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
[ 21, 7, 63, 79 ]
24
[ "63/21=3", "79-7=72", "72/3=24" ]
Current State: 24:[21, 7, 63, 79], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [7, 79, 3] Generated Node #2: [7, 79, 3] from Operation: 63/21=3 Current State: 24:[7, 79, 3], Operations: ['63/21=3'] Exploring Operation: 79-7=72, Resulting Numbers: [3, 72] Generated Node #3: [3, 72] from Operation: 79-7=72 Current State: 24:[3, 72], Operations: ['63/21=3', '79-7=72'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[21, 7, 63, 79], Operations: [] Exploring Operation: 79-63=16, Resulting Numbers: [21, 7, 16] Generated Node #0,0: 24:[21, 7, 16] Operation: 79-63=16 Exploring Operation: 63/7=9, Resulting Numbers: [21, 79, 9] Generated Node #0,1: 24:[21, 79, 9] Operation: 63/7=9 Exploring Operation: 63/21=3, Resulting Numbers: [7, 79, 3] Generated Node #0,2: 24:[7, 79, 3] Operation: 63/21=3 Exploring Operation: 79-21=58, Resulting Numbers: [7, 63, 58] Generated Node #0,3: 24:[7, 63, 58] Operation: 79-21=58 Exploring Operation: 63-21=42, Resulting Numbers: [7, 79, 42] Generated Node #0,4: 24:[7, 79, 42] Operation: 63-21=42 Moving to Node #0,0 Current State: 24:[21, 7, 16], Operations: ['79-63=16'] Exploring Operation: 16-7=9, Resulting Numbers: [21, 9] Generated Node #0,0,0: 24:[21, 9] Operation: 16-7=9 Exploring Operation: 21/7=3, Resulting Numbers: [16, 3] Generated Node #0,0,1: 24:[16, 3] Operation: 21/7=3 Exploring Operation: 21-7=14, Resulting Numbers: [16, 14] Generated Node #0,0,2: 24:[16, 14] Operation: 21-7=14 Exploring Operation: 7+16=23, Resulting Numbers: [21, 23] Generated Node #0,0,3: 24:[21, 23] Operation: 7+16=23 Exploring Operation: 21-16=5, Resulting Numbers: [7, 5] Generated Node #0,0,4: 24:[7, 5] Operation: 21-16=5 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 24:[7, 5], Operations: ['79-63=16', '21-16=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[21, 9], Operations: ['79-63=16', '16-7=9'] Exploring Operation: 21-9=12, Resulting Numbers: [12] 12,24 unequal: No Solution Exploring Operation: 21*9=189, Resulting Numbers: [189] 189,24 unequal: No Solution Exploring Operation: 21+9=30, Resulting Numbers: [30] 30,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[16, 3], Operations: ['79-63=16', '21/7=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,24 unequal: No Solution Exploring Operation: 16*3=48, Resulting Numbers: [48] 48,24 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 24:[21, 23], Operations: ['79-63=16', '7+16=23'] Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,24 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[16, 14], Operations: ['79-63=16', '21-7=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,24 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,24 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: 24:[7, 79, 3], Operations: ['63/21=3'] Exploring Operation: 7*3=21, Resulting Numbers: [79, 21] Generated Node #0,2,0: 24:[79, 21] Operation: 7*3=21 Exploring Operation: 79-7=72, Resulting Numbers: [3, 72] Generated Node #0,2,1: 24:[3, 72] Operation: 79-7=72 Exploring Operation: 79-3=76, Resulting Numbers: [7, 76] Generated Node #0,2,2: 24:[7, 76] Operation: 79-3=76 Exploring Operation: 7-3=4, Resulting Numbers: [79, 4] Generated Node #0,2,3: 24:[79, 4] Operation: 7-3=4 Exploring Operation: 7+3=10, Resulting Numbers: [79, 10] Generated Node #0,2,4: 24:[79, 10] Operation: 7+3=10 Moving to Node #0,1 Current State: 24:[21, 79, 9], Operations: ['63/7=9'] Exploring Operation: 79+9=88, Resulting Numbers: [21, 88] Generated Node #0,1,0: 24:[21, 88] Operation: 79+9=88 Exploring Operation: 21-9=12, Resulting Numbers: [79, 12] Generated Node #0,1,1: 24:[79, 12] Operation: 21-9=12 Exploring Operation: 79-9=70, Resulting Numbers: [21, 70] Generated Node #0,1,2: 24:[21, 70] Operation: 79-9=70 Exploring Operation: 79-21=58, Resulting Numbers: [9, 58] Generated Node #0,1,3: 24:[9, 58] Operation: 79-21=58 Exploring Operation: 21+9=30, Resulting Numbers: [79, 30] Generated Node #0,1,4: 24:[79, 30] Operation: 21+9=30 Moving to Node #0,3 Current State: 24:[7, 63, 58], Operations: ['79-21=58'] Exploring Operation: 63/7=9, Resulting Numbers: [58, 9] Generated Node #0,3,0: 24:[58, 9] Operation: 63/7=9 Exploring Operation: 58-7=51, Resulting Numbers: [63, 51] Generated Node #0,3,1: 24:[63, 51] Operation: 58-7=51 Exploring Operation: 63-58=5, Resulting Numbers: [7, 5] Generated Node #0,3,2: 24:[7, 5] Operation: 63-58=5 Exploring Operation: 63-7=56, Resulting Numbers: [58, 56] Generated Node #0,3,3: 24:[58, 56] Operation: 63-7=56 Exploring Operation: 7+63=70, Resulting Numbers: [58, 70] Generated Node #0,3,4: 24:[58, 70] Operation: 7+63=70 Moving to Node #0,4 Current State: 24:[7, 79, 42], Operations: ['63-21=42'] Exploring Operation: 79-42=37, Resulting Numbers: [7, 37] Generated Node #0,4,0: 24:[7, 37] Operation: 79-42=37 Exploring Operation: 42/7=6, Resulting Numbers: [79, 6] Generated Node #0,4,1: 24:[79, 6] Operation: 42/7=6 Exploring Operation: 79-7=72, Resulting Numbers: [42, 72] Generated Node #0,4,2: 24:[42, 72] Operation: 79-7=72 Exploring Operation: 42-7=35, Resulting Numbers: [79, 35] Generated Node #0,4,3: 24:[79, 35] Operation: 42-7=35 Exploring Operation: 7+79=86, Resulting Numbers: [42, 86] Generated Node #0,4,4: 24:[42, 86] Operation: 7+79=86 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 24:[7, 37], Operations: ['63-21=42', '79-42=37'] Exploring Operation: 7*37=259, Resulting Numbers: [259] 259,24 unequal: No Solution Exploring Operation: 7+37=44, Resulting Numbers: [44] 44,24 unequal: No Solution Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 24:[79, 6], Operations: ['63-21=42', '42/7=6'] Exploring Operation: 79*6=474, Resulting Numbers: [474] 474,24 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,24 unequal: No Solution Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 24:[42, 72], Operations: ['63-21=42', '79-7=72'] Exploring Operation: 72-42=30, Resulting Numbers: [30] 30,24 unequal: No Solution Exploring Operation: 42*72=3024, Resulting Numbers: [3024] 3024,24 unequal: No Solution Exploring Operation: 42+72=114, Resulting Numbers: [114] 114,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 24:[79, 35], Operations: ['63-21=42', '42-7=35'] Exploring Operation: 79*35=2765, Resulting Numbers: [2765] 2765,24 unequal: No Solution Exploring Operation: 79+35=114, Resulting Numbers: [114] 114,24 unequal: No Solution Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 24:[42, 86], Operations: ['63-21=42', '7+79=86'] Exploring Operation: 42+86=128, Resulting Numbers: [128] 128,24 unequal: No Solution Exploring Operation: 42*86=3612, Resulting Numbers: [3612] 3612,24 unequal: No Solution Exploring Operation: 86-42=44, Resulting Numbers: [44] 44,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 24:[7, 5], Operations: ['79-21=58', '63-58=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,24 unequal: No Solution Exploring Operation: 7-5=2, Resulting Numbers: [2] 2,24 unequal: No Solution Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,24 unequal: No Solution Moving to Node #0,3,0 Current State: 24:[58, 9], Operations: ['79-21=58', '63/7=9'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,24 unequal: No Solution Exploring Operation: 58*9=522, Resulting Numbers: [522] 522,24 unequal: No Solution Exploring Operation: 58+9=67, Resulting Numbers: [67] 67,24 unequal: No Solution Moving to Node #0,1,3 Current State: 24:[9, 58], Operations: ['63/7=9', '79-21=58'] Exploring Operation: 9+58=67, Resulting Numbers: [67] 67,24 unequal: No Solution Exploring Operation: 9*58=522, Resulting Numbers: [522] 522,24 unequal: No Solution Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,24 unequal: No Solution Moving to Node #0,2,1 Current State: 24:[3, 72], Operations: ['63/21=3', '79-7=72'] Exploring Operation: 3+72=75, Resulting Numbers: [75] 75,24 unequal: No Solution Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[21, 7, 63, 79], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [7, 79, 3] Generated Node #0,2: 24:[7, 79, 3] Operation: 63/21=3 Moving to Node #0,2 Current State: 24:[7, 79, 3], Operations: ['63/21=3'] Exploring Operation: 79-7=72, Resulting Numbers: [3, 72] Generated Node #0,2,1: 24:[3, 72] Operation: 79-7=72 Moving to Node #0,2,1 Current State: 24:[3, 72], Operations: ['63/21=3', '79-7=72'] Exploring Operation: 72/3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
0.934896
hs_5
sum_heuristic
[ 68, 31, 44, 21 ]
76
[ "68+31=99", "44-21=23", "99-23=76" ]
Current State: 76:[68, 31, 44, 21], Operations: [] Exploring Operation: 68+31=99, Resulting Numbers: [44, 21, 99] Generated Node #2: [44, 21, 99] from Operation: 68+31=99 Current State: 76:[44, 21, 99], Operations: ['68+31=99'] Exploring Operation: 44-21=23, Resulting Numbers: [99, 23] Generated Node #3: [99, 23] from Operation: 44-21=23 Current State: 76:[99, 23], Operations: ['68+31=99', '44-21=23'] Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[68, 31, 44, 21], Operations: [] Exploring Operation: 68-31=37, Resulting Numbers: [44, 21, 37] Generated Node #0,0: 76:[44, 21, 37] Operation: 68-31=37 Moving to Node #0,0 Current State: 76:[44, 21, 37], Operations: ['68-31=37'] Exploring Operation: 44-21=23, Resulting Numbers: [37, 23] Generated Node #0,0,0: 76:[37, 23] Operation: 44-21=23 Moving to Node #0,0,0 Current State: 76:[37, 23], Operations: ['68-31=37', '44-21=23'] Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,76 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 25, 13, 7, 24 ]
55
[ "25+13=38", "24-7=17", "38+17=55" ]
Current State: 55:[25, 13, 7, 24], Operations: [] Exploring Operation: 25+13=38, Resulting Numbers: [7, 24, 38] Generated Node #2: [7, 24, 38] from Operation: 25+13=38 Current State: 55:[7, 24, 38], Operations: ['25+13=38'] Exploring Operation: 24-7=17, Resulting Numbers: [38, 17] Generated Node #3: [38, 17] from Operation: 24-7=17 Current State: 55:[38, 17], Operations: ['25+13=38', '24-7=17'] Exploring Operation: 38+17=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[25, 13, 7, 24], Operations: [] Exploring Operation: 25-24=1, Resulting Numbers: [13, 7, 1] Generated Node #0,0: 55:[13, 7, 1] Operation: 25-24=1 Moving to Node #0,0 Current State: 55:[13, 7, 1], Operations: ['25-24=1'] Exploring Operation: 13-1=12, Resulting Numbers: [7, 12] Generated Node #0,0,0: 55:[7, 12] Operation: 13-1=12 Moving to Node #0,0,0 Current State: 55:[7, 12], Operations: ['25-24=1', '13-1=12'] Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,55 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 19, 70, 21, 12 ]
67
[ "19-12=7", "21/7=3", "70-3=67" ]
Current State: 67:[19, 70, 21, 12], Operations: [] Exploring Operation: 19-12=7, Resulting Numbers: [70, 21, 7] Generated Node #2: [70, 21, 7] from Operation: 19-12=7 Current State: 67:[70, 21, 7], Operations: ['19-12=7'] Exploring Operation: 21/7=3, Resulting Numbers: [70, 3] Generated Node #3: [70, 3] from Operation: 21/7=3 Current State: 67:[70, 3], Operations: ['19-12=7', '21/7=3'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[19, 70, 21, 12], Operations: [] Exploring Operation: 19+21=40, Resulting Numbers: [70, 12, 40] Generated Node #0,0: 67:[70, 12, 40] Operation: 19+21=40 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[70, 12, 40], Operations: ['19+21=40'] Exploring Operation: 12+40=52, Resulting Numbers: [70, 52] Generated Node #0,0,0: 67:[70, 52] Operation: 12+40=52 Moving to Node #0,0,0 Current State: 67:[70, 52], Operations: ['19+21=40', '12+40=52'] Exploring Operation: 70-52=18, Resulting Numbers: [18] 18,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 6, 13, 83, 4 ]
86
[ "13-6=7", "83-4=79", "7+79=86" ]
Current State: 86:[6, 13, 83, 4], Operations: [] Exploring Operation: 13-6=7, Resulting Numbers: [83, 4, 7] Generated Node #2: [83, 4, 7] from Operation: 13-6=7 Current State: 86:[83, 4, 7], Operations: ['13-6=7'] Exploring Operation: 83-4=79, Resulting Numbers: [7, 79] Generated Node #3: [7, 79] from Operation: 83-4=79 Current State: 86:[7, 79], Operations: ['13-6=7', '83-4=79'] Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[6, 13, 83, 4], Operations: [] Exploring Operation: 13-6=7, Resulting Numbers: [83, 4, 7] Generated Node #0,0: 86:[83, 4, 7] Operation: 13-6=7 Exploring Operation: 13-4=9, Resulting Numbers: [6, 83, 9] Generated Node #0,1: 86:[6, 83, 9] Operation: 13-4=9 Exploring Operation: 6*13=78, Resulting Numbers: [83, 4, 78] Generated Node #0,2: 86:[83, 4, 78] Operation: 6*13=78 Exploring Operation: 6-4=2, Resulting Numbers: [13, 83, 2] Generated Node #0,3: 86:[13, 83, 2] Operation: 6-4=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[83, 4, 7], Operations: ['13-6=7'] Exploring Operation: 7-4=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 7-4=3 Exploring Operation: 83+4=87, Resulting Numbers: [7, 87] Generated Node #0,0,1: 86:[7, 87] Operation: 83+4=87 Exploring Operation: 83+7=90, Resulting Numbers: [4, 90] Generated Node #0,0,2: 86:[4, 90] Operation: 83+7=90 Exploring Operation: 83-4=79, Resulting Numbers: [7, 79] Generated Node #0,0,3: 86:[7, 79] Operation: 83-4=79 Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['13-6=7', '7-4=3'] Exploring Operation: 83*3=249, Resulting Numbers: [249] 249,86 unequal: No Solution Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[6, 13, 83, 4], Operations: [] Exploring Operation: 13-6=7, Resulting Numbers: [83, 4, 7] Generated Node #0,0: 86:[83, 4, 7] Operation: 13-6=7 Moving to Node #0,0 Current State: 86:[83, 4, 7], Operations: ['13-6=7'] Exploring Operation: 7-4=3, Resulting Numbers: [83, 3] Generated Node #0,0,0: 86:[83, 3] Operation: 7-4=3 Moving to Node #0,0,0 Current State: 86:[83, 3], Operations: ['13-6=7', '7-4=3'] Exploring Operation: 83+3=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 64, 39, 4, 42 ]
58
[ "64-39=25", "4*25=100", "100-42=58" ]
Current State: 58:[64, 39, 4, 42], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [4, 42, 25] Generated Node #2: [4, 42, 25] from Operation: 64-39=25 Current State: 58:[4, 42, 25], Operations: ['64-39=25'] Exploring Operation: 4*25=100, Resulting Numbers: [42, 100] Generated Node #3: [42, 100] from Operation: 4*25=100 Current State: 58:[42, 100], Operations: ['64-39=25', '4*25=100'] Exploring Operation: 100-42=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[64, 39, 4, 42], Operations: [] Exploring Operation: 64-39=25, Resulting Numbers: [4, 42, 25] Generated Node #0,0: 58:[4, 42, 25] Operation: 64-39=25 Exploring Operation: 64-42=22, Resulting Numbers: [39, 4, 22] Generated Node #0,1: 58:[39, 4, 22] Operation: 64-42=22 Exploring Operation: 42-39=3, Resulting Numbers: [64, 4, 3] Generated Node #0,2: 58:[64, 4, 3] Operation: 42-39=3 Exploring Operation: 64-4=60, Resulting Numbers: [39, 42, 60] Generated Node #0,3: 58:[39, 42, 60] Operation: 64-4=60 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[64, 4, 3], Operations: ['42-39=3'] Exploring Operation: 64+4=68, Resulting Numbers: [3, 68] Generated Node #0,2,0: 58:[3, 68] Operation: 64+4=68 Exploring Operation: 64-4=60, Resulting Numbers: [3, 60] Generated Node #0,2,1: 58:[3, 60] Operation: 64-4=60 Exploring Operation: 64-3=61, Resulting Numbers: [4, 61] Generated Node #0,2,2: 58:[4, 61] Operation: 64-3=61 Exploring Operation: 4-3=1, Resulting Numbers: [64, 1] Generated Node #0,2,3: 58:[64, 1] Operation: 4-3=1 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 58:[3, 60], Operations: ['42-39=3', '64-4=60'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,58 unequal: No Solution Exploring Operation: 3*60=180, Resulting Numbers: [180] 180,58 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 3+60=63, Resulting Numbers: [63] 63,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 58:[4, 61], Operations: ['42-39=3', '64-3=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,58 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 58:[64, 1], Operations: ['42-39=3', '4-3=1'] Exploring Operation: 64+1=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 64/1=64, Resulting Numbers: [64] 64,58 unequal: No Solution Exploring Operation: 64*1=64, Resulting Numbers: [64] 64,58 unequal: No Solution Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 58:[3, 68], Operations: ['42-39=3', '64+4=68'] Exploring Operation: 3+68=71, Resulting Numbers: [71] 71,58 unequal: No Solution Exploring Operation: 68-3=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 3*68=204, Resulting Numbers: [204] 204,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[4, 42, 25], Operations: ['64-39=25'] Exploring Operation: 42-4=38, Resulting Numbers: [25, 38] Generated Node #0,0,0: 58:[25, 38] Operation: 42-4=38 Exploring Operation: 42-25=17, Resulting Numbers: [4, 17] Generated Node #0,0,1: 58:[4, 17] Operation: 42-25=17 Exploring Operation: 42+25=67, Resulting Numbers: [4, 67] Generated Node #0,0,2: 58:[4, 67] Operation: 42+25=67 Exploring Operation: 4+25=29, Resulting Numbers: [42, 29] Generated Node #0,0,3: 58:[42, 29] Operation: 4+25=29 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 58:[4, 67], Operations: ['64-39=25', '42+25=67'] Exploring Operation: 67-4=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 4*67=268, Resulting Numbers: [268] 268,58 unequal: No Solution Exploring Operation: 4+67=71, Resulting Numbers: [71] 71,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[25, 38], Operations: ['64-39=25', '42-4=38'] Exploring Operation: 25+38=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 25*38=950, Resulting Numbers: [950] 950,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 58:[42, 29], Operations: ['64-39=25', '4+25=29'] Exploring Operation: 42-29=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 42*29=1218, Resulting Numbers: [1218] 1218,58 unequal: No Solution Exploring Operation: 42+29=71, Resulting Numbers: [71] 71,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 58:[4, 17], Operations: ['64-39=25', '42-25=17'] Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,58 unequal: No Solution Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[39, 4, 22], Operations: ['64-42=22'] Exploring Operation: 39-4=35, Resulting Numbers: [22, 35] Generated Node #0,1,0: 58:[22, 35] Operation: 39-4=35 Exploring Operation: 39-22=17, Resulting Numbers: [4, 17] Generated Node #0,1,1: 58:[4, 17] Operation: 39-22=17 Exploring Operation: 39+22=61, Resulting Numbers: [4, 61] Generated Node #0,1,2: 58:[4, 61] Operation: 39+22=61 Exploring Operation: 4+22=26, Resulting Numbers: [39, 26] Generated Node #0,1,3: 58:[39, 26] Operation: 4+22=26 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 58:[4, 61], Operations: ['64-42=22', '39+22=61'] Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,58 unequal: No Solution Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,58 unequal: No Solution Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[22, 35], Operations: ['64-42=22', '39-4=35'] Exploring Operation: 22*35=770, Resulting Numbers: [770] 770,58 unequal: No Solution Exploring Operation: 22+35=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 58:[39, 26], Operations: ['64-42=22', '4+22=26'] Exploring Operation: 39-26=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 39*26=1014, Resulting Numbers: [1014] 1014,58 unequal: No Solution Exploring Operation: 39+26=65, Resulting Numbers: [65] 65,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[4, 17], Operations: ['64-42=22', '39-22=17'] Exploring Operation: 4*17=68, Resulting Numbers: [68] 68,58 unequal: No Solution Exploring Operation: 4+17=21, Resulting Numbers: [21] 21,58 unequal: No Solution Exploring Operation: 17-4=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[39, 42, 60], Operations: ['64-4=60'] Exploring Operation: 39+42=81, Resulting Numbers: [60, 81] Generated Node #0,3,0: 58:[60, 81] Operation: 39+42=81 Exploring Operation: 60-39=21, Resulting Numbers: [42, 21] Generated Node #0,3,1: 58:[42, 21] Operation: 60-39=21 Exploring Operation: 60-42=18, Resulting Numbers: [39, 18] Generated Node #0,3,2: 58:[39, 18] Operation: 60-42=18 Exploring Operation: 42-39=3, Resulting Numbers: [60, 3] Generated Node #0,3,3: 58:[60, 3] Operation: 42-39=3 Moving to Node #0,3,3 Current State: 58:[60, 3], Operations: ['64-4=60', '42-39=3'] Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,58 unequal: No Solution Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,58 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,58 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,58 unequal: No Solution Moving to Node #0,3,2 Current State: 58:[39, 18], Operations: ['64-4=60', '60-42=18'] Exploring Operation: 39+18=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 39*18=702, Resulting Numbers: [702] 702,58 unequal: No Solution Exploring Operation: 39-18=21, Resulting Numbers: [21] 21,58 unequal: No Solution Moving to Node #0,3,1 Current State: 58:[42, 21], Operations: ['64-4=60', '60-39=21'] Exploring Operation: 42-21=21, Resulting Numbers: [21] 21,58 unequal: No Solution Exploring Operation: 42/21=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 42*21=882, Resulting Numbers: [882] 882,58 unequal: No Solution Exploring Operation: 42+21=63, Resulting Numbers: [63] 63,58 unequal: No Solution Moving to Node #0,3,0 Current State: 58:[60, 81], Operations: ['64-4=60', '39+42=81'] Exploring Operation: 81-60=21, Resulting Numbers: [21] 21,58 unequal: No Solution Exploring Operation: 60+81=141, Resulting Numbers: [141] 141,58 unequal: No Solution Exploring Operation: 60*81=4860, Resulting Numbers: [4860] 4860,58 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
[ 21, 40, 11, 10 ]
99
[ "40-21=19", "19-10=9", "11*9=99" ]
Current State: 99:[21, 40, 11, 10], Operations: [] Exploring Operation: 40-21=19, Resulting Numbers: [11, 10, 19] Generated Node #2: [11, 10, 19] from Operation: 40-21=19 Current State: 99:[11, 10, 19], Operations: ['40-21=19'] Exploring Operation: 19-10=9, Resulting Numbers: [11, 9] Generated Node #3: [11, 9] from Operation: 19-10=9 Current State: 99:[11, 9], Operations: ['40-21=19', '19-10=9'] Exploring Operation: 11*9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[21, 40, 11, 10], Operations: [] Exploring Operation: 21-10=11, Resulting Numbers: [40, 11, 11] Generated Node #0,0: 99:[40, 11, 11] Operation: 21-10=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[40, 11, 11], Operations: ['21-10=11'] Exploring Operation: 40-11=29, Resulting Numbers: [11, 29] Generated Node #0,0,0: 99:[11, 29] Operation: 40-11=29 Moving to Node #0,0,0 Current State: 99:[11, 29], Operations: ['21-10=11', '40-11=29'] Exploring Operation: 11+29=40, Resulting Numbers: [40] 40,99 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
[ 33, 34, 25, 47 ]
51
[ "33*34=1122", "47-25=22", "1122/22=51" ]
Current State: 51:[33, 34, 25, 47], Operations: [] Exploring Operation: 33*34=1122, Resulting Numbers: [25, 47, 1122] Generated Node #2: [25, 47, 1122] from Operation: 33*34=1122 Current State: 51:[25, 47, 1122], Operations: ['33*34=1122'] Exploring Operation: 47-25=22, Resulting Numbers: [1122, 22] Generated Node #3: [1122, 22] from Operation: 47-25=22 Current State: 51:[1122, 22], Operations: ['33*34=1122', '47-25=22'] Exploring Operation: 1122/22=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[33, 34, 25, 47], Operations: [] Exploring Operation: 33+34=67, Resulting Numbers: [25, 47, 67] Generated Node #0,0: 51:[25, 47, 67] Operation: 33+34=67 Exploring Operation: 34-25=9, Resulting Numbers: [33, 47, 9] Generated Node #0,1: 51:[33, 47, 9] Operation: 34-25=9 Exploring Operation: 33-25=8, Resulting Numbers: [34, 47, 8] Generated Node #0,2: 51:[34, 47, 8] Operation: 33-25=8 Exploring Operation: 34-33=1, Resulting Numbers: [25, 47, 1] Generated Node #0,3: 51:[25, 47, 1] Operation: 34-33=1 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[25, 47, 1], Operations: ['34-33=1'] Exploring Operation: 47-25=22, Resulting Numbers: [1, 22] Generated Node #0,3,0: 51:[1, 22] Operation: 47-25=22 Exploring Operation: 25*1=25, Resulting Numbers: [47, 25] Generated Node #0,3,1: 51:[47, 25] Operation: 25*1=25 Exploring Operation: 25-1=24, Resulting Numbers: [47, 24] Generated Node #0,3,2: 51:[47, 24] Operation: 25-1=24 Exploring Operation: 47+1=48, Resulting Numbers: [25, 48] Generated Node #0,3,3: 51:[25, 48] Operation: 47+1=48 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 51:[1, 22], Operations: ['34-33=1', '47-25=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 1+22=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,51 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 #0,3,2 Current State: 51:[47, 24], Operations: ['34-33=1', '25-1=24'] Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,51 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,51 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 #0,3,3 Current State: 51:[25, 48], Operations: ['34-33=1', '47+1=48'] Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 25*48=1200, Resulting Numbers: [1200] 1200,51 unequal: No Solution Exploring Operation: 25+48=73, Resulting Numbers: [73] 73,51 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 #0,3,1 Current State: 51:[47, 25], Operations: ['34-33=1', '25*1=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,51 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,51 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,51 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 #0,1 Current State: 51:[33, 47, 9], Operations: ['34-25=9'] Exploring Operation: 47-33=14, Resulting Numbers: [9, 14] Generated Node #0,1,0: 51:[9, 14] Operation: 47-33=14 Exploring Operation: 47+9=56, Resulting Numbers: [33, 56] Generated Node #0,1,1: 51:[33, 56] Operation: 47+9=56 Exploring Operation: 33+9=42, Resulting Numbers: [47, 42] Generated Node #0,1,2: 51:[47, 42] Operation: 33+9=42 Exploring Operation: 33-9=24, Resulting Numbers: [47, 24] Generated Node #0,1,3: 51:[47, 24] Operation: 33-9=24 Moving to Node #0,1,0 Current State: 51:[9, 14], Operations: ['34-25=9', '47-33=14'] Exploring Operation: 9*14=126, Resulting Numbers: [126] 126,51 unequal: No Solution Exploring Operation: 9+14=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 14-9=5, Resulting Numbers: [5] 5,51 unequal: No Solution Moving to Node #0,1,3 Current State: 51:[47, 24], Operations: ['34-25=9', '33-9=24'] Exploring Operation: 47*24=1128, Resulting Numbers: [1128] 1128,51 unequal: No Solution Exploring Operation: 47-24=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 47+24=71, Resulting Numbers: [71] 71,51 unequal: No Solution Moving to Node #0,1,2 Current State: 51:[47, 42], Operations: ['34-25=9', '33+9=42'] Exploring Operation: 47+42=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 47*42=1974, Resulting Numbers: [1974] 1974,51 unequal: No Solution Moving to Node #0,1,1 Current State: 51:[33, 56], Operations: ['34-25=9', '47+9=56'] Exploring Operation: 33*56=1848, Resulting Numbers: [1848] 1848,51 unequal: No Solution Exploring Operation: 33+56=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,51 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 #0,2 Current State: 51:[34, 47, 8], Operations: ['33-25=8'] Exploring Operation: 47-34=13, Resulting Numbers: [8, 13] Generated Node #0,2,0: 51:[8, 13] Operation: 47-34=13 Exploring Operation: 47+8=55, Resulting Numbers: [34, 55] Generated Node #0,2,1: 51:[34, 55] Operation: 47+8=55 Exploring Operation: 34+8=42, Resulting Numbers: [47, 42] Generated Node #0,2,2: 51:[47, 42] Operation: 34+8=42 Exploring Operation: 34-8=26, Resulting Numbers: [47, 26] Generated Node #0,2,3: 51:[47, 26] Operation: 34-8=26 Moving to Node #0,2,0 Current State: 51:[8, 13], Operations: ['33-25=8', '47-34=13'] Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 8+13=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 8*13=104, Resulting Numbers: [104] 104,51 unequal: No Solution Moving to Node #0,2,3 Current State: 51:[47, 26], Operations: ['33-25=8', '34-8=26'] Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,51 unequal: No Solution Exploring Operation: 47*26=1222, Resulting Numbers: [1222] 1222,51 unequal: No Solution Moving to Node #0,2,2 Current State: 51:[47, 42], Operations: ['33-25=8', '34+8=42'] Exploring Operation: 47*42=1974, Resulting Numbers: [1974] 1974,51 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 47+42=89, Resulting Numbers: [89] 89,51 unequal: No Solution Moving to Node #0,2,1 Current State: 51:[34, 55], Operations: ['33-25=8', '47+8=55'] Exploring Operation: 34*55=1870, Resulting Numbers: [1870] 1870,51 unequal: No Solution Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,51 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 Current State: 51:[25, 47, 67], Operations: ['33+34=67'] Exploring Operation: 67-47=20, Resulting Numbers: [25, 20] Generated Node #0,0,0: 51:[25, 20] Operation: 67-47=20 Exploring Operation: 25+47=72, Resulting Numbers: [67, 72] Generated Node #0,0,1: 51:[67, 72] Operation: 25+47=72 Exploring Operation: 67-25=42, Resulting Numbers: [47, 42] Generated Node #0,0,2: 51:[47, 42] Operation: 67-25=42 Exploring Operation: 47-25=22, Resulting Numbers: [67, 22] Generated Node #0,0,3: 51:[67, 22] Operation: 47-25=22 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 51:[25, 20], Operations: ['33+34=67', '67-47=20'] Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,51 unequal: No Solution Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,51 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,51 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 #0,0,2 Current State: 51:[47, 42], Operations: ['33+34=67', '67-25=42'] Exploring Operation: 47+42=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 47*42=1974, Resulting Numbers: [1974] 1974,51 unequal: No Solution Exploring Operation: 47-42=5, Resulting Numbers: [5] 5,51 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 #0,0,3 Current State: 51:[67, 22], Operations: ['33+34=67', '47-25=22'] Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,51 unequal: No Solution Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,51 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,51 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 #0,0,1 Current State: 51:[67, 72], Operations: ['33+34=67', '25+47=72'] Exploring Operation: 67*72=4824, Resulting Numbers: [4824] 4824,51 unequal: No Solution Exploring Operation: 72-67=5, Resulting Numbers: [5] 5,51 unequal: No Solution Exploring Operation: 67+72=139, Resulting Numbers: [139] 139,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 2, 1, 11, 5 ]
50
[ "2-1=1", "11-1=10", "5*10=50" ]
Current State: 50:[2, 1, 11, 5], Operations: [] Exploring Operation: 2-1=1, Resulting Numbers: [11, 5, 1] Generated Node #2: [11, 5, 1] from Operation: 2-1=1 Current State: 50:[11, 5, 1], Operations: ['2-1=1'] Exploring Operation: 11-1=10, Resulting Numbers: [5, 10] Generated Node #3: [5, 10] from Operation: 11-1=10 Current State: 50:[5, 10], Operations: ['2-1=1', '11-1=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[2, 1, 11, 5], Operations: [] Exploring Operation: 11-1=10, Resulting Numbers: [2, 5, 10] Generated Node #0,0: 50:[2, 5, 10] Operation: 11-1=10 Exploring Operation: 2*1=2, Resulting Numbers: [11, 5, 2] Generated Node #0,1: 50:[11, 5, 2] Operation: 2*1=2 Moving to Node #0,0 Current State: 50:[2, 5, 10], Operations: ['11-1=10'] Exploring Operation: 2*5=10, Resulting Numbers: [10, 10] Generated Node #0,0,0: 50:[10, 10] Operation: 2*5=10 Exploring Operation: 10/2=5, Resulting Numbers: [5, 5] Generated Node #0,0,1: 50:[5, 5] Operation: 10/2=5 Moving to Node #0,1 Current State: 50:[11, 5, 2], Operations: ['2*1=2'] Exploring Operation: 11-5=6, Resulting Numbers: [2, 6] Generated Node #0,1,0: 50:[2, 6] Operation: 11-5=6 Exploring Operation: 11-2=9, Resulting Numbers: [5, 9] Generated Node #0,1,1: 50:[5, 9] Operation: 11-2=9 Moving to Node #0,0,0 Current State: 50:[10, 10], Operations: ['11-1=10', '2*5=10'] Exploring Operation: 10-10=0, Resulting Numbers: [0] 0,50 unequal: No Solution Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,50 unequal: No Solution Moving to Node #0,0,1 Current State: 50:[5, 5], Operations: ['11-1=10', '10/2=5'] Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,50 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,50 unequal: No Solution Moving to Node #0,1,1 Current State: 50:[5, 9], Operations: ['2*1=2', '11-2=9'] Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,50 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,50 unequal: No Solution Moving to Node #0,1,0 Current State: 50:[2, 6], Operations: ['2*1=2', '11-5=6'] Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,50 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,50 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 66, 28, 23, 2 ]
28
[ "66/2=33", "28-23=5", "33-5=28" ]
Current State: 28:[66, 28, 23, 2], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [28, 23, 33] Generated Node #2: [28, 23, 33] from Operation: 66/2=33 Current State: 28:[28, 23, 33], Operations: ['66/2=33'] Exploring Operation: 28-23=5, Resulting Numbers: [33, 5] Generated Node #3: [33, 5] from Operation: 28-23=5 Current State: 28:[33, 5], Operations: ['66/2=33', '28-23=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[66, 28, 23, 2], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [28, 23, 33] Generated Node #0,0: 28:[28, 23, 33] Operation: 66/2=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[28, 23, 33], Operations: ['66/2=33'] Exploring Operation: 33-23=10, Resulting Numbers: [28, 10] Generated Node #0,0,0: 28:[28, 10] Operation: 33-23=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[28, 10], Operations: ['66/2=33', '33-23=10'] Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 74, 17, 21, 23 ]
59
[ "74-17=57", "23-21=2", "57+2=59" ]
Current State: 59:[74, 17, 21, 23], Operations: [] Exploring Operation: 74-17=57, Resulting Numbers: [21, 23, 57] Generated Node #2: [21, 23, 57] from Operation: 74-17=57 Current State: 59:[21, 23, 57], Operations: ['74-17=57'] Exploring Operation: 23-21=2, Resulting Numbers: [57, 2] Generated Node #3: [57, 2] from Operation: 23-21=2 Current State: 59:[57, 2], Operations: ['74-17=57', '23-21=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[74, 17, 21, 23], Operations: [] Exploring Operation: 17+21=38, Resulting Numbers: [74, 23, 38] Generated Node #0,0: 59:[74, 23, 38] Operation: 17+21=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[74, 23, 38], Operations: ['17+21=38'] Exploring Operation: 23+38=61, Resulting Numbers: [74, 61] Generated Node #0,0,0: 59:[74, 61] Operation: 23+38=61 Moving to Node #0,0,0 Current State: 59:[74, 61], Operations: ['17+21=38', '23+38=61'] Exploring Operation: 74-61=13, Resulting Numbers: [13] 13,59 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, 80, 96, 12 ]
17
[ "80*12=960", "960/96=10", "7+10=17" ]
Current State: 17:[7, 80, 96, 12], Operations: [] Exploring Operation: 80*12=960, Resulting Numbers: [7, 96, 960] Generated Node #2: [7, 96, 960] from Operation: 80*12=960 Current State: 17:[7, 96, 960], Operations: ['80*12=960'] Exploring Operation: 960/96=10, Resulting Numbers: [7, 10] Generated Node #3: [7, 10] from Operation: 960/96=10 Current State: 17:[7, 10], Operations: ['80*12=960', '960/96=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[7, 80, 96, 12], Operations: [] Exploring Operation: 80-12=68, Resulting Numbers: [7, 96, 68] Generated Node #0,0: 17:[7, 96, 68] Operation: 80-12=68 Exploring Operation: 96/12=8, Resulting Numbers: [7, 80, 8] Generated Node #0,1: 17:[7, 80, 8] Operation: 96/12=8 Exploring Operation: 96-80=16, Resulting Numbers: [7, 12, 16] Generated Node #0,2: 17:[7, 12, 16] Operation: 96-80=16 Exploring Operation: 96-7=89, Resulting Numbers: [80, 12, 89] Generated Node #0,3: 17:[80, 12, 89] Operation: 96-7=89 Exploring Operation: 80-7=73, Resulting Numbers: [96, 12, 73] Generated Node #0,4: 17:[96, 12, 73] Operation: 80-7=73 Moving to Node #0,2 Current State: 17:[7, 12, 16], Operations: ['96-80=16'] Exploring Operation: 12+16=28, Resulting Numbers: [7, 28] Generated Node #0,2,0: 17:[7, 28] Operation: 12+16=28 Exploring Operation: 16-7=9, Resulting Numbers: [12, 9] Generated Node #0,2,1: 17:[12, 9] Operation: 16-7=9 Exploring Operation: 7+16=23, Resulting Numbers: [12, 23] Generated Node #0,2,2: 17:[12, 23] Operation: 7+16=23 Exploring Operation: 12-7=5, Resulting Numbers: [16, 5] Generated Node #0,2,3: 17:[16, 5] Operation: 12-7=5 Exploring Operation: 7+12=19, Resulting Numbers: [16, 19] Generated Node #0,2,4: 17:[16, 19] Operation: 7+12=19 Moving to Node #0,1 Current State: 17:[7, 80, 8], Operations: ['96/12=8'] Exploring Operation: 80-7=73, Resulting Numbers: [8, 73] Generated Node #0,1,0: 17:[8, 73] Operation: 80-7=73 Exploring Operation: 7+80=87, Resulting Numbers: [8, 87] Generated Node #0,1,1: 17:[8, 87] Operation: 7+80=87 Exploring Operation: 7+8=15, Resulting Numbers: [80, 15] Generated Node #0,1,2: 17:[80, 15] Operation: 7+8=15 Exploring Operation: 80/8=10, Resulting Numbers: [7, 10] Generated Node #0,1,3: 17:[7, 10] Operation: 80/8=10 Exploring Operation: 80-8=72, Resulting Numbers: [7, 72] Generated Node #0,1,4: 17:[7, 72] Operation: 80-8=72 Moving to Node #0,0 Current State: 17:[7, 96, 68], Operations: ['80-12=68'] Exploring Operation: 96-7=89, Resulting Numbers: [68, 89] Generated Node #0,0,0: 17:[68, 89] Operation: 96-7=89 Exploring Operation: 68-7=61, Resulting Numbers: [96, 61] Generated Node #0,0,1: 17:[96, 61] Operation: 68-7=61 Exploring Operation: 7+96=103, Resulting Numbers: [68, 103] Generated Node #0,0,2: 17:[68, 103] Operation: 7+96=103 Exploring Operation: 96-68=28, Resulting Numbers: [7, 28] Generated Node #0,0,3: 17:[7, 28] Operation: 96-68=28 Exploring Operation: 7+68=75, Resulting Numbers: [96, 75] Generated Node #0,0,4: 17:[96, 75] Operation: 7+68=75 Moving to Node #0,3 Current State: 17:[80, 12, 89], Operations: ['96-7=89'] Exploring Operation: 89-12=77, Resulting Numbers: [80, 77] Generated Node #0,3,0: 17:[80, 77] Operation: 89-12=77 Exploring Operation: 89-80=9, Resulting Numbers: [12, 9] Generated Node #0,3,1: 17:[12, 9] Operation: 89-80=9 Exploring Operation: 80-12=68, Resulting Numbers: [89, 68] Generated Node #0,3,2: 17:[89, 68] Operation: 80-12=68 Exploring Operation: 80+12=92, Resulting Numbers: [89, 92] Generated Node #0,3,3: 17:[89, 92] Operation: 80+12=92 Exploring Operation: 12+89=101, Resulting Numbers: [80, 101] Generated Node #0,3,4: 17:[80, 101] Operation: 12+89=101 Moving to Node #0,4 Current State: 17:[96, 12, 73], Operations: ['80-7=73'] Exploring Operation: 96-12=84, Resulting Numbers: [73, 84] Generated Node #0,4,0: 17:[73, 84] Operation: 96-12=84 Exploring Operation: 96+12=108, Resulting Numbers: [73, 108] Generated Node #0,4,1: 17:[73, 108] Operation: 96+12=108 Exploring Operation: 73-12=61, Resulting Numbers: [96, 61] Generated Node #0,4,2: 17:[96, 61] Operation: 73-12=61 Exploring Operation: 96-73=23, Resulting Numbers: [12, 23] Generated Node #0,4,3: 17:[12, 23] Operation: 96-73=23 Exploring Operation: 96/12=8, Resulting Numbers: [73, 8] Generated Node #0,4,4: 17:[73, 8] Operation: 96/12=8 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 17:[12, 23], Operations: ['80-7=73', '96-73=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,17 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,17 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 #0,4,4 Current State: 17:[73, 8], Operations: ['80-7=73', '96/12=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,17 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,17 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,17 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 #0,4,0 Current State: 17:[73, 84], Operations: ['80-7=73', '96-12=84'] Exploring Operation: 84-73=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 73+84=157, Resulting Numbers: [157] 157,17 unequal: No Solution Exploring Operation: 73*84=6132, Resulting Numbers: [6132] 6132,17 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 #0,4,2 Current State: 17:[96, 61], Operations: ['80-7=73', '73-12=61'] Exploring Operation: 96+61=157, Resulting Numbers: [157] 157,17 unequal: No Solution Exploring Operation: 96-61=35, Resulting Numbers: [35] 35,17 unequal: No Solution Exploring Operation: 96*61=5856, Resulting Numbers: [5856] 5856,17 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 #0,4,1 Current State: 17:[73, 108], Operations: ['80-7=73', '96+12=108'] Exploring Operation: 73*108=7884, Resulting Numbers: [7884] 7884,17 unequal: No Solution Exploring Operation: 73+108=181, Resulting Numbers: [181] 181,17 unequal: No Solution Exploring Operation: 108-73=35, Resulting Numbers: [35] 35,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,4 Current State: 17:[16, 19], Operations: ['96-80=16', '7+12=19'] Exploring Operation: 16*19=304, Resulting Numbers: [304] 304,17 unequal: No Solution Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 16+19=35, Resulting Numbers: [35] 35,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[12, 23], Operations: ['96-80=16', '7+16=23'] Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,17 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[12, 9], Operations: ['96-80=16', '16-7=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,17 unequal: No Solution Moving to Node #0,2,3 Current State: 17:[16, 5], Operations: ['96-80=16', '12-7=5'] Exploring Operation: 16+5=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 16-5=11, Resulting Numbers: [11] 11,17 unequal: No Solution Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,17 unequal: No Solution Moving to Node #0,3,1 Current State: 17:[12, 9], Operations: ['96-7=89', '89-80=9'] Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,17 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,17 unequal: No Solution Moving to Node #0,1,3 Current State: 17:[7, 10], Operations: ['96/12=8', '80/8=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,17 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[7, 80, 96, 12], Operations: [] Exploring Operation: 96/12=8, Resulting Numbers: [7, 80, 8] Generated Node #0,1: 17:[7, 80, 8] Operation: 96/12=8 Moving to Node #0,1 Current State: 17:[7, 80, 8], Operations: ['96/12=8'] Exploring Operation: 80/8=10, Resulting Numbers: [7, 10] Generated Node #0,1,3: 17:[7, 10] Operation: 80/8=10 Moving to Node #0,1,3 Current State: 17:[7, 10], Operations: ['96/12=8', '80/8=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
0.94184
hs_5
sum_heuristic
[ 23, 16, 2, 85 ]
99
[ "23*16=368", "368/2=184", "184-85=99" ]
Current State: 99:[23, 16, 2, 85], Operations: [] Exploring Operation: 23*16=368, Resulting Numbers: [2, 85, 368] Generated Node #2: [2, 85, 368] from Operation: 23*16=368 Current State: 99:[2, 85, 368], Operations: ['23*16=368'] Exploring Operation: 368/2=184, Resulting Numbers: [85, 184] Generated Node #3: [85, 184] from Operation: 368/2=184 Current State: 99:[85, 184], Operations: ['23*16=368', '368/2=184'] Exploring Operation: 184-85=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[23, 16, 2, 85], Operations: [] Exploring Operation: 23+85=108, Resulting Numbers: [16, 2, 108] Generated Node #0,0: 99:[16, 2, 108] Operation: 23+85=108 Exploring Operation: 23+16=39, Resulting Numbers: [2, 85, 39] Generated Node #0,1: 99:[2, 85, 39] Operation: 23+16=39 Exploring Operation: 23-16=7, Resulting Numbers: [2, 85, 7] Generated Node #0,2: 99:[2, 85, 7] Operation: 23-16=7 Exploring Operation: 16+85=101, Resulting Numbers: [23, 2, 101] Generated Node #0,3: 99:[23, 2, 101] Operation: 16+85=101 Moving to Node #0,3 Current State: 99:[23, 2, 101], Operations: ['16+85=101'] Exploring Operation: 23-2=21, Resulting Numbers: [101, 21] Generated Node #0,3,0: 99:[101, 21] Operation: 23-2=21 Exploring Operation: 23+2=25, Resulting Numbers: [101, 25] Generated Node #0,3,1: 99:[101, 25] Operation: 23+2=25 Exploring Operation: 101-2=99, Resulting Numbers: [23, 99] Generated Node #0,3,2: 99:[23, 99] Operation: 101-2=99 Exploring Operation: 2+101=103, Resulting Numbers: [23, 103] Generated Node #0,3,3: 99:[23, 103] Operation: 2+101=103 Moving to Node #0,0 Current State: 99:[16, 2, 108], Operations: ['23+85=108'] Exploring Operation: 16/2=8, Resulting Numbers: [108, 8] Generated Node #0,0,0: 99:[108, 8] Operation: 16/2=8 Exploring Operation: 108-16=92, Resulting Numbers: [2, 92] Generated Node #0,0,1: 99:[2, 92] Operation: 108-16=92 Exploring Operation: 16-2=14, Resulting Numbers: [108, 14] Generated Node #0,0,2: 99:[108, 14] Operation: 16-2=14 Exploring Operation: 16*2=32, Resulting Numbers: [108, 32] Generated Node #0,0,3: 99:[108, 32] Operation: 16*2=32 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 99:[2, 92], Operations: ['23+85=108', '108-16=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 2*92=184, Resulting Numbers: [184] 184,99 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 #0,0,0 Current State: 99:[108, 8], Operations: ['23+85=108', '16/2=8'] Exploring Operation: 108-8=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 108*8=864, Resulting Numbers: [864] 864,99 unequal: No Solution Exploring Operation: 108+8=116, Resulting Numbers: [116] 116,99 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 #0,0,3 Current State: 99:[108, 32], Operations: ['23+85=108', '16*2=32'] Exploring Operation: 108+32=140, Resulting Numbers: [140] 140,99 unequal: No Solution Exploring Operation: 108-32=76, Resulting Numbers: [76] 76,99 unequal: No Solution Exploring Operation: 108*32=3456, Resulting Numbers: [3456] 3456,99 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 #0,0,2 Current State: 99:[108, 14], Operations: ['23+85=108', '16-2=14'] Exploring Operation: 108-14=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 108*14=1512, Resulting Numbers: [1512] 1512,99 unequal: No Solution Exploring Operation: 108+14=122, Resulting Numbers: [122] 122,99 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: 99:[2, 85, 7], Operations: ['23-16=7'] Exploring Operation: 85+7=92, Resulting Numbers: [2, 92] Generated Node #0,2,0: 99:[2, 92] Operation: 85+7=92 Exploring Operation: 7-2=5, Resulting Numbers: [85, 5] Generated Node #0,2,1: 99:[85, 5] Operation: 7-2=5 Exploring Operation: 2+7=9, Resulting Numbers: [85, 9] Generated Node #0,2,2: 99:[85, 9] Operation: 2+7=9 Exploring Operation: 2+85=87, Resulting Numbers: [7, 87] Generated Node #0,2,3: 99:[7, 87] Operation: 2+85=87 Moving to Node #0,1 Current State: 99:[2, 85, 39], Operations: ['23+16=39'] Exploring Operation: 39-2=37, Resulting Numbers: [85, 37] Generated Node #0,1,0: 99:[85, 37] Operation: 39-2=37 Exploring Operation: 85-39=46, Resulting Numbers: [2, 46] Generated Node #0,1,1: 99:[2, 46] Operation: 85-39=46 Exploring Operation: 85-2=83, Resulting Numbers: [39, 83] Generated Node #0,1,2: 99:[39, 83] Operation: 85-2=83 Exploring Operation: 2+85=87, Resulting Numbers: [39, 87] Generated Node #0,1,3: 99:[39, 87] Operation: 2+85=87 Moving to Node #0,2,0 Current State: 99:[2, 92], Operations: ['23-16=7', '85+7=92'] Exploring Operation: 2+92=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 92/2=46, Resulting Numbers: [46] 46,99 unequal: No Solution Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 2*92=184, Resulting Numbers: [184] 184,99 unequal: No Solution Moving to Node #0,3,1 Current State: 99:[101, 25], Operations: ['16+85=101', '23+2=25'] Exploring Operation: 101*25=2525, Resulting Numbers: [2525] 2525,99 unequal: No Solution Exploring Operation: 101-25=76, Resulting Numbers: [76] 76,99 unequal: No Solution Exploring Operation: 101+25=126, Resulting Numbers: [126] 126,99 unequal: No Solution Moving to Node #0,3,2 Current State: 99:[23, 99], Operations: ['16+85=101', '101-2=99'] Exploring Operation: 23*99=2277, Resulting Numbers: [2277] 2277,99 unequal: No Solution Exploring Operation: 23+99=122, Resulting Numbers: [122] 122,99 unequal: No Solution Exploring Operation: 99-23=76, Resulting Numbers: [76] 76,99 unequal: No Solution Moving to Node #0,3,0 Current State: 99:[101, 21], Operations: ['16+85=101', '23-2=21'] Exploring Operation: 101+21=122, Resulting Numbers: [122] 122,99 unequal: No Solution Exploring Operation: 101*21=2121, Resulting Numbers: [2121] 2121,99 unequal: No Solution Exploring Operation: 101-21=80, Resulting Numbers: [80] 80,99 unequal: No Solution Moving to Node #0,2,3 Current State: 99:[7, 87], Operations: ['23-16=7', '2+85=87'] Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,99 unequal: No Solution Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,99 unequal: No Solution Moving to Node #0,2,2 Current State: 99:[85, 9], Operations: ['23-16=7', '2+7=9'] Exploring Operation: 85*9=765, Resulting Numbers: [765] 765,99 unequal: No Solution Exploring Operation: 85-9=76, Resulting Numbers: [76] 76,99 unequal: No Solution Exploring Operation: 85+9=94, Resulting Numbers: [94] 94,99 unequal: No Solution Moving to Node #0,3,3 Current State: 99:[23, 103], Operations: ['16+85=101', '2+101=103'] Exploring Operation: 23+103=126, Resulting Numbers: [126] 126,99 unequal: No Solution Exploring Operation: 103-23=80, Resulting Numbers: [80] 80,99 unequal: No Solution Exploring Operation: 23*103=2369, Resulting Numbers: [2369] 2369,99 unequal: No Solution Moving to Node #0,1,1 Current State: 99:[2, 46], Operations: ['23+16=39', '85-39=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,99 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,99 unequal: No Solution Moving to Node #0,2,1 Current State: 99:[85, 5], Operations: ['23-16=7', '7-2=5'] Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,99 unequal: No Solution Exploring Operation: 85+5=90, Resulting Numbers: [90] 90,99 unequal: No Solution Exploring Operation: 85*5=425, Resulting Numbers: [425] 425,99 unequal: No Solution Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,99 unequal: No Solution Moving to Node #0,1,3 Current State: 99:[39, 87], Operations: ['23+16=39', '2+85=87'] Exploring Operation: 87-39=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 39+87=126, Resulting Numbers: [126] 126,99 unequal: No Solution Exploring Operation: 39*87=3393, Resulting Numbers: [3393] 3393,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[85, 37], Operations: ['23+16=39', '39-2=37'] Exploring Operation: 85+37=122, Resulting Numbers: [122] 122,99 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 85*37=3145, Resulting Numbers: [3145] 3145,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[39, 83], Operations: ['23+16=39', '85-2=83'] Exploring Operation: 39*83=3237, Resulting Numbers: [3237] 3237,99 unequal: No Solution Exploring Operation: 83-39=44, Resulting Numbers: [44] 44,99 unequal: No Solution Exploring Operation: 39+83=122, Resulting Numbers: [122] 122,99 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 49, 3, 6, 54 ]
25
[ "49-6=43", "54/3=18", "43-18=25" ]
Current State: 25:[49, 3, 6, 54], Operations: [] Exploring Operation: 49-6=43, Resulting Numbers: [3, 54, 43] Generated Node #2: [3, 54, 43] from Operation: 49-6=43 Current State: 25:[3, 54, 43], Operations: ['49-6=43'] Exploring Operation: 54/3=18, Resulting Numbers: [43, 18] Generated Node #3: [43, 18] from Operation: 54/3=18 Current State: 25:[43, 18], Operations: ['49-6=43', '54/3=18'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[49, 3, 6, 54], Operations: [] Exploring Operation: 54-49=5, Resulting Numbers: [3, 6, 5] Generated Node #0,0: 25:[3, 6, 5] Operation: 54-49=5 Exploring Operation: 54/3=18, Resulting Numbers: [49, 6, 18] Generated Node #0,1: 25:[49, 6, 18] Operation: 54/3=18 Exploring Operation: 54/6=9, Resulting Numbers: [49, 3, 9] Generated Node #0,2: 25:[49, 3, 9] Operation: 54/6=9 Moving to Node #0,0 Current State: 25:[3, 6, 5], Operations: ['54-49=5'] Exploring Operation: 6/3=2, Resulting Numbers: [5, 2] Generated Node #0,0,0: 25:[5, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [5, 3] Generated Node #0,0,1: 25:[5, 3] Operation: 6-3=3 Exploring Operation: 3+6=9, Resulting Numbers: [5, 9] Generated Node #0,0,2: 25:[5, 9] Operation: 3+6=9 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[5, 3], Operations: ['54-49=5', '6-3=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,25 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[5, 2], Operations: ['54-49=5', '6/3=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,25 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 25:[5, 9], Operations: ['54-49=5', '3+6=9'] Exploring Operation: 5*9=45, Resulting Numbers: [45] 45,25 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 5+9=14, Resulting Numbers: [14] 14,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 25:[49, 3, 9], Operations: ['54/6=9'] Exploring Operation: 9-3=6, Resulting Numbers: [49, 6] Generated Node #0,2,0: 25:[49, 6] Operation: 9-3=6 Exploring Operation: 49-3=46, Resulting Numbers: [9, 46] Generated Node #0,2,1: 25:[9, 46] Operation: 49-3=46 Exploring Operation: 49-9=40, Resulting Numbers: [3, 40] Generated Node #0,2,2: 25:[3, 40] Operation: 49-9=40 Moving to Node #0,1 Current State: 25:[49, 6, 18], Operations: ['54/3=18'] Exploring Operation: 49-18=31, Resulting Numbers: [6, 31] Generated Node #0,1,0: 25:[6, 31] Operation: 49-18=31 Exploring Operation: 49-6=43, Resulting Numbers: [18, 43] Generated Node #0,1,1: 25:[18, 43] Operation: 49-6=43 Exploring Operation: 6+18=24, Resulting Numbers: [49, 24] Generated Node #0,1,2: 25:[49, 24] Operation: 6+18=24 Moving to Node #0,1,0 Current State: 25:[6, 31], Operations: ['54/3=18', '49-18=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,25 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,25 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached Moving to Node #0 Current State: 25:[49, 3, 6, 54], Operations: [] Exploring Operation: 54/3=18, Resulting Numbers: [49, 6, 18] Generated Node #0,1: 25:[49, 6, 18] Operation: 54/3=18 Moving to Node #0,1 Current State: 25:[49, 6, 18], Operations: ['54/3=18'] Exploring Operation: 49-18=31, Resulting Numbers: [6, 31] Generated Node #0,1,0: 25:[6, 31] Operation: 49-18=31 Moving to Node #0,1,0 Current State: 25:[6, 31], Operations: ['54/3=18', '49-18=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
0.975694
hs_3
mult_heuristic
[ 6, 62, 88, 56 ]
24
[ "62-6=56", "88-56=32", "56-32=24" ]
Current State: 24:[6, 62, 88, 56], Operations: [] Exploring Operation: 62-6=56, Resulting Numbers: [88, 56, 56] Generated Node #2: [88, 56, 56] from Operation: 62-6=56 Current State: 24:[88, 56, 56], Operations: ['62-6=56'] Exploring Operation: 88-56=32, Resulting Numbers: [32] 32,24 equal: Goal Reached Exploring Operation: 56-32=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[6, 62, 88, 56], Operations: [] Exploring Operation: 62-56=6, Resulting Numbers: [6, 88, 6] Generated Node #0,0: 24:[6, 88, 6] Operation: 62-56=6 Exploring Operation: 62-6=56, Resulting Numbers: [88, 56, 56] Generated Node #0,1: 24:[88, 56, 56] Operation: 62-6=56 Exploring Operation: 88-62=26, Resulting Numbers: [6, 56, 26] Generated Node #0,2: 24:[6, 56, 26] Operation: 88-62=26 Exploring Operation: 88-56=32, Resulting Numbers: [6, 62, 32] Generated Node #0,3: 24:[6, 62, 32] Operation: 88-56=32 Moving to Node #0,2 Current State: 24:[6, 56, 26], Operations: ['88-62=26'] Exploring Operation: 6+56=62, Resulting Numbers: [26, 62] Generated Node #0,2,0: 24:[26, 62] Operation: 6+56=62 Exploring Operation: 26-6=20, Resulting Numbers: [56, 20] Generated Node #0,2,1: 24:[56, 20] Operation: 26-6=20 Exploring Operation: 56-6=50, Resulting Numbers: [26, 50] Generated Node #0,2,2: 24:[26, 50] Operation: 56-6=50 Exploring Operation: 56-26=30, Resulting Numbers: [6, 30] Generated Node #0,2,3: 24:[6, 30] Operation: 56-26=30 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 24:[6, 30], Operations: ['88-62=26', '56-26=30'] Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,24 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,24 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,24 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[6, 62, 88, 56], Operations: [] Exploring Operation: 88-62=26, Resulting Numbers: [6, 56, 26] Generated Node #0,2: 24:[6, 56, 26] Operation: 88-62=26 Moving to Node #0,2 Current State: 24:[6, 56, 26], Operations: ['88-62=26'] Exploring Operation: 56-26=30, Resulting Numbers: [6, 30] Generated Node #0,2,3: 24:[6, 30] Operation: 56-26=30 Moving to Node #0,2,3 Current State: 24:[6, 30], Operations: ['88-62=26', '56-26=30'] Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 19, 8, 22, 33 ]
19
[ "19-8=11", "33/11=3", "22-3=19" ]
Current State: 19:[19, 8, 22, 33], Operations: [] Exploring Operation: 19-8=11, Resulting Numbers: [22, 33, 11] Generated Node #2: [22, 33, 11] from Operation: 19-8=11 Current State: 19:[22, 33, 11], Operations: ['19-8=11'] Exploring Operation: 33/11=3, Resulting Numbers: [22, 3] Generated Node #3: [22, 3] from Operation: 33/11=3 Current State: 19:[22, 3], Operations: ['19-8=11', '33/11=3'] Exploring Operation: 22-3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[19, 8, 22, 33], Operations: [] Exploring Operation: 19+8=27, Resulting Numbers: [22, 33, 27] Generated Node #0,0: 19:[22, 33, 27] Operation: 19+8=27 Exploring Operation: 33-22=11, Resulting Numbers: [19, 8, 11] Generated Node #0,1: 19:[19, 8, 11] Operation: 33-22=11 Exploring Operation: 22-8=14, Resulting Numbers: [19, 33, 14] Generated Node #0,2: 19:[19, 33, 14] Operation: 22-8=14 Exploring Operation: 33-8=25, Resulting Numbers: [19, 22, 25] Generated Node #0,3: 19:[19, 22, 25] Operation: 33-8=25 Exploring Operation: 33-19=14, Resulting Numbers: [8, 22, 14] Generated Node #0,4: 19:[8, 22, 14] Operation: 33-19=14 Moving to Node #0,3 Current State: 19:[19, 22, 25], Operations: ['33-8=25'] Exploring Operation: 25-22=3, Resulting Numbers: [19, 3] Generated Node #0,3,0: 19:[19, 3] Operation: 25-22=3 Exploring Operation: 19+22=41, Resulting Numbers: [25, 41] Generated Node #0,3,1: 19:[25, 41] Operation: 19+22=41 Exploring Operation: 25-19=6, Resulting Numbers: [22, 6] Generated Node #0,3,2: 19:[22, 6] Operation: 25-19=6 Exploring Operation: 19+25=44, Resulting Numbers: [22, 44] Generated Node #0,3,3: 19:[22, 44] Operation: 19+25=44 Exploring Operation: 22-19=3, Resulting Numbers: [25, 3] Generated Node #0,3,4: 19:[25, 3] Operation: 22-19=3 Moving to Node #0,2 Current State: 19:[19, 33, 14], Operations: ['22-8=14'] Exploring Operation: 33-14=19, Resulting Numbers: [19, 19] Generated Node #0,2,0: 19:[19, 19] Operation: 33-14=19 Exploring Operation: 19-14=5, Resulting Numbers: [33, 5] Generated Node #0,2,1: 19:[33, 5] Operation: 19-14=5 Exploring Operation: 19+14=33, Resulting Numbers: [33, 33] Generated Node #0,2,2: 19:[33, 33] Operation: 19+14=33 Exploring Operation: 33-19=14, Resulting Numbers: [14, 14] Generated Node #0,2,3: 19:[14, 14] Operation: 33-19=14 Exploring Operation: 33+14=47, Resulting Numbers: [19, 47] Generated Node #0,2,4: 19:[19, 47] Operation: 33+14=47 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 19:[19, 19], Operations: ['22-8=14', '33-14=19'] Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,19 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,19 unequal: No Solution No 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: 19:[14, 14], Operations: ['22-8=14', '33-19=14'] Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,19 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,19 unequal: No Solution No 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: 19:[33, 5], Operations: ['22-8=14', '19-14=5'] Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,19 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,19 unequal: No Solution No 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: 19:[33, 33], Operations: ['22-8=14', '19+14=33'] Exploring Operation: 33*33=1089, Resulting Numbers: [1089] 1089,19 unequal: No Solution Exploring Operation: 33+33=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 33-33=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 33/33=1, Resulting Numbers: [1] 1,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 19:[19, 47], Operations: ['22-8=14', '33+14=47'] Exploring Operation: 19*47=893, Resulting Numbers: [893] 893,19 unequal: No Solution Exploring Operation: 19+47=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,19 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: 19:[19, 8, 11], Operations: ['33-22=11'] Exploring Operation: 11-8=3, Resulting Numbers: [19, 3] Generated Node #0,1,0: 19:[19, 3] Operation: 11-8=3 Exploring Operation: 8+11=19, Resulting Numbers: [19, 19] Generated Node #0,1,1: 19:[19, 19] Operation: 8+11=19 Exploring Operation: 19+11=30, Resulting Numbers: [8, 30] Generated Node #0,1,2: 19:[8, 30] Operation: 19+11=30 Exploring Operation: 19-8=11, Resulting Numbers: [11, 11] Generated Node #0,1,3: 19:[11, 11] Operation: 19-8=11 Exploring Operation: 19+8=27, Resulting Numbers: [11, 27] Generated Node #0,1,4: 19:[11, 27] Operation: 19+8=27 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[19, 19], Operations: ['33-22=11', '8+11=19'] Exploring Operation: 19*19=361, Resulting Numbers: [361] 361,19 unequal: No Solution Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 19+19=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 19-19=0, Resulting Numbers: [0] 0,19 unequal: No Solution No 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: 19:[19, 3], Operations: ['33-22=11', '11-8=3'] Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,19 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,19 unequal: No Solution No 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: 19:[11, 11], Operations: ['33-22=11', '19-8=11'] Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 11*11=121, Resulting Numbers: [121] 121,19 unequal: No Solution Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 11-11=0, Resulting Numbers: [0] 0,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 19:[11, 27], Operations: ['33-22=11', '19+8=27'] Exploring Operation: 11+27=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 11*27=297, Resulting Numbers: [297] 297,19 unequal: No Solution Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,19 unequal: No Solution No 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: 19:[8, 30], Operations: ['33-22=11', '19+11=30'] Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 8*30=240, Resulting Numbers: [240] 240,19 unequal: No Solution Exploring Operation: 8+30=38, Resulting Numbers: [38] 38,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 19:[8, 22, 14], Operations: ['33-19=14'] Exploring Operation: 14-8=6, Resulting Numbers: [22, 6] Generated Node #0,4,0: 19:[22, 6] Operation: 14-8=6 Exploring Operation: 8+22=30, Resulting Numbers: [14, 30] Generated Node #0,4,1: 19:[14, 30] Operation: 8+22=30 Exploring Operation: 22-8=14, Resulting Numbers: [14, 14] Generated Node #0,4,2: 19:[14, 14] Operation: 22-8=14 Exploring Operation: 8+14=22, Resulting Numbers: [22, 22] Generated Node #0,4,3: 19:[22, 22] Operation: 8+14=22 Exploring Operation: 22-14=8, Resulting Numbers: [8, 8] Generated Node #0,4,4: 19:[8, 8] Operation: 22-14=8 Moving to Node #0,0 Current State: 19:[22, 33, 27], Operations: ['19+8=27'] Exploring Operation: 22+33=55, Resulting Numbers: [27, 55] Generated Node #0,0,0: 19:[27, 55] Operation: 22+33=55 Exploring Operation: 33-22=11, Resulting Numbers: [27, 11] Generated Node #0,0,1: 19:[27, 11] Operation: 33-22=11 Exploring Operation: 27-22=5, Resulting Numbers: [33, 5] Generated Node #0,0,2: 19:[33, 5] Operation: 27-22=5 Exploring Operation: 33-27=6, Resulting Numbers: [22, 6] Generated Node #0,0,3: 19:[22, 6] Operation: 33-27=6 Exploring Operation: 22+27=49, Resulting Numbers: [33, 49] Generated Node #0,0,4: 19:[33, 49] Operation: 22+27=49 Moving to Node #0,4,3 Current State: 19:[22, 22], Operations: ['33-19=14', '8+14=22'] Exploring Operation: 22*22=484, Resulting Numbers: [484] 484,19 unequal: No Solution Exploring Operation: 22/22=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 22-22=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 22+22=44, Resulting Numbers: [44] 44,19 unequal: No Solution Moving to Node #0,4,2 Current State: 19:[14, 14], Operations: ['33-19=14', '22-8=14'] Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 14*14=196, Resulting Numbers: [196] 196,19 unequal: No Solution Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,19 unequal: No Solution Moving to Node #0,3,0 Current State: 19:[19, 3], Operations: ['33-8=25', '25-22=3'] Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,19 unequal: No Solution Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,19 unequal: No Solution Moving to Node #0,0,3 Current State: 19:[22, 6], Operations: ['19+8=27', '33-27=6'] Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,19 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,19 unequal: No Solution Moving to Node #0,3,2 Current State: 19:[22, 6], Operations: ['33-8=25', '25-19=6'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,19 unequal: No Solution Moving to Node #0,0,1 Current State: 19:[27, 11], Operations: ['19+8=27', '33-22=11'] Exploring Operation: 27-11=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 27+11=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 27*11=297, Resulting Numbers: [297] 297,19 unequal: No Solution Moving to Node #0,4,0 Current State: 19:[22, 6], Operations: ['33-19=14', '14-8=6'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,19 unequal: No Solution Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,19 unequal: No Solution Moving to Node #0,4,1 Current State: 19:[14, 30], Operations: ['33-19=14', '8+22=30'] Exploring Operation: 14*30=420, Resulting Numbers: [420] 420,19 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 14+30=44, Resulting Numbers: [44] 44,19 unequal: No Solution Moving to Node #0,3,4 Current State: 19:[25, 3], Operations: ['33-8=25', '22-19=3'] Exploring Operation: 25*3=75, Resulting Numbers: [75] 75,19 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 25+3=28, Resulting Numbers: [28] 28,19 unequal: No Solution Moving to Node #0,4,4 Current State: 19:[8, 8], Operations: ['33-19=14', '22-14=8'] Exploring Operation: 8/8=1, Resulting Numbers: [1] 1,19 unequal: No Solution Exploring Operation: 8-8=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 8*8=64, Resulting Numbers: [64] 64,19 unequal: No Solution Moving to Node #0,0,2 Current State: 19:[33, 5], Operations: ['19+8=27', '27-22=5'] Exploring Operation: 33*5=165, Resulting Numbers: [165] 165,19 unequal: No Solution Exploring Operation: 33+5=38, Resulting Numbers: [38] 38,19 unequal: No Solution Exploring Operation: 33-5=28, Resulting Numbers: [28] 28,19 unequal: No Solution Moving to Node #0,3,3 Current State: 19:[22, 44], Operations: ['33-8=25', '19+25=44'] Exploring Operation: 44-22=22, Resulting Numbers: [22] 22,19 unequal: No Solution Exploring Operation: 22+44=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 44/22=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 22*44=968, Resulting Numbers: [968] 968,19 unequal: No Solution Moving to Node #0,3,1 Current State: 19:[25, 41], Operations: ['33-8=25', '19+22=41'] Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,19 unequal: No Solution Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,19 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[27, 55], Operations: ['19+8=27', '22+33=55'] Exploring Operation: 27*55=1485, Resulting Numbers: [1485] 1485,19 unequal: No Solution Exploring Operation: 55-27=28, Resulting Numbers: [28] 28,19 unequal: No Solution Exploring Operation: 27+55=82, Resulting Numbers: [82] 82,19 unequal: No Solution Moving to Node #0,0,4 Current State: 19:[33, 49], Operations: ['19+8=27', '22+27=49'] Exploring Operation: 49-33=16, Resulting Numbers: [16] 16,19 unequal: No Solution Exploring Operation: 33+49=82, Resulting Numbers: [82] 82,19 unequal: No Solution Exploring Operation: 33*49=1617, Resulting Numbers: [1617] 1617,19 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 30, 32, 7, 17 ]
59
[ "30-17=13", "7*13=91", "91-32=59" ]
Current State: 59:[30, 32, 7, 17], Operations: [] Exploring Operation: 30-17=13, Resulting Numbers: [32, 7, 13] Generated Node #2: [32, 7, 13] from Operation: 30-17=13 Current State: 59:[32, 7, 13], Operations: ['30-17=13'] Exploring Operation: 7*13=91, Resulting Numbers: [32, 91] Generated Node #3: [32, 91] from Operation: 7*13=91 Current State: 59:[32, 91], Operations: ['30-17=13', '7*13=91'] Exploring Operation: 91-32=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[30, 32, 7, 17], Operations: [] Exploring Operation: 30+7=37, Resulting Numbers: [32, 17, 37] Generated Node #0,0: 59:[32, 17, 37] Operation: 30+7=37 Exploring Operation: 30+17=47, Resulting Numbers: [32, 7, 47] Generated Node #0,1: 59:[32, 7, 47] Operation: 30+17=47 Exploring Operation: 32+17=49, Resulting Numbers: [30, 7, 49] Generated Node #0,2: 59:[30, 7, 49] Operation: 32+17=49 Exploring Operation: 32+7=39, Resulting Numbers: [30, 17, 39] Generated Node #0,3: 59:[30, 17, 39] Operation: 32+7=39 Exploring Operation: 7+17=24, Resulting Numbers: [30, 32, 24] Generated Node #0,4: 59:[30, 32, 24] Operation: 7+17=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[32, 17, 37], Operations: ['30+7=37'] Exploring Operation: 32+37=69, Resulting Numbers: [17, 69] Generated Node #0,0,0: 59:[17, 69] Operation: 32+37=69 Exploring Operation: 32+17=49, Resulting Numbers: [37, 49] Generated Node #0,0,1: 59:[37, 49] Operation: 32+17=49 Exploring Operation: 32-17=15, Resulting Numbers: [37, 15] Generated Node #0,0,2: 59:[37, 15] Operation: 32-17=15 Exploring Operation: 37-17=20, Resulting Numbers: [32, 20] Generated Node #0,0,3: 59:[32, 20] Operation: 37-17=20 Exploring Operation: 17+37=54, Resulting Numbers: [32, 54] Generated Node #0,0,4: 59:[32, 54] Operation: 17+37=54 Moving to Node #0,0,1 Current State: 59:[37, 49], Operations: ['30+7=37', '32+17=49'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 37+49=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 37*49=1813, Resulting Numbers: [1813] 1813,59 unequal: No Solution Moving to Node #0,0,4 Current State: 59:[32, 54], Operations: ['30+7=37', '17+37=54'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[17, 69], Operations: ['30+7=37', '32+37=69'] Exploring Operation: 17*69=1173, Resulting Numbers: [1173] 1173,59 unequal: No Solution Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,59 unequal: No Solution Moving to Node #0,0,2 Current State: 59:[37, 15], Operations: ['30+7=37', '32-17=15'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 37*15=555, Resulting Numbers: [555] 555,59 unequal: No Solution Exploring Operation: 37+15=52, Resulting Numbers: [52] 52,59 unequal: No Solution Moving to Node #0,0,3 Current State: 59:[32, 20], Operations: ['30+7=37', '37-17=20'] Exploring Operation: 32+20=52, Resulting Numbers: [52] 52,59 unequal: No Solution Exploring Operation: 32*20=640, Resulting Numbers: [640] 640,59 unequal: No Solution Exploring Operation: 32-20=12, Resulting Numbers: [12] 12,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[32, 7, 47], Operations: ['30+17=47'] Exploring Operation: 7+47=54, Resulting Numbers: [32, 54] Generated Node #0,1,0: 59:[32, 54] Operation: 7+47=54 Exploring Operation: 47-7=40, Resulting Numbers: [32, 40] Generated Node #0,1,1: 59:[32, 40] Operation: 47-7=40 Exploring Operation: 32+7=39, Resulting Numbers: [47, 39] Generated Node #0,1,2: 59:[47, 39] Operation: 32+7=39 Exploring Operation: 32-7=25, Resulting Numbers: [47, 25] Generated Node #0,1,3: 59:[47, 25] Operation: 32-7=25 Exploring Operation: 32+47=79, Resulting Numbers: [7, 79] Generated Node #0,1,4: 59:[7, 79] Operation: 32+47=79 Moving to Node #0,1,0 Current State: 59:[32, 54], Operations: ['30+17=47', '7+47=54'] Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,59 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[47, 39], Operations: ['30+17=47', '32+7=39'] Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 47*39=1833, Resulting Numbers: [1833] 1833,59 unequal: No Solution Exploring Operation: 47+39=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[32, 40], Operations: ['30+17=47', '47-7=40'] Exploring Operation: 32+40=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 32*40=1280, Resulting Numbers: [1280] 1280,59 unequal: No Solution Exploring Operation: 40-32=8, Resulting Numbers: [8] 8,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[47, 25], Operations: ['30+17=47', '32-7=25'] Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[7, 79], Operations: ['30+17=47', '32+47=79'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 7*79=553, Resulting Numbers: [553] 553,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 59:[30, 7, 49], Operations: ['32+17=49'] Exploring Operation: 30+49=79, Resulting Numbers: [7, 79] Generated Node #0,2,0: 59:[7, 79] Operation: 30+49=79 Exploring Operation: 49-7=42, Resulting Numbers: [30, 42] Generated Node #0,2,1: 59:[30, 42] Operation: 49-7=42 Exploring Operation: 30+7=37, Resulting Numbers: [49, 37] Generated Node #0,2,2: 59:[49, 37] Operation: 30+7=37 Exploring Operation: 7+49=56, Resulting Numbers: [30, 56] Generated Node #0,2,3: 59:[30, 56] Operation: 7+49=56 Exploring Operation: 30-7=23, Resulting Numbers: [49, 23] Generated Node #0,2,4: 59:[49, 23] Operation: 30-7=23 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 59:[49, 37], Operations: ['32+17=49', '30+7=37'] Exploring Operation: 49-37=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 49+37=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 49*37=1813, Resulting Numbers: [1813] 1813,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 59:[30, 56], Operations: ['32+17=49', '7+49=56'] Exploring Operation: 30+56=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 30*56=1680, Resulting Numbers: [1680] 1680,59 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 59:[30, 42], Operations: ['32+17=49', '49-7=42'] Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,59 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 59:[49, 23], Operations: ['32+17=49', '30-7=23'] Exploring Operation: 49-23=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 49*23=1127, Resulting Numbers: [1127] 1127,59 unequal: No Solution Exploring Operation: 49+23=72, Resulting Numbers: [72] 72,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 59:[7, 79], Operations: ['32+17=49', '30+49=79'] Exploring Operation: 79-7=72, Resulting Numbers: [72] 72,59 unequal: No Solution Exploring Operation: 7*79=553, Resulting Numbers: [553] 553,59 unequal: No Solution Exploring Operation: 7+79=86, Resulting Numbers: [86] 86,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[30, 17, 39], Operations: ['32+7=39'] Exploring Operation: 17+39=56, Resulting Numbers: [30, 56] Generated Node #0,3,0: 59:[30, 56] Operation: 17+39=56 Exploring Operation: 39-17=22, Resulting Numbers: [30, 22] Generated Node #0,3,1: 59:[30, 22] Operation: 39-17=22 Exploring Operation: 30+17=47, Resulting Numbers: [39, 47] Generated Node #0,3,2: 59:[39, 47] Operation: 30+17=47 Exploring Operation: 30-17=13, Resulting Numbers: [39, 13] Generated Node #0,3,3: 59:[39, 13] Operation: 30-17=13 Exploring Operation: 30+39=69, Resulting Numbers: [17, 69] Generated Node #0,3,4: 59:[17, 69] Operation: 30+39=69 Moving to Node #0,3,0 Current State: 59:[30, 56], Operations: ['32+7=39', '17+39=56'] Exploring Operation: 30*56=1680, Resulting Numbers: [1680] 1680,59 unequal: No Solution Exploring Operation: 30+56=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,59 unequal: No Solution Moving to Node #0,3,2 Current State: 59:[39, 47], Operations: ['32+7=39', '30+17=47'] Exploring Operation: 47-39=8, Resulting Numbers: [8] 8,59 unequal: No Solution Exploring Operation: 39*47=1833, Resulting Numbers: [1833] 1833,59 unequal: No Solution Exploring Operation: 39+47=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,3,4 Current State: 59:[17, 69], Operations: ['32+7=39', '30+39=69'] Exploring Operation: 17+69=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,59 unequal: No Solution Exploring Operation: 17*69=1173, Resulting Numbers: [1173] 1173,59 unequal: No Solution Moving to Node #0,3,1 Current State: 59:[30, 22], Operations: ['32+7=39', '39-17=22'] Exploring Operation: 30*22=660, Resulting Numbers: [660] 660,59 unequal: No Solution Exploring Operation: 30+22=52, Resulting Numbers: [52] 52,59 unequal: No Solution Exploring Operation: 30-22=8, Resulting Numbers: [8] 8,59 unequal: No Solution Moving to Node #0,3,3 Current State: 59:[39, 13], Operations: ['32+7=39', '30-17=13'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,59 unequal: No Solution Exploring Operation: 39*13=507, Resulting Numbers: [507] 507,59 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 59:[30, 32, 24], Operations: ['7+17=24'] Exploring Operation: 30-24=6, Resulting Numbers: [32, 6] Generated Node #0,4,0: 59:[32, 6] Operation: 30-24=6 Exploring Operation: 30+32=62, Resulting Numbers: [24, 62] Generated Node #0,4,1: 59:[24, 62] Operation: 30+32=62 Exploring Operation: 30+24=54, Resulting Numbers: [32, 54] Generated Node #0,4,2: 59:[32, 54] Operation: 30+24=54 Exploring Operation: 32-24=8, Resulting Numbers: [30, 8] Generated Node #0,4,3: 59:[30, 8] Operation: 32-24=8 Exploring Operation: 32+24=56, Resulting Numbers: [30, 56] Generated Node #0,4,4: 59:[30, 56] Operation: 32+24=56 Moving to Node #0,4,2 Current State: 59:[32, 54], Operations: ['7+17=24', '30+24=54'] Exploring Operation: 54-32=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 32+54=86, Resulting Numbers: [86] 86,59 unequal: No Solution Exploring Operation: 32*54=1728, Resulting Numbers: [1728] 1728,59 unequal: No Solution Moving to Node #0,4,4 Current State: 59:[30, 56], Operations: ['7+17=24', '32+24=56'] Exploring Operation: 56-30=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 30*56=1680, Resulting Numbers: [1680] 1680,59 unequal: No Solution Exploring Operation: 30+56=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,4,1 Current State: 59:[24, 62], Operations: ['7+17=24', '30+32=62'] Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,59 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,59 unequal: No Solution Moving to Node #0,4,0 Current State: 59:[32, 6], Operations: ['7+17=24', '30-24=6'] Exploring Operation: 32+6=38, Resulting Numbers: [38] 38,59 unequal: No Solution Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,59 unequal: No Solution Exploring Operation: 32*6=192, Resulting Numbers: [192] 192,59 unequal: No Solution Moving to Node #0,4,3 Current State: 59:[30, 8], Operations: ['7+17=24', '32-24=8'] Exploring Operation: 30*8=240, Resulting Numbers: [240] 240,59 unequal: No Solution Exploring Operation: 30-8=22, Resulting Numbers: [22] 22,59 unequal: No Solution Exploring Operation: 30+8=38, Resulting Numbers: [38] 38,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 44, 42, 66, 48 ]
76
[ "44*42=1848", "1848/66=28", "48+28=76" ]
Current State: 76:[44, 42, 66, 48], Operations: [] Exploring Operation: 44*42=1848, Resulting Numbers: [66, 48, 1848] Generated Node #2: [66, 48, 1848] from Operation: 44*42=1848 Current State: 76:[66, 48, 1848], Operations: ['44*42=1848'] Exploring Operation: 1848/66=28, Resulting Numbers: [48, 28] Generated Node #3: [48, 28] from Operation: 1848/66=28 Current State: 76:[48, 28], Operations: ['44*42=1848', '1848/66=28'] Exploring Operation: 48+28=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[44, 42, 66, 48], Operations: [] Exploring Operation: 48-42=6, Resulting Numbers: [44, 66, 6] Generated Node #0,0: 76:[44, 66, 6] Operation: 48-42=6 Exploring Operation: 66-48=18, Resulting Numbers: [44, 42, 18] Generated Node #0,1: 76:[44, 42, 18] Operation: 66-48=18 Exploring Operation: 48-44=4, Resulting Numbers: [42, 66, 4] Generated Node #0,2: 76:[42, 66, 4] Operation: 48-44=4 Exploring Operation: 66-44=22, Resulting Numbers: [42, 48, 22] Generated Node #0,3: 76:[42, 48, 22] Operation: 66-44=22 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[44, 42, 18], Operations: ['66-48=18'] Exploring Operation: 44-18=26, Resulting Numbers: [42, 26] Generated Node #0,1,0: 76:[42, 26] Operation: 44-18=26 Exploring Operation: 44+42=86, Resulting Numbers: [18, 86] Generated Node #0,1,1: 76:[18, 86] Operation: 44+42=86 Exploring Operation: 42-18=24, Resulting Numbers: [44, 24] Generated Node #0,1,2: 76:[44, 24] Operation: 42-18=24 Exploring Operation: 44-42=2, Resulting Numbers: [18, 2] Generated Node #0,1,3: 76:[18, 2] Operation: 44-42=2 Moving to Node #0,1,3 Current State: 76:[18, 2], Operations: ['66-48=18', '44-42=2'] Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 18*2=36, Resulting Numbers: [36] 36,76 unequal: No Solution Exploring Operation: 18+2=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[18, 86], Operations: ['66-48=18', '44+42=86'] Exploring Operation: 18+86=104, Resulting Numbers: [104] 104,76 unequal: No Solution Exploring Operation: 18*86=1548, Resulting Numbers: [1548] 1548,76 unequal: No Solution Exploring Operation: 86-18=68, Resulting Numbers: [68] 68,76 unequal: No Solution Moving to Node #0,1,0 Current State: 76:[42, 26], Operations: ['66-48=18', '44-18=26'] Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[44, 24], Operations: ['66-48=18', '42-18=24'] Exploring Operation: 44+24=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 44*24=1056, Resulting Numbers: [1056] 1056,76 unequal: No Solution Exploring Operation: 44-24=20, Resulting Numbers: [20] 20,76 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:[42, 66, 4], Operations: ['48-44=4'] Exploring Operation: 42+4=46, Resulting Numbers: [66, 46] Generated Node #0,2,0: 76:[66, 46] Operation: 42+4=46 Exploring Operation: 66+4=70, Resulting Numbers: [42, 70] Generated Node #0,2,1: 76:[42, 70] Operation: 66+4=70 Exploring Operation: 66-42=24, Resulting Numbers: [4, 24] Generated Node #0,2,2: 76:[4, 24] Operation: 66-42=24 Exploring Operation: 42-4=38, Resulting Numbers: [66, 38] Generated Node #0,2,3: 76:[66, 38] Operation: 42-4=38 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[4, 24], Operations: ['48-44=4', '66-42=24'] Exploring Operation: 4*24=96, Resulting Numbers: [96] 96,76 unequal: No Solution Exploring Operation: 4+24=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[42, 70], Operations: ['48-44=4', '66+4=70'] Exploring Operation: 42*70=2940, Resulting Numbers: [2940] 2940,76 unequal: No Solution Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,76 unequal: No Solution Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[66, 38], Operations: ['48-44=4', '42-4=38'] Exploring Operation: 66*38=2508, Resulting Numbers: [2508] 2508,76 unequal: No Solution Exploring Operation: 66-38=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 66+38=104, Resulting Numbers: [104] 104,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[66, 46], Operations: ['48-44=4', '42+4=46'] Exploring Operation: 66-46=20, Resulting Numbers: [20] 20,76 unequal: No Solution Exploring Operation: 66*46=3036, Resulting Numbers: [3036] 3036,76 unequal: No Solution Exploring Operation: 66+46=112, Resulting Numbers: [112] 112,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 76:[42, 48, 22], Operations: ['66-44=22'] Exploring Operation: 48+22=70, Resulting Numbers: [42, 70] Generated Node #0,3,0: 76:[42, 70] Operation: 48+22=70 Exploring Operation: 48-42=6, Resulting Numbers: [22, 6] Generated Node #0,3,1: 76:[22, 6] Operation: 48-42=6 Exploring Operation: 48-22=26, Resulting Numbers: [42, 26] Generated Node #0,3,2: 76:[42, 26] Operation: 48-22=26 Exploring Operation: 42-22=20, Resulting Numbers: [48, 20] Generated Node #0,3,3: 76:[48, 20] Operation: 42-22=20 Moving to Node #0,3,1 Current State: 76:[22, 6], Operations: ['66-44=22', '48-42=6'] Exploring Operation: 22+6=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 22*6=132, Resulting Numbers: [132] 132,76 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[42, 70], Operations: ['66-44=22', '48+22=70'] Exploring Operation: 70-42=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 42+70=112, Resulting Numbers: [112] 112,76 unequal: No Solution Exploring Operation: 42*70=2940, Resulting Numbers: [2940] 2940,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[48, 20], Operations: ['66-44=22', '42-22=20'] Exploring Operation: 48*20=960, Resulting Numbers: [960] 960,76 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 48+20=68, Resulting Numbers: [68] 68,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[42, 26], Operations: ['66-44=22', '48-22=26'] Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,76 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,76 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 Current State: 76:[44, 66, 6], Operations: ['48-42=6'] Exploring Operation: 66+6=72, Resulting Numbers: [44, 72] Generated Node #0,0,0: 76:[44, 72] Operation: 66+6=72 Exploring Operation: 66/6=11, Resulting Numbers: [44, 11] Generated Node #0,0,1: 76:[44, 11] Operation: 66/6=11 Exploring Operation: 66-44=22, Resulting Numbers: [6, 22] Generated Node #0,0,2: 76:[6, 22] Operation: 66-44=22 Exploring Operation: 44-6=38, Resulting Numbers: [66, 38] Generated Node #0,0,3: 76:[66, 38] Operation: 44-6=38 Moving to Node #0,0,2 Current State: 76:[6, 22], Operations: ['48-42=6', '66-44=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,76 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[66, 38], Operations: ['48-42=6', '44-6=38'] Exploring Operation: 66*38=2508, Resulting Numbers: [2508] 2508,76 unequal: No Solution Exploring Operation: 66-38=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 66+38=104, Resulting Numbers: [104] 104,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[44, 72], Operations: ['48-42=6', '66+6=72'] Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,76 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,76 unequal: No Solution Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,76 unequal: No Solution Moving to Node #0,0,1 Current State: 76:[44, 11], Operations: ['48-42=6', '66/6=11'] Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,76 unequal: No Solution Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,76 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,76 unequal: No Solution Exploring Operation: 44*11=484, Resulting Numbers: [484] 484,76 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
[ 24, 28, 87, 40 ]
97
[ "28-24=4", "40/4=10", "87+10=97" ]
Current State: 97:[24, 28, 87, 40], Operations: [] Exploring Operation: 28-24=4, Resulting Numbers: [87, 40, 4] Generated Node #2: [87, 40, 4] from Operation: 28-24=4 Current State: 97:[87, 40, 4], Operations: ['28-24=4'] Exploring Operation: 40/4=10, Resulting Numbers: [87, 10] Generated Node #3: [87, 10] from Operation: 40/4=10 Current State: 97:[87, 10], Operations: ['28-24=4', '40/4=10'] Exploring Operation: 87+10=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[24, 28, 87, 40], Operations: [] Exploring Operation: 28+40=68, Resulting Numbers: [24, 87, 68] Generated Node #0,0: 97:[24, 87, 68] Operation: 28+40=68 Exploring Operation: 24+28=52, Resulting Numbers: [87, 40, 52] Generated Node #0,1: 97:[87, 40, 52] Operation: 24+28=52 Exploring Operation: 24+40=64, Resulting Numbers: [28, 87, 64] Generated Node #0,2: 97:[28, 87, 64] Operation: 24+40=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[24, 87, 68], Operations: ['28+40=68'] Exploring Operation: 24+87=111, Resulting Numbers: [68, 111] Generated Node #0,0,0: 97:[68, 111] Operation: 24+87=111 Exploring Operation: 87-24=63, Resulting Numbers: [68, 63] Generated Node #0,0,1: 97:[68, 63] Operation: 87-24=63 Exploring Operation: 24+68=92, Resulting Numbers: [87, 92] Generated Node #0,0,2: 97:[87, 92] Operation: 24+68=92 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[87, 92], Operations: ['28+40=68', '24+68=92'] Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,97 unequal: No Solution Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[68, 111], Operations: ['28+40=68', '24+87=111'] Exploring Operation: 111-68=43, Resulting Numbers: [43] 43,97 unequal: No Solution Exploring Operation: 68+111=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 68*111=7548, Resulting Numbers: [7548] 7548,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[68, 63], Operations: ['28+40=68', '87-24=63'] Exploring Operation: 68+63=131, Resulting Numbers: [131] 131,97 unequal: No Solution Exploring Operation: 68*63=4284, Resulting Numbers: [4284] 4284,97 unequal: No Solution Exploring Operation: 68-63=5, Resulting Numbers: [5] 5,97 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: 97:[87, 40, 52], Operations: ['24+28=52'] Exploring Operation: 87+40=127, Resulting Numbers: [52, 127] Generated Node #0,1,0: 97:[52, 127] Operation: 87+40=127 Exploring Operation: 87-40=47, Resulting Numbers: [52, 47] Generated Node #0,1,1: 97:[52, 47] Operation: 87-40=47 Exploring Operation: 40+52=92, Resulting Numbers: [87, 92] Generated Node #0,1,2: 97:[87, 92] Operation: 40+52=92 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[87, 92], Operations: ['24+28=52', '40+52=92'] Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,97 unequal: No Solution Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[52, 127], Operations: ['24+28=52', '87+40=127'] Exploring Operation: 52*127=6604, Resulting Numbers: [6604] 6604,97 unequal: No Solution Exploring Operation: 52+127=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 127-52=75, Resulting Numbers: [75] 75,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[52, 47], Operations: ['24+28=52', '87-40=47'] Exploring Operation: 52+47=99, Resulting Numbers: [99] 99,97 unequal: No Solution Exploring Operation: 52*47=2444, Resulting Numbers: [2444] 2444,97 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,97 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: 97:[28, 87, 64], Operations: ['24+40=64'] Exploring Operation: 28+87=115, Resulting Numbers: [64, 115] Generated Node #0,2,0: 97:[64, 115] Operation: 28+87=115 Exploring Operation: 28+64=92, Resulting Numbers: [87, 92] Generated Node #0,2,1: 97:[87, 92] Operation: 28+64=92 Exploring Operation: 87-28=59, Resulting Numbers: [64, 59] Generated Node #0,2,2: 97:[64, 59] Operation: 87-28=59 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 97:[87, 92], Operations: ['24+40=64', '28+64=92'] Exploring Operation: 87*92=8004, Resulting Numbers: [8004] 8004,97 unequal: No Solution Exploring Operation: 92-87=5, Resulting Numbers: [5] 5,97 unequal: No Solution Exploring Operation: 87+92=179, Resulting Numbers: [179] 179,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 97:[64, 115], Operations: ['24+40=64', '28+87=115'] Exploring Operation: 64*115=7360, Resulting Numbers: [7360] 7360,97 unequal: No Solution Exploring Operation: 64+115=179, Resulting Numbers: [179] 179,97 unequal: No Solution Exploring Operation: 115-64=51, Resulting Numbers: [51] 51,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 97:[64, 59], Operations: ['24+40=64', '87-28=59'] Exploring Operation: 64+59=123, Resulting Numbers: [123] 123,97 unequal: No Solution Exploring Operation: 64*59=3776, Resulting Numbers: [3776] 3776,97 unequal: No Solution Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 32, 60, 20, 15 ]
69
[ "32+60=92", "15*92=1380", "1380/20=69" ]
Current State: 69:[32, 60, 20, 15], Operations: [] Exploring Operation: 32+60=92, Resulting Numbers: [20, 15, 92] Generated Node #2: [20, 15, 92] from Operation: 32+60=92 Current State: 69:[20, 15, 92], Operations: ['32+60=92'] Exploring Operation: 15*92=1380, Resulting Numbers: [20, 1380] Generated Node #3: [20, 1380] from Operation: 15*92=1380 Current State: 69:[20, 1380], Operations: ['32+60=92', '15*92=1380'] Exploring Operation: 1380/20=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[32, 60, 20, 15], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [32, 15, 3] Generated Node #0,0: 69:[32, 15, 3] Operation: 60/20=3 Exploring Operation: 60-32=28, Resulting Numbers: [20, 15, 28] Generated Node #0,1: 69:[20, 15, 28] Operation: 60-32=28 Exploring Operation: 32-15=17, Resulting Numbers: [60, 20, 17] Generated Node #0,2: 69:[60, 20, 17] Operation: 32-15=17 Exploring Operation: 60/15=4, Resulting Numbers: [32, 20, 4] Generated Node #0,3: 69:[32, 20, 4] Operation: 60/15=4 Exploring Operation: 60+15=75, Resulting Numbers: [32, 20, 75] Generated Node #0,4: 69:[32, 20, 75] Operation: 60+15=75 Moving to Node #0,3 Current State: 69:[32, 20, 4], Operations: ['60/15=4'] Exploring Operation: 20/4=5, Resulting Numbers: [32, 5] Generated Node #0,3,0: 69:[32, 5] Operation: 20/4=5 Exploring Operation: 32-4=28, Resulting Numbers: [20, 28] Generated Node #0,3,1: 69:[20, 28] Operation: 32-4=28 Exploring Operation: 32/4=8, Resulting Numbers: [20, 8] Generated Node #0,3,2: 69:[20, 8] Operation: 32/4=8 Exploring Operation: 20+4=24, Resulting Numbers: [32, 24] Generated Node #0,3,3: 69:[32, 24] Operation: 20+4=24 Exploring Operation: 32-20=12, Resulting Numbers: [4, 12] Generated Node #0,3,4: 69:[4, 12] Operation: 32-20=12 Moving to Node #0,1 Current State: 69:[20, 15, 28], Operations: ['60-32=28'] Exploring Operation: 28-20=8, Resulting Numbers: [15, 8] Generated Node #0,1,0: 69:[15, 8] Operation: 28-20=8 Exploring Operation: 20+15=35, Resulting Numbers: [28, 35] Generated Node #0,1,1: 69:[28, 35] Operation: 20+15=35 Exploring Operation: 20-15=5, Resulting Numbers: [28, 5] Generated Node #0,1,2: 69:[28, 5] Operation: 20-15=5 Exploring Operation: 15+28=43, Resulting Numbers: [20, 43] Generated Node #0,1,3: 69:[20, 43] Operation: 15+28=43 Exploring Operation: 28-15=13, Resulting Numbers: [20, 13] Generated Node #0,1,4: 69:[20, 13] Operation: 28-15=13 Moving to Node #0,0 Current State: 69:[32, 15, 3], Operations: ['60/20=3'] Exploring Operation: 15-3=12, Resulting Numbers: [32, 12] Generated Node #0,0,0: 69:[32, 12] Operation: 15-3=12 Exploring Operation: 15/3=5, Resulting Numbers: [32, 5] Generated Node #0,0,1: 69:[32, 5] Operation: 15/3=5 Exploring Operation: 32-15=17, Resulting Numbers: [3, 17] Generated Node #0,0,2: 69:[3, 17] Operation: 32-15=17 Exploring Operation: 32-3=29, Resulting Numbers: [15, 29] Generated Node #0,0,3: 69:[15, 29] Operation: 32-3=29 Exploring Operation: 15+3=18, Resulting Numbers: [32, 18] Generated Node #0,0,4: 69:[32, 18] Operation: 15+3=18 Moving to Node #0,2 Current State: 69:[60, 20, 17], Operations: ['32-15=17'] Exploring Operation: 60+17=77, Resulting Numbers: [20, 77] Generated Node #0,2,0: 69:[20, 77] Operation: 60+17=77 Exploring Operation: 60+20=80, Resulting Numbers: [17, 80] Generated Node #0,2,1: 69:[17, 80] Operation: 60+20=80 Exploring Operation: 20-17=3, Resulting Numbers: [60, 3] Generated Node #0,2,2: 69:[60, 3] Operation: 20-17=3 Exploring Operation: 60-20=40, Resulting Numbers: [17, 40] Generated Node #0,2,3: 69:[17, 40] Operation: 60-20=40 Exploring Operation: 60/20=3, Resulting Numbers: [17, 3] Generated Node #0,2,4: 69:[17, 3] Operation: 60/20=3 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 69:[17, 3], Operations: ['32-15=17', '60/20=3'] Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,69 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,69 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 #0,2,2 Current State: 69:[60, 3], Operations: ['32-15=17', '20-17=3'] Exploring Operation: 60*3=180, Resulting Numbers: [180] 180,69 unequal: No Solution Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 60/3=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 60+3=63, Resulting Numbers: [63] 63,69 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 #0,2,0 Current State: 69:[20, 77], Operations: ['32-15=17', '60+17=77'] Exploring Operation: 20*77=1540, Resulting Numbers: [1540] 1540,69 unequal: No Solution Exploring Operation: 20+77=97, Resulting Numbers: [97] 97,69 unequal: No Solution Exploring Operation: 77-20=57, Resulting Numbers: [57] 57,69 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 #0,2,1 Current State: 69:[17, 80], Operations: ['32-15=17', '60+20=80'] Exploring Operation: 17+80=97, Resulting Numbers: [97] 97,69 unequal: No Solution Exploring Operation: 17*80=1360, Resulting Numbers: [1360] 1360,69 unequal: No Solution Exploring Operation: 80-17=63, Resulting Numbers: [63] 63,69 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 #0,2,3 Current State: 69:[17, 40], Operations: ['32-15=17', '60-20=40'] Exploring Operation: 17+40=57, Resulting Numbers: [57] 57,69 unequal: No Solution Exploring Operation: 40-17=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 17*40=680, Resulting Numbers: [680] 680,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 69:[32, 20, 75], Operations: ['60+15=75'] Exploring Operation: 32-20=12, Resulting Numbers: [75, 12] Generated Node #0,4,0: 69:[75, 12] Operation: 32-20=12 Exploring Operation: 32+20=52, Resulting Numbers: [75, 52] Generated Node #0,4,1: 69:[75, 52] Operation: 32+20=52 Exploring Operation: 75-32=43, Resulting Numbers: [20, 43] Generated Node #0,4,2: 69:[20, 43] Operation: 75-32=43 Exploring Operation: 20+75=95, Resulting Numbers: [32, 95] Generated Node #0,4,3: 69:[32, 95] Operation: 20+75=95 Exploring Operation: 75-20=55, Resulting Numbers: [32, 55] Generated Node #0,4,4: 69:[32, 55] Operation: 75-20=55 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 69:[75, 12], Operations: ['60+15=75', '32-20=12'] Exploring Operation: 75*12=900, Resulting Numbers: [900] 900,69 unequal: No Solution Exploring Operation: 75+12=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 75-12=63, Resulting Numbers: [63] 63,69 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 #0,4,1 Current State: 69:[75, 52], Operations: ['60+15=75', '32+20=52'] Exploring Operation: 75+52=127, Resulting Numbers: [127] 127,69 unequal: No Solution Exploring Operation: 75-52=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 75*52=3900, Resulting Numbers: [3900] 3900,69 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 #0,4,2 Current State: 69:[20, 43], Operations: ['60+15=75', '75-32=43'] Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 20*43=860, Resulting Numbers: [860] 860,69 unequal: No Solution Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,69 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 #0,4,4 Current State: 69:[32, 55], Operations: ['60+15=75', '75-20=55'] Exploring Operation: 55-32=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 32+55=87, Resulting Numbers: [87] 87,69 unequal: No Solution Exploring Operation: 32*55=1760, Resulting Numbers: [1760] 1760,69 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 #0,4,3 Current State: 69:[32, 95], Operations: ['60+15=75', '20+75=95'] Exploring Operation: 32+95=127, Resulting Numbers: [127] 127,69 unequal: No Solution Exploring Operation: 32*95=3040, Resulting Numbers: [3040] 3040,69 unequal: No Solution Exploring Operation: 95-32=63, Resulting Numbers: [63] 63,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 69:[3, 17], Operations: ['60/20=3', '32-15=17'] Exploring Operation: 3*17=51, Resulting Numbers: [51] 51,69 unequal: No Solution Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,69 unequal: No Solution Exploring Operation: 3+17=20, Resulting Numbers: [20] 20,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[28, 5], Operations: ['60-32=28', '20-15=5'] Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[20, 28], Operations: ['60/15=4', '32-4=28'] Exploring Operation: 20*28=560, Resulting Numbers: [560] 560,69 unequal: No Solution Exploring Operation: 20+28=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[20, 8], Operations: ['60/15=4', '32/4=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,69 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,69 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[32, 24], Operations: ['60/15=4', '20+4=24'] Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,69 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[4, 12], Operations: ['60/15=4', '32-20=12'] Exploring Operation: 4+12=16, Resulting Numbers: [16] 16,69 unequal: No Solution Exploring Operation: 12-4=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 4*12=48, Resulting Numbers: [48] 48,69 unequal: No Solution Exploring Operation: 12/4=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[32, 5], Operations: ['60/20=3', '15/3=5'] Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,69 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[32, 5], Operations: ['60/15=4', '20/4=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,69 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,69 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[15, 8], Operations: ['60-32=28', '28-20=8'] Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,69 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,69 unequal: No Solution Moving to Node #0,1,4 Current State: 69:[20, 13], Operations: ['60-32=28', '28-15=13'] Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,69 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,69 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,69 unequal: No Solution Moving to Node #0,0,4 Current State: 69:[32, 18], Operations: ['60/20=3', '15+3=18'] Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,69 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,69 unequal: No Solution Moving to Node #0,0,3 Current State: 69:[15, 29], Operations: ['60/20=3', '32-3=29'] Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,69 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,69 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[28, 35], Operations: ['60-32=28', '20+15=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,69 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[32, 12], Operations: ['60/20=3', '15-3=12'] Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,69 unequal: No Solution Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,69 unequal: No Solution Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,69 unequal: No Solution Moving to Node #0,1,3 Current State: 69:[20, 43], Operations: ['60-32=28', '15+28=43'] Exploring Operation: 20*43=860, Resulting Numbers: [860] 860,69 unequal: No Solution Exploring Operation: 20+43=63, Resulting Numbers: [63] 63,69 unequal: No Solution Exploring Operation: 43-20=23, Resulting Numbers: [23] 23,69 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 62, 57, 23, 59 ]
77
[ "62-57=5", "23+59=82", "82-5=77" ]
Current State: 77:[62, 57, 23, 59], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [23, 59, 5] Generated Node #2: [23, 59, 5] from Operation: 62-57=5 Current State: 77:[23, 59, 5], Operations: ['62-57=5'] Exploring Operation: 23+59=82, Resulting Numbers: [5, 82] Generated Node #3: [5, 82] from Operation: 23+59=82 Current State: 77:[5, 82], Operations: ['62-57=5', '23+59=82'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[62, 57, 23, 59], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [23, 59, 5] Generated Node #0,0: 77:[23, 59, 5] Operation: 62-57=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[23, 59, 5], Operations: ['62-57=5'] Exploring Operation: 23+59=82, Resulting Numbers: [5, 82] Generated Node #0,0,0: 77:[5, 82] Operation: 23+59=82 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 77:[5, 82], Operations: ['62-57=5', '23+59=82'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[62, 57, 23, 59], Operations: [] Exploring Operation: 62-57=5, Resulting Numbers: [23, 59, 5] Generated Node #0,0: 77:[23, 59, 5] Operation: 62-57=5 Moving to Node #0,0 Current State: 77:[23, 59, 5], Operations: ['62-57=5'] Exploring Operation: 23+59=82, Resulting Numbers: [5, 82] Generated Node #0,0,0: 77:[5, 82] Operation: 23+59=82 Moving to Node #0,0,0 Current State: 77:[5, 82], Operations: ['62-57=5', '23+59=82'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 63, 20, 66, 6 ]
22
[ "66-63=3", "6/3=2", "20+2=22" ]
Current State: 22:[63, 20, 66, 6], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [20, 6, 3] Generated Node #2: [20, 6, 3] from Operation: 66-63=3 Current State: 22:[20, 6, 3], Operations: ['66-63=3'] Exploring Operation: 6/3=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 6/3=2 Current State: 22:[20, 2], Operations: ['66-63=3', '6/3=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[63, 20, 66, 6], Operations: [] Exploring Operation: 66-20=46, Resulting Numbers: [63, 6, 46] Generated Node #0,0: 22:[63, 6, 46] Operation: 66-20=46 Exploring Operation: 63-20=43, Resulting Numbers: [66, 6, 43] Generated Node #0,1: 22:[66, 6, 43] Operation: 63-20=43 Exploring Operation: 66-63=3, Resulting Numbers: [20, 6, 3] Generated Node #0,2: 22:[20, 6, 3] Operation: 66-63=3 Exploring Operation: 66/6=11, Resulting Numbers: [63, 20, 11] Generated Node #0,3: 22:[63, 20, 11] Operation: 66/6=11 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[20, 6, 3], Operations: ['66-63=3'] Exploring Operation: 6-3=3, Resulting Numbers: [20, 3] Generated Node #0,2,0: 22:[20, 3] Operation: 6-3=3 Exploring Operation: 6/3=2, Resulting Numbers: [20, 2] Generated Node #0,2,1: 22:[20, 2] Operation: 6/3=2 Exploring Operation: 6+3=9, Resulting Numbers: [20, 9] Generated Node #0,2,2: 22:[20, 9] Operation: 6+3=9 Exploring Operation: 20-6=14, Resulting Numbers: [3, 14] Generated Node #0,2,3: 22:[3, 14] Operation: 20-6=14 Moving to Node #0,2,1 Current State: 22:[20, 2], Operations: ['66-63=3', '6/3=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,22 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,22 unequal: No Solution Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[63, 20, 66, 6], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [20, 6, 3] Generated Node #0,2: 22:[20, 6, 3] Operation: 66-63=3 Moving to Node #0,2 Current State: 22:[20, 6, 3], Operations: ['66-63=3'] Exploring Operation: 6/3=2, Resulting Numbers: [20, 2] Generated Node #0,2,1: 22:[20, 2] Operation: 6/3=2 Moving to Node #0,2,1 Current State: 22:[20, 2], Operations: ['66-63=3', '6/3=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 6, 36, 18, 90 ]
81
[ "36+18=54", "54/6=9", "90-9=81" ]
Current State: 81:[6, 36, 18, 90], Operations: [] Exploring Operation: 36+18=54, Resulting Numbers: [6, 90, 54] Generated Node #2: [6, 90, 54] from Operation: 36+18=54 Current State: 81:[6, 90, 54], Operations: ['36+18=54'] Exploring Operation: 54/6=9, Resulting Numbers: [90, 9] Generated Node #3: [90, 9] from Operation: 54/6=9 Current State: 81:[90, 9], Operations: ['36+18=54', '54/6=9'] Exploring Operation: 90-9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[6, 36, 18, 90], Operations: [] Exploring Operation: 90/18=5, Resulting Numbers: [6, 36, 5] Generated Node #0,0: 81:[6, 36, 5] Operation: 90/18=5 Exploring Operation: 36-6=30, Resulting Numbers: [18, 90, 30] Generated Node #0,1: 81:[18, 90, 30] Operation: 36-6=30 Exploring Operation: 18/6=3, Resulting Numbers: [36, 90, 3] Generated Node #0,2: 81:[36, 90, 3] Operation: 18/6=3 Exploring Operation: 36/18=2, Resulting Numbers: [6, 90, 2] Generated Node #0,3: 81:[6, 90, 2] Operation: 36/18=2 Moving to Node #0,3 Current State: 81:[6, 90, 2], Operations: ['36/18=2'] Exploring Operation: 90/6=15, Resulting Numbers: [2, 15] Generated Node #0,3,0: 81:[2, 15] Operation: 90/6=15 Exploring Operation: 6/2=3, Resulting Numbers: [90, 3] Generated Node #0,3,1: 81:[90, 3] Operation: 6/2=3 Exploring Operation: 6+2=8, Resulting Numbers: [90, 8] Generated Node #0,3,2: 81:[90, 8] Operation: 6+2=8 Exploring Operation: 90-6=84, Resulting Numbers: [2, 84] Generated Node #0,3,3: 81:[2, 84] Operation: 90-6=84 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 81:[2, 84], Operations: ['36/18=2', '90-6=84'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,81 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,81 unequal: No Solution Exploring Operation: 2*84=168, Resulting Numbers: [168] 168,81 unequal: No Solution Exploring Operation: 2+84=86, Resulting Numbers: [86] 86,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 81:[2, 15], Operations: ['36/18=2', '90/6=15'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,81 unequal: No Solution Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 81:[90, 3], Operations: ['36/18=2', '6/2=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,81 unequal: No Solution Exploring Operation: 90/3=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 90*3=270, Resulting Numbers: [270] 270,81 unequal: No Solution Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 81:[90, 8], Operations: ['36/18=2', '6+2=8'] Exploring Operation: 90+8=98, Resulting Numbers: [98] 98,81 unequal: No Solution Exploring Operation: 90*8=720, Resulting Numbers: [720] 720,81 unequal: No Solution Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 81:[6, 36, 5], Operations: ['90/18=5'] Exploring Operation: 36-5=31, Resulting Numbers: [6, 31] Generated Node #0,0,0: 81:[6, 31] Operation: 36-5=31 Exploring Operation: 36/6=6, Resulting Numbers: [5, 6] Generated Node #0,0,1: 81:[5, 6] Operation: 36/6=6 Exploring Operation: 36-6=30, Resulting Numbers: [5, 30] Generated Node #0,0,2: 81:[5, 30] Operation: 36-6=30 Exploring Operation: 6+5=11, Resulting Numbers: [36, 11] Generated Node #0,0,3: 81:[36, 11] Operation: 6+5=11 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 81:[5, 6], Operations: ['90/18=5', '36/6=6'] Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,81 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 81:[5, 30], Operations: ['90/18=5', '36-6=30'] Exploring Operation: 5*30=150, Resulting Numbers: [150] 150,81 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,81 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 81:[6, 31], Operations: ['90/18=5', '36-5=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,81 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 81:[36, 11], Operations: ['90/18=5', '6+5=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 36*11=396, Resulting Numbers: [396] 396,81 unequal: No Solution Exploring Operation: 36+11=47, Resulting Numbers: [47] 47,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 81:[36, 90, 3], Operations: ['18/6=3'] Exploring Operation: 90/3=30, Resulting Numbers: [36, 30] Generated Node #0,2,0: 81:[36, 30] Operation: 90/3=30 Exploring Operation: 36-3=33, Resulting Numbers: [90, 33] Generated Node #0,2,1: 81:[90, 33] Operation: 36-3=33 Exploring Operation: 36/3=12, Resulting Numbers: [90, 12] Generated Node #0,2,2: 81:[90, 12] Operation: 36/3=12 Exploring Operation: 90-3=87, Resulting Numbers: [36, 87] Generated Node #0,2,3: 81:[36, 87] Operation: 90-3=87 Moving to Node #0,1 Current State: 81:[18, 90, 30], Operations: ['36-6=30'] Exploring Operation: 90/30=3, Resulting Numbers: [18, 3] Generated Node #0,1,0: 81:[18, 3] Operation: 90/30=3 Exploring Operation: 30-18=12, Resulting Numbers: [90, 12] Generated Node #0,1,1: 81:[90, 12] Operation: 30-18=12 Exploring Operation: 90/18=5, Resulting Numbers: [30, 5] Generated Node #0,1,2: 81:[30, 5] Operation: 90/18=5 Exploring Operation: 90-18=72, Resulting Numbers: [30, 72] Generated Node #0,1,3: 81:[30, 72] Operation: 90-18=72 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 81:[30, 5], Operations: ['36-6=30', '90/18=5'] Exploring Operation: 30+5=35, Resulting Numbers: [35] 35,81 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 30*5=150, Resulting Numbers: [150] 150,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 81:[18, 3], Operations: ['36-6=30', '90/30=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,81 unequal: No Solution Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,81 unequal: No Solution Exploring Operation: 18+3=21, Resulting Numbers: [21] 21,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[90, 12], Operations: ['36-6=30', '30-18=12'] Exploring Operation: 90+12=102, Resulting Numbers: [102] 102,81 unequal: No Solution Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 90*12=1080, Resulting Numbers: [1080] 1080,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 81:[30, 72], Operations: ['36-6=30', '90-18=72'] Exploring Operation: 30*72=2160, Resulting Numbers: [2160] 2160,81 unequal: No Solution Exploring Operation: 30+72=102, Resulting Numbers: [102] 102,81 unequal: No Solution Exploring Operation: 72-30=42, Resulting Numbers: [42] 42,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 81:[36, 30], Operations: ['18/6=3', '90/3=30'] Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,81 unequal: No Solution Exploring Operation: 36+30=66, Resulting Numbers: [66] 66,81 unequal: No Solution Exploring Operation: 36*30=1080, Resulting Numbers: [1080] 1080,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[90, 12], Operations: ['18/6=3', '36/3=12'] Exploring Operation: 90+12=102, Resulting Numbers: [102] 102,81 unequal: No Solution Exploring Operation: 90*12=1080, Resulting Numbers: [1080] 1080,81 unequal: No Solution Exploring Operation: 90-12=78, Resulting Numbers: [78] 78,81 unequal: No Solution Moving to Node #0,2,3 Current State: 81:[36, 87], Operations: ['18/6=3', '90-3=87'] Exploring Operation: 36*87=3132, Resulting Numbers: [3132] 3132,81 unequal: No Solution Exploring Operation: 36+87=123, Resulting Numbers: [123] 123,81 unequal: No Solution Exploring Operation: 87-36=51, Resulting Numbers: [51] 51,81 unequal: No Solution Moving to Node #0,2,1 Current State: 81:[90, 33], Operations: ['18/6=3', '36-3=33'] Exploring Operation: 90-33=57, Resulting Numbers: [57] 57,81 unequal: No Solution Exploring Operation: 90*33=2970, Resulting Numbers: [2970] 2970,81 unequal: No Solution Exploring Operation: 90+33=123, Resulting Numbers: [123] 123,81 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 4, 3, 82, 88 ]
90
[ "4*88=352", "352-82=270", "270/3=90" ]
Current State: 90:[4, 3, 82, 88], Operations: [] Exploring Operation: 4*88=352, Resulting Numbers: [3, 82, 352] Generated Node #2: [3, 82, 352] from Operation: 4*88=352 Current State: 90:[3, 82, 352], Operations: ['4*88=352'] Exploring Operation: 352-82=270, Resulting Numbers: [3, 270] Generated Node #3: [3, 270] from Operation: 352-82=270 Current State: 90:[3, 270], Operations: ['4*88=352', '352-82=270'] Exploring Operation: 270/3=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[4, 3, 82, 88], Operations: [] Exploring Operation: 4+82=86, Resulting Numbers: [3, 88, 86] Generated Node #0,0: 90:[3, 88, 86] Operation: 4+82=86 Exploring Operation: 88-82=6, Resulting Numbers: [4, 3, 6] Generated Node #0,1: 90:[4, 3, 6] Operation: 88-82=6 Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[4, 3, 6], Operations: ['88-82=6'] Exploring Operation: 6-4=2, Resulting Numbers: [3, 2] Generated Node #0,1,0: 90:[3, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [3, 10] Generated Node #0,1,1: 90:[3, 10] Operation: 4+6=10 Moving to Node #0,1,0 Current State: 90:[3, 2], Operations: ['88-82=6', '6-4=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[3, 10], Operations: ['88-82=6', '4+6=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,90 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[3, 88, 86], Operations: ['4+82=86'] Exploring Operation: 88-86=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 90:[3, 2] Operation: 88-86=2 Exploring Operation: 3+86=89, Resulting Numbers: [88, 89] Generated Node #0,0,1: 90:[88, 89] Operation: 3+86=89 Moving to Node #0,0,0 Current State: 90:[3, 2], Operations: ['4+82=86', '88-86=2'] Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[88, 89], Operations: ['4+82=86', '3+86=89'] Exploring Operation: 89-88=1, Resulting Numbers: [1] 1,90 unequal: No Solution Exploring Operation: 88+89=177, Resulting Numbers: [177] 177,90 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
[ 7, 15, 12, 66 ]
100
[ "7+15=22", "12+66=78", "22+78=100" ]
Current State: 100:[7, 15, 12, 66], Operations: [] Exploring Operation: 7+15=22, Resulting Numbers: [12, 66, 22] Generated Node #2: [12, 66, 22] from Operation: 7+15=22 Current State: 100:[12, 66, 22], Operations: ['7+15=22'] Exploring Operation: 12+66=78, Resulting Numbers: [22, 78] Generated Node #3: [22, 78] from Operation: 12+66=78 Current State: 100:[22, 78], Operations: ['7+15=22', '12+66=78'] Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[7, 15, 12, 66], Operations: [] Exploring Operation: 66-15=51, Resulting Numbers: [7, 12, 51] Generated Node #0,0: 100:[7, 12, 51] Operation: 66-15=51 Exploring Operation: 66-12=54, Resulting Numbers: [7, 15, 54] Generated Node #0,1: 100:[7, 15, 54] Operation: 66-12=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[7, 12, 51], Operations: ['66-15=51'] Exploring Operation: 12-7=5, Resulting Numbers: [51, 5] Generated Node #0,0,0: 100:[51, 5] Operation: 12-7=5 Exploring Operation: 7+12=19, Resulting Numbers: [51, 19] Generated Node #0,0,1: 100:[51, 19] Operation: 7+12=19 Moving to Node #0,0,0 Current State: 100:[51, 5], Operations: ['66-15=51', '12-7=5'] Exploring Operation: 51+5=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 51-5=46, Resulting Numbers: [46] 46,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[51, 19], Operations: ['66-15=51', '7+12=19'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,100 unequal: No Solution Exploring Operation: 51+19=70, Resulting Numbers: [70] 70,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 100:[7, 15, 54], Operations: ['66-12=54'] Exploring Operation: 7+15=22, Resulting Numbers: [54, 22] Generated Node #0,1,0: 100:[54, 22] Operation: 7+15=22 Exploring Operation: 15-7=8, Resulting Numbers: [54, 8] Generated Node #0,1,1: 100:[54, 8] Operation: 15-7=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 100:[54, 22], Operations: ['66-12=54', '7+15=22'] Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,100 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 100:[54, 8], Operations: ['66-12=54', '15-7=8'] Exploring Operation: 54+8=62, Resulting Numbers: [62] 62,100 unequal: No Solution Exploring Operation: 54-8=46, Resulting Numbers: [46] 46,100 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 10, 62, 36, 12 ]
30
[ "10+62=72", "72/12=6", "36-6=30" ]
Current State: 30:[10, 62, 36, 12], Operations: [] Exploring Operation: 10+62=72, Resulting Numbers: [36, 12, 72] Generated Node #2: [36, 12, 72] from Operation: 10+62=72 Current State: 30:[36, 12, 72], Operations: ['10+62=72'] Exploring Operation: 72/12=6, Resulting Numbers: [36, 6] Generated Node #3: [36, 6] from Operation: 72/12=6 Current State: 30:[36, 6], Operations: ['10+62=72', '72/12=6'] Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[10, 62, 36, 12], Operations: [] Exploring Operation: 62-36=26, Resulting Numbers: [10, 12, 26] Generated Node #0,0: 30:[10, 12, 26] Operation: 62-36=26 Exploring Operation: 62-12=50, Resulting Numbers: [10, 36, 50] Generated Node #0,1: 30:[10, 36, 50] Operation: 62-12=50 Moving to Node #0,0 Current State: 30:[10, 12, 26], Operations: ['62-36=26'] Exploring Operation: 26-10=16, Resulting Numbers: [12, 16] Generated Node #0,0,0: 30:[12, 16] Operation: 26-10=16 Exploring Operation: 26-12=14, Resulting Numbers: [10, 14] Generated Node #0,0,1: 30:[10, 14] Operation: 26-12=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 30:[10, 14], Operations: ['62-36=26', '26-12=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 30:[12, 16], Operations: ['62-36=26', '26-10=16'] Exploring Operation: 12+16=28, Resulting Numbers: [28] 28,30 unequal: No Solution Exploring Operation: 16-12=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 30:[10, 36, 50], Operations: ['62-12=50'] Exploring Operation: 50-36=14, Resulting Numbers: [10, 14] Generated Node #0,1,0: 30:[10, 14] Operation: 50-36=14 Exploring Operation: 50/10=5, Resulting Numbers: [36, 5] Generated Node #0,1,1: 30:[36, 5] Operation: 50/10=5 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[10, 14], Operations: ['62-12=50', '50-36=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[36, 5], Operations: ['62-12=50', '50/10=5'] Exploring Operation: 36+5=41, Resulting Numbers: [41] 41,30 unequal: No Solution Exploring Operation: 36-5=31, Resulting Numbers: [31] 31,30 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
[ 72, 84, 24, 66 ]
80
[ "72-66=6", "24/6=4", "84-4=80" ]
Current State: 80:[72, 84, 24, 66], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [84, 24, 6] Generated Node #2: [84, 24, 6] from Operation: 72-66=6 Current State: 80:[84, 24, 6], Operations: ['72-66=6'] Exploring Operation: 24/6=4, Resulting Numbers: [84, 4] Generated Node #3: [84, 4] from Operation: 24/6=4 Current State: 80:[84, 4], Operations: ['72-66=6', '24/6=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[72, 84, 24, 66], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [84, 24, 6] Generated Node #0,0: 80:[84, 24, 6] Operation: 72-66=6 Exploring Operation: 66-24=42, Resulting Numbers: [72, 84, 42] Generated Node #0,1: 80:[72, 84, 42] Operation: 66-24=42 Exploring Operation: 84-66=18, Resulting Numbers: [72, 24, 18] Generated Node #0,2: 80:[72, 24, 18] Operation: 84-66=18 Moving to Node #0,0 Current State: 80:[84, 24, 6], Operations: ['72-66=6'] Exploring Operation: 84/6=14, Resulting Numbers: [24, 14] Generated Node #0,0,0: 80:[24, 14] Operation: 84/6=14 Exploring Operation: 84-6=78, Resulting Numbers: [24, 78] Generated Node #0,0,1: 80:[24, 78] Operation: 84-6=78 Exploring Operation: 24/6=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 80:[84, 4] Operation: 24/6=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[84, 4], Operations: ['72-66=6', '24/6=4'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,80 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[72, 84, 24, 66], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [84, 24, 6] Generated Node #0,0: 80:[84, 24, 6] Operation: 72-66=6 Moving to Node #0,0 Current State: 80:[84, 24, 6], Operations: ['72-66=6'] Exploring Operation: 24/6=4, Resulting Numbers: [84, 4] Generated Node #0,0,2: 80:[84, 4] Operation: 24/6=4 Moving to Node #0,0,2 Current State: 80:[84, 4], Operations: ['72-66=6', '24/6=4'] Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 7, 26, 20, 23 ]
46
[ "20-7=13", "26*23=598", "598/13=46" ]
Current State: 46:[7, 26, 20, 23], Operations: [] Exploring Operation: 20-7=13, Resulting Numbers: [26, 23, 13] Generated Node #2: [26, 23, 13] from Operation: 20-7=13 Current State: 46:[26, 23, 13], Operations: ['20-7=13'] Exploring Operation: 26*23=598, Resulting Numbers: [13, 598] Generated Node #3: [13, 598] from Operation: 26*23=598 Current State: 46:[13, 598], Operations: ['20-7=13', '26*23=598'] Exploring Operation: 598/13=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[7, 26, 20, 23], Operations: [] Exploring Operation: 7+20=27, Resulting Numbers: [26, 23, 27] Generated Node #0,0: 46:[26, 23, 27] Operation: 7+20=27 Exploring Operation: 26+20=46, Resulting Numbers: [7, 23, 46] Generated Node #0,1: 46:[7, 23, 46] Operation: 26+20=46 Exploring Operation: 26-20=6, Resulting Numbers: [7, 23, 6] Generated Node #0,2: 46:[7, 23, 6] Operation: 26-20=6 Exploring Operation: 26-7=19, Resulting Numbers: [20, 23, 19] Generated Node #0,3: 46:[20, 23, 19] Operation: 26-7=19 Moving to Node #0,1 Current State: 46:[7, 23, 46], Operations: ['26+20=46'] Exploring Operation: 46/23=2, Resulting Numbers: [7, 2] Generated Node #0,1,0: 46:[7, 2] Operation: 46/23=2 Exploring Operation: 23-7=16, Resulting Numbers: [46, 16] Generated Node #0,1,1: 46:[46, 16] Operation: 23-7=16 Exploring Operation: 7+23=30, Resulting Numbers: [46, 30] Generated Node #0,1,2: 46:[46, 30] Operation: 7+23=30 Exploring Operation: 46-23=23, Resulting Numbers: [7, 23] Generated Node #0,1,3: 46:[7, 23] Operation: 46-23=23 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[7, 2], Operations: ['26+20=46', '46/23=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 46:[7, 23], Operations: ['26+20=46', '46-23=23'] Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[46, 16], Operations: ['26+20=46', '23-7=16'] Exploring Operation: 46+16=62, Resulting Numbers: [62] 62,46 unequal: No Solution Exploring Operation: 46*16=736, Resulting Numbers: [736] 736,46 unequal: No Solution Exploring Operation: 46-16=30, Resulting Numbers: [30] 30,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[46, 30], Operations: ['26+20=46', '7+23=30'] Exploring Operation: 46*30=1380, Resulting Numbers: [1380] 1380,46 unequal: No Solution Exploring Operation: 46+30=76, Resulting Numbers: [76] 76,46 unequal: No Solution Exploring Operation: 46-30=16, Resulting Numbers: [16] 16,46 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: 46:[20, 23, 19], Operations: ['26-7=19'] Exploring Operation: 20-19=1, Resulting Numbers: [23, 1] Generated Node #0,3,0: 46:[23, 1] Operation: 20-19=1 Exploring Operation: 23-19=4, Resulting Numbers: [20, 4] Generated Node #0,3,1: 46:[20, 4] Operation: 23-19=4 Exploring Operation: 20+23=43, Resulting Numbers: [19, 43] Generated Node #0,3,2: 46:[19, 43] Operation: 20+23=43 Exploring Operation: 23-20=3, Resulting Numbers: [19, 3] Generated Node #0,3,3: 46:[19, 3] Operation: 23-20=3 Moving to Node #0,0 Current State: 46:[26, 23, 27], Operations: ['7+20=27'] Exploring Operation: 26+23=49, Resulting Numbers: [27, 49] Generated Node #0,0,0: 46:[27, 49] Operation: 26+23=49 Exploring Operation: 26-23=3, Resulting Numbers: [27, 3] Generated Node #0,0,1: 46:[27, 3] Operation: 26-23=3 Exploring Operation: 27-26=1, Resulting Numbers: [23, 1] Generated Node #0,0,2: 46:[23, 1] Operation: 27-26=1 Exploring Operation: 27-23=4, Resulting Numbers: [26, 4] Generated Node #0,0,3: 46:[26, 4] Operation: 27-23=4 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 46:[23, 1], Operations: ['7+20=27', '27-26=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,46 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 #0,0,1 Current State: 46:[27, 3], Operations: ['7+20=27', '26-23=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,46 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,46 unequal: No Solution Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,46 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,46 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 #0,0,3 Current State: 46:[26, 4], Operations: ['7+20=27', '27-23=4'] Exploring Operation: 26*4=104, Resulting Numbers: [104] 104,46 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,46 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 #0,0,0 Current State: 46:[27, 49], Operations: ['7+20=27', '26+23=49'] Exploring Operation: 27*49=1323, Resulting Numbers: [1323] 1323,46 unequal: No Solution Exploring Operation: 49-27=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 27+49=76, Resulting Numbers: [76] 76,46 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: 46:[7, 23, 6], Operations: ['26-20=6'] Exploring Operation: 7*6=42, Resulting Numbers: [23, 42] Generated Node #0,2,0: 46:[23, 42] Operation: 7*6=42 Exploring Operation: 7+23=30, Resulting Numbers: [6, 30] Generated Node #0,2,1: 46:[6, 30] Operation: 7+23=30 Exploring Operation: 7-6=1, Resulting Numbers: [23, 1] Generated Node #0,2,2: 46:[23, 1] Operation: 7-6=1 Exploring Operation: 7+6=13, Resulting Numbers: [23, 13] Generated Node #0,2,3: 46:[23, 13] Operation: 7+6=13 Moving to Node #0,3,0 Current State: 46:[23, 1], Operations: ['26-7=19', '20-19=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[23, 1], Operations: ['26-20=6', '7-6=1'] Exploring Operation: 23-1=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 23/1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23*1=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[23, 42], Operations: ['26-20=6', '7*6=42'] Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,46 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[19, 3], Operations: ['26-7=19', '23-20=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,46 unequal: No Solution Exploring Operation: 19*3=57, Resulting Numbers: [57] 57,46 unequal: No Solution Exploring Operation: 19-3=16, Resulting Numbers: [16] 16,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[20, 4], Operations: ['26-7=19', '23-19=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,46 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,46 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[19, 43], Operations: ['26-7=19', '20+23=43'] Exploring Operation: 19*43=817, Resulting Numbers: [817] 817,46 unequal: No Solution Exploring Operation: 43-19=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 19+43=62, Resulting Numbers: [62] 62,46 unequal: No Solution Moving to Node #0,2,3 Current State: 46:[23, 13], Operations: ['26-20=6', '7+6=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,46 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,46 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[6, 30], Operations: ['26-20=6', '7+23=30'] Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,46 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,46 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,46 unequal: No Solution Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,46 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 44, 28, 75, 67 ]
80
[ "44+28=72", "75-67=8", "72+8=80" ]
Current State: 80:[44, 28, 75, 67], Operations: [] Exploring Operation: 44+28=72, Resulting Numbers: [75, 67, 72] Generated Node #2: [75, 67, 72] from Operation: 44+28=72 Current State: 80:[75, 67, 72], Operations: ['44+28=72'] Exploring Operation: 75-67=8, Resulting Numbers: [72, 8] Generated Node #3: [72, 8] from Operation: 75-67=8 Current State: 80:[72, 8], Operations: ['44+28=72', '75-67=8'] Exploring Operation: 72+8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[44, 28, 75, 67], Operations: [] Exploring Operation: 67-28=39, Resulting Numbers: [44, 75, 39] Generated Node #0,0: 80:[44, 75, 39] Operation: 67-28=39 Moving to Node #0,0 Current State: 80:[44, 75, 39], Operations: ['67-28=39'] Exploring Operation: 44-39=5, Resulting Numbers: [75, 5] Generated Node #0,0,0: 80:[75, 5] Operation: 44-39=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[75, 5], Operations: ['67-28=39', '44-39=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[44, 28, 75, 67], Operations: [] Exploring Operation: 67-28=39, Resulting Numbers: [44, 75, 39] Generated Node #0,0: 80:[44, 75, 39] Operation: 67-28=39 Moving to Node #0,0 Current State: 80:[44, 75, 39], Operations: ['67-28=39'] Exploring Operation: 44-39=5, Resulting Numbers: [75, 5] Generated Node #0,0,0: 80:[75, 5] Operation: 44-39=5 Moving to Node #0,0,0 Current State: 80:[75, 5], Operations: ['67-28=39', '44-39=5'] Exploring Operation: 75+5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 39, 54, 41, 24 ]
51
[ "41-39=2", "54/2=27", "24+27=51" ]
Current State: 51:[39, 54, 41, 24], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [54, 24, 2] Generated Node #2: [54, 24, 2] from Operation: 41-39=2 Current State: 51:[54, 24, 2], Operations: ['41-39=2'] Exploring Operation: 54/2=27, Resulting Numbers: [24, 27] Generated Node #3: [24, 27] from Operation: 54/2=27 Current State: 51:[24, 27], Operations: ['41-39=2', '54/2=27'] Exploring Operation: 24+27=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[39, 54, 41, 24], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [54, 24, 2] Generated Node #0,0: 51:[54, 24, 2] Operation: 41-39=2 Exploring Operation: 39-24=15, Resulting Numbers: [54, 41, 15] Generated Node #0,1: 51:[54, 41, 15] Operation: 39-24=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[54, 24, 2], Operations: ['41-39=2'] Exploring Operation: 54-2=52, Resulting Numbers: [24, 52] Generated Node #0,0,0: 51:[24, 52] Operation: 54-2=52 Exploring Operation: 24*2=48, Resulting Numbers: [54, 48] Generated Node #0,0,1: 51:[54, 48] Operation: 24*2=48 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 51:[54, 48], Operations: ['41-39=2', '24*2=48'] Exploring Operation: 54+48=102, Resulting Numbers: [102] 102,51 unequal: No Solution Exploring Operation: 54-48=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 #0,0,0 Current State: 51:[24, 52], Operations: ['41-39=2', '54-2=52'] Exploring Operation: 24+52=76, Resulting Numbers: [76] 76,51 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,51 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 #0,1 Current State: 51:[54, 41, 15], Operations: ['39-24=15'] Exploring Operation: 41+15=56, Resulting Numbers: [54, 56] Generated Node #0,1,0: 51:[54, 56] Operation: 41+15=56 Exploring Operation: 54-41=13, Resulting Numbers: [15, 13] Generated Node #0,1,1: 51:[15, 13] Operation: 54-41=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 51:[15, 13], Operations: ['39-24=15', '54-41=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,51 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,51 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:[54, 56], Operations: ['39-24=15', '41+15=56'] Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,51 unequal: No Solution Exploring Operation: 54+56=110, Resulting Numbers: [110] 110,51 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 87, 54, 46, 75 ]
88
[ "87-54=33", "46+75=121", "121-33=88" ]
Current State: 88:[87, 54, 46, 75], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [46, 75, 33] Generated Node #2: [46, 75, 33] from Operation: 87-54=33 Current State: 88:[46, 75, 33], Operations: ['87-54=33'] Exploring Operation: 46+75=121, Resulting Numbers: [33, 121] Generated Node #3: [33, 121] from Operation: 46+75=121 Current State: 88:[33, 121], Operations: ['87-54=33', '46+75=121'] Exploring Operation: 121-33=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[87, 54, 46, 75], Operations: [] Exploring Operation: 75-54=21, Resulting Numbers: [87, 46, 21] Generated Node #0,0: 88:[87, 46, 21] Operation: 75-54=21 Moving to Node #0,0 Current State: 88:[87, 46, 21], Operations: ['75-54=21'] Exploring Operation: 87-46=41, Resulting Numbers: [21, 41] Generated Node #0,0,0: 88:[21, 41] Operation: 87-46=41 Moving to Node #0,0,0 Current State: 88:[21, 41], Operations: ['75-54=21', '87-46=41'] Exploring Operation: 41-21=20, Resulting Numbers: [20] 20,88 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 31, 82, 22, 50 ]
41
[ "31+82=113", "22+50=72", "113-72=41" ]
Current State: 41:[31, 82, 22, 50], Operations: [] Exploring Operation: 31+82=113, Resulting Numbers: [22, 50, 113] Generated Node #2: [22, 50, 113] from Operation: 31+82=113 Current State: 41:[22, 50, 113], Operations: ['31+82=113'] Exploring Operation: 22+50=72, Resulting Numbers: [113, 72] Generated Node #3: [113, 72] from Operation: 22+50=72 Current State: 41:[113, 72], Operations: ['31+82=113', '22+50=72'] Exploring Operation: 113-72=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[31, 82, 22, 50], Operations: [] Exploring Operation: 82-31=51, Resulting Numbers: [22, 50, 51] Generated Node #0,0: 41:[22, 50, 51] Operation: 82-31=51 Exploring Operation: 31+22=53, Resulting Numbers: [82, 50, 53] Generated Node #0,1: 41:[82, 50, 53] Operation: 31+22=53 Exploring Operation: 82-22=60, Resulting Numbers: [31, 50, 60] Generated Node #0,2: 41:[31, 50, 60] Operation: 82-22=60 Exploring Operation: 82-50=32, Resulting Numbers: [31, 22, 32] Generated Node #0,3: 41:[31, 22, 32] Operation: 82-50=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[22, 50, 51], Operations: ['82-31=51'] Exploring Operation: 50-22=28, Resulting Numbers: [51, 28] Generated Node #0,0,0: 41:[51, 28] Operation: 50-22=28 Exploring Operation: 51-22=29, Resulting Numbers: [50, 29] Generated Node #0,0,1: 41:[50, 29] Operation: 51-22=29 Exploring Operation: 22+50=72, Resulting Numbers: [51, 72] Generated Node #0,0,2: 41:[51, 72] Operation: 22+50=72 Exploring Operation: 22+51=73, Resulting Numbers: [50, 73] Generated Node #0,0,3: 41:[50, 73] Operation: 22+51=73 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[50, 29], Operations: ['82-31=51', '51-22=29'] Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,41 unequal: No Solution Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[51, 28], Operations: ['82-31=51', '50-22=28'] Exploring Operation: 51-28=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 51*28=1428, Resulting Numbers: [1428] 1428,41 unequal: No Solution Exploring Operation: 51+28=79, Resulting Numbers: [79] 79,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[51, 72], Operations: ['82-31=51', '22+50=72'] Exploring Operation: 51+72=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 51*72=3672, Resulting Numbers: [3672] 3672,41 unequal: No Solution Exploring Operation: 72-51=21, Resulting Numbers: [21] 21,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[50, 73], Operations: ['82-31=51', '22+51=73'] Exploring Operation: 73-50=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 50*73=3650, Resulting Numbers: [3650] 3650,41 unequal: No Solution Exploring Operation: 50+73=123, Resulting Numbers: [123] 123,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[31, 50, 60], Operations: ['82-22=60'] Exploring Operation: 50-31=19, Resulting Numbers: [60, 19] Generated Node #0,2,0: 41:[60, 19] Operation: 50-31=19 Exploring Operation: 60-50=10, Resulting Numbers: [31, 10] Generated Node #0,2,1: 41:[31, 10] Operation: 60-50=10 Exploring Operation: 60-31=29, Resulting Numbers: [50, 29] Generated Node #0,2,2: 41:[50, 29] Operation: 60-31=29 Exploring Operation: 31+50=81, Resulting Numbers: [60, 81] Generated Node #0,2,3: 41:[60, 81] Operation: 31+50=81 Moving to Node #0,2,2 Current State: 41:[50, 29], Operations: ['82-22=60', '60-31=29'] Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,41 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[31, 10], Operations: ['82-22=60', '60-50=10'] Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Moving to Node #0 Current State: 41:[31, 82, 22, 50], Operations: [] Exploring Operation: 82-22=60, Resulting Numbers: [31, 50, 60] Generated Node #0,2: 41:[31, 50, 60] Operation: 82-22=60 Moving to Node #0,2 Current State: 41:[31, 50, 60], Operations: ['82-22=60'] Exploring Operation: 60-50=10, Resulting Numbers: [31, 10] Generated Node #0,2,1: 41:[31, 10] Operation: 60-50=10 Moving to Node #0,2,1 Current State: 41:[31, 10], Operations: ['82-22=60', '60-50=10'] Exploring Operation: 31+10=41, Resulting Numbers: [41] 41,41 equal: Goal Reached Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 53, 84, 18, 30 ]
46
[ "30-18=12", "84/12=7", "53-7=46" ]
Current State: 46:[53, 84, 18, 30], Operations: [] Exploring Operation: 30-18=12, Resulting Numbers: [53, 84, 12] Generated Node #2: [53, 84, 12] from Operation: 30-18=12 Current State: 46:[53, 84, 12], Operations: ['30-18=12'] Exploring Operation: 84/12=7, Resulting Numbers: [53, 7] Generated Node #3: [53, 7] from Operation: 84/12=7 Current State: 46:[53, 7], Operations: ['30-18=12', '84/12=7'] Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[53, 84, 18, 30], Operations: [] Exploring Operation: 84-53=31, Resulting Numbers: [18, 30, 31] Generated Node #0,0: 46:[18, 30, 31] Operation: 84-53=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[18, 30, 31], Operations: ['84-53=31'] Exploring Operation: 31-30=1, Resulting Numbers: [18, 1] Generated Node #0,0,0: 46:[18, 1] Operation: 31-30=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[18, 1], Operations: ['84-53=31', '31-30=1'] Exploring Operation: 18+1=19, Resulting Numbers: [19] 19,46 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
[ 77, 81, 68, 29 ]
43
[ "81-77=4", "68-29=39", "4+39=43" ]
Current State: 43:[77, 81, 68, 29], Operations: [] Exploring Operation: 81-77=4, Resulting Numbers: [68, 29, 4] Generated Node #2: [68, 29, 4] from Operation: 81-77=4 Current State: 43:[68, 29, 4], Operations: ['81-77=4'] Exploring Operation: 68-29=39, Resulting Numbers: [4, 39] Generated Node #3: [4, 39] from Operation: 68-29=39 Current State: 43:[4, 39], Operations: ['81-77=4', '68-29=39'] Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[77, 81, 68, 29], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [77, 68, 52] Generated Node #0,0: 43:[77, 68, 52] Operation: 81-29=52 Exploring Operation: 77-29=48, Resulting Numbers: [81, 68, 48] Generated Node #0,1: 43:[81, 68, 48] Operation: 77-29=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[77, 68, 52], Operations: ['81-29=52'] Exploring Operation: 77-52=25, Resulting Numbers: [68, 25] Generated Node #0,0,0: 43:[68, 25] Operation: 77-52=25 Exploring Operation: 77-68=9, Resulting Numbers: [52, 9] Generated Node #0,0,1: 43:[52, 9] Operation: 77-68=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[68, 25], Operations: ['81-29=52', '77-52=25'] Exploring Operation: 68+25=93, Resulting Numbers: [93] 93,43 unequal: No Solution Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[77, 81, 68, 29], Operations: [] Exploring Operation: 81-29=52, Resulting Numbers: [77, 68, 52] Generated Node #0,0: 43:[77, 68, 52] Operation: 81-29=52 Moving to Node #0,0 Current State: 43:[77, 68, 52], Operations: ['81-29=52'] Exploring Operation: 77-52=25, Resulting Numbers: [68, 25] Generated Node #0,0,0: 43:[68, 25] Operation: 77-52=25 Moving to Node #0,0,0 Current State: 43:[68, 25], Operations: ['81-29=52', '77-52=25'] Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 63, 24, 76, 84 ]
39
[ "76-24=52", "63*52=3276", "3276/84=39" ]
Current State: 39:[63, 24, 76, 84], Operations: [] Exploring Operation: 76-24=52, Resulting Numbers: [63, 84, 52] Generated Node #2: [63, 84, 52] from Operation: 76-24=52 Current State: 39:[63, 84, 52], Operations: ['76-24=52'] Exploring Operation: 63*52=3276, Resulting Numbers: [84, 3276] Generated Node #3: [84, 3276] from Operation: 63*52=3276 Current State: 39:[84, 3276], Operations: ['76-24=52', '63*52=3276'] Exploring Operation: 3276/84=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[63, 24, 76, 84], Operations: [] Exploring Operation: 76-63=13, Resulting Numbers: [24, 84, 13] Generated Node #0,0: 39:[24, 84, 13] Operation: 76-63=13 Exploring Operation: 76-24=52, Resulting Numbers: [63, 84, 52] Generated Node #0,1: 39:[63, 84, 52] Operation: 76-24=52 Exploring Operation: 84-63=21, Resulting Numbers: [24, 76, 21] Generated Node #0,2: 39:[24, 76, 21] Operation: 84-63=21 Exploring Operation: 63-24=39, Resulting Numbers: [76, 84, 39] Generated Node #0,3: 39:[76, 84, 39] Operation: 63-24=39 Exploring Operation: 84-76=8, Resulting Numbers: [63, 24, 8] Generated Node #0,4: 39:[63, 24, 8] Operation: 84-76=8 Moving to Node #0,4 Current State: 39:[63, 24, 8], Operations: ['84-76=8'] Exploring Operation: 63-24=39, Resulting Numbers: [8, 39] Generated Node #0,4,0: 39:[8, 39] Operation: 63-24=39 Exploring Operation: 63-8=55, Resulting Numbers: [24, 55] Generated Node #0,4,1: 39:[24, 55] Operation: 63-8=55 Exploring Operation: 24-8=16, Resulting Numbers: [63, 16] Generated Node #0,4,2: 39:[63, 16] Operation: 24-8=16 Exploring Operation: 24/8=3, Resulting Numbers: [63, 3] Generated Node #0,4,3: 39:[63, 3] Operation: 24/8=3 Exploring Operation: 24+8=32, Resulting Numbers: [63, 32] Generated Node #0,4,4: 39:[63, 32] Operation: 24+8=32 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 39:[8, 39], Operations: ['84-76=8', '63-24=39'] Exploring Operation: 8*39=312, Resulting Numbers: [312] 312,39 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 8+39=47, Resulting Numbers: [47] 47,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 39:[63, 3], Operations: ['84-76=8', '24/8=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,39 unequal: No Solution Exploring Operation: 63*3=189, Resulting Numbers: [189] 189,39 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,39 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 39:[24, 55], Operations: ['84-76=8', '63-8=55'] Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,39 unequal: No Solution Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 39:[63, 16], Operations: ['84-76=8', '24-8=16'] Exploring Operation: 63-16=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 63+16=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 63*16=1008, Resulting Numbers: [1008] 1008,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 39:[63, 32], Operations: ['84-76=8', '24+8=32'] Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 63*32=2016, Resulting Numbers: [2016] 2016,39 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 39:[24, 76, 21], Operations: ['84-63=21'] Exploring Operation: 24+76=100, Resulting Numbers: [21, 100] Generated Node #0,2,0: 39:[21, 100] Operation: 24+76=100 Exploring Operation: 24+21=45, Resulting Numbers: [76, 45] Generated Node #0,2,1: 39:[76, 45] Operation: 24+21=45 Exploring Operation: 76-24=52, Resulting Numbers: [21, 52] Generated Node #0,2,2: 39:[21, 52] Operation: 76-24=52 Exploring Operation: 76-21=55, Resulting Numbers: [24, 55] Generated Node #0,2,3: 39:[24, 55] Operation: 76-21=55 Exploring Operation: 24-21=3, Resulting Numbers: [76, 3] Generated Node #0,2,4: 39:[76, 3] Operation: 24-21=3 Moving to Node #0,0 Current State: 39:[24, 84, 13], Operations: ['76-63=13'] Exploring Operation: 84-24=60, Resulting Numbers: [13, 60] Generated Node #0,0,0: 39:[13, 60] Operation: 84-24=60 Exploring Operation: 24+84=108, Resulting Numbers: [13, 108] Generated Node #0,0,1: 39:[13, 108] Operation: 24+84=108 Exploring Operation: 84-13=71, Resulting Numbers: [24, 71] Generated Node #0,0,2: 39:[24, 71] Operation: 84-13=71 Exploring Operation: 24-13=11, Resulting Numbers: [84, 11] Generated Node #0,0,3: 39:[84, 11] Operation: 24-13=11 Exploring Operation: 24+13=37, Resulting Numbers: [84, 37] Generated Node #0,0,4: 39:[84, 37] Operation: 24+13=37 Moving to Node #0,1 Current State: 39:[63, 84, 52], Operations: ['76-24=52'] Exploring Operation: 84-52=32, Resulting Numbers: [63, 32] Generated Node #0,1,0: 39:[63, 32] Operation: 84-52=32 Exploring Operation: 84-63=21, Resulting Numbers: [52, 21] Generated Node #0,1,1: 39:[52, 21] Operation: 84-63=21 Exploring Operation: 63+52=115, Resulting Numbers: [84, 115] Generated Node #0,1,2: 39:[84, 115] Operation: 63+52=115 Exploring Operation: 63-52=11, Resulting Numbers: [84, 11] Generated Node #0,1,3: 39:[84, 11] Operation: 63-52=11 Exploring Operation: 63+84=147, Resulting Numbers: [52, 147] Generated Node #0,1,4: 39:[52, 147] Operation: 63+84=147 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 39:[52, 21], Operations: ['76-24=52', '84-63=21'] Exploring Operation: 52+21=73, Resulting Numbers: [73] 73,39 unequal: No Solution Exploring Operation: 52*21=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 39:[63, 32], Operations: ['76-24=52', '84-52=32'] Exploring Operation: 63*32=2016, Resulting Numbers: [2016] 2016,39 unequal: No Solution Exploring Operation: 63+32=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 63-32=31, Resulting Numbers: [31] 31,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 39:[84, 11], Operations: ['76-24=52', '63-52=11'] Exploring Operation: 84-11=73, Resulting Numbers: [73] 73,39 unequal: No Solution Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 84*11=924, Resulting Numbers: [924] 924,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 39:[84, 115], Operations: ['76-24=52', '63+52=115'] Exploring Operation: 115-84=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 84*115=9660, Resulting Numbers: [9660] 9660,39 unequal: No Solution Exploring Operation: 84+115=199, Resulting Numbers: [199] 199,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 39:[52, 147], Operations: ['76-24=52', '63+84=147'] Exploring Operation: 147-52=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 52+147=199, Resulting Numbers: [199] 199,39 unequal: No Solution Exploring Operation: 52*147=7644, Resulting Numbers: [7644] 7644,39 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: 39:[76, 84, 39], Operations: ['63-24=39'] Exploring Operation: 84-39=45, Resulting Numbers: [76, 45] Generated Node #0,3,0: 39:[76, 45] Operation: 84-39=45 Exploring Operation: 76+84=160, Resulting Numbers: [39, 160] Generated Node #0,3,1: 39:[39, 160] Operation: 76+84=160 Exploring Operation: 76+39=115, Resulting Numbers: [84, 115] Generated Node #0,3,2: 39:[84, 115] Operation: 76+39=115 Exploring Operation: 76-39=37, Resulting Numbers: [84, 37] Generated Node #0,3,3: 39:[84, 37] Operation: 76-39=37 Exploring Operation: 84-76=8, Resulting Numbers: [39, 8] Generated Node #0,3,4: 39:[39, 8] Operation: 84-76=8 Moving to Node #0,3,4 Current State: 39:[39, 8], Operations: ['63-24=39', '84-76=8'] Exploring Operation: 39*8=312, Resulting Numbers: [312] 312,39 unequal: No Solution Exploring Operation: 39-8=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 39+8=47, Resulting Numbers: [47] 47,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[13, 60], Operations: ['76-63=13', '84-24=60'] Exploring Operation: 60-13=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 13*60=780, Resulting Numbers: [780] 780,39 unequal: No Solution Exploring Operation: 13+60=73, Resulting Numbers: [73] 73,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[21, 52], Operations: ['84-63=21', '76-24=52'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 21*52=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution Exploring Operation: 21+52=73, Resulting Numbers: [73] 73,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[24, 55], Operations: ['84-63=21', '76-21=55'] Exploring Operation: 24+55=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 55-24=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 24*55=1320, Resulting Numbers: [1320] 1320,39 unequal: No Solution Moving to Node #0,2,4 Current State: 39:[76, 3], Operations: ['84-63=21', '24-21=3'] Exploring Operation: 76*3=228, Resulting Numbers: [228] 228,39 unequal: No Solution Exploring Operation: 76+3=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 76-3=73, Resulting Numbers: [73] 73,39 unequal: No Solution Moving to Node #0,0,2 Current State: 39:[24, 71], Operations: ['76-63=13', '84-13=71'] Exploring Operation: 24*71=1704, Resulting Numbers: [1704] 1704,39 unequal: No Solution Exploring Operation: 24+71=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 71-24=47, Resulting Numbers: [47] 47,39 unequal: No Solution Moving to Node #0,3,0 Current State: 39:[76, 45], Operations: ['63-24=39', '84-39=45'] Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[76, 45], Operations: ['84-63=21', '24+21=45'] Exploring Operation: 76+45=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 76*45=3420, Resulting Numbers: [3420] 3420,39 unequal: No Solution Exploring Operation: 76-45=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,0,4 Current State: 39:[84, 37], Operations: ['76-63=13', '24+13=37'] Exploring Operation: 84+37=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 84*37=3108, Resulting Numbers: [3108] 3108,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[84, 11], Operations: ['76-63=13', '24-13=11'] Exploring Operation: 84*11=924, Resulting Numbers: [924] 924,39 unequal: No Solution Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,39 unequal: No Solution Exploring Operation: 84-11=73, Resulting Numbers: [73] 73,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[84, 37], Operations: ['63-24=39', '76-39=37'] Exploring Operation: 84*37=3108, Resulting Numbers: [3108] 3108,39 unequal: No Solution Exploring Operation: 84-37=47, Resulting Numbers: [47] 47,39 unequal: No Solution Exploring Operation: 84+37=121, Resulting Numbers: [121] 121,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[13, 108], Operations: ['76-63=13', '24+84=108'] Exploring Operation: 13*108=1404, Resulting Numbers: [1404] 1404,39 unequal: No Solution Exploring Operation: 13+108=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 108-13=95, Resulting Numbers: [95] 95,39 unequal: No Solution Moving to Node #0,2,0 Current State: 39:[21, 100], Operations: ['84-63=21', '24+76=100'] Exploring Operation: 21+100=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 100-21=79, Resulting Numbers: [79] 79,39 unequal: No Solution Exploring Operation: 21*100=2100, Resulting Numbers: [2100] 2100,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[84, 115], Operations: ['63-24=39', '76+39=115'] Exploring Operation: 84+115=199, Resulting Numbers: [199] 199,39 unequal: No Solution Exploring Operation: 84*115=9660, Resulting Numbers: [9660] 9660,39 unequal: No Solution Exploring Operation: 115-84=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[39, 160], Operations: ['63-24=39', '76+84=160'] Exploring Operation: 39+160=199, Resulting Numbers: [199] 199,39 unequal: No Solution Exploring Operation: 160-39=121, Resulting Numbers: [121] 121,39 unequal: No Solution Exploring Operation: 39*160=6240, Resulting Numbers: [6240] 6240,39 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 67, 31, 47, 6 ]
57
[ "67+31=98", "47-6=41", "98-41=57" ]
Current State: 57:[67, 31, 47, 6], Operations: [] Exploring Operation: 67+31=98, Resulting Numbers: [47, 6, 98] Generated Node #2: [47, 6, 98] from Operation: 67+31=98 Current State: 57:[47, 6, 98], Operations: ['67+31=98'] Exploring Operation: 47-6=41, Resulting Numbers: [98, 41] Generated Node #3: [98, 41] from Operation: 47-6=41 Current State: 57:[98, 41], Operations: ['67+31=98', '47-6=41'] Exploring Operation: 98-41=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[67, 31, 47, 6], Operations: [] Exploring Operation: 67-47=20, Resulting Numbers: [31, 6, 20] Generated Node #0,0: 57:[31, 6, 20] Operation: 67-47=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[31, 6, 20], Operations: ['67-47=20'] Exploring Operation: 31-6=25, Resulting Numbers: [20, 25] Generated Node #0,0,0: 57:[20, 25] Operation: 31-6=25 Moving to Node #0,0,0 Current State: 57:[20, 25], Operations: ['67-47=20', '31-6=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 50, 24, 4, 42 ]
29
[ "50+24=74", "42+74=116", "116/4=29" ]
Current State: 29:[50, 24, 4, 42], Operations: [] Exploring Operation: 50+24=74, Resulting Numbers: [4, 42, 74] Generated Node #2: [4, 42, 74] from Operation: 50+24=74 Current State: 29:[4, 42, 74], Operations: ['50+24=74'] Exploring Operation: 42+74=116, Resulting Numbers: [4, 116] Generated Node #3: [4, 116] from Operation: 42+74=116 Current State: 29:[4, 116], Operations: ['50+24=74', '42+74=116'] Exploring Operation: 116/4=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[50, 24, 4, 42], Operations: [] Exploring Operation: 50-4=46, Resulting Numbers: [24, 42, 46] Generated Node #0,0: 29:[24, 42, 46] Operation: 50-4=46 Exploring Operation: 24+4=28, Resulting Numbers: [50, 42, 28] Generated Node #0,1: 29:[50, 42, 28] Operation: 24+4=28 Moving to Node #0,0 Current State: 29:[24, 42, 46], Operations: ['50-4=46'] Exploring Operation: 42-24=18, Resulting Numbers: [46, 18] Generated Node #0,0,0: 29:[46, 18] Operation: 42-24=18 Exploring Operation: 46-24=22, Resulting Numbers: [42, 22] Generated Node #0,0,1: 29:[42, 22] Operation: 46-24=22 Moving to Node #0,1 Current State: 29:[50, 42, 28], Operations: ['24+4=28'] Exploring Operation: 50-28=22, Resulting Numbers: [42, 22] Generated Node #0,1,0: 29:[42, 22] Operation: 50-28=22 Exploring Operation: 50-42=8, Resulting Numbers: [28, 8] Generated Node #0,1,1: 29:[28, 8] Operation: 50-42=8 Moving to Node #0,0,1 Current State: 29:[42, 22], Operations: ['50-4=46', '46-24=22'] Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[42, 22], Operations: ['24+4=28', '50-28=22'] Exploring Operation: 42+22=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 42-22=20, Resulting Numbers: [20] 20,29 unequal: No Solution Moving to Node #0,1,1 Current State: 29:[28, 8], Operations: ['24+4=28', '50-42=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[46, 18], Operations: ['50-4=46', '42-24=18'] Exploring Operation: 46+18=64, Resulting Numbers: [64] 64,29 unequal: No Solution Exploring Operation: 46-18=28, Resulting Numbers: [28] 28,29 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 45, 34, 15, 53 ]
22
[ "45/15=3", "53-34=19", "3+19=22" ]
Current State: 22:[45, 34, 15, 53], Operations: [] Exploring Operation: 45/15=3, Resulting Numbers: [34, 53, 3] Generated Node #2: [34, 53, 3] from Operation: 45/15=3 Current State: 22:[34, 53, 3], Operations: ['45/15=3'] Exploring Operation: 53-34=19, Resulting Numbers: [3, 19] Generated Node #3: [3, 19] from Operation: 53-34=19 Current State: 22:[3, 19], Operations: ['45/15=3', '53-34=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[45, 34, 15, 53], Operations: [] Exploring Operation: 45-34=11, Resulting Numbers: [15, 53, 11] Generated Node #0,0: 22:[15, 53, 11] Operation: 45-34=11 Exploring Operation: 53-34=19, Resulting Numbers: [45, 15, 19] Generated Node #0,1: 22:[45, 15, 19] Operation: 53-34=19 Exploring Operation: 45/15=3, Resulting Numbers: [34, 53, 3] Generated Node #0,2: 22:[34, 53, 3] Operation: 45/15=3 Exploring Operation: 53-45=8, Resulting Numbers: [34, 15, 8] Generated Node #0,3: 22:[34, 15, 8] Operation: 53-45=8 Moving to Node #0,3 Current State: 22:[34, 15, 8], Operations: ['53-45=8'] Exploring Operation: 15+8=23, Resulting Numbers: [34, 23] Generated Node #0,3,0: 22:[34, 23] Operation: 15+8=23 Exploring Operation: 15-8=7, Resulting Numbers: [34, 7] Generated Node #0,3,1: 22:[34, 7] Operation: 15-8=7 Exploring Operation: 34-15=19, Resulting Numbers: [8, 19] Generated Node #0,3,2: 22:[8, 19] Operation: 34-15=19 Exploring Operation: 34-8=26, Resulting Numbers: [15, 26] Generated Node #0,3,3: 22:[15, 26] Operation: 34-8=26 Moving to Node #0,1 Current State: 22:[45, 15, 19], Operations: ['53-34=19'] Exploring Operation: 45-19=26, Resulting Numbers: [15, 26] Generated Node #0,1,0: 22:[15, 26] Operation: 45-19=26 Exploring Operation: 45-15=30, Resulting Numbers: [19, 30] Generated Node #0,1,1: 22:[19, 30] Operation: 45-15=30 Exploring Operation: 19-15=4, Resulting Numbers: [45, 4] Generated Node #0,1,2: 22:[45, 4] Operation: 19-15=4 Exploring Operation: 45/15=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 22:[19, 3] Operation: 45/15=3 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 22:[19, 3], Operations: ['53-34=19', '45/15=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[45, 34, 15, 53], Operations: [] Exploring Operation: 53-34=19, Resulting Numbers: [45, 15, 19] Generated Node #0,1: 22:[45, 15, 19] Operation: 53-34=19 Moving to Node #0,1 Current State: 22:[45, 15, 19], Operations: ['53-34=19'] Exploring Operation: 45/15=3, Resulting Numbers: [19, 3] Generated Node #0,1,3: 22:[19, 3] Operation: 45/15=3 Moving to Node #0,1,3 Current State: 22:[19, 3], Operations: ['53-34=19', '45/15=3'] Exploring Operation: 19+3=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
sum_heuristic
[ 91, 61, 8, 99 ]
80
[ "91+61=152", "152/8=19", "99-19=80" ]
Current State: 80:[91, 61, 8, 99], Operations: [] Exploring Operation: 91+61=152, Resulting Numbers: [8, 99, 152] Generated Node #2: [8, 99, 152] from Operation: 91+61=152 Current State: 80:[8, 99, 152], Operations: ['91+61=152'] Exploring Operation: 152/8=19, Resulting Numbers: [99, 19] Generated Node #3: [99, 19] from Operation: 152/8=19 Current State: 80:[99, 19], Operations: ['91+61=152', '152/8=19'] Exploring Operation: 99-19=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[91, 61, 8, 99], Operations: [] Exploring Operation: 99-61=38, Resulting Numbers: [91, 8, 38] Generated Node #0,0: 80:[91, 8, 38] Operation: 99-61=38 Exploring Operation: 99-91=8, Resulting Numbers: [61, 8, 8] Generated Node #0,1: 80:[61, 8, 8] Operation: 99-91=8 Moving to Node #0,0 Current State: 80:[91, 8, 38], Operations: ['99-61=38'] Exploring Operation: 91-8=83, Resulting Numbers: [38, 83] Generated Node #0,0,0: 80:[38, 83] Operation: 91-8=83 Exploring Operation: 91-38=53, Resulting Numbers: [8, 53] Generated Node #0,0,1: 80:[8, 53] Operation: 91-38=53 Moving to Node #0,1 Current State: 80:[61, 8, 8], Operations: ['99-91=8'] Exploring Operation: 61+8=69, Resulting Numbers: [8, 69] Generated Node #0,1,0: 80:[8, 69] Operation: 61+8=69 Exploring Operation: 61+8=69, Resulting Numbers: [8, 69] Generated Node #0,1,1: 80:[8, 69] Operation: 61+8=69 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[8, 69], Operations: ['99-91=8', '61+8=69'] Exploring Operation: 8+69=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,80 unequal: No Solution No 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: 80:[8, 69], Operations: ['99-91=8', '61+8=69'] Exploring Operation: 69-8=61, Resulting Numbers: [61] 61,80 unequal: No Solution Exploring Operation: 8+69=77, Resulting Numbers: [77] 77,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 80:[38, 83], Operations: ['99-61=38', '91-8=83'] Exploring Operation: 38+83=121, Resulting Numbers: [121] 121,80 unequal: No Solution Exploring Operation: 83-38=45, Resulting Numbers: [45] 45,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[8, 53], Operations: ['99-61=38', '91-38=53'] Exploring Operation: 53-8=45, Resulting Numbers: [45] 45,80 unequal: No Solution Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,80 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 6, 11, 25, 1 ]
92
[ "6*11=66", "25+1=26", "66+26=92" ]
Current State: 92:[6, 11, 25, 1], Operations: [] Exploring Operation: 6*11=66, Resulting Numbers: [25, 1, 66] Generated Node #2: [25, 1, 66] from Operation: 6*11=66 Current State: 92:[25, 1, 66], Operations: ['6*11=66'] Exploring Operation: 25+1=26, Resulting Numbers: [66, 26] Generated Node #3: [66, 26] from Operation: 25+1=26 Current State: 92:[66, 26], Operations: ['6*11=66', '25+1=26'] Exploring Operation: 66+26=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[6, 11, 25, 1], Operations: [] Exploring Operation: 11-6=5, Resulting Numbers: [25, 1, 5] Generated Node #0,0: 92:[25, 1, 5] Operation: 11-6=5 Exploring Operation: 6-1=5, Resulting Numbers: [11, 25, 5] Generated Node #0,1: 92:[11, 25, 5] Operation: 6-1=5 Exploring Operation: 11-1=10, Resulting Numbers: [6, 25, 10] Generated Node #0,2: 92:[6, 25, 10] Operation: 11-1=10 Exploring Operation: 6+11=17, Resulting Numbers: [25, 1, 17] Generated Node #0,3: 92:[25, 1, 17] Operation: 6+11=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[25, 1, 5], Operations: ['11-6=5'] Exploring Operation: 25/5=5, Resulting Numbers: [1, 5] Generated Node #0,0,0: 92:[1, 5] Operation: 25/5=5 Exploring Operation: 5-1=4, Resulting Numbers: [25, 4] Generated Node #0,0,1: 92:[25, 4] Operation: 5-1=4 Exploring Operation: 25*1=25, Resulting Numbers: [5, 25] Generated Node #0,0,2: 92:[5, 25] Operation: 25*1=25 Exploring Operation: 25-1=24, Resulting Numbers: [5, 24] Generated Node #0,0,3: 92:[5, 24] Operation: 25-1=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 92:[1, 5], Operations: ['11-6=5', '25/5=5'] Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,92 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,92 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,92 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:[25, 4], Operations: ['11-6=5', '5-1=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,92 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,92 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,92 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:[5, 24], Operations: ['11-6=5', '25-1=24'] Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 5*24=120, Resulting Numbers: [120] 120,92 unequal: No Solution Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,92 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:[5, 25], Operations: ['11-6=5', '25*1=25'] Exploring Operation: 5+25=30, Resulting Numbers: [30] 30,92 unequal: No Solution Exploring Operation: 5*25=125, Resulting Numbers: [125] 125,92 unequal: No Solution Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,92 unequal: No Solution Exploring Operation: 25/5=5, Resulting Numbers: [5] 5,92 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 #0,3 Current State: 92:[25, 1, 17], Operations: ['6+11=17'] Exploring Operation: 25+17=42, Resulting Numbers: [1, 42] Generated Node #0,3,0: 92:[1, 42] Operation: 25+17=42 Exploring Operation: 1+17=18, Resulting Numbers: [25, 18] Generated Node #0,3,1: 92:[25, 18] Operation: 1+17=18 Exploring Operation: 25-1=24, Resulting Numbers: [17, 24] Generated Node #0,3,2: 92:[17, 24] Operation: 25-1=24 Exploring Operation: 25-17=8, Resulting Numbers: [1, 8] Generated Node #0,3,3: 92:[1, 8] Operation: 25-17=8 Moving to Node #0,3,0 Current State: 92:[1, 42], Operations: ['6+11=17', '25+17=42'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 1*42=42, Resulting Numbers: [42] 42,92 unequal: No Solution Exploring Operation: 42-1=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 1+42=43, Resulting Numbers: [43] 43,92 unequal: No Solution Moving to Node #0,3,3 Current State: 92:[1, 8], Operations: ['6+11=17', '25-17=8'] Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,92 unequal: No Solution Moving to Node #0,3,2 Current State: 92:[17, 24], Operations: ['6+11=17', '25-1=24'] Exploring Operation: 24-17=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 17*24=408, Resulting Numbers: [408] 408,92 unequal: No Solution Exploring Operation: 17+24=41, Resulting Numbers: [41] 41,92 unequal: No Solution Moving to Node #0,3,1 Current State: 92:[25, 18], Operations: ['6+11=17', '1+17=18'] Exploring Operation: 25-18=7, Resulting Numbers: [7] 7,92 unequal: No Solution Exploring Operation: 25*18=450, Resulting Numbers: [450] 450,92 unequal: No Solution Exploring Operation: 25+18=43, Resulting Numbers: [43] 43,92 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:[11, 25, 5], Operations: ['6-1=5'] Exploring Operation: 25-11=14, Resulting Numbers: [5, 14] Generated Node #0,1,0: 92:[5, 14] Operation: 25-11=14 Exploring Operation: 11+5=16, Resulting Numbers: [25, 16] Generated Node #0,1,1: 92:[25, 16] Operation: 11+5=16 Exploring Operation: 11-5=6, Resulting Numbers: [25, 6] Generated Node #0,1,2: 92:[25, 6] Operation: 11-5=6 Exploring Operation: 25/5=5, Resulting Numbers: [11, 5] Generated Node #0,1,3: 92:[11, 5] Operation: 25/5=5 Moving to Node #0,1,2 Current State: 92:[25, 6], Operations: ['6-1=5', '11-5=6'] Exploring Operation: 25-6=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 25*6=150, Resulting Numbers: [150] 150,92 unequal: No Solution Exploring Operation: 25+6=31, Resulting Numbers: [31] 31,92 unequal: No Solution Moving to Node #0,1,3 Current State: 92:[11, 5], Operations: ['6-1=5', '25/5=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,92 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,92 unequal: No Solution Moving to Node #0,1,1 Current State: 92:[25, 16], Operations: ['6-1=5', '11+5=16'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,92 unequal: No Solution Moving to Node #0,1,0 Current State: 92:[5, 14], Operations: ['6-1=5', '25-11=14'] Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,92 unequal: No Solution Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,92 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,92 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 #0,2 Current State: 92:[6, 25, 10], Operations: ['11-1=10'] Exploring Operation: 10-6=4, Resulting Numbers: [25, 4] Generated Node #0,2,0: 92:[25, 4] Operation: 10-6=4 Exploring Operation: 25-10=15, Resulting Numbers: [6, 15] Generated Node #0,2,1: 92:[6, 15] Operation: 25-10=15 Exploring Operation: 6+10=16, Resulting Numbers: [25, 16] Generated Node #0,2,2: 92:[25, 16] Operation: 6+10=16 Exploring Operation: 25-6=19, Resulting Numbers: [10, 19] Generated Node #0,2,3: 92:[10, 19] Operation: 25-6=19 Moving to Node #0,2,0 Current State: 92:[25, 4], Operations: ['11-1=10', '10-6=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,92 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,92 unequal: No Solution Moving to Node #0,2,2 Current State: 92:[25, 16], Operations: ['11-1=10', '6+10=16'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,92 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,92 unequal: No Solution Moving to Node #0,2,3 Current State: 92:[10, 19], Operations: ['11-1=10', '25-6=19'] Exploring Operation: 10*19=190, Resulting Numbers: [190] 190,92 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,92 unequal: No Solution Exploring Operation: 10+19=29, Resulting Numbers: [29] 29,92 unequal: No Solution Moving to Node #0,2,1 Current State: 92:[6, 15], Operations: ['11-1=10', '25-10=15'] Exploring Operation: 6+15=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 6*15=90, Resulting Numbers: [90] 90,92 unequal: No Solution Exploring Operation: 15-6=9, Resulting Numbers: [9] 9,92 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
[ 35, 30, 1, 24 ]
29
[ "35-30=5", "1*24=24", "5+24=29" ]
Current State: 29:[35, 30, 1, 24], Operations: [] Exploring Operation: 35-30=5, Resulting Numbers: [1, 24, 5] Generated Node #2: [1, 24, 5] from Operation: 35-30=5 Current State: 29:[1, 24, 5], Operations: ['35-30=5'] Exploring Operation: 1*24=24, Resulting Numbers: [5, 24] Generated Node #3: [5, 24] from Operation: 1*24=24 Current State: 29:[5, 24], Operations: ['35-30=5', '1*24=24'] Exploring Operation: 5+24=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[35, 30, 1, 24], Operations: [] Exploring Operation: 35-1=34, Resulting Numbers: [30, 24, 34] Generated Node #0,0: 29:[30, 24, 34] Operation: 35-1=34 Exploring Operation: 30-1=29, Resulting Numbers: [35, 24, 29] Generated Node #0,1: 29:[35, 24, 29] Operation: 30-1=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[30, 24, 34], Operations: ['35-1=34'] Exploring Operation: 30-24=6, Resulting Numbers: [34, 6] Generated Node #0,0,0: 29:[34, 6] Operation: 30-24=6 Exploring Operation: 34-24=10, Resulting Numbers: [30, 10] Generated Node #0,0,1: 29:[30, 10] Operation: 34-24=10 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[30, 10], Operations: ['35-1=34', '34-24=10'] Exploring Operation: 30-10=20, Resulting Numbers: [20] 20,29 unequal: No Solution Exploring Operation: 30+10=40, Resulting Numbers: [40] 40,29 unequal: No Solution No 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: 29:[34, 6], Operations: ['35-1=34', '30-24=6'] Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[35, 24, 29], Operations: ['30-1=29'] Exploring Operation: 35-24=11, Resulting Numbers: [29, 11] Generated Node #0,1,0: 29:[29, 11] Operation: 35-24=11 Exploring Operation: 35-29=6, Resulting Numbers: [24, 6] Generated Node #0,1,1: 29:[24, 6] Operation: 35-29=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 29:[29, 11], Operations: ['30-1=29', '35-24=11'] Exploring Operation: 29+11=40, Resulting Numbers: [40] 40,29 unequal: No Solution Exploring Operation: 29-11=18, Resulting Numbers: [18] 18,29 unequal: No Solution No 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: 29:[24, 6], Operations: ['30-1=29', '35-29=6'] Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,29 unequal: No Solution Exploring Operation: 24+6=30, Resulting Numbers: [30] 30,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 57, 41, 4, 47 ]
15
[ "57+47=104", "104/4=26", "41-26=15" ]
Current State: 15:[57, 41, 4, 47], Operations: [] Exploring Operation: 57+47=104, Resulting Numbers: [41, 4, 104] Generated Node #2: [41, 4, 104] from Operation: 57+47=104 Current State: 15:[41, 4, 104], Operations: ['57+47=104'] Exploring Operation: 104/4=26, Resulting Numbers: [41, 26] Generated Node #3: [41, 26] from Operation: 104/4=26 Current State: 15:[41, 26], Operations: ['57+47=104', '104/4=26'] Exploring Operation: 41-26=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[57, 41, 4, 47], Operations: [] Exploring Operation: 47-41=6, Resulting Numbers: [57, 4, 6] Generated Node #0,0: 15:[57, 4, 6] Operation: 47-41=6 Exploring Operation: 57-47=10, Resulting Numbers: [41, 4, 10] Generated Node #0,1: 15:[41, 4, 10] Operation: 57-47=10 Exploring Operation: 57-41=16, Resulting Numbers: [4, 47, 16] Generated Node #0,2: 15:[4, 47, 16] Operation: 57-41=16 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[41, 4, 10], Operations: ['57-47=10'] Exploring Operation: 4+10=14, Resulting Numbers: [41, 14] Generated Node #0,1,0: 15:[41, 14] Operation: 4+10=14 Exploring Operation: 41-4=37, Resulting Numbers: [10, 37] Generated Node #0,1,1: 15:[10, 37] Operation: 41-4=37 Exploring Operation: 41-10=31, Resulting Numbers: [4, 31] Generated Node #0,1,2: 15:[4, 31] Operation: 41-10=31 Moving to Node #0,1,2 Current State: 15:[4, 31], Operations: ['57-47=10', '41-10=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,15 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,15 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,15 unequal: No Solution Moving to Node #0,1,0 Current State: 15:[41, 14], Operations: ['57-47=10', '4+10=14'] Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,15 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[10, 37], Operations: ['57-47=10', '41-4=37'] Exploring Operation: 10+37=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 10*37=370, Resulting Numbers: [370] 370,15 unequal: No Solution Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[4, 47, 16], Operations: ['57-41=16'] Exploring Operation: 47-4=43, Resulting Numbers: [16, 43] Generated Node #0,2,0: 15:[16, 43] Operation: 47-4=43 Exploring Operation: 47-16=31, Resulting Numbers: [4, 31] Generated Node #0,2,1: 15:[4, 31] Operation: 47-16=31 Exploring Operation: 16/4=4, Resulting Numbers: [47, 4] Generated Node #0,2,2: 15:[47, 4] Operation: 16/4=4 Moving to Node #0,2,1 Current State: 15:[4, 31], Operations: ['57-41=16', '47-16=31'] Exploring Operation: 4+31=35, Resulting Numbers: [35] 35,15 unequal: No Solution Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 4*31=124, Resulting Numbers: [124] 124,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[16, 43], Operations: ['57-41=16', '47-4=43'] Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,15 unequal: No Solution Exploring Operation: 16+43=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 16*43=688, Resulting Numbers: [688] 688,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[47, 4], Operations: ['57-41=16', '16/4=4'] Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,15 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[57, 4, 6], Operations: ['47-41=6'] Exploring Operation: 57-4=53, Resulting Numbers: [6, 53] Generated Node #0,0,0: 15:[6, 53] Operation: 57-4=53 Exploring Operation: 6-4=2, Resulting Numbers: [57, 2] Generated Node #0,0,1: 15:[57, 2] Operation: 6-4=2 Exploring Operation: 57-6=51, Resulting Numbers: [4, 51] Generated Node #0,0,2: 15:[4, 51] Operation: 57-6=51 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 15:[4, 51], Operations: ['47-41=6', '57-6=51'] Exploring Operation: 4+51=55, Resulting Numbers: [55] 55,15 unequal: No Solution Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 4*51=204, Resulting Numbers: [204] 204,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[6, 53], Operations: ['47-41=6', '57-4=53'] Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 6+53=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 6*53=318, Resulting Numbers: [318] 318,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[57, 2], Operations: ['47-41=6', '6-4=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,15 unequal: No Solution Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,15 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 36, 84, 24, 58 ]
65
[ "36-24=12", "84/12=7", "58+7=65" ]
Current State: 65:[36, 84, 24, 58], Operations: [] Exploring Operation: 36-24=12, Resulting Numbers: [84, 58, 12] Generated Node #2: [84, 58, 12] from Operation: 36-24=12 Current State: 65:[84, 58, 12], Operations: ['36-24=12'] Exploring Operation: 84/12=7, Resulting Numbers: [58, 7] Generated Node #3: [58, 7] from Operation: 84/12=7 Current State: 65:[58, 7], Operations: ['36-24=12', '84/12=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[36, 84, 24, 58], Operations: [] Exploring Operation: 36+24=60, Resulting Numbers: [84, 58, 60] Generated Node #0,0: 65:[84, 58, 60] Operation: 36+24=60 Exploring Operation: 84-24=60, Resulting Numbers: [36, 58, 60] Generated Node #0,1: 65:[36, 58, 60] Operation: 84-24=60 Exploring Operation: 36-24=12, Resulting Numbers: [84, 58, 12] Generated Node #0,2: 65:[84, 58, 12] Operation: 36-24=12 Exploring Operation: 84-36=48, Resulting Numbers: [24, 58, 48] Generated Node #0,3: 65:[24, 58, 48] Operation: 84-36=48 Exploring Operation: 58-36=22, Resulting Numbers: [84, 24, 22] Generated Node #0,4: 65:[84, 24, 22] Operation: 58-36=22 Moving to Node #0,2 Current State: 65:[84, 58, 12], Operations: ['36-24=12'] Exploring Operation: 58+12=70, Resulting Numbers: [84, 70] Generated Node #0,2,0: 65:[84, 70] Operation: 58+12=70 Exploring Operation: 84/12=7, Resulting Numbers: [58, 7] Generated Node #0,2,1: 65:[58, 7] Operation: 84/12=7 Exploring Operation: 84-58=26, Resulting Numbers: [12, 26] Generated Node #0,2,2: 65:[12, 26] Operation: 84-58=26 Exploring Operation: 84-12=72, Resulting Numbers: [58, 72] Generated Node #0,2,3: 65:[58, 72] Operation: 84-12=72 Exploring Operation: 84+12=96, Resulting Numbers: [58, 96] Generated Node #0,2,4: 65:[58, 96] Operation: 84+12=96 Moving to Node #0,0 Current State: 65:[84, 58, 60], Operations: ['36+24=60'] Exploring Operation: 60-58=2, Resulting Numbers: [84, 2] Generated Node #0,0,0: 65:[84, 2] Operation: 60-58=2 Exploring Operation: 84-58=26, Resulting Numbers: [60, 26] Generated Node #0,0,1: 65:[60, 26] Operation: 84-58=26 Exploring Operation: 58+60=118, Resulting Numbers: [84, 118] Generated Node #0,0,2: 65:[84, 118] Operation: 58+60=118 Exploring Operation: 84+58=142, Resulting Numbers: [60, 142] Generated Node #0,0,3: 65:[60, 142] Operation: 84+58=142 Exploring Operation: 84-60=24, Resulting Numbers: [58, 24] Generated Node #0,0,4: 65:[58, 24] Operation: 84-60=24 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 65:[60, 26], Operations: ['36+24=60', '84-58=26'] Exploring Operation: 60*26=1560, Resulting Numbers: [1560] 1560,65 unequal: No Solution Exploring Operation: 60+26=86, Resulting Numbers: [86] 86,65 unequal: No Solution Exploring Operation: 60-26=34, Resulting Numbers: [34] 34,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 65:[58, 24], Operations: ['36+24=60', '84-60=24'] Exploring Operation: 58*24=1392, Resulting Numbers: [1392] 1392,65 unequal: No Solution Exploring Operation: 58+24=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 65:[84, 2], Operations: ['36+24=60', '60-58=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,65 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,65 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 65:[84, 118], Operations: ['36+24=60', '58+60=118'] Exploring Operation: 84*118=9912, Resulting Numbers: [9912] 9912,65 unequal: No Solution Exploring Operation: 118-84=34, Resulting Numbers: [34] 34,65 unequal: No Solution Exploring Operation: 84+118=202, Resulting Numbers: [202] 202,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 65:[60, 142], Operations: ['36+24=60', '84+58=142'] Exploring Operation: 60+142=202, Resulting Numbers: [202] 202,65 unequal: No Solution Exploring Operation: 60*142=8520, Resulting Numbers: [8520] 8520,65 unequal: No Solution Exploring Operation: 142-60=82, Resulting Numbers: [82] 82,65 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: 65:[36, 58, 60], Operations: ['84-24=60'] Exploring Operation: 58-36=22, Resulting Numbers: [60, 22] Generated Node #0,1,0: 65:[60, 22] Operation: 58-36=22 Exploring Operation: 60-36=24, Resulting Numbers: [58, 24] Generated Node #0,1,1: 65:[58, 24] Operation: 60-36=24 Exploring Operation: 60-58=2, Resulting Numbers: [36, 2] Generated Node #0,1,2: 65:[36, 2] Operation: 60-58=2 Exploring Operation: 36+60=96, Resulting Numbers: [58, 96] Generated Node #0,1,3: 65:[58, 96] Operation: 36+60=96 Exploring Operation: 36+58=94, Resulting Numbers: [60, 94] Generated Node #0,1,4: 65:[60, 94] Operation: 36+58=94 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[60, 22], Operations: ['84-24=60', '58-36=22'] Exploring Operation: 60*22=1320, Resulting Numbers: [1320] 1320,65 unequal: No Solution Exploring Operation: 60+22=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[58, 24], Operations: ['84-24=60', '60-36=24'] Exploring Operation: 58*24=1392, Resulting Numbers: [1392] 1392,65 unequal: No Solution Exploring Operation: 58+24=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 58-24=34, Resulting Numbers: [34] 34,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[36, 2], Operations: ['84-24=60', '60-58=2'] Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,65 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,65 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 65:[60, 94], Operations: ['84-24=60', '36+58=94'] Exploring Operation: 60+94=154, Resulting Numbers: [154] 154,65 unequal: No Solution Exploring Operation: 60*94=5640, Resulting Numbers: [5640] 5640,65 unequal: No Solution Exploring Operation: 94-60=34, Resulting Numbers: [34] 34,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[58, 96], Operations: ['84-24=60', '36+60=96'] Exploring Operation: 96-58=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 58*96=5568, Resulting Numbers: [5568] 5568,65 unequal: No Solution Exploring Operation: 58+96=154, Resulting Numbers: [154] 154,65 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: 65:[24, 58, 48], Operations: ['84-36=48'] Exploring Operation: 24+58=82, Resulting Numbers: [48, 82] Generated Node #0,3,0: 65:[48, 82] Operation: 24+58=82 Exploring Operation: 24+48=72, Resulting Numbers: [58, 72] Generated Node #0,3,1: 65:[58, 72] Operation: 24+48=72 Exploring Operation: 48-24=24, Resulting Numbers: [58, 24] Generated Node #0,3,2: 65:[58, 24] Operation: 48-24=24 Exploring Operation: 48/24=2, Resulting Numbers: [58, 2] Generated Node #0,3,3: 65:[58, 2] Operation: 48/24=2 Exploring Operation: 58-48=10, Resulting Numbers: [24, 10] Generated Node #0,3,4: 65:[24, 10] Operation: 58-48=10 Moving to Node #0,4 Current State: 65:[84, 24, 22], Operations: ['58-36=22'] Exploring Operation: 24-22=2, Resulting Numbers: [84, 2] Generated Node #0,4,0: 65:[84, 2] Operation: 24-22=2 Exploring Operation: 24+22=46, Resulting Numbers: [84, 46] Generated Node #0,4,1: 65:[84, 46] Operation: 24+22=46 Exploring Operation: 84+24=108, Resulting Numbers: [22, 108] Generated Node #0,4,2: 65:[22, 108] Operation: 84+24=108 Exploring Operation: 84-22=62, Resulting Numbers: [24, 62] Generated Node #0,4,3: 65:[24, 62] Operation: 84-22=62 Exploring Operation: 84-24=60, Resulting Numbers: [22, 60] Generated Node #0,4,4: 65:[22, 60] Operation: 84-24=60 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 65:[24, 62], Operations: ['58-36=22', '84-22=62'] Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,65 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 65:[22, 60], Operations: ['58-36=22', '84-24=60'] Exploring Operation: 22+60=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 22*60=1320, Resulting Numbers: [1320] 1320,65 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 65:[84, 2], Operations: ['58-36=22', '24-22=2'] Exploring Operation: 84-2=82, Resulting Numbers: [82] 82,65 unequal: No Solution Exploring Operation: 84*2=168, Resulting Numbers: [168] 168,65 unequal: No Solution Exploring Operation: 84/2=42, Resulting Numbers: [42] 42,65 unequal: No Solution Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 65:[84, 46], Operations: ['58-36=22', '24+22=46'] Exploring Operation: 84-46=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 84+46=130, Resulting Numbers: [130] 130,65 unequal: No Solution Exploring Operation: 84*46=3864, Resulting Numbers: [3864] 3864,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 65:[22, 108], Operations: ['58-36=22', '84+24=108'] Exploring Operation: 22+108=130, Resulting Numbers: [130] 130,65 unequal: No Solution Exploring Operation: 108-22=86, Resulting Numbers: [86] 86,65 unequal: No Solution Exploring Operation: 22*108=2376, Resulting Numbers: [2376] 2376,65 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: 65:[58, 7], Operations: ['36-24=12', '84/12=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[36, 84, 24, 58], Operations: [] Exploring Operation: 36-24=12, Resulting Numbers: [84, 58, 12] Generated Node #0,2: 65:[84, 58, 12] Operation: 36-24=12 Moving to Node #0,2 Current State: 65:[84, 58, 12], Operations: ['36-24=12'] Exploring Operation: 84/12=7, Resulting Numbers: [58, 7] Generated Node #0,2,1: 65:[58, 7] Operation: 84/12=7 Moving to Node #0,2,1 Current State: 65:[58, 7], Operations: ['36-24=12', '84/12=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
0.927951
hs_5
mult_heuristic
[ 20, 59, 95, 97 ]
78
[ "59-20=39", "97-95=2", "39*2=78" ]
Current State: 78:[20, 59, 95, 97], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [95, 97, 39] Generated Node #2: [95, 97, 39] from Operation: 59-20=39 Current State: 78:[95, 97, 39], Operations: ['59-20=39'] Exploring Operation: 97-95=2, Resulting Numbers: [39, 2] Generated Node #3: [39, 2] from Operation: 97-95=2 Current State: 78:[39, 2], Operations: ['59-20=39', '97-95=2'] Exploring Operation: 39*2=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[20, 59, 95, 97], Operations: [] Exploring Operation: 59-20=39, Resulting Numbers: [95, 97, 39] Generated Node #0,0: 78:[95, 97, 39] Operation: 59-20=39 Exploring Operation: 95-59=36, Resulting Numbers: [20, 97, 36] Generated Node #0,1: 78:[20, 97, 36] Operation: 95-59=36 Exploring Operation: 97-59=38, Resulting Numbers: [20, 95, 38] Generated Node #0,2: 78:[20, 95, 38] Operation: 97-59=38 Exploring Operation: 97-95=2, Resulting Numbers: [20, 59, 2] Generated Node #0,3: 78:[20, 59, 2] Operation: 97-95=2 Moving to Node #0,2 Current State: 78:[20, 95, 38], Operations: ['97-59=38'] Exploring Operation: 95-38=57, Resulting Numbers: [20, 57] Generated Node #0,2,0: 78:[20, 57] Operation: 95-38=57 Exploring Operation: 38-20=18, Resulting Numbers: [95, 18] Generated Node #0,2,1: 78:[95, 18] Operation: 38-20=18 Exploring Operation: 20+38=58, Resulting Numbers: [95, 58] Generated Node #0,2,2: 78:[95, 58] Operation: 20+38=58 Exploring Operation: 95-20=75, Resulting Numbers: [38, 75] Generated Node #0,2,3: 78:[38, 75] Operation: 95-20=75 Moving to Node #0,3 Current State: 78:[20, 59, 2], Operations: ['97-95=2'] Exploring Operation: 20+59=79, Resulting Numbers: [2, 79] Generated Node #0,3,0: 78:[2, 79] Operation: 20+59=79 Exploring Operation: 59-20=39, Resulting Numbers: [2, 39] Generated Node #0,3,1: 78:[2, 39] Operation: 59-20=39 Exploring Operation: 20/2=10, Resulting Numbers: [59, 10] Generated Node #0,3,2: 78:[59, 10] Operation: 20/2=10 Exploring Operation: 20*2=40, Resulting Numbers: [59, 40] Generated Node #0,3,3: 78:[59, 40] Operation: 20*2=40 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 78:[2, 39], Operations: ['97-95=2', '59-20=39'] Exploring Operation: 2+39=41, Resulting Numbers: [41] 41,78 unequal: No Solution Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,78 unequal: No Solution Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[20, 59, 95, 97], Operations: [] Exploring Operation: 97-95=2, Resulting Numbers: [20, 59, 2] Generated Node #0,3: 78:[20, 59, 2] Operation: 97-95=2 Moving to Node #0,3 Current State: 78:[20, 59, 2], Operations: ['97-95=2'] Exploring Operation: 59-20=39, Resulting Numbers: [2, 39] Generated Node #0,3,1: 78:[2, 39] Operation: 59-20=39 Moving to Node #0,3,1 Current State: 78:[2, 39], Operations: ['97-95=2', '59-20=39'] Exploring Operation: 2*39=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 65, 29, 32, 52 ]
48
[ "65-29=36", "32+52=84", "84-36=48" ]
Current State: 48:[65, 29, 32, 52], Operations: [] Exploring Operation: 65-29=36, Resulting Numbers: [32, 52, 36] Generated Node #2: [32, 52, 36] from Operation: 65-29=36 Current State: 48:[32, 52, 36], Operations: ['65-29=36'] Exploring Operation: 32+52=84, Resulting Numbers: [36, 84] Generated Node #3: [36, 84] from Operation: 32+52=84 Current State: 48:[36, 84], Operations: ['65-29=36', '32+52=84'] Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[65, 29, 32, 52], Operations: [] Exploring Operation: 65-52=13, Resulting Numbers: [29, 32, 13] Generated Node #0,0: 48:[29, 32, 13] Operation: 65-52=13 Exploring Operation: 32-29=3, Resulting Numbers: [65, 52, 3] Generated Node #0,1: 48:[65, 52, 3] Operation: 32-29=3 Exploring Operation: 65-32=33, Resulting Numbers: [29, 52, 33] Generated Node #0,2: 48:[29, 52, 33] Operation: 65-32=33 Moving to Node #0,0 Current State: 48:[29, 32, 13], Operations: ['65-52=13'] Exploring Operation: 32-29=3, Resulting Numbers: [13, 3] Generated Node #0,0,0: 48:[13, 3] Operation: 32-29=3 Exploring Operation: 32+13=45, Resulting Numbers: [29, 45] Generated Node #0,0,1: 48:[29, 45] Operation: 32+13=45 Exploring Operation: 29-13=16, Resulting Numbers: [32, 16] Generated Node #0,0,2: 48:[32, 16] Operation: 29-13=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 48:[13, 3], Operations: ['65-52=13', '32-29=3'] Exploring Operation: 13-3=10, Resulting Numbers: [10] 10,48 unequal: No Solution Exploring Operation: 13+3=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 13*3=39, Resulting Numbers: [39] 39,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 48:[29, 45], Operations: ['65-52=13', '32+13=45'] Exploring Operation: 29*45=1305, Resulting Numbers: [1305] 1305,48 unequal: No Solution Exploring Operation: 45-29=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 29+45=74, Resulting Numbers: [74] 74,48 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 48:[32, 16], Operations: ['65-52=13', '29-13=16'] Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,48 unequal: No Solution Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[65, 29, 32, 52], Operations: [] Exploring Operation: 65-52=13, Resulting Numbers: [29, 32, 13] Generated Node #0,0: 48:[29, 32, 13] Operation: 65-52=13 Moving to Node #0,0 Current State: 48:[29, 32, 13], Operations: ['65-52=13'] Exploring Operation: 29-13=16, Resulting Numbers: [32, 16] Generated Node #0,0,2: 48:[32, 16] Operation: 29-13=16 Moving to Node #0,0,2 Current State: 48:[32, 16], Operations: ['65-52=13', '29-13=16'] Exploring Operation: 32+16=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 66, 10, 92, 30 ]
46
[ "66+10=76", "92+30=122", "122-76=46" ]
Current State: 46:[66, 10, 92, 30], Operations: [] Exploring Operation: 66+10=76, Resulting Numbers: [92, 30, 76] Generated Node #2: [92, 30, 76] from Operation: 66+10=76 Current State: 46:[92, 30, 76], Operations: ['66+10=76'] Exploring Operation: 92+30=122, Resulting Numbers: [76, 122] Generated Node #3: [76, 122] from Operation: 92+30=122 Current State: 46:[76, 122], Operations: ['66+10=76', '92+30=122'] Exploring Operation: 122-76=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[66, 10, 92, 30], Operations: [] Exploring Operation: 66-10=56, Resulting Numbers: [92, 30, 56] Generated Node #0,0: 46:[92, 30, 56] Operation: 66-10=56 Exploring Operation: 92-30=62, Resulting Numbers: [66, 10, 62] Generated Node #0,1: 46:[66, 10, 62] Operation: 92-30=62 Exploring Operation: 92-66=26, Resulting Numbers: [10, 30, 26] Generated Node #0,2: 46:[10, 30, 26] Operation: 92-66=26 Exploring Operation: 92-10=82, Resulting Numbers: [66, 30, 82] Generated Node #0,3: 46:[66, 30, 82] Operation: 92-10=82 Exploring Operation: 66-30=36, Resulting Numbers: [10, 92, 36] Generated Node #0,4: 46:[10, 92, 36] Operation: 66-30=36 Moving to Node #0,2 Current State: 46:[10, 30, 26], Operations: ['92-66=26'] Exploring Operation: 30-10=20, Resulting Numbers: [26, 20] Generated Node #0,2,0: 46:[26, 20] Operation: 30-10=20 Exploring Operation: 10+30=40, Resulting Numbers: [26, 40] Generated Node #0,2,1: 46:[26, 40] Operation: 10+30=40 Exploring Operation: 30-26=4, Resulting Numbers: [10, 4] Generated Node #0,2,2: 46:[10, 4] Operation: 30-26=4 Exploring Operation: 30/10=3, Resulting Numbers: [26, 3] Generated Node #0,2,3: 46:[26, 3] Operation: 30/10=3 Exploring Operation: 26-10=16, Resulting Numbers: [30, 16] Generated Node #0,2,4: 46:[30, 16] Operation: 26-10=16 Moving to Node #0,1 Current State: 46:[66, 10, 62], Operations: ['92-30=62'] Exploring Operation: 10+62=72, Resulting Numbers: [66, 72] Generated Node #0,1,0: 46:[66, 72] Operation: 10+62=72 Exploring Operation: 66+10=76, Resulting Numbers: [62, 76] Generated Node #0,1,1: 46:[62, 76] Operation: 66+10=76 Exploring Operation: 66-10=56, Resulting Numbers: [62, 56] Generated Node #0,1,2: 46:[62, 56] Operation: 66-10=56 Exploring Operation: 66-62=4, Resulting Numbers: [10, 4] Generated Node #0,1,3: 46:[10, 4] Operation: 66-62=4 Exploring Operation: 62-10=52, Resulting Numbers: [66, 52] Generated Node #0,1,4: 46:[66, 52] Operation: 62-10=52 Moving to Node #0,0 Current State: 46:[92, 30, 56], Operations: ['66-10=56'] Exploring Operation: 92+30=122, Resulting Numbers: [56, 122] Generated Node #0,0,0: 46:[56, 122] Operation: 92+30=122 Exploring Operation: 92-30=62, Resulting Numbers: [56, 62] Generated Node #0,0,1: 46:[56, 62] Operation: 92-30=62 Exploring Operation: 56-30=26, Resulting Numbers: [92, 26] Generated Node #0,0,2: 46:[92, 26] Operation: 56-30=26 Exploring Operation: 92-56=36, Resulting Numbers: [30, 36] Generated Node #0,0,3: 46:[30, 36] Operation: 92-56=36 Exploring Operation: 30+56=86, Resulting Numbers: [92, 86] Generated Node #0,0,4: 46:[92, 86] Operation: 30+56=86 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 46:[30, 36], Operations: ['66-10=56', '92-56=36'] Exploring Operation: 30*36=1080, Resulting Numbers: [1080] 1080,46 unequal: No Solution Exploring Operation: 36-30=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 30+36=66, Resulting Numbers: [66] 66,46 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 #0,0,1 Current State: 46:[56, 62], Operations: ['66-10=56', '92-30=62'] Exploring Operation: 56+62=118, Resulting Numbers: [118] 118,46 unequal: No Solution Exploring Operation: 56*62=3472, Resulting Numbers: [3472] 3472,46 unequal: No Solution Exploring Operation: 62-56=6, Resulting Numbers: [6] 6,46 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 #0,0,2 Current State: 46:[92, 26], Operations: ['66-10=56', '56-30=26'] Exploring Operation: 92*26=2392, Resulting Numbers: [2392] 2392,46 unequal: No Solution Exploring Operation: 92+26=118, Resulting Numbers: [118] 118,46 unequal: No Solution Exploring Operation: 92-26=66, Resulting Numbers: [66] 66,46 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 #0,0,0 Current State: 46:[56, 122], Operations: ['66-10=56', '92+30=122'] Exploring Operation: 56*122=6832, Resulting Numbers: [6832] 6832,46 unequal: No Solution Exploring Operation: 122-56=66, Resulting Numbers: [66] 66,46 unequal: No Solution Exploring Operation: 56+122=178, Resulting Numbers: [178] 178,46 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 #0,0,4 Current State: 46:[92, 86], Operations: ['66-10=56', '30+56=86'] Exploring Operation: 92*86=7912, Resulting Numbers: [7912] 7912,46 unequal: No Solution Exploring Operation: 92+86=178, Resulting Numbers: [178] 178,46 unequal: No Solution Exploring Operation: 92-86=6, Resulting Numbers: [6] 6,46 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: 46:[66, 30, 82], Operations: ['92-10=82'] Exploring Operation: 30+82=112, Resulting Numbers: [66, 112] Generated Node #0,3,0: 46:[66, 112] Operation: 30+82=112 Exploring Operation: 66-30=36, Resulting Numbers: [82, 36] Generated Node #0,3,1: 46:[82, 36] Operation: 66-30=36 Exploring Operation: 82-30=52, Resulting Numbers: [66, 52] Generated Node #0,3,2: 46:[66, 52] Operation: 82-30=52 Exploring Operation: 66+30=96, Resulting Numbers: [82, 96] Generated Node #0,3,3: 46:[82, 96] Operation: 66+30=96 Exploring Operation: 82-66=16, Resulting Numbers: [30, 16] Generated Node #0,3,4: 46:[30, 16] Operation: 82-66=16 Moving to Node #0,4 Current State: 46:[10, 92, 36], Operations: ['66-30=36'] Exploring Operation: 92-10=82, Resulting Numbers: [36, 82] Generated Node #0,4,0: 46:[36, 82] Operation: 92-10=82 Exploring Operation: 10+92=102, Resulting Numbers: [36, 102] Generated Node #0,4,1: 46:[36, 102] Operation: 10+92=102 Exploring Operation: 10+36=46, Resulting Numbers: [92, 46] Generated Node #0,4,2: 46:[92, 46] Operation: 10+36=46 Exploring Operation: 92-36=56, Resulting Numbers: [10, 56] Generated Node #0,4,3: 46:[10, 56] Operation: 92-36=56 Exploring Operation: 36-10=26, Resulting Numbers: [92, 26] Generated Node #0,4,4: 46:[92, 26] Operation: 36-10=26 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 46:[10, 56], Operations: ['66-30=36', '92-36=56'] Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[66, 10, 92, 30], Operations: [] Exploring Operation: 66-30=36, Resulting Numbers: [10, 92, 36] Generated Node #0,4: 46:[10, 92, 36] Operation: 66-30=36 Moving to Node #0,4 Current State: 46:[10, 92, 36], Operations: ['66-30=36'] Exploring Operation: 92-36=56, Resulting Numbers: [10, 56] Generated Node #0,4,3: 46:[10, 56] Operation: 92-36=56 Moving to Node #0,4,3 Current State: 46:[10, 56], Operations: ['66-30=36', '92-36=56'] Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.956597
hs_5
sum_heuristic
[ 6, 27, 18, 54 ]
96
[ "54/27=2", "18-2=16", "6*16=96" ]
Current State: 96:[6, 27, 18, 54], Operations: [] Exploring Operation: 54/27=2, Resulting Numbers: [6, 18, 2] Generated Node #2: [6, 18, 2] from Operation: 54/27=2 Current State: 96:[6, 18, 2], Operations: ['54/27=2'] Exploring Operation: 18-2=16, Resulting Numbers: [6, 16] Generated Node #3: [6, 16] from Operation: 18-2=16 Current State: 96:[6, 16], Operations: ['54/27=2', '18-2=16'] Exploring Operation: 6*16=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[6, 27, 18, 54], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [6, 27, 3] Generated Node #0,0: 96:[6, 27, 3] Operation: 54/18=3 Exploring Operation: 54/27=2, Resulting Numbers: [6, 18, 2] Generated Node #0,1: 96:[6, 18, 2] Operation: 54/27=2 Exploring Operation: 54-6=48, Resulting Numbers: [27, 18, 48] Generated Node #0,2: 96:[27, 18, 48] Operation: 54-6=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[6, 18, 2], Operations: ['54/27=2'] Exploring Operation: 6+18=24, Resulting Numbers: [2, 24] Generated Node #0,1,0: 96:[2, 24] Operation: 6+18=24 Exploring Operation: 18-6=12, Resulting Numbers: [2, 12] Generated Node #0,1,1: 96:[2, 12] Operation: 18-6=12 Exploring Operation: 18/6=3, Resulting Numbers: [2, 3] Generated Node #0,1,2: 96:[2, 3] Operation: 18/6=3 Moving to Node #0,1,0 Current State: 96:[2, 24], Operations: ['54/27=2', '6+18=24'] Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,96 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,96 unequal: No Solution Moving to Node #0,1,1 Current State: 96:[2, 12], Operations: ['54/27=2', '18-6=12'] Exploring Operation: 2*12=24, Resulting Numbers: [24] 24,96 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,96 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[2, 3], Operations: ['54/27=2', '18/6=3'] Exploring Operation: 2+3=5, Resulting Numbers: [5] 5,96 unequal: No Solution Exploring Operation: 2*3=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[6, 27, 3], Operations: ['54/18=3'] Exploring Operation: 27-3=24, Resulting Numbers: [6, 24] Generated Node #0,0,0: 96:[6, 24] Operation: 27-3=24 Exploring Operation: 6+27=33, Resulting Numbers: [3, 33] Generated Node #0,0,1: 96:[3, 33] Operation: 6+27=33 Exploring Operation: 27/3=9, Resulting Numbers: [6, 9] Generated Node #0,0,2: 96:[6, 9] Operation: 27/3=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[6, 24], Operations: ['54/18=3', '27-3=24'] Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,96 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,96 unequal: No Solution No 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: 96:[3, 33], Operations: ['54/18=3', '6+27=33'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,96 unequal: No Solution Exploring Operation: 3*33=99, Resulting Numbers: [99] 99,96 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,96 unequal: No Solution No 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: 96:[6, 9], Operations: ['54/18=3', '27/3=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,96 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,96 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[27, 18, 48], Operations: ['54-6=48'] Exploring Operation: 27-18=9, Resulting Numbers: [48, 9] Generated Node #0,2,0: 96:[48, 9] Operation: 27-18=9 Exploring Operation: 48-27=21, Resulting Numbers: [18, 21] Generated Node #0,2,1: 96:[18, 21] Operation: 48-27=21 Exploring Operation: 27+18=45, Resulting Numbers: [48, 45] Generated Node #0,2,2: 96:[48, 45] Operation: 27+18=45 Moving to Node #0,2,0 Current State: 96:[48, 9], Operations: ['54-6=48', '27-18=9'] Exploring Operation: 48+9=57, Resulting Numbers: [57] 57,96 unequal: No Solution Exploring Operation: 48*9=432, Resulting Numbers: [432] 432,96 unequal: No Solution Exploring Operation: 48-9=39, Resulting Numbers: [39] 39,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[48, 45], Operations: ['54-6=48', '27+18=45'] Exploring Operation: 48+45=93, Resulting Numbers: [93] 93,96 unequal: No Solution Exploring Operation: 48*45=2160, Resulting Numbers: [2160] 2160,96 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[18, 21], Operations: ['54-6=48', '48-27=21'] Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,96 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,96 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 47, 93, 84, 70 ]
86
[ "47+93=140", "140/70=2", "84+2=86" ]
Current State: 86:[47, 93, 84, 70], Operations: [] Exploring Operation: 47+93=140, Resulting Numbers: [84, 70, 140] Generated Node #2: [84, 70, 140] from Operation: 47+93=140 Current State: 86:[84, 70, 140], Operations: ['47+93=140'] Exploring Operation: 140/70=2, Resulting Numbers: [84, 2] Generated Node #3: [84, 2] from Operation: 140/70=2 Current State: 86:[84, 2], Operations: ['47+93=140', '140/70=2'] Exploring Operation: 84+2=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[47, 93, 84, 70], Operations: [] Exploring Operation: 93-47=46, Resulting Numbers: [84, 70, 46] Generated Node #0,0: 86:[84, 70, 46] Operation: 93-47=46 Moving to Node #0,0 Current State: 86:[84, 70, 46], Operations: ['93-47=46'] Exploring Operation: 84-70=14, Resulting Numbers: [46, 14] Generated Node #0,0,0: 86:[46, 14] Operation: 84-70=14 Moving to Node #0,0,0 Current State: 86:[46, 14], Operations: ['93-47=46', '84-70=14'] Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,86 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 9, 26, 5, 35 ]
16
[ "9*5=45", "26+35=61", "61-45=16" ]
Current State: 16:[9, 26, 5, 35], Operations: [] Exploring Operation: 9*5=45, Resulting Numbers: [26, 35, 45] Generated Node #2: [26, 35, 45] from Operation: 9*5=45 Current State: 16:[26, 35, 45], Operations: ['9*5=45'] Exploring Operation: 26+35=61, Resulting Numbers: [45, 61] Generated Node #3: [45, 61] from Operation: 26+35=61 Current State: 16:[45, 61], Operations: ['9*5=45', '26+35=61'] Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[9, 26, 5, 35], Operations: [] Exploring Operation: 35/5=7, Resulting Numbers: [9, 26, 7] Generated Node #0,0: 16:[9, 26, 7] Operation: 35/5=7 Exploring Operation: 35-26=9, Resulting Numbers: [9, 5, 9] Generated Node #0,1: 16:[9, 5, 9] Operation: 35-26=9 Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[9, 5, 9], Operations: ['35-26=9'] Exploring Operation: 9-5=4, Resulting Numbers: [9, 4] Generated Node #0,1,0: 16:[9, 4] Operation: 9-5=4 Exploring Operation: 9-5=4, Resulting Numbers: [9, 4] Generated Node #0,1,1: 16:[9, 4] Operation: 9-5=4 Moving to Node #0,1,0 Current State: 16:[9, 4], Operations: ['35-26=9', '9-5=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[9, 4], Operations: ['35-26=9', '9-5=4'] Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[9, 26, 7], Operations: ['35/5=7'] Exploring Operation: 26-9=17, Resulting Numbers: [7, 17] Generated Node #0,0,0: 16:[7, 17] Operation: 26-9=17 Exploring Operation: 26-7=19, Resulting Numbers: [9, 19] Generated Node #0,0,1: 16:[9, 19] Operation: 26-7=19 Moving to Node #0,0,0 Current State: 16:[7, 17], Operations: ['35/5=7', '26-9=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[9, 19], Operations: ['35/5=7', '26-7=19'] Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,16 unequal: No Solution Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,16 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
[ 22, 61, 27, 32 ]
28
[ "61+27=88", "88/22=4", "32-4=28" ]
Current State: 28:[22, 61, 27, 32], Operations: [] Exploring Operation: 61+27=88, Resulting Numbers: [22, 32, 88] Generated Node #2: [22, 32, 88] from Operation: 61+27=88 Current State: 28:[22, 32, 88], Operations: ['61+27=88'] Exploring Operation: 88/22=4, Resulting Numbers: [32, 4] Generated Node #3: [32, 4] from Operation: 88/22=4 Current State: 28:[32, 4], Operations: ['61+27=88', '88/22=4'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[22, 61, 27, 32], Operations: [] Exploring Operation: 61-27=34, Resulting Numbers: [22, 32, 34] Generated Node #0,0: 28:[22, 32, 34] Operation: 61-27=34 Exploring Operation: 61-32=29, Resulting Numbers: [22, 27, 29] Generated Node #0,1: 28:[22, 27, 29] Operation: 61-32=29 Exploring Operation: 32-22=10, Resulting Numbers: [61, 27, 10] Generated Node #0,2: 28:[61, 27, 10] Operation: 32-22=10 Exploring Operation: 61-22=39, Resulting Numbers: [27, 32, 39] Generated Node #0,3: 28:[27, 32, 39] Operation: 61-22=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 28:[22, 27, 29], Operations: ['61-32=29'] Exploring Operation: 22+27=49, Resulting Numbers: [29, 49] Generated Node #0,1,0: 28:[29, 49] Operation: 22+27=49 Exploring Operation: 27-22=5, Resulting Numbers: [29, 5] Generated Node #0,1,1: 28:[29, 5] Operation: 27-22=5 Exploring Operation: 29-27=2, Resulting Numbers: [22, 2] Generated Node #0,1,2: 28:[22, 2] Operation: 29-27=2 Exploring Operation: 29-22=7, Resulting Numbers: [27, 7] Generated Node #0,1,3: 28:[27, 7] Operation: 29-22=7 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 28:[27, 7], Operations: ['61-32=29', '29-22=7'] Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,28 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 28:[29, 5], Operations: ['61-32=29', '27-22=5'] Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,28 unequal: No Solution Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,28 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 28:[22, 2], Operations: ['61-32=29', '29-27=2'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 28:[29, 49], Operations: ['61-32=29', '22+27=49'] Exploring Operation: 29+49=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 49-29=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 29*49=1421, Resulting Numbers: [1421] 1421,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[22, 32, 34], Operations: ['61-27=34'] Exploring Operation: 34-22=12, Resulting Numbers: [32, 12] Generated Node #0,0,0: 28:[32, 12] Operation: 34-22=12 Exploring Operation: 32-22=10, Resulting Numbers: [34, 10] Generated Node #0,0,1: 28:[34, 10] Operation: 32-22=10 Exploring Operation: 34-32=2, Resulting Numbers: [22, 2] Generated Node #0,0,2: 28:[22, 2] Operation: 34-32=2 Exploring Operation: 22+32=54, Resulting Numbers: [34, 54] Generated Node #0,0,3: 28:[34, 54] Operation: 22+32=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[32, 12], Operations: ['61-27=34', '34-22=12'] Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,28 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 28:[22, 2], Operations: ['61-27=34', '34-32=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,28 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 28:[34, 10], Operations: ['61-27=34', '32-22=10'] Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,28 unequal: No Solution Exploring Operation: 34+10=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 34*10=340, Resulting Numbers: [340] 340,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 28:[34, 54], Operations: ['61-27=34', '22+32=54'] Exploring Operation: 34+54=88, Resulting Numbers: [88] 88,28 unequal: No Solution Exploring Operation: 34*54=1836, Resulting Numbers: [1836] 1836,28 unequal: No Solution Exploring Operation: 54-34=20, Resulting Numbers: [20] 20,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 28:[27, 32, 39], Operations: ['61-22=39'] Exploring Operation: 32-27=5, Resulting Numbers: [39, 5] Generated Node #0,3,0: 28:[39, 5] Operation: 32-27=5 Exploring Operation: 39-27=12, Resulting Numbers: [32, 12] Generated Node #0,3,1: 28:[32, 12] Operation: 39-27=12 Exploring Operation: 39-32=7, Resulting Numbers: [27, 7] Generated Node #0,3,2: 28:[27, 7] Operation: 39-32=7 Exploring Operation: 27+32=59, Resulting Numbers: [39, 59] Generated Node #0,3,3: 28:[39, 59] Operation: 27+32=59 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 28:[27, 7], Operations: ['61-22=39', '39-32=7'] Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,28 unequal: No Solution Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 28:[32, 12], Operations: ['61-22=39', '39-27=12'] Exploring Operation: 32+12=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 32*12=384, Resulting Numbers: [384] 384,28 unequal: No Solution Exploring Operation: 32-12=20, Resulting Numbers: [20] 20,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 28:[39, 5], Operations: ['61-22=39', '32-27=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,28 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 39*5=195, Resulting Numbers: [195] 195,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 28:[39, 59], Operations: ['61-22=39', '27+32=59'] Exploring Operation: 39+59=98, Resulting Numbers: [98] 98,28 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,28 unequal: No Solution Exploring Operation: 39*59=2301, Resulting Numbers: [2301] 2301,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 28:[61, 27, 10], Operations: ['32-22=10'] Exploring Operation: 61-27=34, Resulting Numbers: [10, 34] Generated Node #0,2,0: 28:[10, 34] Operation: 61-27=34 Exploring Operation: 61-10=51, Resulting Numbers: [27, 51] Generated Node #0,2,1: 28:[27, 51] Operation: 61-10=51 Exploring Operation: 27-10=17, Resulting Numbers: [61, 17] Generated Node #0,2,2: 28:[61, 17] Operation: 27-10=17 Exploring Operation: 27+10=37, Resulting Numbers: [61, 37] Generated Node #0,2,3: 28:[61, 37] Operation: 27+10=37 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 28:[10, 34], Operations: ['32-22=10', '61-27=34'] Exploring Operation: 10+34=44, Resulting Numbers: [44] 44,28 unequal: No Solution Exploring Operation: 10*34=340, Resulting Numbers: [340] 340,28 unequal: No Solution Exploring Operation: 34-10=24, Resulting Numbers: [24] 24,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 28:[27, 51], Operations: ['32-22=10', '61-10=51'] Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,28 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 28:[61, 17], Operations: ['32-22=10', '27-10=17'] Exploring Operation: 61*17=1037, Resulting Numbers: [1037] 1037,28 unequal: No Solution Exploring Operation: 61+17=78, Resulting Numbers: [78] 78,28 unequal: No Solution Exploring Operation: 61-17=44, Resulting Numbers: [44] 44,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 28:[61, 37], Operations: ['32-22=10', '27+10=37'] Exploring Operation: 61*37=2257, Resulting Numbers: [2257] 2257,28 unequal: No Solution Exploring Operation: 61+37=98, Resulting Numbers: [98] 98,28 unequal: No Solution Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 66, 11, 75, 49 ]
81
[ "66-11=55", "75-49=26", "55+26=81" ]
Current State: 81:[66, 11, 75, 49], Operations: [] Exploring Operation: 66-11=55, Resulting Numbers: [75, 49, 55] Generated Node #2: [75, 49, 55] from Operation: 66-11=55 Current State: 81:[75, 49, 55], Operations: ['66-11=55'] Exploring Operation: 75-49=26, Resulting Numbers: [55, 26] Generated Node #3: [55, 26] from Operation: 75-49=26 Current State: 81:[55, 26], Operations: ['66-11=55', '75-49=26'] Exploring Operation: 55+26=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[66, 11, 75, 49], Operations: [] Exploring Operation: 66/11=6, Resulting Numbers: [75, 49, 6] Generated Node #0,0: 81:[75, 49, 6] Operation: 66/11=6 Exploring Operation: 75-49=26, Resulting Numbers: [66, 11, 26] Generated Node #0,1: 81:[66, 11, 26] Operation: 75-49=26 Exploring Operation: 75-66=9, Resulting Numbers: [11, 49, 9] Generated Node #0,2: 81:[11, 49, 9] Operation: 75-66=9 Exploring Operation: 66-49=17, Resulting Numbers: [11, 75, 17] Generated Node #0,3: 81:[11, 75, 17] Operation: 66-49=17 Start Sub Search at level 1: Moving to Node #0,3 Current State: 81:[11, 75, 17], Operations: ['66-49=17'] Exploring Operation: 11+17=28, Resulting Numbers: [75, 28] Generated Node #0,3,0: 81:[75, 28] Operation: 11+17=28 Exploring Operation: 11+75=86, Resulting Numbers: [17, 86] Generated Node #0,3,1: 81:[17, 86] Operation: 11+75=86 Exploring Operation: 75+17=92, Resulting Numbers: [11, 92] Generated Node #0,3,2: 81:[11, 92] Operation: 75+17=92 Exploring Operation: 17-11=6, Resulting Numbers: [75, 6] Generated Node #0,3,3: 81:[75, 6] Operation: 17-11=6 Moving to Node #0,3,0 Current State: 81:[75, 28], Operations: ['66-49=17', '11+17=28'] Exploring Operation: 75+28=103, Resulting Numbers: [103] 103,81 unequal: No Solution Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,81 unequal: No Solution Exploring Operation: 75*28=2100, Resulting Numbers: [2100] 2100,81 unequal: No Solution Moving to Node #0,3,3 Current State: 81:[75, 6], Operations: ['66-49=17', '17-11=6'] Exploring Operation: 75-6=69, Resulting Numbers: [69] 69,81 unequal: No Solution Exploring Operation: 75*6=450, Resulting Numbers: [450] 450,81 unequal: No Solution Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[66, 11, 75, 49], Operations: [] Exploring Operation: 66-49=17, Resulting Numbers: [11, 75, 17] Generated Node #0,3: 81:[11, 75, 17] Operation: 66-49=17 Moving to Node #0,3 Current State: 81:[11, 75, 17], Operations: ['66-49=17'] Exploring Operation: 17-11=6, Resulting Numbers: [75, 6] Generated Node #0,3,3: 81:[75, 6] Operation: 17-11=6 Moving to Node #0,3,3 Current State: 81:[75, 6], Operations: ['66-49=17', '17-11=6'] Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 19, 31, 52, 11 ]
93
[ "52-19=33", "31*33=1023", "1023/11=93" ]
Current State: 93:[19, 31, 52, 11], Operations: [] Exploring Operation: 52-19=33, Resulting Numbers: [31, 11, 33] Generated Node #2: [31, 11, 33] from Operation: 52-19=33 Current State: 93:[31, 11, 33], Operations: ['52-19=33'] Exploring Operation: 31*33=1023, Resulting Numbers: [11, 1023] Generated Node #3: [11, 1023] from Operation: 31*33=1023 Current State: 93:[11, 1023], Operations: ['52-19=33', '31*33=1023'] Exploring Operation: 1023/11=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[19, 31, 52, 11], Operations: [] Exploring Operation: 19+11=30, Resulting Numbers: [31, 52, 30] Generated Node #0,0: 93:[31, 52, 30] Operation: 19+11=30 Exploring Operation: 52-19=33, Resulting Numbers: [31, 11, 33] Generated Node #0,1: 93:[31, 11, 33] Operation: 52-19=33 Exploring Operation: 52-11=41, Resulting Numbers: [19, 31, 41] Generated Node #0,2: 93:[19, 31, 41] Operation: 52-11=41 Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[31, 11, 33], Operations: ['52-19=33'] Exploring Operation: 33-31=2, Resulting Numbers: [11, 2] Generated Node #0,1,0: 93:[11, 2] Operation: 33-31=2 Exploring Operation: 33-11=22, Resulting Numbers: [31, 22] Generated Node #0,1,1: 93:[31, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [31, 3] Generated Node #0,1,2: 93:[31, 3] Operation: 33/11=3 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 93:[31, 3], Operations: ['52-19=33', '33/11=3'] Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,93 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[19, 31, 52, 11], Operations: [] Exploring Operation: 52-19=33, Resulting Numbers: [31, 11, 33] Generated Node #0,1: 93:[31, 11, 33] Operation: 52-19=33 Moving to Node #0,1 Current State: 93:[31, 11, 33], Operations: ['52-19=33'] Exploring Operation: 33/11=3, Resulting Numbers: [31, 3] Generated Node #0,1,2: 93:[31, 3] Operation: 33/11=3 Moving to Node #0,1,2 Current State: 93:[31, 3], Operations: ['52-19=33', '33/11=3'] Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 71, 52, 17, 19 ]
97
[ "19-17=2", "52/2=26", "71+26=97" ]
Current State: 97:[71, 52, 17, 19], Operations: [] Exploring Operation: 19-17=2, Resulting Numbers: [71, 52, 2] Generated Node #2: [71, 52, 2] from Operation: 19-17=2 Current State: 97:[71, 52, 2], Operations: ['19-17=2'] Exploring Operation: 52/2=26, Resulting Numbers: [71, 26] Generated Node #3: [71, 26] from Operation: 52/2=26 Current State: 97:[71, 26], Operations: ['19-17=2', '52/2=26'] Exploring Operation: 71+26=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[71, 52, 17, 19], Operations: [] Exploring Operation: 71+17=88, Resulting Numbers: [52, 19, 88] Generated Node #0,0: 97:[52, 19, 88] Operation: 71+17=88 Exploring Operation: 52+17=69, Resulting Numbers: [71, 19, 69] Generated Node #0,1: 97:[71, 19, 69] Operation: 52+17=69 Exploring Operation: 71+19=90, Resulting Numbers: [52, 17, 90] Generated Node #0,2: 97:[52, 17, 90] Operation: 71+19=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[52, 19, 88], Operations: ['71+17=88'] Exploring Operation: 52+19=71, Resulting Numbers: [88, 71] Generated Node #0,0,0: 97:[88, 71] Operation: 52+19=71 Exploring Operation: 52-19=33, Resulting Numbers: [88, 33] Generated Node #0,0,1: 97:[88, 33] Operation: 52-19=33 Exploring Operation: 19+88=107, Resulting Numbers: [52, 107] Generated Node #0,0,2: 97:[52, 107] Operation: 19+88=107 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[88, 71], Operations: ['71+17=88', '52+19=71'] Exploring Operation: 88*71=6248, Resulting Numbers: [6248] 6248,97 unequal: No Solution Exploring Operation: 88+71=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 97:[52, 107], Operations: ['71+17=88', '19+88=107'] Exploring Operation: 52+107=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 52*107=5564, Resulting Numbers: [5564] 5564,97 unequal: No Solution Exploring Operation: 107-52=55, Resulting Numbers: [55] 55,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 97:[88, 33], Operations: ['71+17=88', '52-19=33'] Exploring Operation: 88*33=2904, Resulting Numbers: [2904] 2904,97 unequal: No Solution Exploring Operation: 88+33=121, Resulting Numbers: [121] 121,97 unequal: No Solution Exploring Operation: 88-33=55, Resulting Numbers: [55] 55,97 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: 97:[71, 19, 69], Operations: ['52+17=69'] Exploring Operation: 19+69=88, Resulting Numbers: [71, 88] Generated Node #0,1,0: 97:[71, 88] Operation: 19+69=88 Exploring Operation: 71+19=90, Resulting Numbers: [69, 90] Generated Node #0,1,1: 97:[69, 90] Operation: 71+19=90 Exploring Operation: 71-19=52, Resulting Numbers: [69, 52] Generated Node #0,1,2: 97:[69, 52] Operation: 71-19=52 Moving to Node #0,1,0 Current State: 97:[71, 88], Operations: ['52+17=69', '19+69=88'] Exploring Operation: 88-71=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 71*88=6248, Resulting Numbers: [6248] 6248,97 unequal: No Solution Exploring Operation: 71+88=159, Resulting Numbers: [159] 159,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[69, 90], Operations: ['52+17=69', '71+19=90'] Exploring Operation: 90-69=21, Resulting Numbers: [21] 21,97 unequal: No Solution Exploring Operation: 69+90=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 69*90=6210, Resulting Numbers: [6210] 6210,97 unequal: No Solution Moving to Node #0,1,2 Current State: 97:[69, 52], Operations: ['52+17=69', '71-19=52'] Exploring Operation: 69-52=17, Resulting Numbers: [17] 17,97 unequal: No Solution Exploring Operation: 69*52=3588, Resulting Numbers: [3588] 3588,97 unequal: No Solution Exploring Operation: 69+52=121, Resulting Numbers: [121] 121,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[52, 17, 90], Operations: ['71+19=90'] Exploring Operation: 52+17=69, Resulting Numbers: [90, 69] Generated Node #0,2,0: 97:[90, 69] Operation: 52+17=69 Exploring Operation: 17+90=107, Resulting Numbers: [52, 107] Generated Node #0,2,1: 97:[52, 107] Operation: 17+90=107 Exploring Operation: 52-17=35, Resulting Numbers: [90, 35] Generated Node #0,2,2: 97:[90, 35] Operation: 52-17=35 Moving to Node #0,2,0 Current State: 97:[90, 69], Operations: ['71+19=90', '52+17=69'] Exploring Operation: 90+69=159, Resulting Numbers: [159] 159,97 unequal: No Solution Exploring Operation: 90*69=6210, Resulting Numbers: [6210] 6210,97 unequal: No Solution Exploring Operation: 90-69=21, Resulting Numbers: [21] 21,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[52, 107], Operations: ['71+19=90', '17+90=107'] Exploring Operation: 52*107=5564, Resulting Numbers: [5564] 5564,97 unequal: No Solution Exploring Operation: 107-52=55, Resulting Numbers: [55] 55,97 unequal: No Solution Exploring Operation: 52+107=159, Resulting Numbers: [159] 159,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[90, 35], Operations: ['71+19=90', '52-17=35'] Exploring Operation: 90+35=125, Resulting Numbers: [125] 125,97 unequal: No Solution Exploring Operation: 90*35=3150, Resulting Numbers: [3150] 3150,97 unequal: No Solution Exploring Operation: 90-35=55, Resulting Numbers: [55] 55,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 11, 60, 33, 9 ]
91
[ "60-11=49", "33+9=42", "49+42=91" ]
Current State: 91:[11, 60, 33, 9], Operations: [] Exploring Operation: 60-11=49, Resulting Numbers: [33, 9, 49] Generated Node #2: [33, 9, 49] from Operation: 60-11=49 Current State: 91:[33, 9, 49], Operations: ['60-11=49'] Exploring Operation: 33+9=42, Resulting Numbers: [49, 42] Generated Node #3: [49, 42] from Operation: 33+9=42 Current State: 91:[49, 42], Operations: ['60-11=49', '33+9=42'] Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[11, 60, 33, 9], Operations: [] Exploring Operation: 33-11=22, Resulting Numbers: [60, 9, 22] Generated Node #0,0: 91:[60, 9, 22] Operation: 33-11=22 Exploring Operation: 33/11=3, Resulting Numbers: [60, 9, 3] Generated Node #0,1: 91:[60, 9, 3] Operation: 33/11=3 Exploring Operation: 60-33=27, Resulting Numbers: [11, 9, 27] Generated Node #0,2: 91:[11, 9, 27] Operation: 60-33=27 Exploring Operation: 60+33=93, Resulting Numbers: [11, 9, 93] Generated Node #0,3: 91:[11, 9, 93] Operation: 60+33=93 Exploring Operation: 11+60=71, Resulting Numbers: [33, 9, 71] Generated Node #0,4: 91:[33, 9, 71] Operation: 11+60=71 Start Sub Search at level 1: Moving to Node #0,3 Current State: 91:[11, 9, 93], Operations: ['60+33=93'] Exploring Operation: 11*9=99, Resulting Numbers: [93, 99] Generated Node #0,3,0: 91:[93, 99] Operation: 11*9=99 Exploring Operation: 11-9=2, Resulting Numbers: [93, 2] Generated Node #0,3,1: 91:[93, 2] Operation: 11-9=2 Exploring Operation: 11+9=20, Resulting Numbers: [93, 20] Generated Node #0,3,2: 91:[93, 20] Operation: 11+9=20 Exploring Operation: 93-11=82, Resulting Numbers: [9, 82] Generated Node #0,3,3: 91:[9, 82] Operation: 93-11=82 Exploring Operation: 93-9=84, Resulting Numbers: [11, 84] Generated Node #0,3,4: 91:[11, 84] Operation: 93-9=84 Moving to Node #0,3,1 Current State: 91:[93, 2], Operations: ['60+33=93', '11-9=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[11, 60, 33, 9], Operations: [] Exploring Operation: 60+33=93, Resulting Numbers: [11, 9, 93] Generated Node #0,3: 91:[11, 9, 93] Operation: 60+33=93 Moving to Node #0,3 Current State: 91:[11, 9, 93], Operations: ['60+33=93'] Exploring Operation: 11-9=2, Resulting Numbers: [93, 2] Generated Node #0,3,1: 91:[93, 2] Operation: 11-9=2 Moving to Node #0,3,1 Current State: 91:[93, 2], Operations: ['60+33=93', '11-9=2'] Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 89, 4, 5, 64 ]
81
[ "89-4=85", "85/5=17", "64+17=81" ]
Current State: 81:[89, 4, 5, 64], Operations: [] Exploring Operation: 89-4=85, Resulting Numbers: [5, 64, 85] Generated Node #2: [5, 64, 85] from Operation: 89-4=85 Current State: 81:[5, 64, 85], Operations: ['89-4=85'] Exploring Operation: 85/5=17, Resulting Numbers: [64, 17] Generated Node #3: [64, 17] from Operation: 85/5=17 Current State: 81:[64, 17], Operations: ['89-4=85', '85/5=17'] Exploring Operation: 64+17=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[89, 4, 5, 64], Operations: [] Exploring Operation: 89-64=25, Resulting Numbers: [4, 5, 25] Generated Node #0,0: 81:[4, 5, 25] Operation: 89-64=25 Exploring Operation: 64/4=16, Resulting Numbers: [89, 5, 16] Generated Node #0,1: 81:[89, 5, 16] Operation: 64/4=16 Exploring Operation: 89-5=84, Resulting Numbers: [4, 64, 84] Generated Node #0,2: 81:[4, 64, 84] Operation: 89-5=84 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[4, 5, 25], Operations: ['89-64=25'] Exploring Operation: 4+5=9, Resulting Numbers: [25, 9] Generated Node #0,0,0: 81:[25, 9] Operation: 4+5=9 Exploring Operation: 5-4=1, Resulting Numbers: [25, 1] Generated Node #0,0,1: 81:[25, 1] Operation: 5-4=1 Exploring Operation: 25/5=5, Resulting Numbers: [4, 5] Generated Node #0,0,2: 81:[4, 5] Operation: 25/5=5 Moving to Node #0,0,0 Current State: 81:[25, 9], Operations: ['89-64=25', '4+5=9'] Exploring Operation: 25+9=34, Resulting Numbers: [34] 34,81 unequal: No Solution Exploring Operation: 25*9=225, Resulting Numbers: [225] 225,81 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,81 unequal: No Solution Moving to Node #0,0,2 Current State: 81:[4, 5], Operations: ['89-64=25', '25/5=5'] Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,81 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,81 unequal: No Solution Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[25, 1], Operations: ['89-64=25', '5-4=1'] Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,81 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[89, 5, 16], Operations: ['64/4=16'] Exploring Operation: 89-16=73, Resulting Numbers: [5, 73] Generated Node #0,1,0: 81:[5, 73] Operation: 89-16=73 Exploring Operation: 89-5=84, Resulting Numbers: [16, 84] Generated Node #0,1,1: 81:[16, 84] Operation: 89-5=84 Exploring Operation: 5*16=80, Resulting Numbers: [89, 80] Generated Node #0,1,2: 81:[89, 80] Operation: 5*16=80 Moving to Node #0,1,2 Current State: 81:[89, 80], Operations: ['64/4=16', '5*16=80'] Exploring Operation: 89+80=169, Resulting Numbers: [169] 169,81 unequal: No Solution Exploring Operation: 89-80=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 89*80=7120, Resulting Numbers: [7120] 7120,81 unequal: No Solution Moving to Node #0,1,0 Current State: 81:[5, 73], Operations: ['64/4=16', '89-16=73'] Exploring Operation: 5+73=78, Resulting Numbers: [78] 78,81 unequal: No Solution Exploring Operation: 5*73=365, Resulting Numbers: [365] 365,81 unequal: No Solution Exploring Operation: 73-5=68, Resulting Numbers: [68] 68,81 unequal: No Solution Moving to Node #0,1,1 Current State: 81:[16, 84], Operations: ['64/4=16', '89-5=84'] Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,81 unequal: No Solution Exploring Operation: 16+84=100, Resulting Numbers: [100] 100,81 unequal: No Solution Exploring Operation: 16*84=1344, Resulting Numbers: [1344] 1344,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 81:[4, 64, 84], Operations: ['89-5=84'] Exploring Operation: 4+64=68, Resulting Numbers: [84, 68] Generated Node #0,2,0: 81:[84, 68] Operation: 4+64=68 Exploring Operation: 84-64=20, Resulting Numbers: [4, 20] Generated Node #0,2,1: 81:[4, 20] Operation: 84-64=20 Exploring Operation: 64/4=16, Resulting Numbers: [84, 16] Generated Node #0,2,2: 81:[84, 16] Operation: 64/4=16 Moving to Node #0,2,1 Current State: 81:[4, 20], Operations: ['89-5=84', '84-64=20'] Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,81 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,81 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,81 unequal: No Solution Moving to Node #0,2,2 Current State: 81:[84, 16], Operations: ['89-5=84', '64/4=16'] Exploring Operation: 84-16=68, Resulting Numbers: [68] 68,81 unequal: No Solution Exploring Operation: 84*16=1344, Resulting Numbers: [1344] 1344,81 unequal: No Solution Exploring Operation: 84+16=100, Resulting Numbers: [100] 100,81 unequal: No Solution Moving to Node #0,2,0 Current State: 81:[84, 68], Operations: ['89-5=84', '4+64=68'] Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,81 unequal: No Solution Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,81 unequal: No Solution Exploring Operation: 84*68=5712, Resulting Numbers: [5712] 5712,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 10, 70, 2, 98 ]
84
[ "70/10=7", "2*7=14", "98-14=84" ]
Current State: 84:[10, 70, 2, 98], Operations: [] Exploring Operation: 70/10=7, Resulting Numbers: [2, 98, 7] Generated Node #2: [2, 98, 7] from Operation: 70/10=7 Current State: 84:[2, 98, 7], Operations: ['70/10=7'] Exploring Operation: 2*7=14, Resulting Numbers: [98, 14] Generated Node #3: [98, 14] from Operation: 2*7=14 Current State: 84:[98, 14], Operations: ['70/10=7', '2*7=14'] Exploring Operation: 98-14=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[10, 70, 2, 98], Operations: [] Exploring Operation: 98-10=88, Resulting Numbers: [70, 2, 88] Generated Node #0,0: 84:[70, 2, 88] Operation: 98-10=88 Exploring Operation: 70/10=7, Resulting Numbers: [2, 98, 7] Generated Node #0,1: 84:[2, 98, 7] Operation: 70/10=7 Exploring Operation: 10+70=80, Resulting Numbers: [2, 98, 80] Generated Node #0,2: 84:[2, 98, 80] Operation: 10+70=80 Exploring Operation: 98-70=28, Resulting Numbers: [10, 2, 28] Generated Node #0,3: 84:[10, 2, 28] Operation: 98-70=28 Moving to Node #0,3 Current State: 84:[10, 2, 28], Operations: ['98-70=28'] Exploring Operation: 10*2=20, Resulting Numbers: [28, 20] Generated Node #0,3,0: 84:[28, 20] Operation: 10*2=20 Exploring Operation: 10-2=8, Resulting Numbers: [28, 8] Generated Node #0,3,1: 84:[28, 8] Operation: 10-2=8 Exploring Operation: 10/2=5, Resulting Numbers: [28, 5] Generated Node #0,3,2: 84:[28, 5] Operation: 10/2=5 Exploring Operation: 10+2=12, Resulting Numbers: [28, 12] Generated Node #0,3,3: 84:[28, 12] Operation: 10+2=12 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 84:[28, 12], Operations: ['98-70=28', '10+2=12'] Exploring Operation: 28-12=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 28+12=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 28*12=336, Resulting Numbers: [336] 336,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[28, 20], Operations: ['98-70=28', '10*2=20'] Exploring Operation: 28-20=8, Resulting Numbers: [8] 8,84 unequal: No Solution Exploring Operation: 28+20=48, Resulting Numbers: [48] 48,84 unequal: No Solution Exploring Operation: 28*20=560, Resulting Numbers: [560] 560,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[28, 8], Operations: ['98-70=28', '10-2=8'] Exploring Operation: 28-8=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 28+8=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 28*8=224, Resulting Numbers: [224] 224,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 84:[28, 5], Operations: ['98-70=28', '10/2=5'] Exploring Operation: 28-5=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 28+5=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 28*5=140, Resulting Numbers: [140] 140,84 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: 84:[2, 98, 7], Operations: ['70/10=7'] Exploring Operation: 98-7=91, Resulting Numbers: [2, 91] Generated Node #0,1,0: 84:[2, 91] Operation: 98-7=91 Exploring Operation: 98-2=96, Resulting Numbers: [7, 96] Generated Node #0,1,1: 84:[7, 96] Operation: 98-2=96 Exploring Operation: 98/2=49, Resulting Numbers: [7, 49] Generated Node #0,1,2: 84:[7, 49] Operation: 98/2=49 Exploring Operation: 98/7=14, Resulting Numbers: [2, 14] Generated Node #0,1,3: 84:[2, 14] Operation: 98/7=14 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 84:[2, 14], Operations: ['70/10=7', '98/7=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,84 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 2*14=28, Resulting Numbers: [28] 28,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 84:[2, 91], Operations: ['70/10=7', '98-7=91'] Exploring Operation: 2*91=182, Resulting Numbers: [182] 182,84 unequal: No Solution Exploring Operation: 2+91=93, Resulting Numbers: [93] 93,84 unequal: No Solution Exploring Operation: 91-2=89, Resulting Numbers: [89] 89,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 84:[7, 49], Operations: ['70/10=7', '98/2=49'] Exploring Operation: 7*49=343, Resulting Numbers: [343] 343,84 unequal: No Solution Exploring Operation: 49/7=7, Resulting Numbers: [7] 7,84 unequal: No Solution Exploring Operation: 49-7=42, Resulting Numbers: [42] 42,84 unequal: No Solution Exploring Operation: 7+49=56, Resulting Numbers: [56] 56,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 84:[7, 96], Operations: ['70/10=7', '98-2=96'] Exploring Operation: 7+96=103, Resulting Numbers: [103] 103,84 unequal: No Solution Exploring Operation: 96-7=89, Resulting Numbers: [89] 89,84 unequal: No Solution Exploring Operation: 7*96=672, Resulting Numbers: [672] 672,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 84:[2, 98, 80], Operations: ['10+70=80'] Exploring Operation: 98-2=96, Resulting Numbers: [80, 96] Generated Node #0,2,0: 84:[80, 96] Operation: 98-2=96 Exploring Operation: 2+80=82, Resulting Numbers: [98, 82] Generated Node #0,2,1: 84:[98, 82] Operation: 2+80=82 Exploring Operation: 98-80=18, Resulting Numbers: [2, 18] Generated Node #0,2,2: 84:[2, 18] Operation: 98-80=18 Exploring Operation: 98/2=49, Resulting Numbers: [80, 49] Generated Node #0,2,3: 84:[80, 49] Operation: 98/2=49 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[2, 18], Operations: ['10+70=80', '98-80=18'] Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,84 unequal: No Solution Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[80, 49], Operations: ['10+70=80', '98/2=49'] Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 80*49=3920, Resulting Numbers: [3920] 3920,84 unequal: No Solution Exploring Operation: 80+49=129, Resulting Numbers: [129] 129,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[80, 96], Operations: ['10+70=80', '98-2=96'] Exploring Operation: 80*96=7680, Resulting Numbers: [7680] 7680,84 unequal: No Solution Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 80+96=176, Resulting Numbers: [176] 176,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 84:[98, 82], Operations: ['10+70=80', '2+80=82'] Exploring Operation: 98-82=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 98+82=180, Resulting Numbers: [180] 180,84 unequal: No Solution Exploring Operation: 98*82=8036, Resulting Numbers: [8036] 8036,84 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: 84:[70, 2, 88], Operations: ['98-10=88'] Exploring Operation: 88-2=86, Resulting Numbers: [70, 86] Generated Node #0,0,0: 84:[70, 86] Operation: 88-2=86 Exploring Operation: 70+2=72, Resulting Numbers: [88, 72] Generated Node #0,0,1: 84:[88, 72] Operation: 70+2=72 Exploring Operation: 70/2=35, Resulting Numbers: [88, 35] Generated Node #0,0,2: 84:[88, 35] Operation: 70/2=35 Exploring Operation: 88-70=18, Resulting Numbers: [2, 18] Generated Node #0,0,3: 84:[2, 18] Operation: 88-70=18 Moving to Node #0,0,3 Current State: 84:[2, 18], Operations: ['98-10=88', '88-70=18'] Exploring Operation: 2*18=36, Resulting Numbers: [36] 36,84 unequal: No Solution Exploring Operation: 2+18=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 18-2=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 18/2=9, Resulting Numbers: [9] 9,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[88, 35], Operations: ['98-10=88', '70/2=35'] Exploring Operation: 88-35=53, Resulting Numbers: [53] 53,84 unequal: No Solution Exploring Operation: 88+35=123, Resulting Numbers: [123] 123,84 unequal: No Solution Exploring Operation: 88*35=3080, Resulting Numbers: [3080] 3080,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[88, 72], Operations: ['98-10=88', '70+2=72'] Exploring Operation: 88*72=6336, Resulting Numbers: [6336] 6336,84 unequal: No Solution Exploring Operation: 88+72=160, Resulting Numbers: [160] 160,84 unequal: No Solution Exploring Operation: 88-72=16, Resulting Numbers: [16] 16,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[70, 86], Operations: ['98-10=88', '88-2=86'] Exploring Operation: 86-70=16, Resulting Numbers: [16] 16,84 unequal: No Solution Exploring Operation: 70*86=6020, Resulting Numbers: [6020] 6020,84 unequal: No Solution Exploring Operation: 70+86=156, Resulting Numbers: [156] 156,84 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 96, 8, 98, 4 ]
74
[ "8-4=4", "96/4=24", "98-24=74" ]
Current State: 74:[96, 8, 98, 4], Operations: [] Exploring Operation: 8-4=4, Resulting Numbers: [96, 98, 4] Generated Node #2: [96, 98, 4] from Operation: 8-4=4 Current State: 74:[96, 98, 4], Operations: ['8-4=4'] Exploring Operation: 96/4=24, Resulting Numbers: [98, 24] Generated Node #3: [98, 24] from Operation: 96/4=24 Current State: 74:[98, 24], Operations: ['8-4=4', '96/4=24'] Exploring Operation: 98-24=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[96, 8, 98, 4], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [8, 4, 2] Generated Node #0,0: 74:[8, 4, 2] Operation: 98-96=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[8, 4, 2], Operations: ['98-96=2'] Exploring Operation: 8/4=2, Resulting Numbers: [2, 2] Generated Node #0,0,0: 74:[2, 2] Operation: 8/4=2 Moving to Node #0,0,0 Current State: 74:[2, 2], Operations: ['98-96=2', '8/4=2'] Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,74 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
[ 78, 28, 7, 76 ]
14
[ "78-76=2", "7*2=14", "28-14=14" ]
Current State: 14:[78, 28, 7, 76], Operations: [] Exploring Operation: 78-76=2, Resulting Numbers: [28, 7, 2] Generated Node #2: [28, 7, 2] from Operation: 78-76=2 Current State: 14:[28, 7, 2], Operations: ['78-76=2'] Exploring Operation: 7*2=14, Resulting Numbers: [28, 14] Generated Node #3: [28, 14] from Operation: 7*2=14 Current State: 14:[28, 14], Operations: ['78-76=2', '7*2=14'] Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[78, 28, 7, 76], Operations: [] Exploring Operation: 78-28=50, Resulting Numbers: [7, 76, 50] Generated Node #0,0: 14:[7, 76, 50] Operation: 78-28=50 Exploring Operation: 78-76=2, Resulting Numbers: [28, 7, 2] Generated Node #0,1: 14:[28, 7, 2] Operation: 78-76=2 Exploring Operation: 76-28=48, Resulting Numbers: [78, 7, 48] Generated Node #0,2: 14:[78, 7, 48] Operation: 76-28=48 Moving to Node #0,1 Current State: 14:[28, 7, 2], Operations: ['78-76=2'] Exploring Operation: 28/2=14, Resulting Numbers: [7, 14] Generated Node #0,1,0: 14:[7, 14] Operation: 28/2=14 Exploring Operation: 28/7=4, Resulting Numbers: [2, 4] Generated Node #0,1,1: 14:[2, 4] Operation: 28/7=4 Exploring Operation: 28-7=21, Resulting Numbers: [2, 21] Generated Node #0,1,2: 14:[2, 21] Operation: 28-7=21 Moving to Node #0,0 Current State: 14:[7, 76, 50], Operations: ['78-28=50'] Exploring Operation: 76-7=69, Resulting Numbers: [50, 69] Generated Node #0,0,0: 14:[50, 69] Operation: 76-7=69 Exploring Operation: 76-50=26, Resulting Numbers: [7, 26] Generated Node #0,0,1: 14:[7, 26] Operation: 76-50=26 Exploring Operation: 50-7=43, Resulting Numbers: [76, 43] Generated Node #0,0,2: 14:[76, 43] Operation: 50-7=43 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[7, 26], Operations: ['78-28=50', '76-50=26'] Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,14 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,14 unequal: No Solution Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[50, 69], Operations: ['78-28=50', '76-7=69'] Exploring Operation: 69-50=19, Resulting Numbers: [19] 19,14 unequal: No Solution Exploring Operation: 50+69=119, Resulting Numbers: [119] 119,14 unequal: No Solution Exploring Operation: 50*69=3450, Resulting Numbers: [3450] 3450,14 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:[76, 43], Operations: ['78-28=50', '50-7=43'] Exploring Operation: 76+43=119, Resulting Numbers: [119] 119,14 unequal: No Solution Exploring Operation: 76-43=33, Resulting Numbers: [33] 33,14 unequal: No Solution Exploring Operation: 76*43=3268, Resulting Numbers: [3268] 3268,14 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:[78, 7, 48], Operations: ['76-28=48'] Exploring Operation: 78-48=30, Resulting Numbers: [7, 30] Generated Node #0,2,0: 14:[7, 30] Operation: 78-48=30 Exploring Operation: 48-7=41, Resulting Numbers: [78, 41] Generated Node #0,2,1: 14:[78, 41] Operation: 48-7=41 Exploring Operation: 78-7=71, Resulting Numbers: [48, 71] Generated Node #0,2,2: 14:[48, 71] Operation: 78-7=71 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 14:[7, 30], Operations: ['76-28=48', '78-48=30'] Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,14 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,14 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:[78, 41], Operations: ['76-28=48', '48-7=41'] Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,14 unequal: No Solution Exploring Operation: 78*41=3198, Resulting Numbers: [3198] 3198,14 unequal: No Solution Exploring Operation: 78+41=119, Resulting Numbers: [119] 119,14 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:[48, 71], Operations: ['76-28=48', '78-7=71'] Exploring Operation: 48+71=119, Resulting Numbers: [119] 119,14 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 48*71=3408, Resulting Numbers: [3408] 3408,14 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: 14:[7, 14], Operations: ['78-76=2', '28/2=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,14 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,14 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,1,1 Current State: 14:[2, 4], Operations: ['78-76=2', '28/7=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Exploring Operation: 2+4=6, Resulting Numbers: [6] 6,14 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,14 unequal: No Solution Moving to Node #0,1,2 Current State: 14:[2, 21], Operations: ['78-76=2', '28-7=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,14 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,14 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,14 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 88, 54, 92, 9 ]
49
[ "88-54=34", "92-9=83", "83-34=49" ]
Current State: 49:[88, 54, 92, 9], Operations: [] Exploring Operation: 88-54=34, Resulting Numbers: [92, 9, 34] Generated Node #2: [92, 9, 34] from Operation: 88-54=34 Current State: 49:[92, 9, 34], Operations: ['88-54=34'] Exploring Operation: 92-9=83, Resulting Numbers: [34, 83] Generated Node #3: [34, 83] from Operation: 92-9=83 Current State: 49:[34, 83], Operations: ['88-54=34', '92-9=83'] Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[88, 54, 92, 9], Operations: [] Exploring Operation: 92-88=4, Resulting Numbers: [54, 9, 4] Generated Node #0,0: 49:[54, 9, 4] Operation: 92-88=4 Exploring Operation: 88-54=34, Resulting Numbers: [92, 9, 34] Generated Node #0,1: 49:[92, 9, 34] Operation: 88-54=34 Exploring Operation: 92-54=38, Resulting Numbers: [88, 9, 38] Generated Node #0,2: 49:[88, 9, 38] Operation: 92-54=38 Moving to Node #0,0 Current State: 49:[54, 9, 4], Operations: ['92-88=4'] Exploring Operation: 54-9=45, Resulting Numbers: [4, 45] Generated Node #0,0,0: 49:[4, 45] Operation: 54-9=45 Exploring Operation: 54-4=50, Resulting Numbers: [9, 50] Generated Node #0,0,1: 49:[9, 50] Operation: 54-4=50 Exploring Operation: 54/9=6, Resulting Numbers: [4, 6] Generated Node #0,0,2: 49:[4, 6] Operation: 54/9=6 Moving to Node #0,2 Current State: 49:[88, 9, 38], Operations: ['92-54=38'] Exploring Operation: 88-9=79, Resulting Numbers: [38, 79] Generated Node #0,2,0: 49:[38, 79] Operation: 88-9=79 Exploring Operation: 88-38=50, Resulting Numbers: [9, 50] Generated Node #0,2,1: 49:[9, 50] Operation: 88-38=50 Exploring Operation: 9+38=47, Resulting Numbers: [88, 47] Generated Node #0,2,2: 49:[88, 47] Operation: 9+38=47 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 49:[9, 50], Operations: ['92-54=38', '88-38=50'] Exploring Operation: 50-9=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 9+50=59, Resulting Numbers: [59] 59,49 unequal: No Solution Exploring Operation: 9*50=450, Resulting Numbers: [450] 450,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 49:[38, 79], Operations: ['92-54=38', '88-9=79'] Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 38*79=3002, Resulting Numbers: [3002] 3002,49 unequal: No Solution Exploring Operation: 38+79=117, Resulting Numbers: [117] 117,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 49:[88, 47], Operations: ['92-54=38', '9+38=47'] Exploring Operation: 88-47=41, Resulting Numbers: [41] 41,49 unequal: No Solution Exploring Operation: 88*47=4136, Resulting Numbers: [4136] 4136,49 unequal: No Solution Exploring Operation: 88+47=135, Resulting Numbers: [135] 135,49 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: 49:[92, 9, 34], Operations: ['88-54=34'] Exploring Operation: 92-34=58, Resulting Numbers: [9, 58] Generated Node #0,1,0: 49:[9, 58] Operation: 92-34=58 Exploring Operation: 92-9=83, Resulting Numbers: [34, 83] Generated Node #0,1,1: 49:[34, 83] Operation: 92-9=83 Exploring Operation: 9+34=43, Resulting Numbers: [92, 43] Generated Node #0,1,2: 49:[92, 43] Operation: 9+34=43 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 49:[9, 58], Operations: ['88-54=34', '92-34=58'] Exploring Operation: 9+58=67, Resulting Numbers: [67] 67,49 unequal: No Solution Exploring Operation: 9*58=522, Resulting Numbers: [522] 522,49 unequal: No Solution Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Moving to Node #0 Current State: 49:[88, 54, 92, 9], Operations: [] Exploring Operation: 88-54=34, Resulting Numbers: [92, 9, 34] Generated Node #0,1: 49:[92, 9, 34] Operation: 88-54=34 Moving to Node #0,1 Current State: 49:[92, 9, 34], Operations: ['88-54=34'] Exploring Operation: 92-34=58, Resulting Numbers: [9, 58] Generated Node #0,1,0: 49:[9, 58] Operation: 92-34=58 Moving to Node #0,1,0 Current State: 49:[9, 58], Operations: ['88-54=34', '92-34=58'] Exploring Operation: 58-9=49, Resulting Numbers: [49] 49,49 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
mult_heuristic
[ 18, 57, 64, 19 ]
79
[ "18+64=82", "57/19=3", "82-3=79" ]
Current State: 79:[18, 57, 64, 19], Operations: [] Exploring Operation: 18+64=82, Resulting Numbers: [57, 19, 82] Generated Node #2: [57, 19, 82] from Operation: 18+64=82 Current State: 79:[57, 19, 82], Operations: ['18+64=82'] Exploring Operation: 57/19=3, Resulting Numbers: [82, 3] Generated Node #3: [82, 3] from Operation: 57/19=3 Current State: 79:[82, 3], Operations: ['18+64=82', '57/19=3'] Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[18, 57, 64, 19], Operations: [] Exploring Operation: 18+57=75, Resulting Numbers: [64, 19, 75] Generated Node #0,0: 79:[64, 19, 75] Operation: 18+57=75 Moving to Node #0,0 Current State: 79:[64, 19, 75], Operations: ['18+57=75'] Exploring Operation: 64+19=83, Resulting Numbers: [75, 83] Generated Node #0,0,0: 79:[75, 83] Operation: 64+19=83 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 79:[75, 83], Operations: ['18+57=75', '64+19=83'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,79 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
[ 8, 67, 72, 78 ]
81
[ "8+67=75", "78-72=6", "75+6=81" ]
Current State: 81:[8, 67, 72, 78], Operations: [] Exploring Operation: 8+67=75, Resulting Numbers: [72, 78, 75] Generated Node #2: [72, 78, 75] from Operation: 8+67=75 Current State: 81:[72, 78, 75], Operations: ['8+67=75'] Exploring Operation: 78-72=6, Resulting Numbers: [75, 6] Generated Node #3: [75, 6] from Operation: 78-72=6 Current State: 81:[75, 6], Operations: ['8+67=75', '78-72=6'] Exploring Operation: 75+6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[8, 67, 72, 78], Operations: [] Exploring Operation: 8+67=75, Resulting Numbers: [72, 78, 75] Generated Node #0,0: 81:[72, 78, 75] Operation: 8+67=75 Exploring Operation: 72-67=5, Resulting Numbers: [8, 78, 5] Generated Node #0,1: 81:[8, 78, 5] Operation: 72-67=5 Exploring Operation: 78-67=11, Resulting Numbers: [8, 72, 11] Generated Node #0,2: 81:[8, 72, 11] Operation: 78-67=11 Exploring Operation: 72/8=9, Resulting Numbers: [67, 78, 9] Generated Node #0,3: 81:[67, 78, 9] Operation: 72/8=9 Moving to Node #0,1 Current State: 81:[8, 78, 5], Operations: ['72-67=5'] Exploring Operation: 8+78=86, Resulting Numbers: [5, 86] Generated Node #0,1,0: 81:[5, 86] Operation: 8+78=86 Exploring Operation: 78+5=83, Resulting Numbers: [8, 83] Generated Node #0,1,1: 81:[8, 83] Operation: 78+5=83 Exploring Operation: 8+5=13, Resulting Numbers: [78, 13] Generated Node #0,1,2: 81:[78, 13] Operation: 8+5=13 Exploring Operation: 8-5=3, Resulting Numbers: [78, 3] Generated Node #0,1,3: 81:[78, 3] Operation: 8-5=3 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[8, 83], Operations: ['72-67=5', '78+5=83'] Exploring Operation: 8*83=664, Resulting Numbers: [664] 664,81 unequal: No Solution Exploring Operation: 8+83=91, Resulting Numbers: [91] 91,81 unequal: No Solution Exploring Operation: 83-8=75, Resulting Numbers: [75] 75,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 81:[78, 3], Operations: ['72-67=5', '8-5=3'] Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,81 unequal: No Solution Exploring Operation: 78*3=234, Resulting Numbers: [234] 234,81 unequal: No Solution Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[8, 67, 72, 78], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [8, 78, 5] Generated Node #0,1: 81:[8, 78, 5] Operation: 72-67=5 Moving to Node #0,1 Current State: 81:[8, 78, 5], Operations: ['72-67=5'] Exploring Operation: 8-5=3, Resulting Numbers: [78, 3] Generated Node #0,1,3: 81:[78, 3] Operation: 8-5=3 Moving to Node #0,1,3 Current State: 81:[78, 3], Operations: ['72-67=5', '8-5=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 94, 74, 57, 87 ]
85
[ "94-57=37", "74/37=2", "87-2=85" ]
Current State: 85:[94, 74, 57, 87], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [74, 87, 37] Generated Node #2: [74, 87, 37] from Operation: 94-57=37 Current State: 85:[74, 87, 37], Operations: ['94-57=37'] Exploring Operation: 74/37=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 74/37=2 Current State: 85:[87, 2], Operations: ['94-57=37', '74/37=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[94, 74, 57, 87], Operations: [] Exploring Operation: 87-57=30, Resulting Numbers: [94, 74, 30] Generated Node #0,0: 85:[94, 74, 30] Operation: 87-57=30 Exploring Operation: 94-57=37, Resulting Numbers: [74, 87, 37] Generated Node #0,1: 85:[74, 87, 37] Operation: 94-57=37 Exploring Operation: 94-74=20, Resulting Numbers: [57, 87, 20] Generated Node #0,2: 85:[57, 87, 20] Operation: 94-74=20 Exploring Operation: 74-57=17, Resulting Numbers: [94, 87, 17] Generated Node #0,3: 85:[94, 87, 17] Operation: 74-57=17 Moving to Node #0,3 Current State: 85:[94, 87, 17], Operations: ['74-57=17'] Exploring Operation: 94-17=77, Resulting Numbers: [87, 77] Generated Node #0,3,0: 85:[87, 77] Operation: 94-17=77 Exploring Operation: 94+17=111, Resulting Numbers: [87, 111] Generated Node #0,3,1: 85:[87, 111] Operation: 94+17=111 Exploring Operation: 94-87=7, Resulting Numbers: [17, 7] Generated Node #0,3,2: 85:[17, 7] Operation: 94-87=7 Exploring Operation: 87-17=70, Resulting Numbers: [94, 70] Generated Node #0,3,3: 85:[94, 70] Operation: 87-17=70 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[17, 7], Operations: ['74-57=17', '94-87=7'] Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,85 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 #0,3,0 Current State: 85:[87, 77], Operations: ['74-57=17', '94-17=77'] Exploring Operation: 87*77=6699, Resulting Numbers: [6699] 6699,85 unequal: No Solution Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,85 unequal: No Solution Exploring Operation: 87+77=164, Resulting Numbers: [164] 164,85 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:[94, 70], Operations: ['74-57=17', '87-17=70'] Exploring Operation: 94-70=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 94*70=6580, Resulting Numbers: [6580] 6580,85 unequal: No Solution Exploring Operation: 94+70=164, Resulting Numbers: [164] 164,85 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:[87, 111], Operations: ['74-57=17', '94+17=111'] Exploring Operation: 87+111=198, Resulting Numbers: [198] 198,85 unequal: No Solution Exploring Operation: 87*111=9657, Resulting Numbers: [9657] 9657,85 unequal: No Solution Exploring Operation: 111-87=24, Resulting Numbers: [24] 24,85 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: 85:[74, 87, 37], Operations: ['94-57=37'] Exploring Operation: 74-37=37, Resulting Numbers: [87, 37] Generated Node #0,1,0: 85:[87, 37] Operation: 74-37=37 Exploring Operation: 74/37=2, Resulting Numbers: [87, 2] Generated Node #0,1,1: 85:[87, 2] Operation: 74/37=2 Exploring Operation: 87-74=13, Resulting Numbers: [37, 13] Generated Node #0,1,2: 85:[37, 13] Operation: 87-74=13 Exploring Operation: 74+37=111, Resulting Numbers: [87, 111] Generated Node #0,1,3: 85:[87, 111] Operation: 74+37=111 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[87, 2], Operations: ['94-57=37', '74/37=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[94, 74, 57, 87], Operations: [] Exploring Operation: 94-57=37, Resulting Numbers: [74, 87, 37] Generated Node #0,1: 85:[74, 87, 37] Operation: 94-57=37 Moving to Node #0,1 Current State: 85:[74, 87, 37], Operations: ['94-57=37'] Exploring Operation: 74/37=2, Resulting Numbers: [87, 2] Generated Node #0,1,1: 85:[87, 2] Operation: 74/37=2 Moving to Node #0,1,1 Current State: 85:[87, 2], Operations: ['94-57=37', '74/37=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.973958
hs_4
mult_heuristic
[ 97, 99, 2, 56 ]
45
[ "97+56=153", "99*2=198", "198-153=45" ]
Current State: 45:[97, 99, 2, 56], Operations: [] Exploring Operation: 97+56=153, Resulting Numbers: [99, 2, 153] Generated Node #2: [99, 2, 153] from Operation: 97+56=153 Current State: 45:[99, 2, 153], Operations: ['97+56=153'] Exploring Operation: 99*2=198, Resulting Numbers: [153, 198] Generated Node #3: [153, 198] from Operation: 99*2=198 Current State: 45:[153, 198], Operations: ['97+56=153', '99*2=198'] Exploring Operation: 198-153=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[97, 99, 2, 56], Operations: [] Exploring Operation: 99-97=2, Resulting Numbers: [2, 56, 2] Generated Node #0,0: 45:[2, 56, 2] Operation: 99-97=2 Exploring Operation: 99-56=43, Resulting Numbers: [97, 2, 43] Generated Node #0,1: 45:[97, 2, 43] Operation: 99-56=43 Moving to Node #0,0 Current State: 45:[2, 56, 2], Operations: ['99-97=2'] Exploring Operation: 56-2=54, Resulting Numbers: [2, 54] Generated Node #0,0,0: 45:[2, 54] Operation: 56-2=54 Exploring Operation: 56-2=54, Resulting Numbers: [2, 54] Generated Node #0,0,1: 45:[2, 54] Operation: 56-2=54 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 45:[2, 54], Operations: ['99-97=2', '56-2=54'] Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 45:[2, 54], Operations: ['99-97=2', '56-2=54'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,45 unequal: No Solution Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 45:[97, 2, 43], Operations: ['99-56=43'] Exploring Operation: 97-2=95, Resulting Numbers: [43, 95] Generated Node #0,1,0: 45:[43, 95] Operation: 97-2=95 Exploring Operation: 97-43=54, Resulting Numbers: [2, 54] Generated Node #0,1,1: 45:[2, 54] Operation: 97-43=54 Moving to Node #0,1,1 Current State: 45:[2, 54], Operations: ['99-56=43', '97-43=54'] Exploring Operation: 2+54=56, Resulting Numbers: [56] 56,45 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,45 unequal: No Solution Moving to Node #0,1,0 Current State: 45:[43, 95], Operations: ['99-56=43', '97-2=95'] Exploring Operation: 95-43=52, Resulting Numbers: [52] 52,45 unequal: No Solution Exploring Operation: 43+95=138, Resulting Numbers: [138] 138,45 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 83, 62, 48, 46 ]
51
[ "83+62=145", "48+46=94", "145-94=51" ]
Current State: 51:[83, 62, 48, 46], Operations: [] Exploring Operation: 83+62=145, Resulting Numbers: [48, 46, 145] Generated Node #2: [48, 46, 145] from Operation: 83+62=145 Current State: 51:[48, 46, 145], Operations: ['83+62=145'] Exploring Operation: 48+46=94, Resulting Numbers: [145, 94] Generated Node #3: [145, 94] from Operation: 48+46=94 Current State: 51:[145, 94], Operations: ['83+62=145', '48+46=94'] Exploring Operation: 145-94=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[83, 62, 48, 46], Operations: [] Exploring Operation: 62-46=16, Resulting Numbers: [83, 48, 16] Generated Node #0,0: 51:[83, 48, 16] Operation: 62-46=16 Exploring Operation: 83-48=35, Resulting Numbers: [62, 46, 35] Generated Node #0,1: 51:[62, 46, 35] Operation: 83-48=35 Exploring Operation: 83-46=37, Resulting Numbers: [62, 48, 37] Generated Node #0,2: 51:[62, 48, 37] Operation: 83-46=37 Exploring Operation: 83-62=21, Resulting Numbers: [48, 46, 21] Generated Node #0,3: 51:[48, 46, 21] Operation: 83-62=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 51:[48, 46, 21], Operations: ['83-62=21'] Exploring Operation: 46+21=67, Resulting Numbers: [48, 67] Generated Node #0,3,0: 51:[48, 67] Operation: 46+21=67 Exploring Operation: 48-46=2, Resulting Numbers: [21, 2] Generated Node #0,3,1: 51:[21, 2] Operation: 48-46=2 Exploring Operation: 48-21=27, Resulting Numbers: [46, 27] Generated Node #0,3,2: 51:[46, 27] Operation: 48-21=27 Exploring Operation: 46-21=25, Resulting Numbers: [48, 25] Generated Node #0,3,3: 51:[48, 25] Operation: 46-21=25 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 51:[21, 2], Operations: ['83-62=21', '48-46=2'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,51 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 #0,3,3 Current State: 51:[48, 25], Operations: ['83-62=21', '46-21=25'] Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 48*25=1200, Resulting Numbers: [1200] 1200,51 unequal: No Solution Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,51 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 #0,3,2 Current State: 51:[46, 27], Operations: ['83-62=21', '48-21=27'] Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,51 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,51 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 #0,3,0 Current State: 51:[48, 67], Operations: ['83-62=21', '46+21=67'] Exploring Operation: 67-48=19, Resulting Numbers: [19] 19,51 unequal: No Solution Exploring Operation: 48*67=3216, Resulting Numbers: [3216] 3216,51 unequal: No Solution Exploring Operation: 48+67=115, Resulting Numbers: [115] 115,51 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 #0,2 Current State: 51:[62, 48, 37], Operations: ['83-46=37'] Exploring Operation: 48-37=11, Resulting Numbers: [62, 11] Generated Node #0,2,0: 51:[62, 11] Operation: 48-37=11 Exploring Operation: 48+37=85, Resulting Numbers: [62, 85] Generated Node #0,2,1: 51:[62, 85] Operation: 48+37=85 Exploring Operation: 62-37=25, Resulting Numbers: [48, 25] Generated Node #0,2,2: 51:[48, 25] Operation: 62-37=25 Exploring Operation: 62-48=14, Resulting Numbers: [37, 14] Generated Node #0,2,3: 51:[37, 14] Operation: 62-48=14 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 51:[48, 25], Operations: ['83-46=37', '62-37=25'] Exploring Operation: 48+25=73, Resulting Numbers: [73] 73,51 unequal: No Solution Exploring Operation: 48-25=23, Resulting Numbers: [23] 23,51 unequal: No Solution Exploring Operation: 48*25=1200, Resulting Numbers: [1200] 1200,51 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 #0,2,0 Current State: 51:[62, 11], Operations: ['83-46=37', '48-37=11'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[83, 62, 48, 46], Operations: [] Exploring Operation: 83-46=37, Resulting Numbers: [62, 48, 37] Generated Node #0,2: 51:[62, 48, 37] Operation: 83-46=37 Moving to Node #0,2 Current State: 51:[62, 48, 37], Operations: ['83-46=37'] Exploring Operation: 48-37=11, Resulting Numbers: [62, 11] Generated Node #0,2,0: 51:[62, 11] Operation: 48-37=11 Moving to Node #0,2,0 Current State: 51:[62, 11], Operations: ['83-46=37', '48-37=11'] Exploring Operation: 62-11=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.972222
hs_4
mult_heuristic
[ 8, 66, 86, 56 ]
84
[ "66-8=58", "86+56=142", "142-58=84" ]
Current State: 84:[8, 66, 86, 56], Operations: [] Exploring Operation: 66-8=58, Resulting Numbers: [86, 56, 58] Generated Node #2: [86, 56, 58] from Operation: 66-8=58 Current State: 84:[86, 56, 58], Operations: ['66-8=58'] Exploring Operation: 86+56=142, Resulting Numbers: [58, 142] Generated Node #3: [58, 142] from Operation: 86+56=142 Current State: 84:[58, 142], Operations: ['66-8=58', '86+56=142'] Exploring Operation: 142-58=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[8, 66, 86, 56], Operations: [] Exploring Operation: 86-66=20, Resulting Numbers: [8, 56, 20] Generated Node #0,0: 84:[8, 56, 20] Operation: 86-66=20 Exploring Operation: 66-56=10, Resulting Numbers: [8, 86, 10] Generated Node #0,1: 84:[8, 86, 10] Operation: 66-56=10 Exploring Operation: 56/8=7, Resulting Numbers: [66, 86, 7] Generated Node #0,2: 84:[66, 86, 7] Operation: 56/8=7 Exploring Operation: 86-56=30, Resulting Numbers: [8, 66, 30] Generated Node #0,3: 84:[8, 66, 30] Operation: 86-56=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[8, 86, 10], Operations: ['66-56=10'] Exploring Operation: 8*10=80, Resulting Numbers: [86, 80] Generated Node #0,1,0: 84:[86, 80] Operation: 8*10=80 Exploring Operation: 86-8=78, Resulting Numbers: [10, 78] Generated Node #0,1,1: 84:[10, 78] Operation: 86-8=78 Exploring Operation: 10-8=2, Resulting Numbers: [86, 2] Generated Node #0,1,2: 84:[86, 2] Operation: 10-8=2 Exploring Operation: 8+10=18, Resulting Numbers: [86, 18] Generated Node #0,1,3: 84:[86, 18] Operation: 8+10=18 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 84:[86, 2], Operations: ['66-56=10', '10-8=2'] Exploring Operation: 86*2=172, Resulting Numbers: [172] 172,84 unequal: No Solution Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[8, 66, 86, 56], Operations: [] Exploring Operation: 66-56=10, Resulting Numbers: [8, 86, 10] Generated Node #0,1: 84:[8, 86, 10] Operation: 66-56=10 Moving to Node #0,1 Current State: 84:[8, 86, 10], Operations: ['66-56=10'] Exploring Operation: 10-8=2, Resulting Numbers: [86, 2] Generated Node #0,1,2: 84:[86, 2] Operation: 10-8=2 Moving to Node #0,1,2 Current State: 84:[86, 2], Operations: ['66-56=10', '10-8=2'] Exploring Operation: 86-2=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 55, 20, 12, 69 ]
10
[ "55+12=67", "69-67=2", "20/2=10" ]
Current State: 10:[55, 20, 12, 69], Operations: [] Exploring Operation: 55+12=67, Resulting Numbers: [20, 69, 67] Generated Node #2: [20, 69, 67] from Operation: 55+12=67 Current State: 10:[20, 69, 67], Operations: ['55+12=67'] Exploring Operation: 69-67=2, Resulting Numbers: [20, 2] Generated Node #3: [20, 2] from Operation: 69-67=2 Current State: 10:[20, 2], Operations: ['55+12=67', '69-67=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[55, 20, 12, 69], Operations: [] Exploring Operation: 69-20=49, Resulting Numbers: [55, 12, 49] Generated Node #0,0: 10:[55, 12, 49] Operation: 69-20=49 Exploring Operation: 69-12=57, Resulting Numbers: [55, 20, 57] Generated Node #0,1: 10:[55, 20, 57] Operation: 69-12=57 Exploring Operation: 69-55=14, Resulting Numbers: [20, 12, 14] Generated Node #0,2: 10:[20, 12, 14] Operation: 69-55=14 Exploring Operation: 55-20=35, Resulting Numbers: [12, 69, 35] Generated Node #0,3: 10:[12, 69, 35] Operation: 55-20=35 Exploring Operation: 55-12=43, Resulting Numbers: [20, 69, 43] Generated Node #0,4: 10:[20, 69, 43] Operation: 55-12=43 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[20, 12, 14], Operations: ['69-55=14'] Exploring Operation: 20+12=32, Resulting Numbers: [14, 32] Generated Node #0,2,0: 10:[14, 32] Operation: 20+12=32 Exploring Operation: 20-12=8, Resulting Numbers: [14, 8] Generated Node #0,2,1: 10:[14, 8] Operation: 20-12=8 Exploring Operation: 20-14=6, Resulting Numbers: [12, 6] Generated Node #0,2,2: 10:[12, 6] Operation: 20-14=6 Exploring Operation: 20+14=34, Resulting Numbers: [12, 34] Generated Node #0,2,3: 10:[12, 34] Operation: 20+14=34 Exploring Operation: 14-12=2, Resulting Numbers: [20, 2] Generated Node #0,2,4: 10:[20, 2] Operation: 14-12=2 Moving to Node #0,2,2 Current State: 10:[12, 6], Operations: ['69-55=14', '20-14=6'] Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,10 unequal: No Solution Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,10 unequal: No Solution Moving to Node #0,2,1 Current State: 10:[14, 8], Operations: ['69-55=14', '20-12=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,10 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,10 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,10 unequal: No Solution Moving to Node #0,2,4 Current State: 10:[20, 2], Operations: ['69-55=14', '14-12=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,10 unequal: No Solution Exploring Operation: 20*2=40, Resulting Numbers: [40] 40,10 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[55, 20, 12, 69], Operations: [] Exploring Operation: 69-55=14, Resulting Numbers: [20, 12, 14] Generated Node #0,2: 10:[20, 12, 14] Operation: 69-55=14 Moving to Node #0,2 Current State: 10:[20, 12, 14], Operations: ['69-55=14'] Exploring Operation: 14-12=2, Resulting Numbers: [20, 2] Generated Node #0,2,4: 10:[20, 2] Operation: 14-12=2 Moving to Node #0,2,4 Current State: 10:[20, 2], Operations: ['69-55=14', '14-12=2'] Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_5
sum_heuristic
[ 15, 92, 89, 70 ]
52
[ "15+92=107", "89+70=159", "159-107=52" ]
Current State: 52:[15, 92, 89, 70], Operations: [] Exploring Operation: 15+92=107, Resulting Numbers: [89, 70, 107] Generated Node #2: [89, 70, 107] from Operation: 15+92=107 Current State: 52:[89, 70, 107], Operations: ['15+92=107'] Exploring Operation: 89+70=159, Resulting Numbers: [107, 159] Generated Node #3: [107, 159] from Operation: 89+70=159 Current State: 52:[107, 159], Operations: ['15+92=107', '89+70=159'] Exploring Operation: 159-107=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[15, 92, 89, 70], Operations: [] Exploring Operation: 92-70=22, Resulting Numbers: [15, 89, 22] Generated Node #0,0: 52:[15, 89, 22] Operation: 92-70=22 Exploring Operation: 89-70=19, Resulting Numbers: [15, 92, 19] Generated Node #0,1: 52:[15, 92, 19] Operation: 89-70=19 Exploring Operation: 92-15=77, Resulting Numbers: [89, 70, 77] Generated Node #0,2: 52:[89, 70, 77] Operation: 92-15=77 Exploring Operation: 89-15=74, Resulting Numbers: [92, 70, 74] Generated Node #0,3: 52:[92, 70, 74] Operation: 89-15=74 Exploring Operation: 92-89=3, Resulting Numbers: [15, 70, 3] Generated Node #0,4: 52:[15, 70, 3] Operation: 92-89=3 Moving to Node #0,4 Current State: 52:[15, 70, 3], Operations: ['92-89=3'] Exploring Operation: 70-3=67, Resulting Numbers: [15, 67] Generated Node #0,4,0: 52:[15, 67] Operation: 70-3=67 Exploring Operation: 15/3=5, Resulting Numbers: [70, 5] Generated Node #0,4,1: 52:[70, 5] Operation: 15/3=5 Exploring Operation: 15-3=12, Resulting Numbers: [70, 12] Generated Node #0,4,2: 52:[70, 12] Operation: 15-3=12 Exploring Operation: 15+3=18, Resulting Numbers: [70, 18] Generated Node #0,4,3: 52:[70, 18] Operation: 15+3=18 Exploring Operation: 70-15=55, Resulting Numbers: [3, 55] Generated Node #0,4,4: 52:[3, 55] Operation: 70-15=55 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 52:[3, 55], Operations: ['92-89=3', '70-15=55'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[15, 92, 89, 70], Operations: [] Exploring Operation: 92-89=3, Resulting Numbers: [15, 70, 3] Generated Node #0,4: 52:[15, 70, 3] Operation: 92-89=3 Moving to Node #0,4 Current State: 52:[15, 70, 3], Operations: ['92-89=3'] Exploring Operation: 70-15=55, Resulting Numbers: [3, 55] Generated Node #0,4,4: 52:[3, 55] Operation: 70-15=55 Moving to Node #0,4,4 Current State: 52:[3, 55], Operations: ['92-89=3', '70-15=55'] Exploring Operation: 55-3=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 33, 62, 11, 43 ]
61
[ "62-33=29", "43-11=32", "29+32=61" ]
Current State: 61:[33, 62, 11, 43], Operations: [] Exploring Operation: 62-33=29, Resulting Numbers: [11, 43, 29] Generated Node #2: [11, 43, 29] from Operation: 62-33=29 Current State: 61:[11, 43, 29], Operations: ['62-33=29'] Exploring Operation: 43-11=32, Resulting Numbers: [29, 32] Generated Node #3: [29, 32] from Operation: 43-11=32 Current State: 61:[29, 32], Operations: ['62-33=29', '43-11=32'] Exploring Operation: 29+32=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[33, 62, 11, 43], Operations: [] Exploring Operation: 11+43=54, Resulting Numbers: [33, 62, 54] Generated Node #0,0: 61:[33, 62, 54] Operation: 11+43=54 Exploring Operation: 33-11=22, Resulting Numbers: [62, 43, 22] Generated Node #0,1: 61:[62, 43, 22] Operation: 33-11=22 Exploring Operation: 62+11=73, Resulting Numbers: [33, 43, 73] Generated Node #0,2: 61:[33, 43, 73] Operation: 62+11=73 Exploring Operation: 33+11=44, Resulting Numbers: [62, 43, 44] Generated Node #0,3: 61:[62, 43, 44] Operation: 33+11=44 Exploring Operation: 62-11=51, Resulting Numbers: [33, 43, 51] Generated Node #0,4: 61:[33, 43, 51] Operation: 62-11=51 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[33, 62, 54], Operations: ['11+43=54'] Exploring Operation: 33+54=87, Resulting Numbers: [62, 87] Generated Node #0,0,0: 61:[62, 87] Operation: 33+54=87 Exploring Operation: 33+62=95, Resulting Numbers: [54, 95] Generated Node #0,0,1: 61:[54, 95] Operation: 33+62=95 Exploring Operation: 54-33=21, Resulting Numbers: [62, 21] Generated Node #0,0,2: 61:[62, 21] Operation: 54-33=21 Exploring Operation: 62-33=29, Resulting Numbers: [54, 29] Generated Node #0,0,3: 61:[54, 29] Operation: 62-33=29 Exploring Operation: 62-54=8, Resulting Numbers: [33, 8] Generated Node #0,0,4: 61:[33, 8] Operation: 62-54=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 61:[62, 87], Operations: ['11+43=54', '33+54=87'] Exploring Operation: 62+87=149, Resulting Numbers: [149] 149,61 unequal: No Solution Exploring Operation: 62*87=5394, Resulting Numbers: [5394] 5394,61 unequal: No Solution Exploring Operation: 87-62=25, Resulting Numbers: [25] 25,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 61:[54, 29], Operations: ['11+43=54', '62-33=29'] Exploring Operation: 54+29=83, Resulting Numbers: [83] 83,61 unequal: No Solution Exploring Operation: 54*29=1566, Resulting Numbers: [1566] 1566,61 unequal: No Solution Exploring Operation: 54-29=25, Resulting Numbers: [25] 25,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 61:[54, 95], Operations: ['11+43=54', '33+62=95'] Exploring Operation: 95-54=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 54*95=5130, Resulting Numbers: [5130] 5130,61 unequal: No Solution Exploring Operation: 54+95=149, Resulting Numbers: [149] 149,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 61:[62, 21], Operations: ['11+43=54', '54-33=21'] Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,61 unequal: No Solution Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 62*21=1302, Resulting Numbers: [1302] 1302,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 61:[33, 8], Operations: ['11+43=54', '62-54=8'] Exploring Operation: 33+8=41, Resulting Numbers: [41] 41,61 unequal: No Solution Exploring Operation: 33-8=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 33*8=264, Resulting Numbers: [264] 264,61 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 61:[62, 43, 44], Operations: ['33+11=44'] Exploring Operation: 62-44=18, Resulting Numbers: [43, 18] Generated Node #0,3,0: 61:[43, 18] Operation: 62-44=18 Exploring Operation: 43+44=87, Resulting Numbers: [62, 87] Generated Node #0,3,1: 61:[62, 87] Operation: 43+44=87 Exploring Operation: 44-43=1, Resulting Numbers: [62, 1] Generated Node #0,3,2: 61:[62, 1] Operation: 44-43=1 Exploring Operation: 62+43=105, Resulting Numbers: [44, 105] Generated Node #0,3,3: 61:[44, 105] Operation: 62+43=105 Exploring Operation: 62-43=19, Resulting Numbers: [44, 19] Generated Node #0,3,4: 61:[44, 19] Operation: 62-43=19 Moving to Node #0,3,1 Current State: 61:[62, 87], Operations: ['33+11=44', '43+44=87'] Exploring Operation: 87-62=25, Resulting Numbers: [25] 25,61 unequal: No Solution Exploring Operation: 62+87=149, Resulting Numbers: [149] 149,61 unequal: No Solution Exploring Operation: 62*87=5394, Resulting Numbers: [5394] 5394,61 unequal: No Solution Moving to Node #0,3,4 Current State: 61:[44, 19], Operations: ['33+11=44', '62-43=19'] Exploring Operation: 44*19=836, Resulting Numbers: [836] 836,61 unequal: No Solution Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,61 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,61 unequal: No Solution Moving to Node #0,3,0 Current State: 61:[43, 18], Operations: ['33+11=44', '62-44=18'] Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Moving to Node #0 Current State: 61:[33, 62, 11, 43], Operations: [] Exploring Operation: 33+11=44, Resulting Numbers: [62, 43, 44] Generated Node #0,3: 61:[62, 43, 44] Operation: 33+11=44 Moving to Node #0,3 Current State: 61:[62, 43, 44], Operations: ['33+11=44'] Exploring Operation: 62-44=18, Resulting Numbers: [43, 18] Generated Node #0,3,0: 61:[43, 18] Operation: 62-44=18 Moving to Node #0,3,0 Current State: 61:[43, 18], Operations: ['33+11=44', '62-44=18'] Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,61 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 28, 22, 57, 90 ]
72
[ "28-22=6", "90/6=15", "57+15=72" ]
Current State: 72:[28, 22, 57, 90], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [57, 90, 6] Generated Node #2: [57, 90, 6] from Operation: 28-22=6 Current State: 72:[57, 90, 6], Operations: ['28-22=6'] Exploring Operation: 90/6=15, Resulting Numbers: [57, 15] Generated Node #3: [57, 15] from Operation: 90/6=15 Current State: 72:[57, 15], Operations: ['28-22=6', '90/6=15'] Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[28, 22, 57, 90], Operations: [] Exploring Operation: 57-22=35, Resulting Numbers: [28, 90, 35] Generated Node #0,0: 72:[28, 90, 35] Operation: 57-22=35 Exploring Operation: 90-22=68, Resulting Numbers: [28, 57, 68] Generated Node #0,1: 72:[28, 57, 68] Operation: 90-22=68 Exploring Operation: 90-57=33, Resulting Numbers: [28, 22, 33] Generated Node #0,2: 72:[28, 22, 33] Operation: 90-57=33 Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[28, 22, 33], Operations: ['90-57=33'] Exploring Operation: 33-22=11, Resulting Numbers: [28, 11] Generated Node #0,2,0: 72:[28, 11] Operation: 33-22=11 Exploring Operation: 28-22=6, Resulting Numbers: [33, 6] Generated Node #0,2,1: 72:[33, 6] Operation: 28-22=6 Exploring Operation: 33-28=5, Resulting Numbers: [22, 5] Generated Node #0,2,2: 72:[22, 5] Operation: 33-28=5 Moving to Node #0,2,1 Current State: 72:[33, 6], Operations: ['90-57=33', '28-22=6'] Exploring Operation: 33-6=27, Resulting Numbers: [27] 27,72 unequal: No Solution Exploring Operation: 33+6=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 33*6=198, Resulting Numbers: [198] 198,72 unequal: No Solution Moving to Node #0,2,2 Current State: 72:[22, 5], Operations: ['90-57=33', '33-28=5'] Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,72 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,72 unequal: No Solution Moving to Node #0,2,0 Current State: 72:[28, 11], Operations: ['90-57=33', '33-22=11'] Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,72 unequal: No Solution Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,72 unequal: No Solution No 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: 72:[28, 90, 35], Operations: ['57-22=35'] Exploring Operation: 90-28=62, Resulting Numbers: [35, 62] Generated Node #0,0,0: 72:[35, 62] Operation: 90-28=62 Exploring Operation: 90-35=55, Resulting Numbers: [28, 55] Generated Node #0,0,1: 72:[28, 55] Operation: 90-35=55 Exploring Operation: 35-28=7, Resulting Numbers: [90, 7] Generated Node #0,0,2: 72:[90, 7] Operation: 35-28=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[35, 62], Operations: ['57-22=35', '90-28=62'] Exploring Operation: 35*62=2170, Resulting Numbers: [2170] 2170,72 unequal: No Solution Exploring Operation: 35+62=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 72:[90, 7], Operations: ['57-22=35', '35-28=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,72 unequal: No Solution Exploring Operation: 90*7=630, Resulting Numbers: [630] 630,72 unequal: No Solution Exploring Operation: 90+7=97, Resulting Numbers: [97] 97,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 72:[28, 55], Operations: ['57-22=35', '90-35=55'] Exploring Operation: 28*55=1540, Resulting Numbers: [1540] 1540,72 unequal: No Solution Exploring Operation: 28+55=83, Resulting Numbers: [83] 83,72 unequal: No Solution Exploring Operation: 55-28=27, Resulting Numbers: [27] 27,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[28, 57, 68], Operations: ['90-22=68'] Exploring Operation: 68-57=11, Resulting Numbers: [28, 11] Generated Node #0,1,0: 72:[28, 11] Operation: 68-57=11 Exploring Operation: 57-28=29, Resulting Numbers: [68, 29] Generated Node #0,1,1: 72:[68, 29] Operation: 57-28=29 Exploring Operation: 28+57=85, Resulting Numbers: [68, 85] Generated Node #0,1,2: 72:[68, 85] Operation: 28+57=85 Moving to Node #0,1,0 Current State: 72:[28, 11], Operations: ['90-22=68', '68-57=11'] Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,72 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[68, 29], Operations: ['90-22=68', '57-28=29'] Exploring Operation: 68+29=97, Resulting Numbers: [97] 97,72 unequal: No Solution Exploring Operation: 68*29=1972, Resulting Numbers: [1972] 1972,72 unequal: No Solution Exploring Operation: 68-29=39, Resulting Numbers: [39] 39,72 unequal: No Solution Moving to Node #0,1,2 Current State: 72:[68, 85], Operations: ['90-22=68', '28+57=85'] Exploring Operation: 85-68=17, Resulting Numbers: [17] 17,72 unequal: No Solution Exploring Operation: 68+85=153, Resulting Numbers: [153] 153,72 unequal: No Solution Exploring Operation: 68*85=5780, Resulting Numbers: [5780] 5780,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 5, 95, 71, 70 ]
54
[ "95-70=25", "5*25=125", "125-71=54" ]
Current State: 54:[5, 95, 71, 70], Operations: [] Exploring Operation: 95-70=25, Resulting Numbers: [5, 71, 25] Generated Node #2: [5, 71, 25] from Operation: 95-70=25 Current State: 54:[5, 71, 25], Operations: ['95-70=25'] Exploring Operation: 5*25=125, Resulting Numbers: [71, 125] Generated Node #3: [71, 125] from Operation: 5*25=125 Current State: 54:[71, 125], Operations: ['95-70=25', '5*25=125'] Exploring Operation: 125-71=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[5, 95, 71, 70], Operations: [] Exploring Operation: 95-70=25, Resulting Numbers: [5, 71, 25] Generated Node #0,0: 54:[5, 71, 25] Operation: 95-70=25 Exploring Operation: 95-71=24, Resulting Numbers: [5, 70, 24] Generated Node #0,1: 54:[5, 70, 24] Operation: 95-71=24 Moving to Node #0,0 Current State: 54:[5, 71, 25], Operations: ['95-70=25'] Exploring Operation: 71-25=46, Resulting Numbers: [5, 46] Generated Node #0,0,0: 54:[5, 46] Operation: 71-25=46 Exploring Operation: 71-5=66, Resulting Numbers: [25, 66] Generated Node #0,0,1: 54:[25, 66] Operation: 71-5=66 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 54:[5, 46], Operations: ['95-70=25', '71-25=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,54 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[25, 66], Operations: ['95-70=25', '71-5=66'] Exploring Operation: 66-25=41, Resulting Numbers: [41] 41,54 unequal: No Solution Exploring Operation: 25+66=91, Resulting Numbers: [91] 91,54 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: 54:[5, 70, 24], Operations: ['95-71=24'] Exploring Operation: 70/5=14, Resulting Numbers: [24, 14] Generated Node #0,1,0: 54:[24, 14] Operation: 70/5=14 Exploring Operation: 70-24=46, Resulting Numbers: [5, 46] Generated Node #0,1,1: 54:[5, 46] Operation: 70-24=46 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[24, 14], Operations: ['95-71=24', '70/5=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,54 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[5, 46], Operations: ['95-71=24', '70-24=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,54 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,54 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
[ 23, 2, 24, 23 ]
21
[ "23-2=21", "24-23=1", "21*1=21" ]
Current State: 21:[23, 2, 24, 23], Operations: [] Exploring Operation: 23-2=21, Resulting Numbers: [24, 21] Generated Node #2: [24, 21] from Operation: 23-2=21 Current State: 21:[24, 21], Operations: ['23-2=21'] Exploring Operation: 24-23=1, Resulting Numbers: [21, 1] Generated Node #3: [21, 1] from Operation: 24-23=1 Current State: 21:[21, 1], Operations: ['23-2=21', '24-23=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[23, 2, 24, 23], Operations: [] Exploring Operation: 23-2=21, Resulting Numbers: [24, 23, 21] Generated Node #0,0: 21:[24, 23, 21] Operation: 23-2=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[24, 23, 21], Operations: ['23-2=21'] Exploring Operation: 24-23=1, Resulting Numbers: [21, 1] Generated Node #0,0,0: 21:[21, 1] Operation: 24-23=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[21, 1], Operations: ['23-2=21', '24-23=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[23, 2, 24, 23], Operations: [] Exploring Operation: 23-2=21, Resulting Numbers: [24, 23, 21] Generated Node #0,0: 21:[24, 23, 21] Operation: 23-2=21 Moving to Node #0,0 Current State: 21:[24, 23, 21], Operations: ['23-2=21'] Exploring Operation: 24-23=1, Resulting Numbers: [21, 1] Generated Node #0,0,0: 21:[21, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 21:[21, 1], Operations: ['23-2=21', '24-23=1'] Exploring Operation: 21*1=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 49, 41, 96, 3 ]
91
[ "49-41=8", "96+3=99", "99-8=91" ]
Current State: 91:[49, 41, 96, 3], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [96, 3, 8] Generated Node #2: [96, 3, 8] from Operation: 49-41=8 Current State: 91:[96, 3, 8], Operations: ['49-41=8'] Exploring Operation: 96+3=99, Resulting Numbers: [8, 99] Generated Node #3: [8, 99] from Operation: 96+3=99 Current State: 91:[8, 99], Operations: ['49-41=8', '96+3=99'] Exploring Operation: 99-8=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[49, 41, 96, 3], Operations: [] Exploring Operation: 49+41=90, Resulting Numbers: [96, 3, 90] Generated Node #0,0: 91:[96, 3, 90] Operation: 49+41=90 Exploring Operation: 49-3=46, Resulting Numbers: [41, 96, 46] Generated Node #0,1: 91:[41, 96, 46] Operation: 49-3=46 Exploring Operation: 49-41=8, Resulting Numbers: [96, 3, 8] Generated Node #0,2: 91:[96, 3, 8] Operation: 49-41=8 Exploring Operation: 96-49=47, Resulting Numbers: [41, 3, 47] Generated Node #0,3: 91:[41, 3, 47] Operation: 96-49=47 Moving to Node #0,0 Current State: 91:[96, 3, 90], Operations: ['49+41=90'] Exploring Operation: 3+90=93, Resulting Numbers: [96, 93] Generated Node #0,0,0: 91:[96, 93] Operation: 3+90=93 Exploring Operation: 96-3=93, Resulting Numbers: [90, 93] Generated Node #0,0,1: 91:[90, 93] Operation: 96-3=93 Exploring Operation: 96+3=99, Resulting Numbers: [90, 99] Generated Node #0,0,2: 91:[90, 99] Operation: 96+3=99 Exploring Operation: 96-90=6, Resulting Numbers: [3, 6] Generated Node #0,0,3: 91:[3, 6] Operation: 96-90=6 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 91:[90, 93], Operations: ['49+41=90', '96-3=93'] Exploring Operation: 90+93=183, Resulting Numbers: [183] 183,91 unequal: No Solution Exploring Operation: 90*93=8370, Resulting Numbers: [8370] 8370,91 unequal: No Solution Exploring Operation: 93-90=3, Resulting Numbers: [3] 3,91 unequal: No Solution No 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: 91:[3, 6], Operations: ['49+41=90', '96-90=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,91 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,91 unequal: No Solution No 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: 91:[96, 93], Operations: ['49+41=90', '3+90=93'] Exploring Operation: 96-93=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 96*93=8928, Resulting Numbers: [8928] 8928,91 unequal: No Solution Exploring Operation: 96+93=189, Resulting Numbers: [189] 189,91 unequal: No Solution No 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: 91:[90, 99], Operations: ['49+41=90', '96+3=99'] Exploring Operation: 90*99=8910, Resulting Numbers: [8910] 8910,91 unequal: No Solution Exploring Operation: 90+99=189, Resulting Numbers: [189] 189,91 unequal: No Solution Exploring Operation: 99-90=9, Resulting Numbers: [9] 9,91 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: 91:[96, 3, 8], Operations: ['49-41=8'] Exploring Operation: 96-3=93, Resulting Numbers: [8, 93] Generated Node #0,2,0: 91:[8, 93] Operation: 96-3=93 Exploring Operation: 96/8=12, Resulting Numbers: [3, 12] Generated Node #0,2,1: 91:[3, 12] Operation: 96/8=12 Exploring Operation: 96-8=88, Resulting Numbers: [3, 88] Generated Node #0,2,2: 91:[3, 88] Operation: 96-8=88 Exploring Operation: 3+8=11, Resulting Numbers: [96, 11] Generated Node #0,2,3: 91:[96, 11] Operation: 3+8=11 Moving to Node #0,3 Current State: 91:[41, 3, 47], Operations: ['96-49=47'] Exploring Operation: 41+47=88, Resulting Numbers: [3, 88] Generated Node #0,3,0: 91:[3, 88] Operation: 41+47=88 Exploring Operation: 47-41=6, Resulting Numbers: [3, 6] Generated Node #0,3,1: 91:[3, 6] Operation: 47-41=6 Exploring Operation: 47-3=44, Resulting Numbers: [41, 44] Generated Node #0,3,2: 91:[41, 44] Operation: 47-3=44 Exploring Operation: 41-3=38, Resulting Numbers: [47, 38] Generated Node #0,3,3: 91:[47, 38] Operation: 41-3=38 Moving to Node #0,1 Current State: 91:[41, 96, 46], Operations: ['49-3=46'] Exploring Operation: 41+46=87, Resulting Numbers: [96, 87] Generated Node #0,1,0: 91:[96, 87] Operation: 41+46=87 Exploring Operation: 96-41=55, Resulting Numbers: [46, 55] Generated Node #0,1,1: 91:[46, 55] Operation: 96-41=55 Exploring Operation: 46-41=5, Resulting Numbers: [96, 5] Generated Node #0,1,2: 91:[96, 5] Operation: 46-41=5 Exploring Operation: 96-46=50, Resulting Numbers: [41, 50] Generated Node #0,1,3: 91:[41, 50] Operation: 96-46=50 Moving to Node #0,2,0 Current State: 91:[8, 93], Operations: ['49-41=8', '96-3=93'] Exploring Operation: 8+93=101, Resulting Numbers: [101] 101,91 unequal: No Solution Exploring Operation: 8*93=744, Resulting Numbers: [744] 744,91 unequal: No Solution Exploring Operation: 93-8=85, Resulting Numbers: [85] 85,91 unequal: No Solution Moving to Node #0,2,1 Current State: 91:[3, 12], Operations: ['49-41=8', '96/8=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,91 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,91 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[3, 6], Operations: ['96-49=47', '47-41=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,91 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,91 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,91 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[3, 88], Operations: ['49-41=8', '96-8=88'] Exploring Operation: 88-3=85, Resulting Numbers: [85] 85,91 unequal: No Solution Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,91 equal: Goal Reached Moving to Node #0 Current State: 91:[49, 41, 96, 3], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [96, 3, 8] Generated Node #0,2: 91:[96, 3, 8] Operation: 49-41=8 Moving to Node #0,2 Current State: 91:[96, 3, 8], Operations: ['49-41=8'] Exploring Operation: 96-8=88, Resulting Numbers: [3, 88] Generated Node #0,2,2: 91:[3, 88] Operation: 96-8=88 Moving to Node #0,2,2 Current State: 91:[3, 88], Operations: ['49-41=8', '96-8=88'] Exploring Operation: 3+88=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
0.956597
hs_4
sum_heuristic
[ 64, 29, 94, 28 ]
58
[ "94-64=30", "30-28=2", "29*2=58" ]
Current State: 58:[64, 29, 94, 28], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [29, 28, 30] Generated Node #2: [29, 28, 30] from Operation: 94-64=30 Current State: 58:[29, 28, 30], Operations: ['94-64=30'] Exploring Operation: 30-28=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 30-28=2 Current State: 58:[29, 2], Operations: ['94-64=30', '30-28=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[64, 29, 94, 28], Operations: [] Exploring Operation: 94-64=30, Resulting Numbers: [29, 28, 30] Generated Node #0,0: 58:[29, 28, 30] Operation: 94-64=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[29, 28, 30], Operations: ['94-64=30'] Exploring Operation: 28+30=58, Resulting Numbers: [29, 58] Generated Node #0,0,0: 58:[29, 58] Operation: 28+30=58 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[29, 58], Operations: ['94-64=30', '28+30=58'] Exploring Operation: 58-29=29, Resulting Numbers: [29] 29,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 55, 73, 64, 59 ]
23
[ "73-55=18", "64-59=5", "18+5=23" ]
Current State: 23:[55, 73, 64, 59], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [64, 59, 18] Generated Node #2: [64, 59, 18] from Operation: 73-55=18 Current State: 23:[64, 59, 18], Operations: ['73-55=18'] Exploring Operation: 64-59=5, Resulting Numbers: [18, 5] Generated Node #3: [18, 5] from Operation: 64-59=5 Current State: 23:[18, 5], Operations: ['73-55=18', '64-59=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[55, 73, 64, 59], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [64, 59, 18] Generated Node #0,0: 23:[64, 59, 18] Operation: 73-55=18 Exploring Operation: 73-64=9, Resulting Numbers: [55, 59, 9] Generated Node #0,1: 23:[55, 59, 9] Operation: 73-64=9 Exploring Operation: 73-59=14, Resulting Numbers: [55, 64, 14] Generated Node #0,2: 23:[55, 64, 14] Operation: 73-59=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[64, 59, 18], Operations: ['73-55=18'] Exploring Operation: 59-18=41, Resulting Numbers: [64, 41] Generated Node #0,0,0: 23:[64, 41] Operation: 59-18=41 Exploring Operation: 64-18=46, Resulting Numbers: [59, 46] Generated Node #0,0,1: 23:[59, 46] Operation: 64-18=46 Exploring Operation: 64-59=5, Resulting Numbers: [18, 5] Generated Node #0,0,2: 23:[18, 5] Operation: 64-59=5 Moving to Node #0,0,2 Current State: 23:[18, 5], Operations: ['73-55=18', '64-59=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[55, 73, 64, 59], Operations: [] Exploring Operation: 73-55=18, Resulting Numbers: [64, 59, 18] Generated Node #0,0: 23:[64, 59, 18] Operation: 73-55=18 Moving to Node #0,0 Current State: 23:[64, 59, 18], Operations: ['73-55=18'] Exploring Operation: 64-59=5, Resulting Numbers: [18, 5] Generated Node #0,0,2: 23:[18, 5] Operation: 64-59=5 Moving to Node #0,0,2 Current State: 23:[18, 5], Operations: ['73-55=18', '64-59=5'] Exploring Operation: 18+5=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 62, 84, 43, 9 ]
94
[ "62+84=146", "43+9=52", "146-52=94" ]
Current State: 94:[62, 84, 43, 9], Operations: [] Exploring Operation: 62+84=146, Resulting Numbers: [43, 9, 146] Generated Node #2: [43, 9, 146] from Operation: 62+84=146 Current State: 94:[43, 9, 146], Operations: ['62+84=146'] Exploring Operation: 43+9=52, Resulting Numbers: [146, 52] Generated Node #3: [146, 52] from Operation: 43+9=52 Current State: 94:[146, 52], Operations: ['62+84=146', '43+9=52'] Exploring Operation: 146-52=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[62, 84, 43, 9], Operations: [] Exploring Operation: 62+43=105, Resulting Numbers: [84, 9, 105] Generated Node #0,0: 94:[84, 9, 105] Operation: 62+43=105 Exploring Operation: 84+9=93, Resulting Numbers: [62, 43, 93] Generated Node #0,1: 94:[62, 43, 93] Operation: 84+9=93 Exploring Operation: 62-9=53, Resulting Numbers: [84, 43, 53] Generated Node #0,2: 94:[84, 43, 53] Operation: 62-9=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[62, 43, 93], Operations: ['84+9=93'] Exploring Operation: 62-43=19, Resulting Numbers: [93, 19] Generated Node #0,1,0: 94:[93, 19] Operation: 62-43=19 Exploring Operation: 62+43=105, Resulting Numbers: [93, 105] Generated Node #0,1,1: 94:[93, 105] Operation: 62+43=105 Exploring Operation: 93-43=50, Resulting Numbers: [62, 50] Generated Node #0,1,2: 94:[62, 50] Operation: 93-43=50 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 94:[93, 105], Operations: ['84+9=93', '62+43=105'] Exploring Operation: 93*105=9765, Resulting Numbers: [9765] 9765,94 unequal: No Solution Exploring Operation: 105-93=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 93+105=198, Resulting Numbers: [198] 198,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 94:[93, 19], Operations: ['84+9=93', '62-43=19'] Exploring Operation: 93*19=1767, Resulting Numbers: [1767] 1767,94 unequal: No Solution Exploring Operation: 93-19=74, Resulting Numbers: [74] 74,94 unequal: No Solution Exploring Operation: 93+19=112, Resulting Numbers: [112] 112,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 94:[62, 50], Operations: ['84+9=93', '93-43=50'] Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 62+50=112, Resulting Numbers: [112] 112,94 unequal: No Solution Exploring Operation: 62*50=3100, Resulting Numbers: [3100] 3100,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[84, 43, 53], Operations: ['62-9=53'] Exploring Operation: 43+53=96, Resulting Numbers: [84, 96] Generated Node #0,2,0: 94:[84, 96] Operation: 43+53=96 Exploring Operation: 53-43=10, Resulting Numbers: [84, 10] Generated Node #0,2,1: 94:[84, 10] Operation: 53-43=10 Exploring Operation: 84-43=41, Resulting Numbers: [53, 41] Generated Node #0,2,2: 94:[53, 41] Operation: 84-43=41 Moving to Node #0,2,0 Current State: 94:[84, 96], Operations: ['62-9=53', '43+53=96'] Exploring Operation: 84+96=180, Resulting Numbers: [180] 180,94 unequal: No Solution Exploring Operation: 96-84=12, Resulting Numbers: [12] 12,94 unequal: No Solution Exploring Operation: 84*96=8064, Resulting Numbers: [8064] 8064,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[53, 41], Operations: ['62-9=53', '84-43=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[62, 84, 43, 9], Operations: [] Exploring Operation: 62-9=53, Resulting Numbers: [84, 43, 53] Generated Node #0,2: 94:[84, 43, 53] Operation: 62-9=53 Moving to Node #0,2 Current State: 94:[84, 43, 53], Operations: ['62-9=53'] Exploring Operation: 84-43=41, Resulting Numbers: [53, 41] Generated Node #0,2,2: 94:[53, 41] Operation: 84-43=41 Moving to Node #0,2,2 Current State: 94:[53, 41], Operations: ['62-9=53', '84-43=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
sum_heuristic
[ 87, 7, 70, 39 ]
15
[ "87+7=94", "70+39=109", "109-94=15" ]
Current State: 15:[87, 7, 70, 39], Operations: [] Exploring Operation: 87+7=94, Resulting Numbers: [70, 39, 94] Generated Node #2: [70, 39, 94] from Operation: 87+7=94 Current State: 15:[70, 39, 94], Operations: ['87+7=94'] Exploring Operation: 70+39=109, Resulting Numbers: [94, 109] Generated Node #3: [94, 109] from Operation: 70+39=109 Current State: 15:[94, 109], Operations: ['87+7=94', '70+39=109'] Exploring Operation: 109-94=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[87, 7, 70, 39], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [7, 39, 17] Generated Node #0,0: 15:[7, 39, 17] Operation: 87-70=17 Exploring Operation: 70-39=31, Resulting Numbers: [87, 7, 31] Generated Node #0,1: 15:[87, 7, 31] Operation: 70-39=31 Exploring Operation: 87-39=48, Resulting Numbers: [7, 70, 48] Generated Node #0,2: 15:[7, 70, 48] Operation: 87-39=48 Moving to Node #0,0 Current State: 15:[7, 39, 17], Operations: ['87-70=17'] Exploring Operation: 17-7=10, Resulting Numbers: [39, 10] Generated Node #0,0,0: 15:[39, 10] Operation: 17-7=10 Exploring Operation: 39-7=32, Resulting Numbers: [17, 32] Generated Node #0,0,1: 15:[17, 32] Operation: 39-7=32 Exploring Operation: 39-17=22, Resulting Numbers: [7, 22] Generated Node #0,0,2: 15:[7, 22] Operation: 39-17=22 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[7, 22], Operations: ['87-70=17', '39-17=22'] Exploring Operation: 7*22=154, Resulting Numbers: [154] 154,15 unequal: No Solution Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[87, 7, 70, 39], Operations: [] Exploring Operation: 87-70=17, Resulting Numbers: [7, 39, 17] Generated Node #0,0: 15:[7, 39, 17] Operation: 87-70=17 Moving to Node #0,0 Current State: 15:[7, 39, 17], Operations: ['87-70=17'] Exploring Operation: 39-17=22, Resulting Numbers: [7, 22] Generated Node #0,0,2: 15:[7, 22] Operation: 39-17=22 Moving to Node #0,0,2 Current State: 15:[7, 22], Operations: ['87-70=17', '39-17=22'] Exploring Operation: 22-7=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 25, 22, 19, 11 ]
69
[ "25*22=550", "550/11=50", "19+50=69" ]
Current State: 69:[25, 22, 19, 11], Operations: [] Exploring Operation: 25*22=550, Resulting Numbers: [19, 11, 550] Generated Node #2: [19, 11, 550] from Operation: 25*22=550 Current State: 69:[19, 11, 550], Operations: ['25*22=550'] Exploring Operation: 550/11=50, Resulting Numbers: [19, 50] Generated Node #3: [19, 50] from Operation: 550/11=50 Current State: 69:[19, 50], Operations: ['25*22=550', '550/11=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[25, 22, 19, 11], Operations: [] Exploring Operation: 19+11=30, Resulting Numbers: [25, 22, 30] Generated Node #0,0: 69:[25, 22, 30] Operation: 19+11=30 Exploring Operation: 22/11=2, Resulting Numbers: [25, 19, 2] Generated Node #0,1: 69:[25, 19, 2] Operation: 22/11=2 Exploring Operation: 22-19=3, Resulting Numbers: [25, 11, 3] Generated Node #0,2: 69:[25, 11, 3] Operation: 22-19=3 Exploring Operation: 25-22=3, Resulting Numbers: [19, 11, 3] Generated Node #0,3: 69:[19, 11, 3] Operation: 25-22=3 Exploring Operation: 19-11=8, Resulting Numbers: [25, 22, 8] Generated Node #0,4: 69:[25, 22, 8] Operation: 19-11=8 Moving to Node #0,1 Current State: 69:[25, 19, 2], Operations: ['22/11=2'] Exploring Operation: 25-2=23, Resulting Numbers: [19, 23] Generated Node #0,1,0: 69:[19, 23] Operation: 25-2=23 Exploring Operation: 19+2=21, Resulting Numbers: [25, 21] Generated Node #0,1,1: 69:[25, 21] Operation: 19+2=21 Exploring Operation: 25-19=6, Resulting Numbers: [2, 6] Generated Node #0,1,2: 69:[2, 6] Operation: 25-19=6 Exploring Operation: 19-2=17, Resulting Numbers: [25, 17] Generated Node #0,1,3: 69:[25, 17] Operation: 19-2=17 Exploring Operation: 25+2=27, Resulting Numbers: [19, 27] Generated Node #0,1,4: 69:[19, 27] Operation: 25+2=27 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[19, 23], Operations: ['22/11=2', '25-2=23'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[25, 21], Operations: ['22/11=2', '19+2=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,69 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[2, 6], Operations: ['22/11=2', '25-19=6'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[25, 17], Operations: ['22/11=2', '19-2=17'] Exploring Operation: 25+17=42, Resulting Numbers: [42] 42,69 unequal: No Solution Exploring Operation: 25*17=425, Resulting Numbers: [425] 425,69 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 69:[19, 27], Operations: ['22/11=2', '25+2=27'] Exploring Operation: 19*27=513, Resulting Numbers: [513] 513,69 unequal: No Solution Exploring Operation: 27-19=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 19+27=46, Resulting Numbers: [46] 46,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 69:[25, 22, 8], Operations: ['19-11=8'] Exploring Operation: 22+8=30, Resulting Numbers: [25, 30] Generated Node #0,4,0: 69:[25, 30] Operation: 22+8=30 Exploring Operation: 25+8=33, Resulting Numbers: [22, 33] Generated Node #0,4,1: 69:[22, 33] Operation: 25+8=33 Exploring Operation: 25-8=17, Resulting Numbers: [22, 17] Generated Node #0,4,2: 69:[22, 17] Operation: 25-8=17 Exploring Operation: 22-8=14, Resulting Numbers: [25, 14] Generated Node #0,4,3: 69:[25, 14] Operation: 22-8=14 Exploring Operation: 25-22=3, Resulting Numbers: [8, 3] Generated Node #0,4,4: 69:[8, 3] Operation: 25-22=3 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 69:[8, 3], Operations: ['19-11=8', '25-22=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,69 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 #0,4,2 Current State: 69:[22, 17], Operations: ['19-11=8', '25-8=17'] Exploring Operation: 22-17=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 22*17=374, Resulting Numbers: [374] 374,69 unequal: No Solution Exploring Operation: 22+17=39, Resulting Numbers: [39] 39,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 69:[25, 30], Operations: ['19-11=8', '22+8=30'] Exploring Operation: 30-25=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 25+30=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 25*30=750, Resulting Numbers: [750] 750,69 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 #0,4,1 Current State: 69:[22, 33], Operations: ['19-11=8', '25+8=33'] Exploring Operation: 22+33=55, Resulting Numbers: [55] 55,69 unequal: No Solution Exploring Operation: 22*33=726, Resulting Numbers: [726] 726,69 unequal: No Solution Exploring Operation: 33-22=11, Resulting Numbers: [11] 11,69 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 #0,4,3 Current State: 69:[25, 14], Operations: ['19-11=8', '22-8=14'] Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 25+14=39, Resulting Numbers: [39] 39,69 unequal: No Solution Exploring Operation: 25*14=350, Resulting Numbers: [350] 350,69 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: 69:[25, 22, 30], Operations: ['19+11=30'] Exploring Operation: 25-22=3, Resulting Numbers: [30, 3] Generated Node #0,0,0: 69:[30, 3] Operation: 25-22=3 Exploring Operation: 22+30=52, Resulting Numbers: [25, 52] Generated Node #0,0,1: 69:[25, 52] Operation: 22+30=52 Exploring Operation: 30-22=8, Resulting Numbers: [25, 8] Generated Node #0,0,2: 69:[25, 8] Operation: 30-22=8 Exploring Operation: 30-25=5, Resulting Numbers: [22, 5] Generated Node #0,0,3: 69:[22, 5] Operation: 30-25=5 Exploring Operation: 25+30=55, Resulting Numbers: [22, 55] Generated Node #0,0,4: 69:[22, 55] Operation: 25+30=55 Moving to Node #0,2 Current State: 69:[25, 11, 3], Operations: ['22-19=3'] Exploring Operation: 11*3=33, Resulting Numbers: [25, 33] Generated Node #0,2,0: 69:[25, 33] Operation: 11*3=33 Exploring Operation: 25-3=22, Resulting Numbers: [11, 22] Generated Node #0,2,1: 69:[11, 22] Operation: 25-3=22 Exploring Operation: 25-11=14, Resulting Numbers: [3, 14] Generated Node #0,2,2: 69:[3, 14] Operation: 25-11=14 Exploring Operation: 11+3=14, Resulting Numbers: [25, 14] Generated Node #0,2,3: 69:[25, 14] Operation: 11+3=14 Exploring Operation: 11-3=8, Resulting Numbers: [25, 8] Generated Node #0,2,4: 69:[25, 8] Operation: 11-3=8 Moving to Node #0,3 Current State: 69:[19, 11, 3], Operations: ['25-22=3'] Exploring Operation: 19+3=22, Resulting Numbers: [11, 22] Generated Node #0,3,0: 69:[11, 22] Operation: 19+3=22 Exploring Operation: 19-11=8, Resulting Numbers: [3, 8] Generated Node #0,3,1: 69:[3, 8] Operation: 19-11=8 Exploring Operation: 19+11=30, Resulting Numbers: [3, 30] Generated Node #0,3,2: 69:[3, 30] Operation: 19+11=30 Exploring Operation: 11+3=14, Resulting Numbers: [19, 14] Generated Node #0,3,3: 69:[19, 14] Operation: 11+3=14 Exploring Operation: 11-3=8, Resulting Numbers: [19, 8] Generated Node #0,3,4: 69:[19, 8] Operation: 11-3=8 Moving to Node #0,0,3 Current State: 69:[22, 5], Operations: ['19+11=30', '30-25=5'] Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,69 unequal: No Solution Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[3, 8], Operations: ['25-22=3', '19-11=8'] Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[25, 8], Operations: ['19+11=30', '30-22=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,69 unequal: No Solution Moving to Node #0,2,4 Current State: 69:[25, 8], Operations: ['22-19=3', '11-3=8'] Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[3, 30], Operations: ['25-22=3', '19+11=30'] Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,69 unequal: No Solution Exploring Operation: 3*30=90, Resulting Numbers: [90] 90,69 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[30, 3], Operations: ['19+11=30', '25-22=3'] Exploring Operation: 30*3=90, Resulting Numbers: [90] 90,69 unequal: No Solution Exploring Operation: 30+3=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 30-3=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,69 unequal: No Solution Moving to Node #0,2,1 Current State: 69:[11, 22], Operations: ['22-19=3', '25-3=22'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[11, 22], Operations: ['25-22=3', '19+3=22'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,69 unequal: No Solution Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,69 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[19, 8], Operations: ['25-22=3', '11-3=8'] Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,69 unequal: No Solution Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[3, 14], Operations: ['22-19=3', '25-11=14'] Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,69 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[25, 14], Operations: ['22-19=3', '11+3=14'] Exploring Operation: 25*14=350, Resulting Numbers: [350] 350,69 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,69 unequal: No Solution Exploring Operation: 25+14=39, Resulting Numbers: [39] 39,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[25, 33], Operations: ['22-19=3', '11*3=33'] Exploring Operation: 33-25=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 25+33=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 25*33=825, Resulting Numbers: [825] 825,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[19, 14], Operations: ['25-22=3', '11+3=14'] Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 19+14=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 19*14=266, Resulting Numbers: [266] 266,69 unequal: No Solution Moving to Node #0,0,4 Current State: 69:[22, 55], Operations: ['19+11=30', '25+30=55'] Exploring Operation: 22*55=1210, Resulting Numbers: [1210] 1210,69 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 22+55=77, Resulting Numbers: [77] 77,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[25, 52], Operations: ['19+11=30', '22+30=52'] Exploring Operation: 25+52=77, Resulting Numbers: [77] 77,69 unequal: No Solution Exploring Operation: 25*52=1300, Resulting Numbers: [1300] 1300,69 unequal: No Solution Exploring Operation: 52-25=27, Resulting Numbers: [27] 27,69 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 83, 2, 80, 46 ]
15
[ "80-46=34", "2*34=68", "83-68=15" ]
Current State: 15:[83, 2, 80, 46], Operations: [] Exploring Operation: 80-46=34, Resulting Numbers: [83, 2, 34] Generated Node #2: [83, 2, 34] from Operation: 80-46=34 Current State: 15:[83, 2, 34], Operations: ['80-46=34'] Exploring Operation: 2*34=68, Resulting Numbers: [83, 68] Generated Node #3: [83, 68] from Operation: 2*34=68 Current State: 15:[83, 68], Operations: ['80-46=34', '2*34=68'] Exploring Operation: 83-68=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[83, 2, 80, 46], Operations: [] Exploring Operation: 83-46=37, Resulting Numbers: [2, 80, 37] Generated Node #0,0: 15:[2, 80, 37] Operation: 83-46=37 Exploring Operation: 83-80=3, Resulting Numbers: [2, 46, 3] Generated Node #0,1: 15:[2, 46, 3] Operation: 83-80=3 Exploring Operation: 46/2=23, Resulting Numbers: [83, 80, 23] Generated Node #0,2: 15:[83, 80, 23] Operation: 46/2=23 Exploring Operation: 80-46=34, Resulting Numbers: [83, 2, 34] Generated Node #0,3: 15:[83, 2, 34] Operation: 80-46=34 Exploring Operation: 80/2=40, Resulting Numbers: [83, 46, 40] Generated Node #0,4: 15:[83, 46, 40] Operation: 80/2=40 Start Sub Search at level 1: Moving to Node #0,1 Current State: 15:[2, 46, 3], Operations: ['83-80=3'] Exploring Operation: 46/2=23, Resulting Numbers: [3, 23] Generated Node #0,1,0: 15:[3, 23] Operation: 46/2=23 Exploring Operation: 46-3=43, Resulting Numbers: [2, 43] Generated Node #0,1,1: 15:[2, 43] Operation: 46-3=43 Exploring Operation: 2+3=5, Resulting Numbers: [46, 5] Generated Node #0,1,2: 15:[46, 5] Operation: 2+3=5 Exploring Operation: 46-2=44, Resulting Numbers: [3, 44] Generated Node #0,1,3: 15:[3, 44] Operation: 46-2=44 Exploring Operation: 2*3=6, Resulting Numbers: [46, 6] Generated Node #0,1,4: 15:[46, 6] Operation: 2*3=6 Moving to Node #0,1,0 Current State: 15:[3, 23], Operations: ['83-80=3', '46/2=23'] Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 3*23=69, Resulting Numbers: [69] 69,15 unequal: No Solution Exploring Operation: 3+23=26, Resulting Numbers: [26] 26,15 unequal: No Solution Moving to Node #0,1,3 Current State: 15:[3, 44], Operations: ['83-80=3', '46-2=44'] Exploring Operation: 3+44=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 44-3=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 3*44=132, Resulting Numbers: [132] 132,15 unequal: No Solution Moving to Node #0,1,1 Current State: 15:[2, 43], Operations: ['83-80=3', '46-3=43'] Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,15 unequal: No Solution Moving to Node #0,1,2 Current State: 15:[46, 5], Operations: ['83-80=3', '2+3=5'] Exploring Operation: 46+5=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 46*5=230, Resulting Numbers: [230] 230,15 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,15 unequal: No Solution Moving to Node #0,1,4 Current State: 15:[46, 6], Operations: ['83-80=3', '2*3=6'] Exploring Operation: 46+6=52, Resulting Numbers: [52] 52,15 unequal: No Solution Exploring Operation: 46-6=40, Resulting Numbers: [40] 40,15 unequal: No Solution Exploring Operation: 46*6=276, Resulting Numbers: [276] 276,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 15:[2, 80, 37], Operations: ['83-46=37'] Exploring Operation: 80/2=40, Resulting Numbers: [37, 40] Generated Node #0,0,0: 15:[37, 40] Operation: 80/2=40 Exploring Operation: 80-2=78, Resulting Numbers: [37, 78] Generated Node #0,0,1: 15:[37, 78] Operation: 80-2=78 Exploring Operation: 2+80=82, Resulting Numbers: [37, 82] Generated Node #0,0,2: 15:[37, 82] Operation: 2+80=82 Exploring Operation: 80-37=43, Resulting Numbers: [2, 43] Generated Node #0,0,3: 15:[2, 43] Operation: 80-37=43 Exploring Operation: 37-2=35, Resulting Numbers: [80, 35] Generated Node #0,0,4: 15:[80, 35] Operation: 37-2=35 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 15:[2, 43], Operations: ['83-46=37', '80-37=43'] Exploring Operation: 2+43=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 43-2=41, Resulting Numbers: [41] 41,15 unequal: No Solution Exploring Operation: 2*43=86, Resulting Numbers: [86] 86,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 15:[37, 40], Operations: ['83-46=37', '80/2=40'] Exploring Operation: 37*40=1480, Resulting Numbers: [1480] 1480,15 unequal: No Solution Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 37+40=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 15:[37, 78], Operations: ['83-46=37', '80-2=78'] Exploring Operation: 37*78=2886, Resulting Numbers: [2886] 2886,15 unequal: No Solution Exploring Operation: 37+78=115, Resulting Numbers: [115] 115,15 unequal: No Solution Exploring Operation: 78-37=41, Resulting Numbers: [41] 41,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 15:[80, 35], Operations: ['83-46=37', '37-2=35'] Exploring Operation: 80-35=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 80+35=115, Resulting Numbers: [115] 115,15 unequal: No Solution Exploring Operation: 80*35=2800, Resulting Numbers: [2800] 2800,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 15:[37, 82], Operations: ['83-46=37', '2+80=82'] Exploring Operation: 37+82=119, Resulting Numbers: [119] 119,15 unequal: No Solution Exploring Operation: 82-37=45, Resulting Numbers: [45] 45,15 unequal: No Solution Exploring Operation: 37*82=3034, Resulting Numbers: [3034] 3034,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 15:[83, 2, 34], Operations: ['80-46=34'] Exploring Operation: 83-2=81, Resulting Numbers: [34, 81] Generated Node #0,3,0: 15:[34, 81] Operation: 83-2=81 Exploring Operation: 34/2=17, Resulting Numbers: [83, 17] Generated Node #0,3,1: 15:[83, 17] Operation: 34/2=17 Exploring Operation: 83-34=49, Resulting Numbers: [2, 49] Generated Node #0,3,2: 15:[2, 49] Operation: 83-34=49 Exploring Operation: 34-2=32, Resulting Numbers: [83, 32] Generated Node #0,3,3: 15:[83, 32] Operation: 34-2=32 Exploring Operation: 83+2=85, Resulting Numbers: [34, 85] Generated Node #0,3,4: 15:[34, 85] Operation: 83+2=85 Moving to Node #0,3,2 Current State: 15:[2, 49], Operations: ['80-46=34', '83-34=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,15 unequal: No Solution Moving to Node #0,3,1 Current State: 15:[83, 17], Operations: ['80-46=34', '34/2=17'] Exploring Operation: 83+17=100, Resulting Numbers: [100] 100,15 unequal: No Solution Exploring Operation: 83-17=66, Resulting Numbers: [66] 66,15 unequal: No Solution Exploring Operation: 83*17=1411, Resulting Numbers: [1411] 1411,15 unequal: No Solution Moving to Node #0,3,0 Current State: 15:[34, 81], Operations: ['80-46=34', '83-2=81'] Exploring Operation: 81-34=47, Resulting Numbers: [47] 47,15 unequal: No Solution Exploring Operation: 34+81=115, Resulting Numbers: [115] 115,15 unequal: No Solution Exploring Operation: 34*81=2754, Resulting Numbers: [2754] 2754,15 unequal: No Solution Moving to Node #0,3,3 Current State: 15:[83, 32], Operations: ['80-46=34', '34-2=32'] Exploring Operation: 83+32=115, Resulting Numbers: [115] 115,15 unequal: No Solution Exploring Operation: 83-32=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 83*32=2656, Resulting Numbers: [2656] 2656,15 unequal: No Solution Moving to Node #0,3,4 Current State: 15:[34, 85], Operations: ['80-46=34', '83+2=85'] Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,15 unequal: No Solution Exploring Operation: 34*85=2890, Resulting Numbers: [2890] 2890,15 unequal: No Solution Exploring Operation: 34+85=119, Resulting Numbers: [119] 119,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 15:[83, 46, 40], Operations: ['80/2=40'] Exploring Operation: 46-40=6, Resulting Numbers: [83, 6] Generated Node #0,4,0: 15:[83, 6] Operation: 46-40=6 Exploring Operation: 83+46=129, Resulting Numbers: [40, 129] Generated Node #0,4,1: 15:[40, 129] Operation: 83+46=129 Exploring Operation: 83-40=43, Resulting Numbers: [46, 43] Generated Node #0,4,2: 15:[46, 43] Operation: 83-40=43 Exploring Operation: 83-46=37, Resulting Numbers: [40, 37] Generated Node #0,4,3: 15:[40, 37] Operation: 83-46=37 Exploring Operation: 83+40=123, Resulting Numbers: [46, 123] Generated Node #0,4,4: 15:[46, 123] Operation: 83+40=123 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 15:[40, 37], Operations: ['80/2=40', '83-46=37'] Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 15:[46, 43], Operations: ['80/2=40', '83-40=43'] Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,15 unequal: No Solution Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,15 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 15:[83, 6], Operations: ['80/2=40', '46-40=6'] Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,15 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 15:[40, 129], Operations: ['80/2=40', '83+46=129'] Exploring Operation: 40*129=5160, Resulting Numbers: [5160] 5160,15 unequal: No Solution Exploring Operation: 40+129=169, Resulting Numbers: [169] 169,15 unequal: No Solution Exploring Operation: 129-40=89, Resulting Numbers: [89] 89,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 15:[46, 123], Operations: ['80/2=40', '83+40=123'] Exploring Operation: 123-46=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 46+123=169, Resulting Numbers: [169] 169,15 unequal: No Solution Exploring Operation: 46*123=5658, Resulting Numbers: [5658] 5658,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 15:[83, 80, 23], Operations: ['46/2=23'] Exploring Operation: 83-80=3, Resulting Numbers: [23, 3] Generated Node #0,2,0: 15:[23, 3] Operation: 83-80=3 Exploring Operation: 83+23=106, Resulting Numbers: [80, 106] Generated Node #0,2,1: 15:[80, 106] Operation: 83+23=106 Exploring Operation: 83+80=163, Resulting Numbers: [23, 163] Generated Node #0,2,2: 15:[23, 163] Operation: 83+80=163 Exploring Operation: 80-23=57, Resulting Numbers: [83, 57] Generated Node #0,2,3: 15:[83, 57] Operation: 80-23=57 Exploring Operation: 83-23=60, Resulting Numbers: [80, 60] Generated Node #0,2,4: 15:[80, 60] Operation: 83-23=60 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 15:[23, 3], Operations: ['46/2=23', '83-80=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 15:[83, 57], Operations: ['46/2=23', '80-23=57'] Exploring Operation: 83+57=140, Resulting Numbers: [140] 140,15 unequal: No Solution Exploring Operation: 83-57=26, Resulting Numbers: [26] 26,15 unequal: No Solution Exploring Operation: 83*57=4731, Resulting Numbers: [4731] 4731,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 15:[80, 60], Operations: ['46/2=23', '83-23=60'] Exploring Operation: 80+60=140, Resulting Numbers: [140] 140,15 unequal: No Solution Exploring Operation: 80-60=20, Resulting Numbers: [20] 20,15 unequal: No Solution Exploring Operation: 80*60=4800, Resulting Numbers: [4800] 4800,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 15:[80, 106], Operations: ['46/2=23', '83+23=106'] Exploring Operation: 80+106=186, Resulting Numbers: [186] 186,15 unequal: No Solution Exploring Operation: 80*106=8480, Resulting Numbers: [8480] 8480,15 unequal: No Solution Exploring Operation: 106-80=26, Resulting Numbers: [26] 26,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 15:[23, 163], Operations: ['46/2=23', '83+80=163'] Exploring Operation: 23*163=3749, Resulting Numbers: [3749] 3749,15 unequal: No Solution Exploring Operation: 163-23=140, Resulting Numbers: [140] 140,15 unequal: No Solution Exploring Operation: 23+163=186, Resulting Numbers: [186] 186,15 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 13, 74, 18, 76 ]
49
[ "76-74=2", "18*2=36", "13+36=49" ]
Current State: 49:[13, 74, 18, 76], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [13, 18, 2] Generated Node #2: [13, 18, 2] from Operation: 76-74=2 Current State: 49:[13, 18, 2], Operations: ['76-74=2'] Exploring Operation: 18*2=36, Resulting Numbers: [13, 36] Generated Node #3: [13, 36] from Operation: 18*2=36 Current State: 49:[13, 36], Operations: ['76-74=2', '18*2=36'] Exploring Operation: 13+36=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[13, 74, 18, 76], Operations: [] Exploring Operation: 76-74=2, Resulting Numbers: [13, 18, 2] Generated Node #0,0: 49:[13, 18, 2] Operation: 76-74=2 Moving to Node #0,0 Current State: 49:[13, 18, 2], Operations: ['76-74=2'] Exploring Operation: 18-13=5, Resulting Numbers: [2, 5] Generated Node #0,0,0: 49:[2, 5] Operation: 18-13=5 Moving to Node #0,0,0 Current State: 49:[2, 5], Operations: ['76-74=2', '18-13=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,49 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 1, 63, 65, 22 ]
22
[ "1+63=64", "65-64=1", "22*1=22" ]
Current State: 22:[1, 63, 65, 22], Operations: [] Exploring Operation: 1+63=64, Resulting Numbers: [65, 22, 64] Generated Node #2: [65, 22, 64] from Operation: 1+63=64 Current State: 22:[65, 22, 64], Operations: ['1+63=64'] Exploring Operation: 65-64=1, Resulting Numbers: [22, 1] Generated Node #3: [22, 1] from Operation: 65-64=1 Current State: 22:[22, 1], Operations: ['1+63=64', '65-64=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[1, 63, 65, 22], Operations: [] Exploring Operation: 65-63=2, Resulting Numbers: [1, 22, 2] Generated Node #0,0: 22:[1, 22, 2] Operation: 65-63=2 Moving to Node #0,0 Current State: 22:[1, 22, 2], Operations: ['65-63=2'] Exploring Operation: 1*22=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 22:[2, 22] Operation: 1*22=22 Moving to Node #0,0,0 Current State: 22:[2, 22], Operations: ['65-63=2', '1*22=22'] Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,22 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 96, 52, 65, 57 ]
78
[ "96-52=44", "65+57=122", "122-44=78" ]
Current State: 78:[96, 52, 65, 57], Operations: [] Exploring Operation: 96-52=44, Resulting Numbers: [65, 57, 44] Generated Node #2: [65, 57, 44] from Operation: 96-52=44 Current State: 78:[65, 57, 44], Operations: ['96-52=44'] Exploring Operation: 65+57=122, Resulting Numbers: [44, 122] Generated Node #3: [44, 122] from Operation: 65+57=122 Current State: 78:[44, 122], Operations: ['96-52=44', '65+57=122'] Exploring Operation: 122-44=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[96, 52, 65, 57], Operations: [] Exploring Operation: 65-57=8, Resulting Numbers: [96, 52, 8] Generated Node #0,0: 78:[96, 52, 8] Operation: 65-57=8 Exploring Operation: 96-57=39, Resulting Numbers: [52, 65, 39] Generated Node #0,1: 78:[52, 65, 39] Operation: 96-57=39 Exploring Operation: 57-52=5, Resulting Numbers: [96, 65, 5] Generated Node #0,2: 78:[96, 65, 5] Operation: 57-52=5 Moving to Node #0,1 Current State: 78:[52, 65, 39], Operations: ['96-57=39'] Exploring Operation: 52-39=13, Resulting Numbers: [65, 13] Generated Node #0,1,0: 78:[65, 13] Operation: 52-39=13 Exploring Operation: 65-39=26, Resulting Numbers: [52, 26] Generated Node #0,1,1: 78:[52, 26] Operation: 65-39=26 Exploring Operation: 65-52=13, Resulting Numbers: [39, 13] Generated Node #0,1,2: 78:[39, 13] Operation: 65-52=13 Moving to Node #0,2 Current State: 78:[96, 65, 5], Operations: ['57-52=5'] Exploring Operation: 96-65=31, Resulting Numbers: [5, 31] Generated Node #0,2,0: 78:[5, 31] Operation: 96-65=31 Exploring Operation: 65/5=13, Resulting Numbers: [96, 13] Generated Node #0,2,1: 78:[96, 13] Operation: 65/5=13 Exploring Operation: 96-5=91, Resulting Numbers: [65, 91] Generated Node #0,2,2: 78:[65, 91] Operation: 96-5=91 Moving to Node #0,0 Current State: 78:[96, 52, 8], Operations: ['65-57=8'] Exploring Operation: 96-52=44, Resulting Numbers: [8, 44] Generated Node #0,0,0: 78:[8, 44] Operation: 96-52=44 Exploring Operation: 96-8=88, Resulting Numbers: [52, 88] Generated Node #0,0,1: 78:[52, 88] Operation: 96-8=88 Exploring Operation: 96/8=12, Resulting Numbers: [52, 12] Generated Node #0,0,2: 78:[52, 12] Operation: 96/8=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[8, 44], Operations: ['65-57=8', '96-52=44'] Exploring Operation: 8*44=352, Resulting Numbers: [352] 352,78 unequal: No Solution Exploring Operation: 44-8=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 8+44=52, Resulting Numbers: [52] 52,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[52, 12], Operations: ['65-57=8', '96/8=12'] Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,78 unequal: No Solution Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,78 unequal: No Solution Exploring Operation: 52*12=624, Resulting Numbers: [624] 624,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[52, 88], Operations: ['65-57=8', '96-8=88'] Exploring Operation: 52*88=4576, Resulting Numbers: [4576] 4576,78 unequal: No Solution Exploring Operation: 88-52=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 52+88=140, Resulting Numbers: [140] 140,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 78:[39, 13], Operations: ['96-57=39', '65-52=13'] Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,78 unequal: No Solution Exploring Operation: 39-13=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[5, 31], Operations: ['57-52=5', '96-65=31'] Exploring Operation: 5*31=155, Resulting Numbers: [155] 155,78 unequal: No Solution Exploring Operation: 31-5=26, Resulting Numbers: [26] 26,78 unequal: No Solution Exploring Operation: 5+31=36, Resulting Numbers: [36] 36,78 unequal: No Solution Moving to Node #0,1,1 Current State: 78:[52, 26], Operations: ['96-57=39', '65-39=26'] Exploring Operation: 52/26=2, Resulting Numbers: [2] 2,78 unequal: No Solution Exploring Operation: 52+26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[96, 52, 65, 57], Operations: [] Exploring Operation: 96-57=39, Resulting Numbers: [52, 65, 39] Generated Node #0,1: 78:[52, 65, 39] Operation: 96-57=39 Moving to Node #0,1 Current State: 78:[52, 65, 39], Operations: ['96-57=39'] Exploring Operation: 65-39=26, Resulting Numbers: [52, 26] Generated Node #0,1,1: 78:[52, 26] Operation: 65-39=26 Moving to Node #0,1,1 Current State: 78:[52, 26], Operations: ['96-57=39', '65-39=26'] Exploring Operation: 52+26=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.971354
hs_3
mult_heuristic
[ 78, 28, 26, 5 ]
71
[ "78-28=50", "26-5=21", "50+21=71" ]
Current State: 71:[78, 28, 26, 5], Operations: [] Exploring Operation: 78-28=50, Resulting Numbers: [26, 5, 50] Generated Node #2: [26, 5, 50] from Operation: 78-28=50 Current State: 71:[26, 5, 50], Operations: ['78-28=50'] Exploring Operation: 26-5=21, Resulting Numbers: [50, 21] Generated Node #3: [50, 21] from Operation: 26-5=21 Current State: 71:[50, 21], Operations: ['78-28=50', '26-5=21'] Exploring Operation: 50+21=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[78, 28, 26, 5], Operations: [] Exploring Operation: 28+26=54, Resulting Numbers: [78, 5, 54] Generated Node #0,0: 71:[78, 5, 54] Operation: 28+26=54 Exploring Operation: 78-5=73, Resulting Numbers: [28, 26, 73] Generated Node #0,1: 71:[28, 26, 73] Operation: 78-5=73 Moving to Node #0,0 Current State: 71:[78, 5, 54], Operations: ['28+26=54'] Exploring Operation: 5+54=59, Resulting Numbers: [78, 59] Generated Node #0,0,0: 71:[78, 59] Operation: 5+54=59 Exploring Operation: 78-5=73, Resulting Numbers: [54, 73] Generated Node #0,0,1: 71:[54, 73] Operation: 78-5=73 Moving to Node #0,1 Current State: 71:[28, 26, 73], Operations: ['78-5=73'] Exploring Operation: 28+26=54, Resulting Numbers: [73, 54] Generated Node #0,1,0: 71:[73, 54] Operation: 28+26=54 Exploring Operation: 73-26=47, Resulting Numbers: [28, 47] Generated Node #0,1,1: 71:[28, 47] Operation: 73-26=47 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 71:[73, 54], Operations: ['78-5=73', '28+26=54'] Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 73+54=127, Resulting Numbers: [127] 127,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 71:[28, 47], Operations: ['78-5=73', '73-26=47'] Exploring Operation: 28+47=75, Resulting Numbers: [75] 75,71 unequal: No Solution Exploring Operation: 47-28=19, Resulting Numbers: [19] 19,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 71:[78, 59], Operations: ['28+26=54', '5+54=59'] Exploring Operation: 78-59=19, Resulting Numbers: [19] 19,71 unequal: No Solution Exploring Operation: 78+59=137, Resulting Numbers: [137] 137,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[54, 73], Operations: ['28+26=54', '78-5=73'] Exploring Operation: 54+73=127, Resulting Numbers: [127] 127,71 unequal: No Solution Exploring Operation: 73-54=19, Resulting Numbers: [19] 19,71 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 87, 47, 36, 24 ]
96
[ "87-47=40", "40-36=4", "24*4=96" ]
Current State: 96:[87, 47, 36, 24], Operations: [] Exploring Operation: 87-47=40, Resulting Numbers: [36, 24, 40] Generated Node #2: [36, 24, 40] from Operation: 87-47=40 Current State: 96:[36, 24, 40], Operations: ['87-47=40'] Exploring Operation: 40-36=4, Resulting Numbers: [24, 4] Generated Node #3: [24, 4] from Operation: 40-36=4 Current State: 96:[24, 4], Operations: ['87-47=40', '40-36=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[87, 47, 36, 24], Operations: [] Exploring Operation: 36-24=12, Resulting Numbers: [87, 47, 12] Generated Node #0,0: 96:[87, 47, 12] Operation: 36-24=12 Exploring Operation: 47-36=11, Resulting Numbers: [87, 24, 11] Generated Node #0,1: 96:[87, 24, 11] Operation: 47-36=11 Exploring Operation: 87-47=40, Resulting Numbers: [36, 24, 40] Generated Node #0,2: 96:[36, 24, 40] Operation: 87-47=40 Exploring Operation: 47-24=23, Resulting Numbers: [87, 36, 23] Generated Node #0,3: 96:[87, 36, 23] Operation: 47-24=23 Exploring Operation: 87-36=51, Resulting Numbers: [47, 24, 51] Generated Node #0,4: 96:[47, 24, 51] Operation: 87-36=51 Moving to Node #0,4 Current State: 96:[47, 24, 51], Operations: ['87-36=51'] Exploring Operation: 51-47=4, Resulting Numbers: [24, 4] Generated Node #0,4,0: 96:[24, 4] Operation: 51-47=4 Exploring Operation: 51-24=27, Resulting Numbers: [47, 27] Generated Node #0,4,1: 96:[47, 27] Operation: 51-24=27 Exploring Operation: 24+51=75, Resulting Numbers: [47, 75] Generated Node #0,4,2: 96:[47, 75] Operation: 24+51=75 Exploring Operation: 47+51=98, Resulting Numbers: [24, 98] Generated Node #0,4,3: 96:[24, 98] Operation: 47+51=98 Exploring Operation: 47-24=23, Resulting Numbers: [51, 23] Generated Node #0,4,4: 96:[51, 23] Operation: 47-24=23 Moving to Node #0,1 Current State: 96:[87, 24, 11], Operations: ['47-36=11'] Exploring Operation: 24-11=13, Resulting Numbers: [87, 13] Generated Node #0,1,0: 96:[87, 13] Operation: 24-11=13 Exploring Operation: 87-24=63, Resulting Numbers: [11, 63] Generated Node #0,1,1: 96:[11, 63] Operation: 87-24=63 Exploring Operation: 87+11=98, Resulting Numbers: [24, 98] Generated Node #0,1,2: 96:[24, 98] Operation: 87+11=98 Exploring Operation: 24+11=35, Resulting Numbers: [87, 35] Generated Node #0,1,3: 96:[87, 35] Operation: 24+11=35 Exploring Operation: 87+24=111, Resulting Numbers: [11, 111] Generated Node #0,1,4: 96:[11, 111] Operation: 87+24=111 Moving to Node #0,0 Current State: 96:[87, 47, 12], Operations: ['36-24=12'] Exploring Operation: 87-12=75, Resulting Numbers: [47, 75] Generated Node #0,0,0: 96:[47, 75] Operation: 87-12=75 Exploring Operation: 87+12=99, Resulting Numbers: [47, 99] Generated Node #0,0,1: 96:[47, 99] Operation: 87+12=99 Exploring Operation: 87-47=40, Resulting Numbers: [12, 40] Generated Node #0,0,2: 96:[12, 40] Operation: 87-47=40 Exploring Operation: 47+12=59, Resulting Numbers: [87, 59] Generated Node #0,0,3: 96:[87, 59] Operation: 47+12=59 Exploring Operation: 47-12=35, Resulting Numbers: [87, 35] Generated Node #0,0,4: 96:[87, 35] Operation: 47-12=35 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 96:[47, 99], Operations: ['36-24=12', '87+12=99'] Exploring Operation: 47+99=146, Resulting Numbers: [146] 146,96 unequal: No Solution Exploring Operation: 99-47=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 47*99=4653, Resulting Numbers: [4653] 4653,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 96:[12, 40], Operations: ['36-24=12', '87-47=40'] Exploring Operation: 12+40=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 12*40=480, Resulting Numbers: [480] 480,96 unequal: No Solution Exploring Operation: 40-12=28, Resulting Numbers: [28] 28,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 96:[87, 35], Operations: ['36-24=12', '47-12=35'] Exploring Operation: 87+35=122, Resulting Numbers: [122] 122,96 unequal: No Solution Exploring Operation: 87-35=52, Resulting Numbers: [52] 52,96 unequal: No Solution Exploring Operation: 87*35=3045, Resulting Numbers: [3045] 3045,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 96:[87, 59], Operations: ['36-24=12', '47+12=59'] Exploring Operation: 87-59=28, Resulting Numbers: [28] 28,96 unequal: No Solution Exploring Operation: 87+59=146, Resulting Numbers: [146] 146,96 unequal: No Solution Exploring Operation: 87*59=5133, Resulting Numbers: [5133] 5133,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 96:[47, 75], Operations: ['36-24=12', '87-12=75'] Exploring Operation: 75-47=28, Resulting Numbers: [28] 28,96 unequal: No Solution Exploring Operation: 47+75=122, Resulting Numbers: [122] 122,96 unequal: No Solution Exploring Operation: 47*75=3525, Resulting Numbers: [3525] 3525,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 96:[36, 24, 40], Operations: ['87-47=40'] Exploring Operation: 36-24=12, Resulting Numbers: [40, 12] Generated Node #0,2,0: 96:[40, 12] Operation: 36-24=12 Exploring Operation: 36+40=76, Resulting Numbers: [24, 76] Generated Node #0,2,1: 96:[24, 76] Operation: 36+40=76 Exploring Operation: 40-24=16, Resulting Numbers: [36, 16] Generated Node #0,2,2: 96:[36, 16] Operation: 40-24=16 Exploring Operation: 36+24=60, Resulting Numbers: [40, 60] Generated Node #0,2,3: 96:[40, 60] Operation: 36+24=60 Exploring Operation: 40-36=4, Resulting Numbers: [24, 4] Generated Node #0,2,4: 96:[24, 4] Operation: 40-36=4 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 96:[24, 4], Operations: ['87-47=40', '40-36=4'] Exploring Operation: 24/4=6, Resulting Numbers: [6] 6,96 unequal: No Solution Exploring Operation: 24-4=20, Resulting Numbers: [20] 20,96 unequal: No Solution Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[87, 47, 36, 24], Operations: [] Exploring Operation: 87-47=40, Resulting Numbers: [36, 24, 40] Generated Node #0,2: 96:[36, 24, 40] Operation: 87-47=40 Moving to Node #0,2 Current State: 96:[36, 24, 40], Operations: ['87-47=40'] Exploring Operation: 40-36=4, Resulting Numbers: [24, 4] Generated Node #0,2,4: 96:[24, 4] Operation: 40-36=4 Moving to Node #0,2,4 Current State: 96:[24, 4], Operations: ['87-47=40', '40-36=4'] Exploring Operation: 24*4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.959201
hs_5
sum_heuristic
[ 23, 98, 80, 64 ]
69
[ "98-23=75", "80+64=144", "144-75=69" ]
Current State: 69:[23, 98, 80, 64], Operations: [] Exploring Operation: 98-23=75, Resulting Numbers: [80, 64, 75] Generated Node #2: [80, 64, 75] from Operation: 98-23=75 Current State: 69:[80, 64, 75], Operations: ['98-23=75'] Exploring Operation: 80+64=144, Resulting Numbers: [75, 144] Generated Node #3: [75, 144] from Operation: 80+64=144 Current State: 69:[75, 144], Operations: ['98-23=75', '80+64=144'] Exploring Operation: 144-75=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[23, 98, 80, 64], Operations: [] Exploring Operation: 80-64=16, Resulting Numbers: [23, 98, 16] Generated Node #0,0: 69:[23, 98, 16] Operation: 80-64=16 Exploring Operation: 80-23=57, Resulting Numbers: [98, 64, 57] Generated Node #0,1: 69:[98, 64, 57] Operation: 80-23=57 Exploring Operation: 98-64=34, Resulting Numbers: [23, 80, 34] Generated Node #0,2: 69:[23, 80, 34] Operation: 98-64=34 Exploring Operation: 98-80=18, Resulting Numbers: [23, 64, 18] Generated Node #0,3: 69:[23, 64, 18] Operation: 98-80=18 Exploring Operation: 98-23=75, Resulting Numbers: [80, 64, 75] Generated Node #0,4: 69:[80, 64, 75] Operation: 98-23=75 Start Sub Search at level 1: Moving to Node #0,3 Current State: 69:[23, 64, 18], Operations: ['98-80=18'] Exploring Operation: 23+64=87, Resulting Numbers: [18, 87] Generated Node #0,3,0: 69:[18, 87] Operation: 23+64=87 Exploring Operation: 64+18=82, Resulting Numbers: [23, 82] Generated Node #0,3,1: 69:[23, 82] Operation: 64+18=82 Exploring Operation: 23-18=5, Resulting Numbers: [64, 5] Generated Node #0,3,2: 69:[64, 5] Operation: 23-18=5 Exploring Operation: 23+18=41, Resulting Numbers: [64, 41] Generated Node #0,3,3: 69:[64, 41] Operation: 23+18=41 Exploring Operation: 64-23=41, Resulting Numbers: [18, 41] Generated Node #0,3,4: 69:[18, 41] Operation: 64-23=41 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 69:[64, 5], Operations: ['98-80=18', '23-18=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Moving to Node #0 Current State: 69:[23, 98, 80, 64], Operations: [] Exploring Operation: 98-80=18, Resulting Numbers: [23, 64, 18] Generated Node #0,3: 69:[23, 64, 18] Operation: 98-80=18 Moving to Node #0,3 Current State: 69:[23, 64, 18], Operations: ['98-80=18'] Exploring Operation: 23-18=5, Resulting Numbers: [64, 5] Generated Node #0,3,2: 69:[64, 5] Operation: 23-18=5 Moving to Node #0,3,2 Current State: 69:[64, 5], Operations: ['98-80=18', '23-18=5'] Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,69 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 99, 51, 79, 86 ]
55
[ "99-51=48", "86-79=7", "48+7=55" ]
Current State: 55:[99, 51, 79, 86], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [79, 86, 48] Generated Node #2: [79, 86, 48] from Operation: 99-51=48 Current State: 55:[79, 86, 48], Operations: ['99-51=48'] Exploring Operation: 86-79=7, Resulting Numbers: [48, 7] Generated Node #3: [48, 7] from Operation: 86-79=7 Current State: 55:[48, 7], Operations: ['99-51=48', '86-79=7'] Exploring Operation: 48+7=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[99, 51, 79, 86], Operations: [] Exploring Operation: 99-51=48, Resulting Numbers: [79, 86, 48] Generated Node #0,0: 55:[79, 86, 48] Operation: 99-51=48 Exploring Operation: 86-79=7, Resulting Numbers: [99, 51, 7] Generated Node #0,1: 55:[99, 51, 7] Operation: 86-79=7 Exploring Operation: 99-79=20, Resulting Numbers: [51, 86, 20] Generated Node #0,2: 55:[51, 86, 20] Operation: 99-79=20 Exploring Operation: 99-86=13, Resulting Numbers: [51, 79, 13] Generated Node #0,3: 55:[51, 79, 13] Operation: 99-86=13 Moving to Node #0,3 Current State: 55:[51, 79, 13], Operations: ['99-86=13'] Exploring Operation: 79-51=28, Resulting Numbers: [13, 28] Generated Node #0,3,0: 55:[13, 28] Operation: 79-51=28 Exploring Operation: 51+13=64, Resulting Numbers: [79, 64] Generated Node #0,3,1: 55:[79, 64] Operation: 51+13=64 Exploring Operation: 79-13=66, Resulting Numbers: [51, 66] Generated Node #0,3,2: 55:[51, 66] Operation: 79-13=66 Exploring Operation: 51-13=38, Resulting Numbers: [79, 38] Generated Node #0,3,3: 55:[79, 38] Operation: 51-13=38 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 55:[51, 66], Operations: ['99-86=13', '79-13=66'] Exploring Operation: 51*66=3366, Resulting Numbers: [3366] 3366,55 unequal: No Solution Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 51+66=117, Resulting Numbers: [117] 117,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 55:[13, 28], Operations: ['99-86=13', '79-51=28'] Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 13*28=364, Resulting Numbers: [364] 364,55 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 55:[79, 64], Operations: ['99-86=13', '51+13=64'] Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,55 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,55 unequal: No Solution Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 55:[79, 38], Operations: ['99-86=13', '51-13=38'] Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,55 unequal: No Solution Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 79*38=3002, Resulting Numbers: [3002] 3002,55 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: 55:[51, 86, 20], Operations: ['99-79=20'] Exploring Operation: 51+20=71, Resulting Numbers: [86, 71] Generated Node #0,2,0: 55:[86, 71] Operation: 51+20=71 Exploring Operation: 51-20=31, Resulting Numbers: [86, 31] Generated Node #0,2,1: 55:[86, 31] Operation: 51-20=31 Exploring Operation: 86-20=66, Resulting Numbers: [51, 66] Generated Node #0,2,2: 55:[51, 66] Operation: 86-20=66 Exploring Operation: 86-51=35, Resulting Numbers: [20, 35] Generated Node #0,2,3: 55:[20, 35] Operation: 86-51=35 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 55:[51, 66], Operations: ['99-79=20', '86-20=66'] Exploring Operation: 66-51=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 51+66=117, Resulting Numbers: [117] 117,55 unequal: No Solution Exploring Operation: 51*66=3366, Resulting Numbers: [3366] 3366,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 55:[20, 35], Operations: ['99-79=20', '86-51=35'] Exploring Operation: 20*35=700, Resulting Numbers: [700] 700,55 unequal: No Solution Exploring Operation: 35-20=15, Resulting Numbers: [15] 15,55 unequal: No Solution Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[99, 51, 79, 86], Operations: [] Exploring Operation: 99-79=20, Resulting Numbers: [51, 86, 20] Generated Node #0,2: 55:[51, 86, 20] Operation: 99-79=20 Moving to Node #0,2 Current State: 55:[51, 86, 20], Operations: ['99-79=20'] Exploring Operation: 86-51=35, Resulting Numbers: [20, 35] Generated Node #0,2,3: 55:[20, 35] Operation: 86-51=35 Moving to Node #0,2,3 Current State: 55:[20, 35], Operations: ['99-79=20', '86-51=35'] Exploring Operation: 20+35=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_4
mult_heuristic
[ 32, 18, 11, 74 ]
99
[ "32-18=14", "11+74=85", "14+85=99" ]
Current State: 99:[32, 18, 11, 74], Operations: [] Exploring Operation: 32-18=14, Resulting Numbers: [11, 74, 14] Generated Node #2: [11, 74, 14] from Operation: 32-18=14 Current State: 99:[11, 74, 14], Operations: ['32-18=14'] Exploring Operation: 11+74=85, Resulting Numbers: [14, 85] Generated Node #3: [14, 85] from Operation: 11+74=85 Current State: 99:[14, 85], Operations: ['32-18=14', '11+74=85'] Exploring Operation: 14+85=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[32, 18, 11, 74], Operations: [] Exploring Operation: 18+74=92, Resulting Numbers: [32, 11, 92] Generated Node #0,0: 99:[32, 11, 92] Operation: 18+74=92 Moving to Node #0,0 Current State: 99:[32, 11, 92], Operations: ['18+74=92'] Exploring Operation: 11+92=103, Resulting Numbers: [32, 103] Generated Node #0,0,0: 99:[32, 103] Operation: 11+92=103 Moving to Node #0,0,0 Current State: 99:[32, 103], Operations: ['18+74=92', '11+92=103'] Exploring Operation: 103-32=71, Resulting Numbers: [71] 71,99 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 91, 6, 26, 26 ]
84
[ "91-6=85", "26/26=1", "85-1=84" ]
Current State: 84:[91, 6, 26, 26], Operations: [] Exploring Operation: 91-6=85, Resulting Numbers: [26, 26, 85] Generated Node #2: [26, 26, 85] from Operation: 91-6=85 Current State: 84:[26, 26, 85], Operations: ['91-6=85'] Exploring Operation: 26/26=1, Resulting Numbers: [85, 1] Generated Node #3: [85, 1] from Operation: 26/26=1 Current State: 84:[85, 1], Operations: ['91-6=85', '26/26=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[91, 6, 26, 26], Operations: [] Exploring Operation: 26/26=1, Resulting Numbers: [91, 6, 1] Generated Node #0,0: 84:[91, 6, 1] Operation: 26/26=1 Exploring Operation: 26-26=0, Resulting Numbers: [91, 6, 0] Generated Node #0,1: 84:[91, 6, 0] Operation: 26-26=0 Exploring Operation: 91-6=85, Resulting Numbers: [26, 26, 85] Generated Node #0,2: 84:[26, 26, 85] Operation: 91-6=85 Moving to Node #0,2 Current State: 84:[26, 26, 85], Operations: ['91-6=85'] Exploring Operation: 26/26=1, Resulting Numbers: [85, 1] Generated Node #0,2,0: 84:[85, 1] Operation: 26/26=1 Exploring Operation: 26-26=0, Resulting Numbers: [85, 0] Generated Node #0,2,1: 84:[85, 0] Operation: 26-26=0 Exploring Operation: 26+26=52, Resulting Numbers: [85, 52] Generated Node #0,2,2: 84:[85, 52] Operation: 26+26=52 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[85, 1], Operations: ['91-6=85', '26/26=1'] Exploring Operation: 85/1=85, Resulting Numbers: [85] 85,84 unequal: No Solution Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[91, 6, 26, 26], Operations: [] Exploring Operation: 91-6=85, Resulting Numbers: [26, 26, 85] Generated Node #0,2: 84:[26, 26, 85] Operation: 91-6=85 Moving to Node #0,2 Current State: 84:[26, 26, 85], Operations: ['91-6=85'] Exploring Operation: 26/26=1, Resulting Numbers: [85, 1] Generated Node #0,2,0: 84:[85, 1] Operation: 26/26=1 Moving to Node #0,2,0 Current State: 84:[85, 1], Operations: ['91-6=85', '26/26=1'] Exploring Operation: 85-1=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 92, 36, 61, 34 ]
29
[ "92-36=56", "61-34=27", "56-27=29" ]
Current State: 29:[92, 36, 61, 34], Operations: [] Exploring Operation: 92-36=56, Resulting Numbers: [61, 34, 56] Generated Node #2: [61, 34, 56] from Operation: 92-36=56 Current State: 29:[61, 34, 56], Operations: ['92-36=56'] Exploring Operation: 61-34=27, Resulting Numbers: [56, 27] Generated Node #3: [56, 27] from Operation: 61-34=27 Current State: 29:[56, 27], Operations: ['92-36=56', '61-34=27'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[92, 36, 61, 34], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [36, 34, 31] Generated Node #0,0: 29:[36, 34, 31] Operation: 92-61=31 Exploring Operation: 61-34=27, Resulting Numbers: [92, 36, 27] Generated Node #0,1: 29:[92, 36, 27] Operation: 61-34=27 Exploring Operation: 92-34=58, Resulting Numbers: [36, 61, 58] Generated Node #0,2: 29:[36, 61, 58] Operation: 92-34=58 Exploring Operation: 61-36=25, Resulting Numbers: [92, 34, 25] Generated Node #0,3: 29:[92, 34, 25] Operation: 61-36=25 Exploring Operation: 92-36=56, Resulting Numbers: [61, 34, 56] Generated Node #0,4: 29:[61, 34, 56] Operation: 92-36=56 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[36, 34, 31], Operations: ['92-61=31'] Exploring Operation: 36-31=5, Resulting Numbers: [34, 5] Generated Node #0,0,0: 29:[34, 5] Operation: 36-31=5 Exploring Operation: 36+34=70, Resulting Numbers: [31, 70] Generated Node #0,0,1: 29:[31, 70] Operation: 36+34=70 Exploring Operation: 34-31=3, Resulting Numbers: [36, 3] Generated Node #0,0,2: 29:[36, 3] Operation: 34-31=3 Exploring Operation: 36+31=67, Resulting Numbers: [34, 67] Generated Node #0,0,3: 29:[34, 67] Operation: 36+31=67 Exploring Operation: 36-34=2, Resulting Numbers: [31, 2] Generated Node #0,0,4: 29:[31, 2] Operation: 36-34=2 Moving to Node #0,0,0 Current State: 29:[34, 5], Operations: ['92-61=31', '36-31=5'] Exploring Operation: 34*5=170, Resulting Numbers: [170] 170,29 unequal: No Solution Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[92, 36, 61, 34], Operations: [] Exploring Operation: 92-61=31, Resulting Numbers: [36, 34, 31] Generated Node #0,0: 29:[36, 34, 31] Operation: 92-61=31 Moving to Node #0,0 Current State: 29:[36, 34, 31], Operations: ['92-61=31'] Exploring Operation: 36-31=5, Resulting Numbers: [34, 5] Generated Node #0,0,0: 29:[34, 5] Operation: 36-31=5 Moving to Node #0,0,0 Current State: 29:[34, 5], Operations: ['92-61=31', '36-31=5'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 10, 2, 2, 32 ]
12
[ "10-2=8", "32-8=24", "24/2=12" ]
Current State: 12:[10, 2, 2, 32], Operations: [] Exploring Operation: 10-2=8, Resulting Numbers: [32, 8] Generated Node #2: [32, 8] from Operation: 10-2=8 Current State: 12:[32, 8], Operations: ['10-2=8'] Exploring Operation: 32-8=24, Resulting Numbers: [24] 24,12 equal: Goal Reached Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[10, 2, 2, 32], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [10, 2, 16] Generated Node #0,0: 12:[10, 2, 16] Operation: 32/2=16 Exploring Operation: 32-10=22, Resulting Numbers: [2, 2, 22] Generated Node #0,1: 12:[2, 2, 22] Operation: 32-10=22 Exploring Operation: 32/2=16, Resulting Numbers: [10, 2, 16] Generated Node #0,2: 12:[10, 2, 16] Operation: 32/2=16 Exploring Operation: 10+2=12, Resulting Numbers: [2, 32, 12] Generated Node #0,3: 12:[2, 32, 12] Operation: 10+2=12 Moving to Node #0,0 Current State: 12:[10, 2, 16], Operations: ['32/2=16'] Exploring Operation: 16/2=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 12:[10, 8] Operation: 16/2=8 Exploring Operation: 10+2=12, Resulting Numbers: [16, 12] Generated Node #0,0,1: 12:[16, 12] Operation: 10+2=12 Exploring Operation: 16-10=6, Resulting Numbers: [2, 6] Generated Node #0,0,2: 12:[2, 6] Operation: 16-10=6 Exploring Operation: 16-2=14, Resulting Numbers: [10, 14] Generated Node #0,0,3: 12:[10, 14] Operation: 16-2=14 Moving to Node #0,2 Current State: 12:[10, 2, 16], Operations: ['32/2=16'] Exploring Operation: 16/2=8, Resulting Numbers: [10, 8] Generated Node #0,2,0: 12:[10, 8] Operation: 16/2=8 Exploring Operation: 10+2=12, Resulting Numbers: [16, 12] Generated Node #0,2,1: 12:[16, 12] Operation: 10+2=12 Exploring Operation: 16-10=6, Resulting Numbers: [2, 6] Generated Node #0,2,2: 12:[2, 6] Operation: 16-10=6 Exploring Operation: 16-2=14, Resulting Numbers: [10, 14] Generated Node #0,2,3: 12:[10, 14] Operation: 16-2=14 Moving to Node #0,1 Current State: 12:[2, 2, 22], Operations: ['32-10=22'] Exploring Operation: 22/2=11, Resulting Numbers: [2, 11] Generated Node #0,1,0: 12:[2, 11] Operation: 22/2=11 Exploring Operation: 22-2=20, Resulting Numbers: [2, 20] Generated Node #0,1,1: 12:[2, 20] Operation: 22-2=20 Exploring Operation: 22/2=11, Resulting Numbers: [2, 11] Generated Node #0,1,2: 12:[2, 11] Operation: 22/2=11 Exploring Operation: 22-2=20, Resulting Numbers: [2, 20] Generated Node #0,1,3: 12:[2, 20] Operation: 22-2=20 Moving to Node #0,3 Current State: 12:[2, 32, 12], Operations: ['10+2=12'] Exploring Operation: 32/2=16, Resulting Numbers: [12, 16] Generated Node #0,3,0: 12:[12, 16] Operation: 32/2=16 Exploring Operation: 12/2=6, Resulting Numbers: [32, 6] Generated Node #0,3,1: 12:[32, 6] Operation: 12/2=6 Exploring Operation: 32-2=30, Resulting Numbers: [12, 30] Generated Node #0,3,2: 12:[12, 30] Operation: 32-2=30 Exploring Operation: 32-12=20, Resulting Numbers: [2, 20] Generated Node #0,3,3: 12:[2, 20] Operation: 32-12=20 Moving to Node #0,0,2 Current State: 12:[2, 6], Operations: ['32/2=16', '16-10=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,12 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,12 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,12 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[10, 2, 2, 32], Operations: [] Exploring Operation: 32/2=16, Resulting Numbers: [10, 2, 16] Generated Node #0,0: 12:[10, 2, 16] Operation: 32/2=16 Moving to Node #0,0 Current State: 12:[10, 2, 16], Operations: ['32/2=16'] Exploring Operation: 16-10=6, Resulting Numbers: [2, 6] Generated Node #0,0,2: 12:[2, 6] Operation: 16-10=6 Moving to Node #0,0,2 Current State: 12:[2, 6], Operations: ['32/2=16', '16-10=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
0.975694
hs_4
sum_heuristic
[ 12, 49, 89, 93 ]
97
[ "93-89=4", "12*4=48", "49+48=97" ]
Current State: 97:[12, 49, 89, 93], Operations: [] Exploring Operation: 93-89=4, Resulting Numbers: [12, 49, 4] Generated Node #2: [12, 49, 4] from Operation: 93-89=4 Current State: 97:[12, 49, 4], Operations: ['93-89=4'] Exploring Operation: 12*4=48, Resulting Numbers: [49, 48] Generated Node #3: [49, 48] from Operation: 12*4=48 Current State: 97:[49, 48], Operations: ['93-89=4', '12*4=48'] Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[12, 49, 89, 93], Operations: [] Exploring Operation: 12+49=61, Resulting Numbers: [89, 93, 61] Generated Node #0,0: 97:[89, 93, 61] Operation: 12+49=61 Exploring Operation: 12+89=101, Resulting Numbers: [49, 93, 101] Generated Node #0,1: 97:[49, 93, 101] Operation: 12+89=101 Moving to Node #0,0 Current State: 97:[89, 93, 61], Operations: ['12+49=61'] Exploring Operation: 93+61=154, Resulting Numbers: [89, 154] Generated Node #0,0,0: 97:[89, 154] Operation: 93+61=154 Exploring Operation: 89+61=150, Resulting Numbers: [93, 150] Generated Node #0,0,1: 97:[93, 150] Operation: 89+61=150 Moving to Node #0,1 Current State: 97:[49, 93, 101], Operations: ['12+89=101'] Exploring Operation: 49+93=142, Resulting Numbers: [101, 142] Generated Node #0,1,0: 97:[101, 142] Operation: 49+93=142 Exploring Operation: 101-49=52, Resulting Numbers: [93, 52] Generated Node #0,1,1: 97:[93, 52] Operation: 101-49=52 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 97:[101, 142], Operations: ['12+89=101', '49+93=142'] Exploring Operation: 142-101=41, Resulting Numbers: [41] 41,97 unequal: No Solution Exploring Operation: 101+142=243, Resulting Numbers: [243] 243,97 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:[93, 52], Operations: ['12+89=101', '101-49=52'] Exploring Operation: 93+52=145, Resulting Numbers: [145] 145,97 unequal: No Solution Exploring Operation: 93-52=41, Resulting Numbers: [41] 41,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 97:[93, 150], Operations: ['12+49=61', '89+61=150'] Exploring Operation: 93+150=243, Resulting Numbers: [243] 243,97 unequal: No Solution Exploring Operation: 150-93=57, Resulting Numbers: [57] 57,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[89, 154], Operations: ['12+49=61', '93+61=154'] Exploring Operation: 154-89=65, Resulting Numbers: [65] 65,97 unequal: No Solution Exploring Operation: 89+154=243, Resulting Numbers: [243] 243,97 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 4, 17, 92, 88 ]
33
[ "92-88=4", "4*4=16", "17+16=33" ]
Current State: 33:[4, 17, 92, 88], Operations: [] Exploring Operation: 92-88=4, Resulting Numbers: [4, 17, 4] Generated Node #2: [4, 17, 4] from Operation: 92-88=4 Current State: 33:[4, 17, 4], Operations: ['92-88=4'] Exploring Operation: 4*4=16, Resulting Numbers: [17, 16] Generated Node #3: [17, 16] from Operation: 4*4=16 Current State: 33:[17, 16], Operations: ['92-88=4', '4*4=16'] Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[4, 17, 92, 88], Operations: [] Exploring Operation: 92/4=23, Resulting Numbers: [17, 88, 23] Generated Node #0,0: 33:[17, 88, 23] Operation: 92/4=23 Exploring Operation: 92-88=4, Resulting Numbers: [4, 17, 4] Generated Node #0,1: 33:[4, 17, 4] Operation: 92-88=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[4, 17, 4], Operations: ['92-88=4'] Exploring Operation: 17-4=13, Resulting Numbers: [4, 13] Generated Node #0,1,0: 33:[4, 13] Operation: 17-4=13 Exploring Operation: 17-4=13, Resulting Numbers: [4, 13] Generated Node #0,1,1: 33:[4, 13] Operation: 17-4=13 Moving to Node #0,1,0 Current State: 33:[4, 13], Operations: ['92-88=4', '17-4=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,33 unequal: No Solution Moving to Node #0,1,1 Current State: 33:[4, 13], Operations: ['92-88=4', '17-4=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,33 unequal: No Solution Exploring Operation: 4+13=17, Resulting Numbers: [17] 17,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[17, 88, 23], Operations: ['92/4=23'] Exploring Operation: 88-23=65, Resulting Numbers: [17, 65] Generated Node #0,0,0: 33:[17, 65] Operation: 88-23=65 Exploring Operation: 88-17=71, Resulting Numbers: [23, 71] Generated Node #0,0,1: 33:[23, 71] Operation: 88-17=71 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[17, 65], Operations: ['92/4=23', '88-23=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,33 unequal: No Solution Exploring Operation: 17+65=82, Resulting Numbers: [82] 82,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[23, 71], Operations: ['92/4=23', '88-17=71'] Exploring Operation: 71-23=48, Resulting Numbers: [48] 48,33 unequal: No Solution Exploring Operation: 23+71=94, Resulting Numbers: [94] 94,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 9, 39, 99, 79 ]
29
[ "99/9=11", "79-39=40", "40-11=29" ]
Current State: 29:[9, 39, 99, 79], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [39, 79, 11] Generated Node #2: [39, 79, 11] from Operation: 99/9=11 Current State: 29:[39, 79, 11], Operations: ['99/9=11'] Exploring Operation: 79-39=40, Resulting Numbers: [11, 40] Generated Node #3: [11, 40] from Operation: 79-39=40 Current State: 29:[11, 40], Operations: ['99/9=11', '79-39=40'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[9, 39, 99, 79], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [39, 79, 11] Generated Node #0,0: 29:[39, 79, 11] Operation: 99/9=11 Exploring Operation: 99-39=60, Resulting Numbers: [9, 79, 60] Generated Node #0,1: 29:[9, 79, 60] Operation: 99-39=60 Exploring Operation: 99-79=20, Resulting Numbers: [9, 39, 20] Generated Node #0,2: 29:[9, 39, 20] Operation: 99-79=20 Moving to Node #0,2 Current State: 29:[9, 39, 20], Operations: ['99-79=20'] Exploring Operation: 9+20=29, Resulting Numbers: [39, 29] Generated Node #0,2,0: 29:[39, 29] Operation: 9+20=29 Exploring Operation: 39-9=30, Resulting Numbers: [20, 30] Generated Node #0,2,1: 29:[20, 30] Operation: 39-9=30 Exploring Operation: 9+39=48, Resulting Numbers: [20, 48] Generated Node #0,2,2: 29:[20, 48] Operation: 9+39=48 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 29:[39, 29], Operations: ['99-79=20', '9+20=29'] Exploring Operation: 39-29=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 39*29=1131, Resulting Numbers: [1131] 1131,29 unequal: No Solution Exploring Operation: 39+29=68, Resulting Numbers: [68] 68,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 29:[20, 30], Operations: ['99-79=20', '39-9=30'] Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,29 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,29 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 29:[20, 48], Operations: ['99-79=20', '9+39=48'] Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,29 unequal: No Solution Exploring Operation: 48-20=28, Resulting Numbers: [28] 28,29 unequal: No Solution Exploring Operation: 20*48=960, Resulting Numbers: [960] 960,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 29:[39, 79, 11], Operations: ['99/9=11'] Exploring Operation: 79-39=40, Resulting Numbers: [11, 40] Generated Node #0,0,0: 29:[11, 40] Operation: 79-39=40 Exploring Operation: 79-11=68, Resulting Numbers: [39, 68] Generated Node #0,0,1: 29:[39, 68] Operation: 79-11=68 Exploring Operation: 39-11=28, Resulting Numbers: [79, 28] Generated Node #0,0,2: 29:[79, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[11, 40], Operations: ['99/9=11', '79-39=40'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[9, 39, 99, 79], Operations: [] Exploring Operation: 99/9=11, Resulting Numbers: [39, 79, 11] Generated Node #0,0: 29:[39, 79, 11] Operation: 99/9=11 Moving to Node #0,0 Current State: 29:[39, 79, 11], Operations: ['99/9=11'] Exploring Operation: 79-39=40, Resulting Numbers: [11, 40] Generated Node #0,0,0: 29:[11, 40] Operation: 79-39=40 Moving to Node #0,0,0 Current State: 29:[11, 40], Operations: ['99/9=11', '79-39=40'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 58, 63, 43, 80 ]
59
[ "63-58=5", "80/5=16", "43+16=59" ]
Current State: 59:[58, 63, 43, 80], Operations: [] Exploring Operation: 63-58=5, Resulting Numbers: [43, 80, 5] Generated Node #2: [43, 80, 5] from Operation: 63-58=5 Current State: 59:[43, 80, 5], Operations: ['63-58=5'] Exploring Operation: 80/5=16, Resulting Numbers: [43, 16] Generated Node #3: [43, 16] from Operation: 80/5=16 Current State: 59:[43, 16], Operations: ['63-58=5', '80/5=16'] Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[58, 63, 43, 80], Operations: [] Exploring Operation: 80-43=37, Resulting Numbers: [58, 63, 37] Generated Node #0,0: 59:[58, 63, 37] Operation: 80-43=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[58, 63, 37], Operations: ['80-43=37'] Exploring Operation: 63-37=26, Resulting Numbers: [58, 26] Generated Node #0,0,0: 59:[58, 26] Operation: 63-37=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 59:[58, 26], Operations: ['80-43=37', '63-37=26'] Exploring Operation: 58+26=84, Resulting Numbers: [84] 84,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 76, 95, 3, 2 ]
25
[ "95-76=19", "3*2=6", "19+6=25" ]
Current State: 25:[76, 95, 3, 2], Operations: [] Exploring Operation: 95-76=19, Resulting Numbers: [3, 2, 19] Generated Node #2: [3, 2, 19] from Operation: 95-76=19 Current State: 25:[3, 2, 19], Operations: ['95-76=19'] Exploring Operation: 3*2=6, Resulting Numbers: [19, 6] Generated Node #3: [19, 6] from Operation: 3*2=6 Current State: 25:[19, 6], Operations: ['95-76=19', '3*2=6'] Exploring Operation: 19+6=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[76, 95, 3, 2], Operations: [] Exploring Operation: 95-76=19, Resulting Numbers: [3, 2, 19] Generated Node #0,0: 25:[3, 2, 19] Operation: 95-76=19 Exploring Operation: 76/2=38, Resulting Numbers: [95, 3, 38] Generated Node #0,1: 25:[95, 3, 38] Operation: 76/2=38 Exploring Operation: 76-3=73, Resulting Numbers: [95, 2, 73] Generated Node #0,2: 25:[95, 2, 73] Operation: 76-3=73 Moving to Node #0,0 Current State: 25:[3, 2, 19], Operations: ['95-76=19'] Exploring Operation: 3+19=22, Resulting Numbers: [2, 22] Generated Node #0,0,0: 25:[2, 22] Operation: 3+19=22 Exploring Operation: 3+2=5, Resulting Numbers: [19, 5] Generated Node #0,0,1: 25:[19, 5] Operation: 3+2=5 Exploring Operation: 2+19=21, Resulting Numbers: [3, 21] Generated Node #0,0,2: 25:[3, 21] Operation: 2+19=21 Moving to Node #0,1 Current State: 25:[95, 3, 38], Operations: ['76/2=38'] Exploring Operation: 95-38=57, Resulting Numbers: [3, 57] Generated Node #0,1,0: 25:[3, 57] Operation: 95-38=57 Exploring Operation: 95-3=92, Resulting Numbers: [38, 92] Generated Node #0,1,1: 25:[38, 92] Operation: 95-3=92 Exploring Operation: 38-3=35, Resulting Numbers: [95, 35] Generated Node #0,1,2: 25:[95, 35] Operation: 38-3=35 Moving to Node #0,2 Current State: 25:[95, 2, 73], Operations: ['76-3=73'] Exploring Operation: 95-2=93, Resulting Numbers: [73, 93] Generated Node #0,2,0: 25:[73, 93] Operation: 95-2=93 Exploring Operation: 95-73=22, Resulting Numbers: [2, 22] Generated Node #0,2,1: 25:[2, 22] Operation: 95-73=22 Exploring Operation: 73-2=71, Resulting Numbers: [95, 71] Generated Node #0,2,2: 25:[95, 71] Operation: 73-2=71 Moving to Node #0,0,0 Current State: 25:[2, 22], Operations: ['95-76=19', '3+19=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[3, 21], Operations: ['95-76=19', '2+19=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,25 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[2, 22], Operations: ['76-3=73', '95-73=22'] Exploring Operation: 2+22=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 22/2=11, Resulting Numbers: [11] 11,25 unequal: No Solution Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[19, 5], Operations: ['95-76=19', '3+2=5'] Exploring Operation: 19*5=95, Resulting Numbers: [95] 95,25 unequal: No Solution Exploring Operation: 19+5=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 19-5=14, Resulting Numbers: [14] 14,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[3, 57], Operations: ['76/2=38', '95-38=57'] Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,25 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[95, 35], Operations: ['76/2=38', '38-3=35'] Exploring Operation: 95+35=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 95-35=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 95*35=3325, Resulting Numbers: [3325] 3325,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[38, 92], Operations: ['76/2=38', '95-3=92'] Exploring Operation: 92-38=54, Resulting Numbers: [54] 54,25 unequal: No Solution Exploring Operation: 38*92=3496, Resulting Numbers: [3496] 3496,25 unequal: No Solution Exploring Operation: 38+92=130, Resulting Numbers: [130] 130,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[95, 71], Operations: ['76-3=73', '73-2=71'] Exploring Operation: 95*71=6745, Resulting Numbers: [6745] 6745,25 unequal: No Solution Exploring Operation: 95+71=166, Resulting Numbers: [166] 166,25 unequal: No Solution Exploring Operation: 95-71=24, Resulting Numbers: [24] 24,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[73, 93], Operations: ['76-3=73', '95-2=93'] Exploring Operation: 73*93=6789, Resulting Numbers: [6789] 6789,25 unequal: No Solution Exploring Operation: 73+93=166, Resulting Numbers: [166] 166,25 unequal: No Solution Exploring Operation: 93-73=20, Resulting Numbers: [20] 20,25 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 76, 95, 21, 94 ]
47
[ "95-76=19", "21-19=2", "94/2=47" ]
Current State: 47:[76, 95, 21, 94], Operations: [] Exploring Operation: 95-76=19, Resulting Numbers: [21, 94, 19] Generated Node #2: [21, 94, 19] from Operation: 95-76=19 Current State: 47:[21, 94, 19], Operations: ['95-76=19'] Exploring Operation: 21-19=2, Resulting Numbers: [94, 2] Generated Node #3: [94, 2] from Operation: 21-19=2 Current State: 47:[94, 2], Operations: ['95-76=19', '21-19=2'] Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[76, 95, 21, 94], Operations: [] Exploring Operation: 95-76=19, Resulting Numbers: [21, 94, 19] Generated Node #0,0: 47:[21, 94, 19] Operation: 95-76=19 Exploring Operation: 95-94=1, Resulting Numbers: [76, 21, 1] Generated Node #0,1: 47:[76, 21, 1] Operation: 95-94=1 Moving to Node #0,0 Current State: 47:[21, 94, 19], Operations: ['95-76=19'] Exploring Operation: 94-21=73, Resulting Numbers: [19, 73] Generated Node #0,0,0: 47:[19, 73] Operation: 94-21=73 Exploring Operation: 21+19=40, Resulting Numbers: [94, 40] Generated Node #0,0,1: 47:[94, 40] Operation: 21+19=40 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[19, 73], Operations: ['95-76=19', '94-21=73'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 19+73=92, Resulting Numbers: [92] 92,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[94, 40], Operations: ['95-76=19', '21+19=40'] Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 94+40=134, Resulting Numbers: [134] 134,47 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: 47:[76, 21, 1], Operations: ['95-94=1'] Exploring Operation: 76-21=55, Resulting Numbers: [1, 55] Generated Node #0,1,0: 47:[1, 55] Operation: 76-21=55 Exploring Operation: 76-1=75, Resulting Numbers: [21, 75] Generated Node #0,1,1: 47:[21, 75] Operation: 76-1=75 Moving to Node #0,1,0 Current State: 47:[1, 55], Operations: ['95-94=1', '76-21=55'] Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 1*55=55, Resulting Numbers: [55] 55,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[21, 75], Operations: ['95-94=1', '76-1=75'] Exploring Operation: 75-21=54, Resulting Numbers: [54] 54,47 unequal: No Solution Exploring Operation: 21+75=96, Resulting Numbers: [96] 96,47 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 12, 23, 59, 63 ]
21
[ "12*63=756", "59-23=36", "756/36=21" ]
Current State: 21:[12, 23, 59, 63], Operations: [] Exploring Operation: 12*63=756, Resulting Numbers: [23, 59, 756] Generated Node #2: [23, 59, 756] from Operation: 12*63=756 Current State: 21:[23, 59, 756], Operations: ['12*63=756'] Exploring Operation: 59-23=36, Resulting Numbers: [756, 36] Generated Node #3: [756, 36] from Operation: 59-23=36 Current State: 21:[756, 36], Operations: ['12*63=756', '59-23=36'] Exploring Operation: 756/36=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[12, 23, 59, 63], Operations: [] Exploring Operation: 59-23=36, Resulting Numbers: [12, 63, 36] Generated Node #0,0: 21:[12, 63, 36] Operation: 59-23=36 Exploring Operation: 63-23=40, Resulting Numbers: [12, 59, 40] Generated Node #0,1: 21:[12, 59, 40] Operation: 63-23=40 Exploring Operation: 63-59=4, Resulting Numbers: [12, 23, 4] Generated Node #0,2: 21:[12, 23, 4] Operation: 63-59=4 Moving to Node #0,2 Current State: 21:[12, 23, 4], Operations: ['63-59=4'] Exploring Operation: 12-4=8, Resulting Numbers: [23, 8] Generated Node #0,2,0: 21:[23, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [23, 3] Generated Node #0,2,1: 21:[23, 3] Operation: 12/4=3 Exploring Operation: 23-12=11, Resulting Numbers: [4, 11] Generated Node #0,2,2: 21:[4, 11] Operation: 23-12=11 Moving to Node #0,0 Current State: 21:[12, 63, 36], Operations: ['59-23=36'] Exploring Operation: 63-12=51, Resulting Numbers: [36, 51] Generated Node #0,0,0: 21:[36, 51] Operation: 63-12=51 Exploring Operation: 36/12=3, Resulting Numbers: [63, 3] Generated Node #0,0,1: 21:[63, 3] Operation: 36/12=3 Exploring Operation: 63-36=27, Resulting Numbers: [12, 27] Generated Node #0,0,2: 21:[12, 27] Operation: 63-36=27 Moving to Node #0,1 Current State: 21:[12, 59, 40], Operations: ['63-23=40'] Exploring Operation: 40-12=28, Resulting Numbers: [59, 28] Generated Node #0,1,0: 21:[59, 28] Operation: 40-12=28 Exploring Operation: 59-40=19, Resulting Numbers: [12, 19] Generated Node #0,1,1: 21:[12, 19] Operation: 59-40=19 Exploring Operation: 59-12=47, Resulting Numbers: [40, 47] Generated Node #0,1,2: 21:[40, 47] Operation: 59-12=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[12, 19], Operations: ['63-23=40', '59-40=19'] Exploring Operation: 12+19=31, Resulting Numbers: [31] 31,21 unequal: No Solution Exploring Operation: 19-12=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 12*19=228, Resulting Numbers: [228] 228,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[59, 28], Operations: ['63-23=40', '40-12=28'] Exploring Operation: 59+28=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 59-28=31, Resulting Numbers: [31] 31,21 unequal: No Solution Exploring Operation: 59*28=1652, Resulting Numbers: [1652] 1652,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[40, 47], Operations: ['63-23=40', '59-12=47'] Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,21 unequal: No Solution Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,21 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,21 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: 21:[23, 3], Operations: ['63-59=4', '12/4=3'] Exploring Operation: 23+3=26, Resulting Numbers: [26] 26,21 unequal: No Solution Exploring Operation: 23*3=69, Resulting Numbers: [69] 69,21 unequal: No Solution Exploring Operation: 23-3=20, Resulting Numbers: [20] 20,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[23, 8], Operations: ['63-59=4', '12-4=8'] Exploring Operation: 23*8=184, Resulting Numbers: [184] 184,21 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 23+8=31, Resulting Numbers: [31] 31,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[4, 11], Operations: ['63-59=4', '23-12=11'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 4+11=15, Resulting Numbers: [15] 15,21 unequal: No Solution Exploring Operation: 4*11=44, Resulting Numbers: [44] 44,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[12, 27], Operations: ['59-23=36', '63-36=27'] Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,21 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,21 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,21 unequal: No Solution Moving to Node #0,0,1 Current State: 21:[63, 3], Operations: ['59-23=36', '36/12=3'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[12, 23, 59, 63], Operations: [] Exploring Operation: 59-23=36, Resulting Numbers: [12, 63, 36] Generated Node #0,0: 21:[12, 63, 36] Operation: 59-23=36 Moving to Node #0,0 Current State: 21:[12, 63, 36], Operations: ['59-23=36'] Exploring Operation: 36/12=3, Resulting Numbers: [63, 3] Generated Node #0,0,1: 21:[63, 3] Operation: 36/12=3 Moving to Node #0,0,1 Current State: 21:[63, 3], Operations: ['59-23=36', '36/12=3'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.967014
hs_3
sum_heuristic
[ 39, 46, 16, 54 ]
63
[ "46-39=7", "16+54=70", "70-7=63" ]
Current State: 63:[39, 46, 16, 54], Operations: [] Exploring Operation: 46-39=7, Resulting Numbers: [16, 54, 7] Generated Node #2: [16, 54, 7] from Operation: 46-39=7 Current State: 63:[16, 54, 7], Operations: ['46-39=7'] Exploring Operation: 16+54=70, Resulting Numbers: [7, 70] Generated Node #3: [7, 70] from Operation: 16+54=70 Current State: 63:[7, 70], Operations: ['46-39=7', '16+54=70'] Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[39, 46, 16, 54], Operations: [] Exploring Operation: 46-39=7, Resulting Numbers: [16, 54, 7] Generated Node #0,0: 63:[16, 54, 7] Operation: 46-39=7 Exploring Operation: 54-46=8, Resulting Numbers: [39, 16, 8] Generated Node #0,1: 63:[39, 16, 8] Operation: 54-46=8 Exploring Operation: 39-16=23, Resulting Numbers: [46, 54, 23] Generated Node #0,2: 63:[46, 54, 23] Operation: 39-16=23 Exploring Operation: 54-39=15, Resulting Numbers: [46, 16, 15] Generated Node #0,3: 63:[46, 16, 15] Operation: 54-39=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[16, 54, 7], Operations: ['46-39=7'] Exploring Operation: 54+7=61, Resulting Numbers: [16, 61] Generated Node #0,0,0: 63:[16, 61] Operation: 54+7=61 Exploring Operation: 16-7=9, Resulting Numbers: [54, 9] Generated Node #0,0,1: 63:[54, 9] Operation: 16-7=9 Exploring Operation: 16+54=70, Resulting Numbers: [7, 70] Generated Node #0,0,2: 63:[7, 70] Operation: 16+54=70 Exploring Operation: 16+7=23, Resulting Numbers: [54, 23] Generated Node #0,0,3: 63:[54, 23] Operation: 16+7=23 Moving to Node #0,0,0 Current State: 63:[16, 61], Operations: ['46-39=7', '54+7=61'] Exploring Operation: 16*61=976, Resulting Numbers: [976] 976,63 unequal: No Solution Exploring Operation: 16+61=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,63 unequal: No Solution Moving to Node #0,0,2 Current State: 63:[7, 70], Operations: ['46-39=7', '16+54=70'] Exploring Operation: 7+70=77, Resulting Numbers: [77] 77,63 unequal: No Solution Exploring Operation: 7*70=490, Resulting Numbers: [490] 490,63 unequal: No Solution Exploring Operation: 70/7=10, Resulting Numbers: [10] 10,63 unequal: No Solution Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[39, 46, 16, 54], Operations: [] Exploring Operation: 46-39=7, Resulting Numbers: [16, 54, 7] Generated Node #0,0: 63:[16, 54, 7] Operation: 46-39=7 Moving to Node #0,0 Current State: 63:[16, 54, 7], Operations: ['46-39=7'] Exploring Operation: 16+54=70, Resulting Numbers: [7, 70] Generated Node #0,0,2: 63:[7, 70] Operation: 16+54=70 Moving to Node #0,0,2 Current State: 63:[7, 70], Operations: ['46-39=7', '16+54=70'] Exploring Operation: 70-7=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 69, 7, 77, 10 ]
76
[ "69+77=146", "7*10=70", "146-70=76" ]
Current State: 76:[69, 7, 77, 10], Operations: [] Exploring Operation: 69+77=146, Resulting Numbers: [7, 10, 146] Generated Node #2: [7, 10, 146] from Operation: 69+77=146 Current State: 76:[7, 10, 146], Operations: ['69+77=146'] Exploring Operation: 7*10=70, Resulting Numbers: [146, 70] Generated Node #3: [146, 70] from Operation: 7*10=70 Current State: 76:[146, 70], Operations: ['69+77=146', '7*10=70'] Exploring Operation: 146-70=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[69, 7, 77, 10], Operations: [] Exploring Operation: 10-7=3, Resulting Numbers: [69, 77, 3] Generated Node #0,0: 76:[69, 77, 3] Operation: 10-7=3 Exploring Operation: 69+7=76, Resulting Numbers: [77, 10, 76] Generated Node #0,1: 76:[77, 10, 76] Operation: 69+7=76 Exploring Operation: 69+10=79, Resulting Numbers: [7, 77, 79] Generated Node #0,2: 76:[7, 77, 79] Operation: 69+10=79 Exploring Operation: 7+10=17, Resulting Numbers: [69, 77, 17] Generated Node #0,3: 76:[69, 77, 17] Operation: 7+10=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[77, 10, 76], Operations: ['69+7=76'] Exploring Operation: 77-76=1, Resulting Numbers: [10, 1] Generated Node #0,1,0: 76:[10, 1] Operation: 77-76=1 Exploring Operation: 77+10=87, Resulting Numbers: [76, 87] Generated Node #0,1,1: 76:[76, 87] Operation: 77+10=87 Exploring Operation: 77-10=67, Resulting Numbers: [76, 67] Generated Node #0,1,2: 76:[76, 67] Operation: 77-10=67 Exploring Operation: 10+76=86, Resulting Numbers: [77, 86] Generated Node #0,1,3: 76:[77, 86] Operation: 10+76=86 Moving to Node #0,1,0 Current State: 76:[10, 1], Operations: ['69+7=76', '77-76=1'] Exploring Operation: 10/1=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 10+1=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 10*1=10, Resulting Numbers: [10] 10,76 unequal: No Solution Exploring Operation: 10-1=9, Resulting Numbers: [9] 9,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[76, 67], Operations: ['69+7=76', '77-10=67'] Exploring Operation: 76-67=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 76+67=143, Resulting Numbers: [143] 143,76 unequal: No Solution Exploring Operation: 76*67=5092, Resulting Numbers: [5092] 5092,76 unequal: No Solution Moving to Node #0,1,3 Current State: 76:[77, 86], Operations: ['69+7=76', '10+76=86'] Exploring Operation: 86-77=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 77+86=163, Resulting Numbers: [163] 163,76 unequal: No Solution Exploring Operation: 77*86=6622, Resulting Numbers: [6622] 6622,76 unequal: No Solution Moving to Node #0,1,1 Current State: 76:[76, 87], Operations: ['69+7=76', '77+10=87'] Exploring Operation: 76*87=6612, Resulting Numbers: [6612] 6612,76 unequal: No Solution Exploring Operation: 87-76=11, Resulting Numbers: [11] 11,76 unequal: No Solution Exploring Operation: 76+87=163, Resulting Numbers: [163] 163,76 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:[7, 77, 79], Operations: ['69+10=79'] Exploring Operation: 79-77=2, Resulting Numbers: [7, 2] Generated Node #0,2,0: 76:[7, 2] Operation: 79-77=2 Exploring Operation: 77-7=70, Resulting Numbers: [79, 70] Generated Node #0,2,1: 76:[79, 70] Operation: 77-7=70 Exploring Operation: 77/7=11, Resulting Numbers: [79, 11] Generated Node #0,2,2: 76:[79, 11] Operation: 77/7=11 Exploring Operation: 79-7=72, Resulting Numbers: [77, 72] Generated Node #0,2,3: 76:[77, 72] Operation: 79-7=72 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 76:[7, 2], Operations: ['69+10=79', '79-77=2'] Exploring Operation: 7*2=14, Resulting Numbers: [14] 14,76 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 76:[77, 72], Operations: ['69+10=79', '79-7=72'] Exploring Operation: 77*72=5544, Resulting Numbers: [5544] 5544,76 unequal: No Solution Exploring Operation: 77+72=149, Resulting Numbers: [149] 149,76 unequal: No Solution Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 76:[79, 70], Operations: ['69+10=79', '77-7=70'] Exploring Operation: 79+70=149, Resulting Numbers: [149] 149,76 unequal: No Solution Exploring Operation: 79-70=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 79*70=5530, Resulting Numbers: [5530] 5530,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 76:[79, 11], Operations: ['69+10=79', '77/7=11'] Exploring Operation: 79*11=869, Resulting Numbers: [869] 869,76 unequal: No Solution Exploring Operation: 79-11=68, Resulting Numbers: [68] 68,76 unequal: No Solution Exploring Operation: 79+11=90, Resulting Numbers: [90] 90,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[69, 77, 3], Operations: ['10-7=3'] Exploring Operation: 77-3=74, Resulting Numbers: [69, 74] Generated Node #0,0,0: 76:[69, 74] Operation: 77-3=74 Exploring Operation: 69/3=23, Resulting Numbers: [77, 23] Generated Node #0,0,1: 76:[77, 23] Operation: 69/3=23 Exploring Operation: 69+3=72, Resulting Numbers: [77, 72] Generated Node #0,0,2: 76:[77, 72] Operation: 69+3=72 Exploring Operation: 77-69=8, Resulting Numbers: [3, 8] Generated Node #0,0,3: 76:[3, 8] Operation: 77-69=8 Moving to Node #0,0,1 Current State: 76:[77, 23], Operations: ['10-7=3', '69/3=23'] Exploring Operation: 77-23=54, Resulting Numbers: [54] 54,76 unequal: No Solution Exploring Operation: 77+23=100, Resulting Numbers: [100] 100,76 unequal: No Solution Exploring Operation: 77*23=1771, Resulting Numbers: [1771] 1771,76 unequal: No Solution Moving to Node #0,0,3 Current State: 76:[3, 8], Operations: ['10-7=3', '77-69=8'] Exploring Operation: 3*8=24, Resulting Numbers: [24] 24,76 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 3+8=11, Resulting Numbers: [11] 11,76 unequal: No Solution Moving to Node #0,0,2 Current State: 76:[77, 72], Operations: ['10-7=3', '69+3=72'] Exploring Operation: 77-72=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 77*72=5544, Resulting Numbers: [5544] 5544,76 unequal: No Solution Exploring Operation: 77+72=149, Resulting Numbers: [149] 149,76 unequal: No Solution Moving to Node #0,0,0 Current State: 76:[69, 74], Operations: ['10-7=3', '77-3=74'] Exploring Operation: 69+74=143, Resulting Numbers: [143] 143,76 unequal: No Solution Exploring Operation: 74-69=5, Resulting Numbers: [5] 5,76 unequal: No Solution Exploring Operation: 69*74=5106, Resulting Numbers: [5106] 5106,76 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:[69, 77, 17], Operations: ['7+10=17'] Exploring Operation: 69-17=52, Resulting Numbers: [77, 52] Generated Node #0,3,0: 76:[77, 52] Operation: 69-17=52 Exploring Operation: 77-69=8, Resulting Numbers: [17, 8] Generated Node #0,3,1: 76:[17, 8] Operation: 77-69=8 Exploring Operation: 69+17=86, Resulting Numbers: [77, 86] Generated Node #0,3,2: 76:[77, 86] Operation: 69+17=86 Exploring Operation: 77-17=60, Resulting Numbers: [69, 60] Generated Node #0,3,3: 76:[69, 60] Operation: 77-17=60 Moving to Node #0,3,1 Current State: 76:[17, 8], Operations: ['7+10=17', '77-69=8'] Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,76 unequal: No Solution Moving to Node #0,3,2 Current State: 76:[77, 86], Operations: ['7+10=17', '69+17=86'] Exploring Operation: 77+86=163, Resulting Numbers: [163] 163,76 unequal: No Solution Exploring Operation: 86-77=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 77*86=6622, Resulting Numbers: [6622] 6622,76 unequal: No Solution Moving to Node #0,3,0 Current State: 76:[77, 52], Operations: ['7+10=17', '69-17=52'] Exploring Operation: 77*52=4004, Resulting Numbers: [4004] 4004,76 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,76 unequal: No Solution Exploring Operation: 77+52=129, Resulting Numbers: [129] 129,76 unequal: No Solution Moving to Node #0,3,3 Current State: 76:[69, 60], Operations: ['7+10=17', '77-17=60'] Exploring Operation: 69*60=4140, Resulting Numbers: [4140] 4140,76 unequal: No Solution Exploring Operation: 69-60=9, Resulting Numbers: [9] 9,76 unequal: No Solution Exploring Operation: 69+60=129, Resulting Numbers: [129] 129,76 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
[ 75, 95, 57, 66 ]
21
[ "75*57=4275", "4275/95=45", "66-45=21" ]
Current State: 21:[75, 95, 57, 66], Operations: [] Exploring Operation: 75*57=4275, Resulting Numbers: [95, 66, 4275] Generated Node #2: [95, 66, 4275] from Operation: 75*57=4275 Current State: 21:[95, 66, 4275], Operations: ['75*57=4275'] Exploring Operation: 4275/95=45, Resulting Numbers: [66, 45] Generated Node #3: [66, 45] from Operation: 4275/95=45 Current State: 21:[66, 45], Operations: ['75*57=4275', '4275/95=45'] Exploring Operation: 66-45=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[75, 95, 57, 66], Operations: [] Exploring Operation: 95-75=20, Resulting Numbers: [57, 66, 20] Generated Node #0,0: 21:[57, 66, 20] Operation: 95-75=20 Exploring Operation: 95-66=29, Resulting Numbers: [75, 57, 29] Generated Node #0,1: 21:[75, 57, 29] Operation: 95-66=29 Exploring Operation: 75-66=9, Resulting Numbers: [95, 57, 9] Generated Node #0,2: 21:[95, 57, 9] Operation: 75-66=9 Moving to Node #0,0 Current State: 21:[57, 66, 20], Operations: ['95-75=20'] Exploring Operation: 66-20=46, Resulting Numbers: [57, 46] Generated Node #0,0,0: 21:[57, 46] Operation: 66-20=46 Exploring Operation: 66-57=9, Resulting Numbers: [20, 9] Generated Node #0,0,1: 21:[20, 9] Operation: 66-57=9 Exploring Operation: 57-20=37, Resulting Numbers: [66, 37] Generated Node #0,0,2: 21:[66, 37] Operation: 57-20=37 Moving to Node #0,1 Current State: 21:[75, 57, 29], Operations: ['95-66=29'] Exploring Operation: 57-29=28, Resulting Numbers: [75, 28] Generated Node #0,1,0: 21:[75, 28] Operation: 57-29=28 Exploring Operation: 75-57=18, Resulting Numbers: [29, 18] Generated Node #0,1,1: 21:[29, 18] Operation: 75-57=18 Exploring Operation: 75-29=46, Resulting Numbers: [57, 46] Generated Node #0,1,2: 21:[57, 46] Operation: 75-29=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 21:[29, 18], Operations: ['95-66=29', '75-57=18'] Exploring Operation: 29-18=11, Resulting Numbers: [11] 11,21 unequal: No Solution Exploring Operation: 29+18=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 29*18=522, Resulting Numbers: [522] 522,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[75, 28], Operations: ['95-66=29', '57-29=28'] Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 75+28=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 75*28=2100, Resulting Numbers: [2100] 2100,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 21:[57, 46], Operations: ['95-66=29', '75-29=46'] Exploring Operation: 57*46=2622, Resulting Numbers: [2622] 2622,21 unequal: No Solution Exploring Operation: 57+46=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,21 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: 21:[95, 57, 9], Operations: ['75-66=9'] Exploring Operation: 95-57=38, Resulting Numbers: [9, 38] Generated Node #0,2,0: 21:[9, 38] Operation: 95-57=38 Exploring Operation: 95-9=86, Resulting Numbers: [57, 86] Generated Node #0,2,1: 21:[57, 86] Operation: 95-9=86 Exploring Operation: 57-9=48, Resulting Numbers: [95, 48] Generated Node #0,2,2: 21:[95, 48] Operation: 57-9=48 Moving to Node #0,0,1 Current State: 21:[20, 9], Operations: ['95-75=20', '66-57=9'] Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,21 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,21 unequal: No Solution Moving to Node #0,2,0 Current State: 21:[9, 38], Operations: ['75-66=9', '95-57=38'] Exploring Operation: 9*38=342, Resulting Numbers: [342] 342,21 unequal: No Solution Exploring Operation: 9+38=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 38-9=29, Resulting Numbers: [29] 29,21 unequal: No Solution Moving to Node #0,0,2 Current State: 21:[66, 37], Operations: ['95-75=20', '57-20=37'] Exploring Operation: 66+37=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 66*37=2442, Resulting Numbers: [2442] 2442,21 unequal: No Solution Exploring Operation: 66-37=29, Resulting Numbers: [29] 29,21 unequal: No Solution Moving to Node #0,0,0 Current State: 21:[57, 46], Operations: ['95-75=20', '66-20=46'] Exploring Operation: 57+46=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 57*46=2622, Resulting Numbers: [2622] 2622,21 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,21 unequal: No Solution Moving to Node #0,2,2 Current State: 21:[95, 48], Operations: ['75-66=9', '57-9=48'] Exploring Operation: 95*48=4560, Resulting Numbers: [4560] 4560,21 unequal: No Solution Exploring Operation: 95+48=143, Resulting Numbers: [143] 143,21 unequal: No Solution Exploring Operation: 95-48=47, Resulting Numbers: [47] 47,21 unequal: No Solution Moving to Node #0,2,1 Current State: 21:[57, 86], Operations: ['75-66=9', '95-9=86'] Exploring Operation: 86-57=29, Resulting Numbers: [29] 29,21 unequal: No Solution Exploring Operation: 57*86=4902, Resulting Numbers: [4902] 4902,21 unequal: No Solution Exploring Operation: 57+86=143, Resulting Numbers: [143] 143,21 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 73, 46, 17, 26 ]
70
[ "73-46=27", "17+26=43", "27+43=70" ]
Current State: 70:[73, 46, 17, 26], Operations: [] Exploring Operation: 73-46=27, Resulting Numbers: [17, 26, 27] Generated Node #2: [17, 26, 27] from Operation: 73-46=27 Current State: 70:[17, 26, 27], Operations: ['73-46=27'] Exploring Operation: 17+26=43, Resulting Numbers: [27, 43] Generated Node #3: [27, 43] from Operation: 17+26=43 Current State: 70:[27, 43], Operations: ['73-46=27', '17+26=43'] Exploring Operation: 27+43=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[73, 46, 17, 26], Operations: [] Exploring Operation: 26-17=9, Resulting Numbers: [73, 46, 9] Generated Node #0,0: 70:[73, 46, 9] Operation: 26-17=9 Exploring Operation: 46+26=72, Resulting Numbers: [73, 17, 72] Generated Node #0,1: 70:[73, 17, 72] Operation: 46+26=72 Exploring Operation: 46-26=20, Resulting Numbers: [73, 17, 20] Generated Node #0,2: 70:[73, 17, 20] Operation: 46-26=20 Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[73, 17, 72], Operations: ['46+26=72'] Exploring Operation: 73-17=56, Resulting Numbers: [72, 56] Generated Node #0,1,0: 70:[72, 56] Operation: 73-17=56 Exploring Operation: 72-17=55, Resulting Numbers: [73, 55] Generated Node #0,1,1: 70:[73, 55] Operation: 72-17=55 Exploring Operation: 73-72=1, Resulting Numbers: [17, 1] Generated Node #0,1,2: 70:[17, 1] Operation: 73-72=1 Moving to Node #0,1,2 Current State: 70:[17, 1], Operations: ['46+26=72', '73-72=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 17/1=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 17*1=17, Resulting Numbers: [17] 17,70 unequal: No Solution Moving to Node #0,1,0 Current State: 70:[72, 56], Operations: ['46+26=72', '73-17=56'] Exploring Operation: 72*56=4032, Resulting Numbers: [4032] 4032,70 unequal: No Solution Exploring Operation: 72+56=128, Resulting Numbers: [128] 128,70 unequal: No Solution Exploring Operation: 72-56=16, Resulting Numbers: [16] 16,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[73, 55], Operations: ['46+26=72', '72-17=55'] Exploring Operation: 73*55=4015, Resulting Numbers: [4015] 4015,70 unequal: No Solution Exploring Operation: 73+55=128, Resulting Numbers: [128] 128,70 unequal: No Solution Exploring Operation: 73-55=18, Resulting Numbers: [18] 18,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[73, 17, 20], Operations: ['46-26=20'] Exploring Operation: 73-17=56, Resulting Numbers: [20, 56] Generated Node #0,2,0: 70:[20, 56] Operation: 73-17=56 Exploring Operation: 17+20=37, Resulting Numbers: [73, 37] Generated Node #0,2,1: 70:[73, 37] Operation: 17+20=37 Exploring Operation: 20-17=3, Resulting Numbers: [73, 3] Generated Node #0,2,2: 70:[73, 3] Operation: 20-17=3 Moving to Node #0,2,2 Current State: 70:[73, 3], Operations: ['46-26=20', '20-17=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[73, 46, 17, 26], Operations: [] Exploring Operation: 46-26=20, Resulting Numbers: [73, 17, 20] Generated Node #0,2: 70:[73, 17, 20] Operation: 46-26=20 Moving to Node #0,2 Current State: 70:[73, 17, 20], Operations: ['46-26=20'] Exploring Operation: 20-17=3, Resulting Numbers: [73, 3] Generated Node #0,2,2: 70:[73, 3] Operation: 20-17=3 Moving to Node #0,2,2 Current State: 70:[73, 3], Operations: ['46-26=20', '20-17=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
mult_heuristic