, 63], Operations: [] Exploring Operation: 83-63=20, Resulting Numbers: [56, 40, 20] Generated Node #2: [56, 40, 20] from Operation: 83-63=20 Current State: 28:[56, 40, 20], Operations: ['83-63=20'] Exploring Operation: 56*20=1120, Resulting Numbers: [40, 1120] Generated Node #3: [40, 1120] from Operation: 56*20=1120 Current State: 28:[40, 1120], Operations: ['83-63=20', '56*20=1120'] Exploring Operation: 1120/40=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[56, 40, 83, 63], Operations: [] Exploring Operation: 83-63=20, Resulting Numbers: [56, 40, 20] Generated Node #0,0: 28:[56, 40, 20] Operation: 83-63=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[56, 40, 20], Operations: ['83-63=20'] Exploring Operation: 56-40=16, Resulting Numbers: [20, 16] Generated Node #0,0,0: 28:[20, 16] Operation: 56-40=16 Moving to Node #0,0,0 Current State: 28:[20, 16], Operations: ['83-63=20', '56-40=16'] Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,28 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, 11, 27, 13 ]
75
[ "7*13=91", "27-11=16", "91-16=75" ]
Current State: 75:[7, 11, 27, 13], Operations: [] Exploring Operation: 7*13=91, Resulting Numbers: [11, 27, 91] Generated Node #2: [11, 27, 91] from Operation: 7*13=91 Current State: 75:[11, 27, 91], Operations: ['7*13=91'] Exploring Operation: 27-11=16, Resulting Numbers: [91, 16] Generated Node #3: [91, 16] from Operation: 27-11=16 Current State: 75:[91, 16], Operations: ['7*13=91', '27-11=16'] Exploring Operation: 91-16=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[7, 11, 27, 13], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [27, 13, 4] Generated Node #0,0: 75:[27, 13, 4] Operation: 11-7=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[27, 13, 4], Operations: ['11-7=4'] Exploring Operation: 27-13=14, Resulting Numbers: [4, 14] Generated Node #0,0,0: 75:[4, 14] Operation: 27-13=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 75:[4, 14], Operations: ['11-7=4', '27-13=14'] Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,75 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 59, 17, 37, 55 ]
50
[ "59-17=42", "37+55=92", "92-42=50" ]
Current State: 50:[59, 17, 37, 55], Operations: [] Exploring Operation: 59-17=42, Resulting Numbers: [37, 55, 42] Generated Node #2: [37, 55, 42] from Operation: 59-17=42 Current State: 50:[37, 55, 42], Operations: ['59-17=42'] Exploring Operation: 37+55=92, Resulting Numbers: [42, 92] Generated Node #3: [42, 92] from Operation: 37+55=92 Current State: 50:[42, 92], Operations: ['59-17=42', '37+55=92'] Exploring Operation: 92-42=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[59, 17, 37, 55], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [17, 55, 22] Generated Node #0,0: 50:[17, 55, 22] Operation: 59-37=22 Exploring Operation: 17+37=54, Resulting Numbers: [59, 55, 54] Generated Node #0,1: 50:[59, 55, 54] Operation: 17+37=54 Exploring Operation: 37-17=20, Resulting Numbers: [59, 55, 20] Generated Node #0,2: 50:[59, 55, 20] Operation: 37-17=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[17, 55, 22], Operations: ['59-37=22'] Exploring Operation: 55-17=38, Resulting Numbers: [22, 38] Generated Node #0,0,0: 50:[22, 38] Operation: 55-17=38 Exploring Operation: 55-22=33, Resulting Numbers: [17, 33] Generated Node #0,0,1: 50:[17, 33] Operation: 55-22=33 Exploring Operation: 22-17=5, Resulting Numbers: [55, 5] Generated Node #0,0,2: 50:[55, 5] Operation: 22-17=5 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 50:[55, 5], Operations: ['59-37=22', '22-17=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,50 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,50 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[59, 17, 37, 55], Operations: [] Exploring Operation: 59-37=22, Resulting Numbers: [17, 55, 22] Generated Node #0,0: 50:[17, 55, 22] Operation: 59-37=22 Moving to Node #0,0 Current State: 50:[17, 55, 22], Operations: ['59-37=22'] Exploring Operation: 22-17=5, Resulting Numbers: [55, 5] Generated Node #0,0,2: 50:[55, 5] Operation: 22-17=5 Moving to Node #0,0,2 Current State: 50:[55, 5], Operations: ['59-37=22', '22-17=5'] Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 20, 60, 44, 78 ]
70
[ "60/20=3", "78/3=26", "44+26=70" ]
Current State: 70:[20, 60, 44, 78], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [44, 78, 3] Generated Node #2: [44, 78, 3] from Operation: 60/20=3 Current State: 70:[44, 78, 3], Operations: ['60/20=3'] Exploring Operation: 78/3=26, Resulting Numbers: [44, 26] Generated Node #3: [44, 26] from Operation: 78/3=26 Current State: 70:[44, 26], Operations: ['60/20=3', '78/3=26'] Exploring Operation: 44+26=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[20, 60, 44, 78], Operations: [] Exploring Operation: 60-44=16, Resulting Numbers: [20, 78, 16] Generated Node #0,0: 70:[20, 78, 16] Operation: 60-44=16 Moving to Node #0,0 Current State: 70:[20, 78, 16], Operations: ['60-44=16'] Exploring Operation: 20+16=36, Resulting Numbers: [78, 36] Generated Node #0,0,0: 70:[78, 36] Operation: 20+16=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[78, 36], Operations: ['60-44=16', '20+16=36'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 45, 9, 20, 52 ]
18
[ "45+9=54", "20+52=72", "72-54=18" ]
Current State: 18:[45, 9, 20, 52], Operations: [] Exploring Operation: 45+9=54, Resulting Numbers: [20, 52, 54] Generated Node #2: [20, 52, 54] from Operation: 45+9=54 Current State: 18:[20, 52, 54], Operations: ['45+9=54'] Exploring Operation: 20+52=72, Resulting Numbers: [54, 72] Generated Node #3: [54, 72] from Operation: 20+52=72 Current State: 18:[54, 72], Operations: ['45+9=54', '20+52=72'] Exploring Operation: 72-54=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[45, 9, 20, 52], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [9, 20, 7] Generated Node #0,0: 18:[9, 20, 7] Operation: 52-45=7 Exploring Operation: 45/9=5, Resulting Numbers: [20, 52, 5] Generated Node #0,1: 18:[20, 52, 5] Operation: 45/9=5 Exploring Operation: 52-20=32, Resulting Numbers: [45, 9, 32] Generated Node #0,2: 18:[45, 9, 32] Operation: 52-20=32 Exploring Operation: 45-20=25, Resulting Numbers: [9, 52, 25] Generated Node #0,3: 18:[9, 52, 25] Operation: 45-20=25 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[9, 20, 7], Operations: ['52-45=7'] Exploring Operation: 9-7=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 18:[20, 2] Operation: 9-7=2 Exploring Operation: 20-7=13, Resulting Numbers: [9, 13] Generated Node #0,0,1: 18:[9, 13] Operation: 20-7=13 Exploring Operation: 20-9=11, Resulting Numbers: [7, 11] Generated Node #0,0,2: 18:[7, 11] Operation: 20-9=11 Exploring Operation: 9+7=16, Resulting Numbers: [20, 16] Generated Node #0,0,3: 18:[20, 16] Operation: 9+7=16 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 18:[20, 2], Operations: ['52-45=7', '9-7=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[45, 9, 20, 52], Operations: [] Exploring Operation: 52-45=7, Resulting Numbers: [9, 20, 7] Generated Node #0,0: 18:[9, 20, 7] Operation: 52-45=7 Moving to Node #0,0 Current State: 18:[9, 20, 7], Operations: ['52-45=7'] Exploring Operation: 9-7=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 18:[20, 2] Operation: 9-7=2 Moving to Node #0,0,0 Current State: 18:[20, 2], Operations: ['52-45=7', '9-7=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 69, 96, 97, 31 ]
92
[ "97+31=128", "69*128=8832", "8832/96=92" ]
Current State: 92:[69, 96, 97, 31], Operations: [] Exploring Operation: 97+31=128, Resulting Numbers: [69, 96, 128] Generated Node #2: [69, 96, 128] from Operation: 97+31=128 Current State: 92:[69, 96, 128], Operations: ['97+31=128'] Exploring Operation: 69*128=8832, Resulting Numbers: [96, 8832] Generated Node #3: [96, 8832] from Operation: 69*128=8832 Current State: 92:[96, 8832], Operations: ['97+31=128', '69*128=8832'] Exploring Operation: 8832/96=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[69, 96, 97, 31], Operations: [] Exploring Operation: 96-69=27, Resulting Numbers: [97, 31, 27] Generated Node #0,0: 92:[97, 31, 27] Operation: 96-69=27 Exploring Operation: 97-69=28, Resulting Numbers: [96, 31, 28] Generated Node #0,1: 92:[96, 31, 28] Operation: 97-69=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[97, 31, 27], Operations: ['96-69=27'] Exploring Operation: 31+27=58, Resulting Numbers: [97, 58] Generated Node #0,0,0: 92:[97, 58] Operation: 31+27=58 Exploring Operation: 31-27=4, Resulting Numbers: [97, 4] Generated Node #0,0,1: 92:[97, 4] Operation: 31-27=4 Moving to Node #0,0,1 Current State: 92:[97, 4], Operations: ['96-69=27', '31-27=4'] Exploring Operation: 97+4=101, Resulting Numbers: [101] 101,92 unequal: No Solution Exploring Operation: 97-4=93, Resulting Numbers: [93] 93,92 unequal: No Solution Moving to Node #0,0,0 Current State: 92:[97, 58], Operations: ['96-69=27', '31+27=58'] Exploring Operation: 97+58=155, Resulting Numbers: [155] 155,92 unequal: No Solution Exploring Operation: 97-58=39, Resulting Numbers: [39] 39,92 unequal: No Solution No 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: 92:[96, 31, 28], Operations: ['97-69=28'] Exploring Operation: 31+28=59, Resulting Numbers: [96, 59] Generated Node #0,1,0: 92:[96, 59] Operation: 31+28=59 Exploring Operation: 31-28=3, Resulting Numbers: [96, 3] Generated Node #0,1,1: 92:[96, 3] Operation: 31-28=3 Moving to Node #0,1,1 Current State: 92:[96, 3], Operations: ['97-69=28', '31-28=3'] Exploring Operation: 96+3=99, Resulting Numbers: [99] 99,92 unequal: No Solution Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[96, 59], Operations: ['97-69=28', '31+28=59'] Exploring Operation: 96+59=155, Resulting Numbers: [155] 155,92 unequal: No Solution Exploring Operation: 96-59=37, Resulting Numbers: [37] 37,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 71, 68, 65, 67 ]
69
[ "71+65=136", "136/68=2", "67+2=69" ]
Current State: 69:[71, 68, 65, 67], Operations: [] Exploring Operation: 71+65=136, Resulting Numbers: [68, 67, 136] Generated Node #2: [68, 67, 136] from Operation: 71+65=136 Current State: 69:[68, 67, 136], Operations: ['71+65=136'] Exploring Operation: 136/68=2, Resulting Numbers: [67, 2] Generated Node #3: [67, 2] from Operation: 136/68=2 Current State: 69:[67, 2], Operations: ['71+65=136', '136/68=2'] Exploring Operation: 67+2=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[71, 68, 65, 67], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [71, 67, 3] Generated Node #0,0: 69:[71, 67, 3] Operation: 68-65=3 Exploring Operation: 67-65=2, Resulting Numbers: [71, 68, 2] Generated Node #0,1: 69:[71, 68, 2] Operation: 67-65=2 Moving to Node #0,0 Current State: 69:[71, 67, 3], Operations: ['68-65=3'] Exploring Operation: 71-67=4, Resulting Numbers: [3, 4] Generated Node #0,0,0: 69:[3, 4] Operation: 71-67=4 Exploring Operation: 71-3=68, Resulting Numbers: [67, 68] Generated Node #0,0,1: 69:[67, 68] Operation: 71-3=68 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[3, 4], Operations: ['68-65=3', '71-67=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[67, 68], Operations: ['68-65=3', '71-3=68'] Exploring Operation: 68-67=1, Resulting Numbers: [1] 1,69 unequal: No Solution Exploring Operation: 67+68=135, Resulting Numbers: [135] 135,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 69:[71, 68, 2], Operations: ['67-65=2'] Exploring Operation: 71-68=3, Resulting Numbers: [2, 3] Generated Node #0,1,0: 69:[2, 3] Operation: 71-68=3 Exploring Operation: 71-2=69, Resulting Numbers: [68, 69] Generated Node #0,1,1: 69:[68, 69] Operation: 71-2=69 Moving to Node #0,1,0 Current State: 69:[2, 3], Operations: ['67-65=2', '71-68=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[68, 69], Operations: ['67-65=2', '71-2=69'] Exploring Operation: 68+69=137, Resulting Numbers: [137] 137,69 unequal: No Solution Exploring Operation: 69-68=1, Resulting Numbers: [1] 1,69 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 40, 92, 18, 19 ]
51
[ "92-40=52", "19-18=1", "52-1=51" ]
Current State: 51:[40, 92, 18, 19], Operations: [] Exploring Operation: 92-40=52, Resulting Numbers: [18, 19, 52] Generated Node #2: [18, 19, 52] from Operation: 92-40=52 Current State: 51:[18, 19, 52], Operations: ['92-40=52'] Exploring Operation: 19-18=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 19-18=1 Current State: 51:[52, 1], Operations: ['92-40=52', '19-18=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[40, 92, 18, 19], Operations: [] Exploring Operation: 40-19=21, Resulting Numbers: [92, 18, 21] Generated Node #0,0: 51:[92, 18, 21] Operation: 40-19=21 Exploring Operation: 92-19=73, Resulting Numbers: [40, 18, 73] Generated Node #0,1: 51:[40, 18, 73] Operation: 92-19=73 Exploring Operation: 92-40=52, Resulting Numbers: [18, 19, 52] Generated Node #0,2: 51:[18, 19, 52] Operation: 92-40=52 Exploring Operation: 40-18=22, Resulting Numbers: [92, 19, 22] Generated Node #0,3: 51:[92, 19, 22] Operation: 40-18=22 Exploring Operation: 92-18=74, Resulting Numbers: [40, 19, 74] Generated Node #0,4: 51:[40, 19, 74] Operation: 92-18=74 Start Sub Search at level 1: Moving to Node #0,2 Current State: 51:[18, 19, 52], Operations: ['92-40=52'] Exploring Operation: 52-18=34, Resulting Numbers: [19, 34] Generated Node #0,2,0: 51:[19, 34] Operation: 52-18=34 Exploring Operation: 18+52=70, Resulting Numbers: [19, 70] Generated Node #0,2,1: 51:[19, 70] Operation: 18+52=70 Exploring Operation: 19-18=1, Resulting Numbers: [52, 1] Generated Node #0,2,2: 51:[52, 1] Operation: 19-18=1 Exploring Operation: 52-19=33, Resulting Numbers: [18, 33] Generated Node #0,2,3: 51:[18, 33] Operation: 52-19=33 Exploring Operation: 18+19=37, Resulting Numbers: [52, 37] Generated Node #0,2,4: 51:[52, 37] Operation: 18+19=37 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[52, 1], Operations: ['92-40=52', '19-18=1'] Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,51 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,51 unequal: No Solution Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[40, 92, 18, 19], Operations: [] Exploring Operation: 92-40=52, Resulting Numbers: [18, 19, 52] Generated Node #0,2: 51:[18, 19, 52] Operation: 92-40=52 Moving to Node #0,2 Current State: 51:[18, 19, 52], Operations: ['92-40=52'] Exploring Operation: 19-18=1, Resulting Numbers: [52, 1] Generated Node #0,2,2: 51:[52, 1] Operation: 19-18=1 Moving to Node #0,2,2 Current State: 51:[52, 1], Operations: ['92-40=52', '19-18=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_5
mult_heuristic
[ 65, 93, 98, 84 ]
97
[ "98-93=5", "65/5=13", "84+13=97" ]
Current State: 97:[65, 93, 98, 84], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [65, 84, 5] Generated Node #2: [65, 84, 5] from Operation: 98-93=5 Current State: 97:[65, 84, 5], Operations: ['98-93=5'] Exploring Operation: 65/5=13, Resulting Numbers: [84, 13] Generated Node #3: [84, 13] from Operation: 65/5=13 Current State: 97:[84, 13], Operations: ['98-93=5', '65/5=13'] Exploring Operation: 84+13=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[65, 93, 98, 84], Operations: [] Exploring Operation: 65+93=158, Resulting Numbers: [98, 84, 158] Generated Node #0,0: 97:[98, 84, 158] Operation: 65+93=158 Exploring Operation: 98-65=33, Resulting Numbers: [93, 84, 33] Generated Node #0,1: 97:[93, 84, 33] Operation: 98-65=33 Exploring Operation: 65+84=149, Resulting Numbers: [93, 98, 149] Generated Node #0,2: 97:[93, 98, 149] Operation: 65+84=149 Exploring Operation: 93-65=28, Resulting Numbers: [98, 84, 28] Generated Node #0,3: 97:[98, 84, 28] Operation: 93-65=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[93, 98, 149], Operations: ['65+84=149'] Exploring Operation: 149-93=56, Resulting Numbers: [98, 56] Generated Node #0,2,0: 97:[98, 56] Operation: 149-93=56 Exploring Operation: 93+98=191, Resulting Numbers: [149, 191] Generated Node #0,2,1: 97:[149, 191] Operation: 93+98=191 Exploring Operation: 98-93=5, Resulting Numbers: [149, 5] Generated Node #0,2,2: 97:[149, 5] Operation: 98-93=5 Exploring Operation: 149-98=51, Resulting Numbers: [93, 51] Generated Node #0,2,3: 97:[93, 51] Operation: 149-98=51 Moving to Node #0,2,0 Current State: 97:[98, 56], Operations: ['65+84=149', '149-93=56'] Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 98+56=154, Resulting Numbers: [154] 154,97 unequal: No Solution Exploring Operation: 98*56=5488, Resulting Numbers: [5488] 5488,97 unequal: No Solution Moving to Node #0,2,3 Current State: 97:[93, 51], Operations: ['65+84=149', '149-98=51'] Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 93*51=4743, Resulting Numbers: [4743] 4743,97 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[149, 5], Operations: ['65+84=149', '98-93=5'] Exploring Operation: 149-5=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 149+5=154, Resulting Numbers: [154] 154,97 unequal: No Solution Exploring Operation: 149*5=745, Resulting Numbers: [745] 745,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[149, 191], Operations: ['65+84=149', '93+98=191'] Exploring Operation: 149+191=340, Resulting Numbers: [340] 340,97 unequal: No Solution Exploring Operation: 149*191=28459, Resulting Numbers: [28459] 28459,97 unequal: No Solution Exploring Operation: 191-149=42, Resulting Numbers: [42] 42,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[98, 84, 158], Operations: ['65+93=158'] Exploring Operation: 98-84=14, Resulting Numbers: [158, 14] Generated Node #0,0,0: 97:[158, 14] Operation: 98-84=14 Exploring Operation: 158-98=60, Resulting Numbers: [84, 60] Generated Node #0,0,1: 97:[84, 60] Operation: 158-98=60 Exploring Operation: 98+84=182, Resulting Numbers: [158, 182] Generated Node #0,0,2: 97:[158, 182] Operation: 98+84=182 Exploring Operation: 158-84=74, Resulting Numbers: [98, 74] Generated Node #0,0,3: 97:[98, 74] Operation: 158-84=74 Moving to Node #0,0,3 Current State: 97:[98, 74], Operations: ['65+93=158', '158-84=74'] Exploring Operation: 98*74=7252, Resulting Numbers: [7252] 7252,97 unequal: No Solution Exploring Operation: 98+74=172, Resulting Numbers: [172] 172,97 unequal: No Solution Exploring Operation: 98-74=24, Resulting Numbers: [24] 24,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[84, 60], Operations: ['65+93=158', '158-98=60'] Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[158, 14], Operations: ['65+93=158', '98-84=14'] Exploring Operation: 158*14=2212, Resulting Numbers: [2212] 2212,97 unequal: No Solution Exploring Operation: 158-14=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 158+14=172, Resulting Numbers: [172] 172,97 unequal: No Solution Moving to Node #0,0,2 Current State: 97:[158, 182], Operations: ['65+93=158', '98+84=182'] Exploring Operation: 158*182=28756, Resulting Numbers: [28756] 28756,97 unequal: No Solution Exploring Operation: 182-158=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 158+182=340, Resulting Numbers: [340] 340,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[93, 84, 33], Operations: ['98-65=33'] Exploring Operation: 93-33=60, Resulting Numbers: [84, 60] Generated Node #0,1,0: 97:[84, 60] Operation: 93-33=60 Exploring Operation: 84+33=117, Resulting Numbers: [93, 117] Generated Node #0,1,1: 97:[93, 117] Operation: 84+33=117 Exploring Operation: 84-33=51, Resulting Numbers: [93, 51] Generated Node #0,1,2: 97:[93, 51] Operation: 84-33=51 Exploring Operation: 93+33=126, Resulting Numbers: [84, 126] Generated Node #0,1,3: 97:[84, 126] Operation: 93+33=126 Moving to Node #0,1,1 Current State: 97:[93, 117], Operations: ['98-65=33', '84+33=117'] Exploring Operation: 117-93=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 93+117=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 93*117=10881, Resulting Numbers: [10881] 10881,97 unequal: No Solution Moving to Node #0,1,3 Current State: 97:[84, 126], Operations: ['98-65=33', '93+33=126'] Exploring Operation: 126-84=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 84*126=10584, Resulting Numbers: [10584] 10584,97 unequal: No Solution Exploring Operation: 84+126=210, Resulting Numbers: [210] 210,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[93, 51], Operations: ['98-65=33', '84-33=51'] Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 93*51=4743, Resulting Numbers: [4743] 4743,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[84, 60], Operations: ['98-65=33', '93-33=60'] Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 97:[98, 84, 28], Operations: ['93-65=28'] Exploring Operation: 98-28=70, Resulting Numbers: [84, 70] Generated Node #0,3,0: 97:[84, 70] Operation: 98-28=70 Exploring Operation: 98+28=126, Resulting Numbers: [84, 126] Generated Node #0,3,1: 97:[84, 126] Operation: 98+28=126 Exploring Operation: 84+28=112, Resulting Numbers: [98, 112] Generated Node #0,3,2: 97:[98, 112] Operation: 84+28=112 Exploring Operation: 84-28=56, Resulting Numbers: [98, 56] Generated Node #0,3,3: 97:[98, 56] Operation: 84-28=56 Moving to Node #0,3,2 Current State: 97:[98, 112], Operations: ['93-65=28', '84+28=112'] Exploring Operation: 98*112=10976, Resulting Numbers: [10976] 10976,97 unequal: No Solution Exploring Operation: 98+112=210, Resulting Numbers: [210] 210,97 unequal: No Solution Exploring Operation: 112-98=14, Resulting Numbers: [14] 14,97 unequal: No Solution Moving to Node #0,3,0 Current State: 97:[84, 70], Operations: ['93-65=28', '98-28=70'] Exploring Operation: 84-70=14, Resulting Numbers: [14] 14,97 unequal: No Solution Exploring Operation: 84+70=154, Resulting Numbers: [154] 154,97 unequal: No Solution Exploring Operation: 84*70=5880, Resulting Numbers: [5880] 5880,97 unequal: No Solution Moving to Node #0,3,3 Current State: 97:[98, 56], Operations: ['93-65=28', '84-28=56'] Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 98+56=154, Resulting Numbers: [154] 154,97 unequal: No Solution Exploring Operation: 98*56=5488, Resulting Numbers: [5488] 5488,97 unequal: No Solution Moving to Node #0,3,1 Current State: 97:[84, 126], Operations: ['93-65=28', '98+28=126'] Exploring Operation: 84*126=10584, Resulting Numbers: [10584] 10584,97 unequal: No Solution Exploring Operation: 126-84=42, Resulting Numbers: [42] 42,97 unequal: No Solution Exploring Operation: 84+126=210, Resulting Numbers: [210] 210,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 53, 29, 54, 58 ]
52
[ "53*58=3074", "3074/29=106", "106-54=52" ]
Current State: 52:[53, 29, 54, 58], Operations: [] Exploring Operation: 53*58=3074, Resulting Numbers: [29, 54, 3074] Generated Node #2: [29, 54, 3074] from Operation: 53*58=3074 Current State: 52:[29, 54, 3074], Operations: ['53*58=3074'] Exploring Operation: 3074/29=106, Resulting Numbers: [54, 106] Generated Node #3: [54, 106] from Operation: 3074/29=106 Current State: 52:[54, 106], Operations: ['53*58=3074', '3074/29=106'] Exploring Operation: 106-54=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[53, 29, 54, 58], Operations: [] Exploring Operation: 58/29=2, Resulting Numbers: [53, 54, 2] Generated Node #0,0: 52:[53, 54, 2] Operation: 58/29=2 Moving to Node #0,0 Current State: 52:[53, 54, 2], Operations: ['58/29=2'] Exploring Operation: 54-53=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 52:[2, 1] Operation: 54-53=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 52:[2, 1], Operations: ['58/29=2', '54-53=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,52 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
[ 40, 12, 96, 47 ]
91
[ "40+12=52", "96+47=143", "143-52=91" ]
Current State: 91:[40, 12, 96, 47], Operations: [] Exploring Operation: 40+12=52, Resulting Numbers: [96, 47, 52] Generated Node #2: [96, 47, 52] from Operation: 40+12=52 Current State: 91:[96, 47, 52], Operations: ['40+12=52'] Exploring Operation: 96+47=143, Resulting Numbers: [52, 143] Generated Node #3: [52, 143] from Operation: 96+47=143 Current State: 91:[52, 143], Operations: ['40+12=52', '96+47=143'] Exploring Operation: 143-52=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[40, 12, 96, 47], Operations: [] Exploring Operation: 47-40=7, Resulting Numbers: [12, 96, 7] Generated Node #0,0: 91:[12, 96, 7] Operation: 47-40=7 Moving to Node #0,0 Current State: 91:[12, 96, 7], Operations: ['47-40=7'] Exploring Operation: 96/12=8, Resulting Numbers: [7, 8] Generated Node #0,0,0: 91:[7, 8] Operation: 96/12=8 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 91:[7, 8], Operations: ['47-40=7', '96/12=8'] Exploring Operation: 7+8=15, Resulting Numbers: [15] 15,91 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
[ 72, 44, 52, 22 ]
92
[ "72*44=3168", "3168/22=144", "144-52=92" ]
Current State: 92:[72, 44, 52, 22], Operations: [] Exploring Operation: 72*44=3168, Resulting Numbers: [52, 22, 3168] Generated Node #2: [52, 22, 3168] from Operation: 72*44=3168 Current State: 92:[52, 22, 3168], Operations: ['72*44=3168'] Exploring Operation: 3168/22=144, Resulting Numbers: [52, 144] Generated Node #3: [52, 144] from Operation: 3168/22=144 Current State: 92:[52, 144], Operations: ['72*44=3168', '3168/22=144'] Exploring Operation: 144-52=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[72, 44, 52, 22], Operations: [] Exploring Operation: 72+22=94, Resulting Numbers: [44, 52, 94] Generated Node #0,0: 92:[44, 52, 94] Operation: 72+22=94 Exploring Operation: 72-22=50, Resulting Numbers: [44, 52, 50] Generated Node #0,1: 92:[44, 52, 50] Operation: 72-22=50 Exploring Operation: 72-52=20, Resulting Numbers: [44, 22, 20] Generated Node #0,2: 92:[44, 22, 20] Operation: 72-52=20 Exploring Operation: 72-44=28, Resulting Numbers: [52, 22, 28] Generated Node #0,3: 92:[52, 22, 28] Operation: 72-44=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 92:[44, 22, 20], Operations: ['72-52=20'] Exploring Operation: 44/22=2, Resulting Numbers: [20, 2] Generated Node #0,2,0: 92:[20, 2] Operation: 44/22=2 Exploring Operation: 44-22=22, Resulting Numbers: [20, 22] Generated Node #0,2,1: 92:[20, 22] Operation: 44-22=22 Exploring Operation: 22-20=2, Resulting Numbers: [44, 2] Generated Node #0,2,2: 92:[44, 2] Operation: 22-20=2 Exploring Operation: 44-20=24, Resulting Numbers: [22, 24] Generated Node #0,2,3: 92:[22, 24] Operation: 44-20=24 Moving to Node #0,2,2 Current State: 92:[44, 2], Operations: ['72-52=20', '22-20=2'] Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[22, 24], Operations: ['72-52=20', '44-20=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,92 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,92 unequal: No Solution Moving to Node #0,2,0 Current State: 92:[20, 2], Operations: ['72-52=20', '44/22=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,92 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,92 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[20, 22], Operations: ['72-52=20', '44-22=22'] Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,92 unequal: No Solution Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,92 unequal: No Solution No 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: 92:[44, 52, 94], Operations: ['72+22=94'] Exploring Operation: 52-44=8, Resulting Numbers: [94, 8] Generated Node #0,0,0: 92:[94, 8] Operation: 52-44=8 Exploring Operation: 94-52=42, Resulting Numbers: [44, 42] Generated Node #0,0,1: 92:[44, 42] Operation: 94-52=42 Exploring Operation: 44+52=96, Resulting Numbers: [94, 96] Generated Node #0,0,2: 92:[94, 96] Operation: 44+52=96 Exploring Operation: 94-44=50, Resulting Numbers: [52, 50] Generated Node #0,0,3: 92:[52, 50] Operation: 94-44=50 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[94, 8], Operations: ['72+22=94', '52-44=8'] Exploring Operation: 94-8=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 94+8=102, Resulting Numbers: [102] 102,92 unequal: No Solution Exploring Operation: 94*8=752, Resulting Numbers: [752] 752,92 unequal: No Solution No 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: 92:[44, 42], Operations: ['72+22=94', '94-52=42'] Exploring Operation: 44-42=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 44+42=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 44*42=1848, Resulting Numbers: [1848] 1848,92 unequal: No Solution No 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: 92:[94, 96], Operations: ['72+22=94', '44+52=96'] Exploring Operation: 94+96=190, Resulting Numbers: [190] 190,92 unequal: No Solution Exploring Operation: 94*96=9024, Resulting Numbers: [9024] 9024,92 unequal: No Solution Exploring Operation: 96-94=2, Resulting Numbers: [2] 2,92 unequal: No Solution No 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: 92:[52, 50], Operations: ['72+22=94', '94-44=50'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,92 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,92 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: 92:[44, 52, 50], Operations: ['72-22=50'] Exploring Operation: 52-50=2, Resulting Numbers: [44, 2] Generated Node #0,1,0: 92:[44, 2] Operation: 52-50=2 Exploring Operation: 44+52=96, Resulting Numbers: [50, 96] Generated Node #0,1,1: 92:[50, 96] Operation: 44+52=96 Exploring Operation: 52-44=8, Resulting Numbers: [50, 8] Generated Node #0,1,2: 92:[50, 8] Operation: 52-44=8 Exploring Operation: 44+50=94, Resulting Numbers: [52, 94] Generated Node #0,1,3: 92:[52, 94] Operation: 44+50=94 Moving to Node #0,1,0 Current State: 92:[44, 2], Operations: ['72-22=50', '52-50=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,92 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,92 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,92 unequal: No Solution Moving to Node #0,1,2 Current State: 92:[50, 8], Operations: ['72-22=50', '52-44=8'] Exploring Operation: 50-8=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 50+8=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 50*8=400, Resulting Numbers: [400] 400,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[50, 96], Operations: ['72-22=50', '44+52=96'] Exploring Operation: 96-50=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 50*96=4800, Resulting Numbers: [4800] 4800,92 unequal: No Solution Exploring Operation: 50+96=146, Resulting Numbers: [146] 146,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[52, 94], Operations: ['72-22=50', '44+50=94'] Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 52*94=4888, Resulting Numbers: [4888] 4888,92 unequal: No Solution Exploring Operation: 52+94=146, Resulting Numbers: [146] 146,92 unequal: No Solution No 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: 92:[52, 22, 28], Operations: ['72-44=28'] Exploring Operation: 52-22=30, Resulting Numbers: [28, 30] Generated Node #0,3,0: 92:[28, 30] Operation: 52-22=30 Exploring Operation: 52-28=24, Resulting Numbers: [22, 24] Generated Node #0,3,1: 92:[22, 24] Operation: 52-28=24 Exploring Operation: 22+28=50, Resulting Numbers: [52, 50] Generated Node #0,3,2: 92:[52, 50] Operation: 22+28=50 Exploring Operation: 28-22=6, Resulting Numbers: [52, 6] Generated Node #0,3,3: 92:[52, 6] Operation: 28-22=6 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 92:[22, 24], Operations: ['72-44=28', '52-28=24'] Exploring Operation: 22*24=528, Resulting Numbers: [528] 528,92 unequal: No Solution Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,92 unequal: No Solution No 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: 92:[52, 6], Operations: ['72-44=28', '28-22=6'] Exploring Operation: 52+6=58, Resulting Numbers: [58] 58,92 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,92 unequal: No Solution Exploring Operation: 52*6=312, Resulting Numbers: [312] 312,92 unequal: No Solution No 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: 92:[52, 50], Operations: ['72-44=28', '22+28=50'] Exploring Operation: 52-50=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 52+50=102, Resulting Numbers: [102] 102,92 unequal: No Solution Exploring Operation: 52*50=2600, Resulting Numbers: [2600] 2600,92 unequal: No Solution No 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: 92:[28, 30], Operations: ['72-44=28', '52-22=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,92 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,92 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,92 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 44, 37, 68, 95 ]
65
[ "37+95=132", "132/44=3", "68-3=65" ]
Current State: 65:[44, 37, 68, 95], Operations: [] Exploring Operation: 37+95=132, Resulting Numbers: [44, 68, 132] Generated Node #2: [44, 68, 132] from Operation: 37+95=132 Current State: 65:[44, 68, 132], Operations: ['37+95=132'] Exploring Operation: 132/44=3, Resulting Numbers: [68, 3] Generated Node #3: [68, 3] from Operation: 132/44=3 Current State: 65:[68, 3], Operations: ['37+95=132', '132/44=3'] Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[44, 37, 68, 95], Operations: [] Exploring Operation: 95-37=58, Resulting Numbers: [44, 68, 58] Generated Node #0,0: 65:[44, 68, 58] Operation: 95-37=58 Moving to Node #0,0 Current State: 65:[44, 68, 58], Operations: ['95-37=58'] Exploring Operation: 58-44=14, Resulting Numbers: [68, 14] Generated Node #0,0,0: 65:[68, 14] Operation: 58-44=14 Moving to Node #0,0,0 Current State: 65:[68, 14], Operations: ['95-37=58', '58-44=14'] Exploring Operation: 68-14=54, Resulting Numbers: [54] 54,65 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 37, 20, 24, 58 ]
99
[ "37-20=17", "24+58=82", "17+82=99" ]
Current State: 99:[37, 20, 24, 58], Operations: [] Exploring Operation: 37-20=17, Resulting Numbers: [24, 58, 17] Generated Node #2: [24, 58, 17] from Operation: 37-20=17 Current State: 99:[24, 58, 17], Operations: ['37-20=17'] Exploring Operation: 24+58=82, Resulting Numbers: [17, 82] Generated Node #3: [17, 82] from Operation: 24+58=82 Current State: 99:[17, 82], Operations: ['37-20=17', '24+58=82'] Exploring Operation: 17+82=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[37, 20, 24, 58], Operations: [] Exploring Operation: 58-24=34, Resulting Numbers: [37, 20, 34] Generated Node #0,0: 99:[37, 20, 34] Operation: 58-24=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[37, 20, 34], Operations: ['58-24=34'] Exploring Operation: 37-20=17, Resulting Numbers: [34, 17] Generated Node #0,0,0: 99:[34, 17] Operation: 37-20=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[34, 17], Operations: ['58-24=34', '37-20=17'] Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,99 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
[ 72, 76, 88, 30 ]
54
[ "76-72=4", "88-30=58", "58-4=54" ]
Current State: 54:[72, 76, 88, 30], Operations: [] Exploring Operation: 76-72=4, Resulting Numbers: [88, 30, 4] Generated Node #2: [88, 30, 4] from Operation: 76-72=4 Current State: 54:[88, 30, 4], Operations: ['76-72=4'] Exploring Operation: 88-30=58, Resulting Numbers: [4, 58] Generated Node #3: [4, 58] from Operation: 88-30=58 Current State: 54:[4, 58], Operations: ['76-72=4', '88-30=58'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[72, 76, 88, 30], Operations: [] Exploring Operation: 88-76=12, Resulting Numbers: [72, 30, 12] Generated Node #0,0: 54:[72, 30, 12] Operation: 88-76=12 Moving to Node #0,0 Current State: 54:[72, 30, 12], Operations: ['88-76=12'] Exploring Operation: 72/12=6, Resulting Numbers: [30, 6] Generated Node #0,0,0: 54:[30, 6] Operation: 72/12=6 Moving to Node #0,0,0 Current State: 54:[30, 6], Operations: ['88-76=12', '72/12=6'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,54 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 14, 16, 58, 56 ]
57
[ "16-14=2", "58+56=114", "114/2=57" ]
Current State: 57:[14, 16, 58, 56], Operations: [] Exploring Operation: 16-14=2, Resulting Numbers: [58, 56, 2] Generated Node #2: [58, 56, 2] from Operation: 16-14=2 Current State: 57:[58, 56, 2], Operations: ['16-14=2'] Exploring Operation: 58+56=114, Resulting Numbers: [2, 114] Generated Node #3: [2, 114] from Operation: 58+56=114 Current State: 57:[2, 114], Operations: ['16-14=2', '58+56=114'] Exploring Operation: 114/2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[14, 16, 58, 56], Operations: [] Exploring Operation: 56/14=4, Resulting Numbers: [16, 58, 4] Generated Node #0,0: 57:[16, 58, 4] Operation: 56/14=4 Exploring Operation: 16-14=2, Resulting Numbers: [58, 56, 2] Generated Node #0,1: 57:[58, 56, 2] Operation: 16-14=2 Moving to Node #0,1 Current State: 57:[58, 56, 2], Operations: ['16-14=2'] Exploring Operation: 58-56=2, Resulting Numbers: [2, 2] Generated Node #0,1,0: 57:[2, 2] Operation: 58-56=2 Exploring Operation: 58-2=56, Resulting Numbers: [56, 56] Generated Node #0,1,1: 57:[56, 56] Operation: 58-2=56 Moving to Node #0,0 Current State: 57:[16, 58, 4], Operations: ['56/14=4'] Exploring Operation: 16+4=20, Resulting Numbers: [58, 20] Generated Node #0,0,0: 57:[58, 20] Operation: 16+4=20 Exploring Operation: 16/4=4, Resulting Numbers: [58, 4] Generated Node #0,0,1: 57:[58, 4] Operation: 16/4=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 57:[58, 20], Operations: ['56/14=4', '16+4=20'] Exploring Operation: 58-20=38, Resulting Numbers: [38] 38,57 unequal: No Solution Exploring Operation: 58+20=78, Resulting Numbers: [78] 78,57 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 #0,0,1 Current State: 57:[58, 4], Operations: ['56/14=4', '16/4=4'] Exploring Operation: 58-4=54, Resulting Numbers: [54] 54,57 unequal: No Solution Exploring Operation: 58+4=62, Resulting Numbers: [62] 62,57 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: 57:[2, 2], Operations: ['16-14=2', '58-56=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,57 unequal: No Solution Moving to Node #0,1,1 Current State: 57:[56, 56], Operations: ['16-14=2', '58-2=56'] Exploring Operation: 56-56=0, Resulting Numbers: [0] 0,57 unequal: No Solution Exploring Operation: 56/56=1, Resulting Numbers: [1] 1,57 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 25, 83, 41, 11 ]
93
[ "41-25=16", "11*16=176", "176-83=93" ]
Current State: 93:[25, 83, 41, 11], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [83, 11, 16] Generated Node #2: [83, 11, 16] from Operation: 41-25=16 Current State: 93:[83, 11, 16], Operations: ['41-25=16'] Exploring Operation: 11*16=176, Resulting Numbers: [83, 176] Generated Node #3: [83, 176] from Operation: 11*16=176 Current State: 93:[83, 176], Operations: ['41-25=16', '11*16=176'] Exploring Operation: 176-83=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[25, 83, 41, 11], Operations: [] Exploring Operation: 41-11=30, Resulting Numbers: [25, 83, 30] Generated Node #0,0: 93:[25, 83, 30] Operation: 41-11=30 Exploring Operation: 83+11=94, Resulting Numbers: [25, 41, 94] Generated Node #0,1: 93:[25, 41, 94] Operation: 83+11=94 Moving to Node #0,0 Current State: 93:[25, 83, 30], Operations: ['41-11=30'] Exploring Operation: 25+83=108, Resulting Numbers: [30, 108] Generated Node #0,0,0: 93:[30, 108] Operation: 25+83=108 Exploring Operation: 30-25=5, Resulting Numbers: [83, 5] Generated Node #0,0,1: 93:[83, 5] Operation: 30-25=5 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 93:[83, 5], Operations: ['41-11=30', '30-25=5'] Exploring Operation: 83+5=88, Resulting Numbers: [88] 88,93 unequal: No Solution Exploring Operation: 83-5=78, Resulting Numbers: [78] 78,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[30, 108], Operations: ['41-11=30', '25+83=108'] Exploring Operation: 30+108=138, Resulting Numbers: [138] 138,93 unequal: No Solution Exploring Operation: 108-30=78, Resulting Numbers: [78] 78,93 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: 93:[25, 41, 94], Operations: ['83+11=94'] Exploring Operation: 25+41=66, Resulting Numbers: [94, 66] Generated Node #0,1,0: 93:[94, 66] Operation: 25+41=66 Exploring Operation: 41-25=16, Resulting Numbers: [94, 16] Generated Node #0,1,1: 93:[94, 16] Operation: 41-25=16 Moving to Node #0,1,1 Current State: 93:[94, 16], Operations: ['83+11=94', '41-25=16'] Exploring Operation: 94+16=110, Resulting Numbers: [110] 110,93 unequal: No Solution Exploring Operation: 94-16=78, Resulting Numbers: [78] 78,93 unequal: No Solution Moving to Node #0,1,0 Current State: 93:[94, 66], Operations: ['83+11=94', '25+41=66'] Exploring Operation: 94+66=160, Resulting Numbers: [160] 160,93 unequal: No Solution Exploring Operation: 94-66=28, Resulting Numbers: [28] 28,93 unequal: No Solution No solution found.
0
hs_2
mult_heuristic