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
[ 76, 7, 96, 2 ]
11
[ "76+7=83", "96-2=94", "94-83=11" ]
Current State: 11:[76, 7, 96, 2], Operations: [] Exploring Operation: 76+7=83, Resulting Numbers: [96, 2, 83] Generated Node #2: [96, 2, 83] from Operation: 76+7=83 Current State: 11:[96, 2, 83], Operations: ['76+7=83'] Exploring Operation: 96-2=94, Resulting Numbers: [83, 94] Generated Node #3: [83, 94] from Operation: 96-2=94 Current State: 11:[83, 94], Operations: ['76+7=83', '96-2=94'] Exploring Operation: 94-83=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[76, 7, 96, 2], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [7, 2, 20] Generated Node #0,0: 11:[7, 2, 20] Operation: 96-76=20 Exploring Operation: 96/2=48, Resulting Numbers: [76, 7, 48] Generated Node #0,1: 11:[76, 7, 48] Operation: 96/2=48 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[7, 2, 20], Operations: ['96-76=20'] Exploring Operation: 20/2=10, Resulting Numbers: [7, 10] Generated Node #0,0,0: 11:[7, 10] Operation: 20/2=10 Exploring Operation: 7+2=9, Resulting Numbers: [20, 9] Generated Node #0,0,1: 11:[20, 9] Operation: 7+2=9 Moving to Node #0,0,0 Current State: 11:[7, 10], Operations: ['96-76=20', '20/2=10'] Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,11 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,11 unequal: No Solution Moving to Node #0,0,1 Current State: 11:[20, 9], Operations: ['96-76=20', '7+2=9'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[76, 7, 96, 2], Operations: [] Exploring Operation: 96-76=20, Resulting Numbers: [7, 2, 20] Generated Node #0,0: 11:[7, 2, 20] Operation: 96-76=20 Moving to Node #0,0 Current State: 11:[7, 2, 20], Operations: ['96-76=20'] Exploring Operation: 7+2=9, Resulting Numbers: [20, 9] Generated Node #0,0,1: 11:[20, 9] Operation: 7+2=9 Moving to Node #0,0,1 Current State: 11:[20, 9], Operations: ['96-76=20', '7+2=9'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 20, 51, 26, 23 ]
18
[ "51-20=31", "26+23=49", "49-31=18" ]
Current State: 18:[20, 51, 26, 23], Operations: [] Exploring Operation: 51-20=31, Resulting Numbers: [26, 23, 31] Generated Node #2: [26, 23, 31] from Operation: 51-20=31 Current State: 18:[26, 23, 31], Operations: ['51-20=31'] Exploring Operation: 26+23=49, Resulting Numbers: [31, 49] Generated Node #3: [31, 49] from Operation: 26+23=49 Current State: 18:[31, 49], Operations: ['51-20=31', '26+23=49'] Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[20, 51, 26, 23], Operations: [] Exploring Operation: 51-26=25, Resulting Numbers: [20, 23, 25] Generated Node #0,0: 18:[20, 23, 25] Operation: 51-26=25 Exploring Operation: 51-23=28, Resulting Numbers: [20, 26, 28] Generated Node #0,1: 18:[20, 26, 28] Operation: 51-23=28 Exploring Operation: 51-20=31, Resulting Numbers: [26, 23, 31] Generated Node #0,2: 18:[26, 23, 31] Operation: 51-20=31 Moving to Node #0,0 Current State: 18:[20, 23, 25], Operations: ['51-26=25'] Exploring Operation: 25-23=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 18:[20, 2] Operation: 25-23=2 Exploring Operation: 25-20=5, Resulting Numbers: [23, 5] Generated Node #0,0,1: 18:[23, 5] Operation: 25-20=5 Exploring Operation: 23-20=3, Resulting Numbers: [25, 3] Generated Node #0,0,2: 18:[25, 3] Operation: 23-20=3 Moving to Node #0,1 Current State: 18:[20, 26, 28], Operations: ['51-23=28'] Exploring Operation: 28-20=8, Resulting Numbers: [26, 8] Generated Node #0,1,0: 18:[26, 8] Operation: 28-20=8 Exploring Operation: 28-26=2, Resulting Numbers: [20, 2] Generated Node #0,1,1: 18:[20, 2] Operation: 28-26=2 Exploring Operation: 26-20=6, Resulting Numbers: [28, 6] Generated Node #0,1,2: 18:[28, 6] Operation: 26-20=6 Moving to Node #0,2 Current State: 18:[26, 23, 31], Operations: ['51-20=31'] Exploring Operation: 26-23=3, Resulting Numbers: [31, 3] Generated Node #0,2,0: 18:[31, 3] Operation: 26-23=3 Exploring Operation: 31-26=5, Resulting Numbers: [23, 5] Generated Node #0,2,1: 18:[23, 5] Operation: 31-26=5 Exploring Operation: 31-23=8, Resulting Numbers: [26, 8] Generated Node #0,2,2: 18:[26, 8] Operation: 31-23=8 Moving to Node #0,0,0 Current State: 18:[20, 2], Operations: ['51-26=25', '25-23=2'] Exploring Operation: 20+2=22, Resulting Numbers: [22] 22,18 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[20, 51, 26, 23], Operations: [] Exploring Operation: 51-26=25, Resulting Numbers: [20, 23, 25] Generated Node #0,0: 18:[20, 23, 25] Operation: 51-26=25 Moving to Node #0,0 Current State: 18:[20, 23, 25], Operations: ['51-26=25'] Exploring Operation: 25-23=2, Resulting Numbers: [20, 2] Generated Node #0,0,0: 18:[20, 2] Operation: 25-23=2 Moving to Node #0,0,0 Current State: 18:[20, 2], Operations: ['51-26=25', '25-23=2'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.983507
hs_3
mult_heuristic
[ 84, 60, 68, 44 ]
16
[ "84+44=128", "68-60=8", "128/8=16" ]
Current State: 16:[84, 60, 68, 44], Operations: [] Exploring Operation: 84+44=128, Resulting Numbers: [60, 68, 128] Generated Node #2: [60, 68, 128] from Operation: 84+44=128 Current State: 16:[60, 68, 128], Operations: ['84+44=128'] Exploring Operation: 68-60=8, Resulting Numbers: [128, 8] Generated Node #3: [128, 8] from Operation: 68-60=8 Current State: 16:[128, 8], Operations: ['84+44=128', '68-60=8'] Exploring Operation: 128/8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[84, 60, 68, 44], Operations: [] Exploring Operation: 68-60=8, Resulting Numbers: [84, 44, 8] Generated Node #0,0: 16:[84, 44, 8] Operation: 68-60=8 Exploring Operation: 84-44=40, Resulting Numbers: [60, 68, 40] Generated Node #0,1: 16:[60, 68, 40] Operation: 84-44=40 Exploring Operation: 84-68=16, Resulting Numbers: [60, 44, 16] Generated Node #0,2: 16:[60, 44, 16] Operation: 84-68=16 Exploring Operation: 84-60=24, Resulting Numbers: [68, 44, 24] Generated Node #0,3: 16:[68, 44, 24] Operation: 84-60=24 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[60, 44, 16], Operations: ['84-68=16'] Exploring Operation: 60+44=104, Resulting Numbers: [16, 104] Generated Node #0,2,0: 16:[16, 104] Operation: 60+44=104 Exploring Operation: 60-44=16, Resulting Numbers: [16, 16] Generated Node #0,2,1: 16:[16, 16] Operation: 60-44=16 Exploring Operation: 44-16=28, Resulting Numbers: [60, 28] Generated Node #0,2,2: 16:[60, 28] Operation: 44-16=28 Exploring Operation: 60-16=44, Resulting Numbers: [44, 44] Generated Node #0,2,3: 16:[44, 44] Operation: 60-16=44 Moving to Node #0,2,1 Current State: 16:[16, 16], Operations: ['84-68=16', '60-44=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,16 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,16 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,16 unequal: No Solution Moving to Node #0,2,3 Current State: 16:[44, 44], Operations: ['84-68=16', '60-16=44'] Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,16 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,2,2 Current State: 16:[60, 28], Operations: ['84-68=16', '44-16=28'] Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 60*28=1680, Resulting Numbers: [1680] 1680,16 unequal: No Solution Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,16 unequal: No Solution Moving to Node #0,2,0 Current State: 16:[16, 104], Operations: ['84-68=16', '60+44=104'] Exploring Operation: 16*104=1664, Resulting Numbers: [1664] 1664,16 unequal: No Solution Exploring Operation: 104-16=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 16+104=120, Resulting Numbers: [120] 120,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[68, 44, 24], Operations: ['84-60=24'] Exploring Operation: 68+44=112, Resulting Numbers: [24, 112] Generated Node #0,3,0: 16:[24, 112] Operation: 68+44=112 Exploring Operation: 68-44=24, Resulting Numbers: [24, 24] Generated Node #0,3,1: 16:[24, 24] Operation: 68-44=24 Exploring Operation: 44-24=20, Resulting Numbers: [68, 20] Generated Node #0,3,2: 16:[68, 20] Operation: 44-24=20 Exploring Operation: 68-24=44, Resulting Numbers: [44, 44] Generated Node #0,3,3: 16:[44, 44] Operation: 68-24=44 Moving to Node #0,3,1 Current State: 16:[24, 24], Operations: ['84-60=24', '68-44=24'] Exploring Operation: 24-24=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 24*24=576, Resulting Numbers: [576] 576,16 unequal: No Solution Exploring Operation: 24+24=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 24/24=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,3,3 Current State: 16:[44, 44], Operations: ['84-60=24', '68-24=44'] Exploring Operation: 44*44=1936, Resulting Numbers: [1936] 1936,16 unequal: No Solution Exploring Operation: 44+44=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 44-44=0, Resulting Numbers: [0] 0,16 unequal: No Solution Exploring Operation: 44/44=1, Resulting Numbers: [1] 1,16 unequal: No Solution Moving to Node #0,3,2 Current State: 16:[68, 20], Operations: ['84-60=24', '44-24=20'] Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,16 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,16 unequal: No Solution Moving to Node #0,3,0 Current State: 16:[24, 112], Operations: ['84-60=24', '68+44=112'] Exploring Operation: 24*112=2688, Resulting Numbers: [2688] 2688,16 unequal: No Solution Exploring Operation: 112-24=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 24+112=136, Resulting Numbers: [136] 136,16 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:[84, 44, 8], Operations: ['68-60=8'] Exploring Operation: 84+8=92, Resulting Numbers: [44, 92] Generated Node #0,0,0: 16:[44, 92] Operation: 84+8=92 Exploring Operation: 44-8=36, Resulting Numbers: [84, 36] Generated Node #0,0,1: 16:[84, 36] Operation: 44-8=36 Exploring Operation: 84-44=40, Resulting Numbers: [8, 40] Generated Node #0,0,2: 16:[8, 40] Operation: 84-44=40 Exploring Operation: 84-8=76, Resulting Numbers: [44, 76] Generated Node #0,0,3: 16:[44, 76] Operation: 84-8=76 Moving to Node #0,0,2 Current State: 16:[8, 40], Operations: ['68-60=8', '84-44=40'] Exploring Operation: 8+40=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 8*40=320, Resulting Numbers: [320] 320,16 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[44, 76], Operations: ['68-60=8', '84-8=76'] Exploring Operation: 44+76=120, Resulting Numbers: [120] 120,16 unequal: No Solution Exploring Operation: 76-44=32, Resulting Numbers: [32] 32,16 unequal: No Solution Exploring Operation: 44*76=3344, Resulting Numbers: [3344] 3344,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[84, 36], Operations: ['68-60=8', '44-8=36'] Exploring Operation: 84+36=120, Resulting Numbers: [120] 120,16 unequal: No Solution Exploring Operation: 84-36=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 84*36=3024, Resulting Numbers: [3024] 3024,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[44, 92], Operations: ['68-60=8', '84+8=92'] Exploring Operation: 92-44=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 44*92=4048, Resulting Numbers: [4048] 4048,16 unequal: No Solution Exploring Operation: 44+92=136, Resulting Numbers: [136] 136,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[60, 68, 40], Operations: ['84-44=40'] Exploring Operation: 60-40=20, Resulting Numbers: [68, 20] Generated Node #0,1,0: 16:[68, 20] Operation: 60-40=20 Exploring Operation: 68-40=28, Resulting Numbers: [60, 28] Generated Node #0,1,1: 16:[60, 28] Operation: 68-40=28 Exploring Operation: 60+68=128, Resulting Numbers: [40, 128] Generated Node #0,1,2: 16:[40, 128] Operation: 60+68=128 Exploring Operation: 68-60=8, Resulting Numbers: [40, 8] Generated Node #0,1,3: 16:[40, 8] Operation: 68-60=8 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 16:[40, 8], Operations: ['84-44=40', '68-60=8'] Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,16 unequal: No Solution Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,16 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 16:[68, 20], Operations: ['84-44=40', '60-40=20'] Exploring Operation: 68-20=48, Resulting Numbers: [48] 48,16 unequal: No Solution Exploring Operation: 68+20=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 68*20=1360, Resulting Numbers: [1360] 1360,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 16:[60, 28], Operations: ['84-44=40', '68-40=28'] Exploring Operation: 60*28=1680, Resulting Numbers: [1680] 1680,16 unequal: No Solution Exploring Operation: 60-28=32, Resulting Numbers: [32] 32,16 unequal: No Solution Exploring Operation: 60+28=88, Resulting Numbers: [88] 88,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 16:[40, 128], Operations: ['84-44=40', '60+68=128'] Exploring Operation: 128-40=88, Resulting Numbers: [88] 88,16 unequal: No Solution Exploring Operation: 40+128=168, Resulting Numbers: [168] 168,16 unequal: No Solution Exploring Operation: 40*128=5120, Resulting Numbers: [5120] 5120,16 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 35, 57, 39, 25 ]
78
[ "35+57=92", "39-25=14", "92-14=78" ]
Current State: 78:[35, 57, 39, 25], Operations: [] Exploring Operation: 35+57=92, Resulting Numbers: [39, 25, 92] Generated Node #2: [39, 25, 92] from Operation: 35+57=92 Current State: 78:[39, 25, 92], Operations: ['35+57=92'] Exploring Operation: 39-25=14, Resulting Numbers: [92, 14] Generated Node #3: [92, 14] from Operation: 39-25=14 Current State: 78:[92, 14], Operations: ['35+57=92', '39-25=14'] Exploring Operation: 92-14=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[35, 57, 39, 25], Operations: [] Exploring Operation: 57-35=22, Resulting Numbers: [39, 25, 22] Generated Node #0,0: 78:[39, 25, 22] Operation: 57-35=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 78:[39, 25, 22], Operations: ['57-35=22'] Exploring Operation: 25-22=3, Resulting Numbers: [39, 3] Generated Node #0,0,0: 78:[39, 3] Operation: 25-22=3 Moving to Node #0,0,0 Current State: 78:[39, 3], Operations: ['57-35=22', '25-22=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,78 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
[ 65, 6, 7, 41 ]
93
[ "65-6=59", "41-7=34", "59+34=93" ]
Current State: 93:[65, 6, 7, 41], Operations: [] Exploring Operation: 65-6=59, Resulting Numbers: [7, 41, 59] Generated Node #2: [7, 41, 59] from Operation: 65-6=59 Current State: 93:[7, 41, 59], Operations: ['65-6=59'] Exploring Operation: 41-7=34, Resulting Numbers: [59, 34] Generated Node #3: [59, 34] from Operation: 41-7=34 Current State: 93:[59, 34], Operations: ['65-6=59', '41-7=34'] Exploring Operation: 59+34=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[65, 6, 7, 41], Operations: [] Exploring Operation: 65+41=106, Resulting Numbers: [6, 7, 106] Generated Node #0,0: 93:[6, 7, 106] Operation: 65+41=106 Exploring Operation: 65+6=71, Resulting Numbers: [7, 41, 71] Generated Node #0,1: 93:[7, 41, 71] Operation: 65+6=71 Exploring Operation: 65+7=72, Resulting Numbers: [6, 41, 72] Generated Node #0,2: 93:[6, 41, 72] Operation: 65+7=72 Exploring Operation: 41-7=34, Resulting Numbers: [65, 6, 34] Generated Node #0,3: 93:[65, 6, 34] Operation: 41-7=34 Exploring Operation: 65-41=24, Resulting Numbers: [6, 7, 24] Generated Node #0,4: 93:[6, 7, 24] Operation: 65-41=24 Moving to Node #0,4 Current State: 93:[6, 7, 24], Operations: ['65-41=24'] Exploring Operation: 6+24=30, Resulting Numbers: [7, 30] Generated Node #0,4,0: 93:[7, 30] Operation: 6+24=30 Exploring Operation: 7+24=31, Resulting Numbers: [6, 31] Generated Node #0,4,1: 93:[6, 31] Operation: 7+24=31 Exploring Operation: 24/6=4, Resulting Numbers: [7, 4] Generated Node #0,4,2: 93:[7, 4] Operation: 24/6=4 Exploring Operation: 7-6=1, Resulting Numbers: [24, 1] Generated Node #0,4,3: 93:[24, 1] Operation: 7-6=1 Exploring Operation: 6+7=13, Resulting Numbers: [24, 13] Generated Node #0,4,4: 93:[24, 13] Operation: 6+7=13 Moving to Node #0,0 Current State: 93:[6, 7, 106], Operations: ['65+41=106'] Exploring Operation: 7-6=1, Resulting Numbers: [106, 1] Generated Node #0,0,0: 93:[106, 1] Operation: 7-6=1 Exploring Operation: 106-6=100, Resulting Numbers: [7, 100] Generated Node #0,0,1: 93:[7, 100] Operation: 106-6=100 Exploring Operation: 6+106=112, Resulting Numbers: [7, 112] Generated Node #0,0,2: 93:[7, 112] Operation: 6+106=112 Exploring Operation: 106-7=99, Resulting Numbers: [6, 99] Generated Node #0,0,3: 93:[6, 99] Operation: 106-7=99 Exploring Operation: 6+7=13, Resulting Numbers: [106, 13] Generated Node #0,0,4: 93:[106, 13] Operation: 6+7=13 Moving to Node #0,2 Current State: 93:[6, 41, 72], Operations: ['65+7=72'] Exploring Operation: 6+72=78, Resulting Numbers: [41, 78] Generated Node #0,2,0: 93:[41, 78] Operation: 6+72=78 Exploring Operation: 41+72=113, Resulting Numbers: [6, 113] Generated Node #0,2,1: 93:[6, 113] Operation: 41+72=113 Exploring Operation: 72/6=12, Resulting Numbers: [41, 12] Generated Node #0,2,2: 93:[41, 12] Operation: 72/6=12 Exploring Operation: 72-41=31, Resulting Numbers: [6, 31] Generated Node #0,2,3: 93:[6, 31] Operation: 72-41=31 Exploring Operation: 41-6=35, Resulting Numbers: [72, 35] Generated Node #0,2,4: 93:[72, 35] Operation: 41-6=35 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 93:[6, 31], Operations: ['65+7=72', '72-41=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,93 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 93:[41, 12], Operations: ['65+7=72', '72/6=12'] Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,93 unequal: No Solution Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,93 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 93:[6, 113], Operations: ['65+7=72', '41+72=113'] Exploring Operation: 113-6=107, Resulting Numbers: [107] 107,93 unequal: No Solution Exploring Operation: 6*113=678, Resulting Numbers: [678] 678,93 unequal: No Solution Exploring Operation: 6+113=119, Resulting Numbers: [119] 119,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 93:[41, 78], Operations: ['65+7=72', '6+72=78'] Exploring Operation: 41+78=119, Resulting Numbers: [119] 119,93 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 41*78=3198, Resulting Numbers: [3198] 3198,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 93:[72, 35], Operations: ['65+7=72', '41-6=35'] Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 72+35=107, Resulting Numbers: [107] 107,93 unequal: No Solution Exploring Operation: 72*35=2520, Resulting Numbers: [2520] 2520,93 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: 93:[65, 6, 34], Operations: ['41-7=34'] Exploring Operation: 65+34=99, Resulting Numbers: [6, 99] Generated Node #0,3,0: 93:[6, 99] Operation: 65+34=99 Exploring Operation: 65-34=31, Resulting Numbers: [6, 31] Generated Node #0,3,1: 93:[6, 31] Operation: 65-34=31 Exploring Operation: 65+6=71, Resulting Numbers: [34, 71] Generated Node #0,3,2: 93:[34, 71] Operation: 65+6=71 Exploring Operation: 34-6=28, Resulting Numbers: [65, 28] Generated Node #0,3,3: 93:[65, 28] Operation: 34-6=28 Exploring Operation: 65-6=59, Resulting Numbers: [34, 59] Generated Node #0,3,4: 93:[34, 59] Operation: 65-6=59 Moving to Node #0,1 Current State: 93:[7, 41, 71], Operations: ['65+6=71'] Exploring Operation: 41-7=34, Resulting Numbers: [71, 34] Generated Node #0,1,0: 93:[71, 34] Operation: 41-7=34 Exploring Operation: 41+71=112, Resulting Numbers: [7, 112] Generated Node #0,1,1: 93:[7, 112] Operation: 41+71=112 Exploring Operation: 7+71=78, Resulting Numbers: [41, 78] Generated Node #0,1,2: 93:[41, 78] Operation: 7+71=78 Exploring Operation: 71-41=30, Resulting Numbers: [7, 30] Generated Node #0,1,3: 93:[7, 30] Operation: 71-41=30 Exploring Operation: 7+41=48, Resulting Numbers: [71, 48] Generated Node #0,1,4: 93:[71, 48] Operation: 7+41=48 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 93:[7, 30], Operations: ['65+6=71', '71-41=30'] Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,93 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,93 unequal: No Solution Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 93:[7, 112], Operations: ['65+6=71', '41+71=112'] Exploring Operation: 7*112=784, Resulting Numbers: [784] 784,93 unequal: No Solution Exploring Operation: 112/7=16, Resulting Numbers: [16] 16,93 unequal: No Solution Exploring Operation: 112-7=105, Resulting Numbers: [105] 105,93 unequal: No Solution Exploring Operation: 7+112=119, Resulting Numbers: [119] 119,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 93:[71, 34], Operations: ['65+6=71', '41-7=34'] Exploring Operation: 71-34=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 71+34=105, Resulting Numbers: [105] 105,93 unequal: No Solution Exploring Operation: 71*34=2414, Resulting Numbers: [2414] 2414,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 93:[41, 78], Operations: ['65+6=71', '7+71=78'] Exploring Operation: 41+78=119, Resulting Numbers: [119] 119,93 unequal: No Solution Exploring Operation: 78-41=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 41*78=3198, Resulting Numbers: [3198] 3198,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 93:[71, 48], Operations: ['65+6=71', '7+41=48'] Exploring Operation: 71+48=119, Resulting Numbers: [119] 119,93 unequal: No Solution Exploring Operation: 71*48=3408, Resulting Numbers: [3408] 3408,93 unequal: No Solution Exploring Operation: 71-48=23, Resulting Numbers: [23] 23,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,1 Current State: 93:[6, 31], Operations: ['65-41=24', '7+24=31'] Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,93 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,93 unequal: No Solution Moving to Node #0,3,1 Current State: 93:[6, 31], Operations: ['41-7=34', '65-34=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,93 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,93 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,93 unequal: No Solution Moving to Node #0,4,2 Current State: 93:[7, 4], Operations: ['65-41=24', '24/6=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,93 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,93 unequal: No Solution Exploring Operation: 7*4=28, Resulting Numbers: [28] 28,93 unequal: No Solution Moving to Node #0,4,0 Current State: 93:[7, 30], Operations: ['65-41=24', '6+24=30'] Exploring Operation: 7*30=210, Resulting Numbers: [210] 210,93 unequal: No Solution Exploring Operation: 7+30=37, Resulting Numbers: [37] 37,93 unequal: No Solution Exploring Operation: 30-7=23, Resulting Numbers: [23] 23,93 unequal: No Solution Moving to Node #0,0,3 Current State: 93:[6, 99], Operations: ['65+41=106', '106-7=99'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[65, 6, 7, 41], Operations: [] Exploring Operation: 65+41=106, Resulting Numbers: [6, 7, 106] Generated Node #0,0: 93:[6, 7, 106] Operation: 65+41=106 Moving to Node #0,0 Current State: 93:[6, 7, 106], Operations: ['65+41=106'] Exploring Operation: 106-7=99, Resulting Numbers: [6, 99] Generated Node #0,0,3: 93:[6, 99] Operation: 106-7=99 Moving to Node #0,0,3 Current State: 93:[6, 99], Operations: ['65+41=106', '106-7=99'] Exploring Operation: 99-6=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
0.932292
hs_5
mult_heuristic
[ 2, 52, 18, 14 ]
40
[ "52-18=34", "34-14=20", "2*20=40" ]
Current State: 40:[2, 52, 18, 14], Operations: [] Exploring Operation: 52-18=34, Resulting Numbers: [2, 14, 34] Generated Node #2: [2, 14, 34] from Operation: 52-18=34 Current State: 40:[2, 14, 34], Operations: ['52-18=34'] Exploring Operation: 34-14=20, Resulting Numbers: [2, 20] Generated Node #3: [2, 20] from Operation: 34-14=20 Current State: 40:[2, 20], Operations: ['52-18=34', '34-14=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[2, 52, 18, 14], Operations: [] Exploring Operation: 52-18=34, Resulting Numbers: [2, 14, 34] Generated Node #0,0: 40:[2, 14, 34] Operation: 52-18=34 Exploring Operation: 18-14=4, Resulting Numbers: [2, 52, 4] Generated Node #0,1: 40:[2, 52, 4] Operation: 18-14=4 Exploring Operation: 52/2=26, Resulting Numbers: [18, 14, 26] Generated Node #0,2: 40:[18, 14, 26] Operation: 52/2=26 Exploring Operation: 52-14=38, Resulting Numbers: [2, 18, 38] Generated Node #0,3: 40:[2, 18, 38] Operation: 52-14=38 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[2, 18, 38], Operations: ['52-14=38'] Exploring Operation: 2+18=20, Resulting Numbers: [38, 20] Generated Node #0,3,0: 40:[38, 20] Operation: 2+18=20 Exploring Operation: 2+38=40, Resulting Numbers: [18, 40] Generated Node #0,3,1: 40:[18, 40] Operation: 2+38=40 Exploring Operation: 38-18=20, Resulting Numbers: [2, 20] Generated Node #0,3,2: 40:[2, 20] Operation: 38-18=20 Exploring Operation: 18/2=9, Resulting Numbers: [38, 9] Generated Node #0,3,3: 40:[38, 9] Operation: 18/2=9 Moving to Node #0,3,2 Current State: 40:[2, 20], Operations: ['52-14=38', '38-18=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,40 unequal: No Solution Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[2, 52, 18, 14], Operations: [] Exploring Operation: 52-14=38, Resulting Numbers: [2, 18, 38] Generated Node #0,3: 40:[2, 18, 38] Operation: 52-14=38 Moving to Node #0,3 Current State: 40:[2, 18, 38], Operations: ['52-14=38'] Exploring Operation: 38-18=20, Resulting Numbers: [2, 20] Generated Node #0,3,2: 40:[2, 20] Operation: 38-18=20 Moving to Node #0,3,2 Current State: 40:[2, 20], Operations: ['52-14=38', '38-18=20'] Exploring Operation: 2*20=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
sum_heuristic
[ 9, 34, 12, 97 ]
66
[ "9+34=43", "12+97=109", "109-43=66" ]
Current State: 66:[9, 34, 12, 97], Operations: [] Exploring Operation: 9+34=43, Resulting Numbers: [12, 97, 43] Generated Node #2: [12, 97, 43] from Operation: 9+34=43 Current State: 66:[12, 97, 43], Operations: ['9+34=43'] Exploring Operation: 12+97=109, Resulting Numbers: [43, 109] Generated Node #3: [43, 109] from Operation: 12+97=109 Current State: 66:[43, 109], Operations: ['9+34=43', '12+97=109'] Exploring Operation: 109-43=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[9, 34, 12, 97], Operations: [] Exploring Operation: 97-12=85, Resulting Numbers: [9, 34, 85] Generated Node #0,0: 66:[9, 34, 85] Operation: 97-12=85 Exploring Operation: 97-9=88, Resulting Numbers: [34, 12, 88] Generated Node #0,1: 66:[34, 12, 88] Operation: 97-9=88 Exploring Operation: 97-34=63, Resulting Numbers: [9, 12, 63] Generated Node #0,2: 66:[9, 12, 63] Operation: 97-34=63 Moving to Node #0,2 Current State: 66:[9, 12, 63], Operations: ['97-34=63'] Exploring Operation: 9+12=21, Resulting Numbers: [63, 21] Generated Node #0,2,0: 66:[63, 21] Operation: 9+12=21 Exploring Operation: 63/9=7, Resulting Numbers: [12, 7] Generated Node #0,2,1: 66:[12, 7] Operation: 63/9=7 Exploring Operation: 12-9=3, Resulting Numbers: [63, 3] Generated Node #0,2,2: 66:[63, 3] Operation: 12-9=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 66:[12, 7], Operations: ['97-34=63', '63/9=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,66 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,66 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 66:[63, 3], Operations: ['97-34=63', '12-9=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,66 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,66 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[9, 34, 12, 97], Operations: [] Exploring Operation: 97-34=63, Resulting Numbers: [9, 12, 63] Generated Node #0,2: 66:[9, 12, 63] Operation: 97-34=63 Moving to Node #0,2 Current State: 66:[9, 12, 63], Operations: ['97-34=63'] Exploring Operation: 12-9=3, Resulting Numbers: [63, 3] Generated Node #0,2,2: 66:[63, 3] Operation: 12-9=3 Moving to Node #0,2,2 Current State: 66:[63, 3], Operations: ['97-34=63', '12-9=3'] Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 4, 77, 30, 93 ]
95
[ "77-30=47", "4*47=188", "188-93=95" ]
Current State: 95:[4, 77, 30, 93], Operations: [] Exploring Operation: 77-30=47, Resulting Numbers: [4, 93, 47] Generated Node #2: [4, 93, 47] from Operation: 77-30=47 Current State: 95:[4, 93, 47], Operations: ['77-30=47'] Exploring Operation: 4*47=188, Resulting Numbers: [93, 188] Generated Node #3: [93, 188] from Operation: 4*47=188 Current State: 95:[93, 188], Operations: ['77-30=47', '4*47=188'] Exploring Operation: 188-93=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[4, 77, 30, 93], Operations: [] Exploring Operation: 30-4=26, Resulting Numbers: [77, 93, 26] Generated Node #0,0: 95:[77, 93, 26] Operation: 30-4=26 Exploring Operation: 4+77=81, Resulting Numbers: [30, 93, 81] Generated Node #0,1: 95:[30, 93, 81] Operation: 4+77=81 Exploring Operation: 77+30=107, Resulting Numbers: [4, 93, 107] Generated Node #0,2: 95:[4, 93, 107] Operation: 77+30=107 Exploring Operation: 93-77=16, Resulting Numbers: [4, 30, 16] Generated Node #0,3: 95:[4, 30, 16] Operation: 93-77=16 Start Sub Search at level 1: Moving to Node #0,2 Current State: 95:[4, 93, 107], Operations: ['77+30=107'] Exploring Operation: 107-4=103, Resulting Numbers: [93, 103] Generated Node #0,2,0: 95:[93, 103] Operation: 107-4=103 Exploring Operation: 107-93=14, Resulting Numbers: [4, 14] Generated Node #0,2,1: 95:[4, 14] Operation: 107-93=14 Exploring Operation: 4+93=97, Resulting Numbers: [107, 97] Generated Node #0,2,2: 95:[107, 97] Operation: 4+93=97 Exploring Operation: 93-4=89, Resulting Numbers: [107, 89] Generated Node #0,2,3: 95:[107, 89] Operation: 93-4=89 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 95:[4, 14], Operations: ['77+30=107', '107-93=14'] Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,95 unequal: No Solution No 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: 95:[93, 103], Operations: ['77+30=107', '107-4=103'] Exploring Operation: 93*103=9579, Resulting Numbers: [9579] 9579,95 unequal: No Solution Exploring Operation: 93+103=196, Resulting Numbers: [196] 196,95 unequal: No Solution Exploring Operation: 103-93=10, Resulting Numbers: [10] 10,95 unequal: No Solution No 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: 95:[107, 97], Operations: ['77+30=107', '4+93=97'] Exploring Operation: 107-97=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 107+97=204, Resulting Numbers: [204] 204,95 unequal: No Solution Exploring Operation: 107*97=10379, Resulting Numbers: [10379] 10379,95 unequal: No Solution No 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: 95:[107, 89], Operations: ['77+30=107', '93-4=89'] Exploring Operation: 107+89=196, Resulting Numbers: [196] 196,95 unequal: No Solution Exploring Operation: 107*89=9523, Resulting Numbers: [9523] 9523,95 unequal: No Solution Exploring Operation: 107-89=18, Resulting Numbers: [18] 18,95 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: 95:[4, 30, 16], Operations: ['93-77=16'] Exploring Operation: 30-4=26, Resulting Numbers: [16, 26] Generated Node #0,3,0: 95:[16, 26] Operation: 30-4=26 Exploring Operation: 16/4=4, Resulting Numbers: [30, 4] Generated Node #0,3,1: 95:[30, 4] Operation: 16/4=4 Exploring Operation: 4+16=20, Resulting Numbers: [30, 20] Generated Node #0,3,2: 95:[30, 20] Operation: 4+16=20 Exploring Operation: 30-16=14, Resulting Numbers: [4, 14] Generated Node #0,3,3: 95:[4, 14] Operation: 30-16=14 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 95:[4, 14], Operations: ['93-77=16', '30-16=14'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 4*14=56, Resulting Numbers: [56] 56,95 unequal: No Solution Exploring Operation: 4+14=18, Resulting Numbers: [18] 18,95 unequal: No Solution No 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: 95:[16, 26], Operations: ['93-77=16', '30-4=26'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 16+26=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 16*26=416, Resulting Numbers: [416] 416,95 unequal: No Solution No 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: 95:[30, 4], Operations: ['93-77=16', '16/4=4'] Exploring Operation: 30*4=120, Resulting Numbers: [120] 120,95 unequal: No Solution Exploring Operation: 30+4=34, Resulting Numbers: [34] 34,95 unequal: No Solution Exploring Operation: 30-4=26, Resulting Numbers: [26] 26,95 unequal: No Solution No 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: 95:[30, 20], Operations: ['93-77=16', '4+16=20'] Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,95 unequal: No Solution Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,95 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,95 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: 95:[77, 93, 26], Operations: ['30-4=26'] Exploring Operation: 77+26=103, Resulting Numbers: [93, 103] Generated Node #0,0,0: 95:[93, 103] Operation: 77+26=103 Exploring Operation: 77-26=51, Resulting Numbers: [93, 51] Generated Node #0,0,1: 95:[93, 51] Operation: 77-26=51 Exploring Operation: 93-77=16, Resulting Numbers: [26, 16] Generated Node #0,0,2: 95:[26, 16] Operation: 93-77=16 Exploring Operation: 93+26=119, Resulting Numbers: [77, 119] Generated Node #0,0,3: 95:[77, 119] Operation: 93+26=119 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 95:[93, 103], Operations: ['30-4=26', '77+26=103'] Exploring Operation: 93*103=9579, Resulting Numbers: [9579] 9579,95 unequal: No Solution Exploring Operation: 103-93=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 93+103=196, Resulting Numbers: [196] 196,95 unequal: No Solution No 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: 95:[26, 16], Operations: ['30-4=26', '93-77=16'] Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,95 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,95 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,95 unequal: No Solution No 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: 95:[93, 51], Operations: ['30-4=26', '77-26=51'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 93*51=4743, Resulting Numbers: [4743] 4743,95 unequal: No Solution Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,95 unequal: No Solution No 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: 95:[77, 119], Operations: ['30-4=26', '93+26=119'] Exploring Operation: 77+119=196, Resulting Numbers: [196] 196,95 unequal: No Solution Exploring Operation: 77*119=9163, Resulting Numbers: [9163] 9163,95 unequal: No Solution Exploring Operation: 119-77=42, Resulting Numbers: [42] 42,95 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: 95:[30, 93, 81], Operations: ['4+77=81'] Exploring Operation: 30+81=111, Resulting Numbers: [93, 111] Generated Node #0,1,0: 95:[93, 111] Operation: 30+81=111 Exploring Operation: 30+93=123, Resulting Numbers: [81, 123] Generated Node #0,1,1: 95:[81, 123] Operation: 30+93=123 Exploring Operation: 81-30=51, Resulting Numbers: [93, 51] Generated Node #0,1,2: 95:[93, 51] Operation: 81-30=51 Exploring Operation: 93-81=12, Resulting Numbers: [30, 12] Generated Node #0,1,3: 95:[30, 12] Operation: 93-81=12 Moving to Node #0,1,0 Current State: 95:[93, 111], Operations: ['4+77=81', '30+81=111'] Exploring Operation: 111-93=18, Resulting Numbers: [18] 18,95 unequal: No Solution Exploring Operation: 93*111=10323, Resulting Numbers: [10323] 10323,95 unequal: No Solution Exploring Operation: 93+111=204, Resulting Numbers: [204] 204,95 unequal: No Solution Moving to Node #0,1,3 Current State: 95:[30, 12], Operations: ['4+77=81', '93-81=12'] Exploring Operation: 30*12=360, Resulting Numbers: [360] 360,95 unequal: No Solution Exploring Operation: 30+12=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 30-12=18, Resulting Numbers: [18] 18,95 unequal: No Solution Moving to Node #0,1,2 Current State: 95:[93, 51], Operations: ['4+77=81', '81-30=51'] Exploring Operation: 93-51=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 93+51=144, Resulting Numbers: [144] 144,95 unequal: No Solution Exploring Operation: 93*51=4743, Resulting Numbers: [4743] 4743,95 unequal: No Solution Moving to Node #0,1,1 Current State: 95:[81, 123], Operations: ['4+77=81', '30+93=123'] Exploring Operation: 123-81=42, Resulting Numbers: [42] 42,95 unequal: No Solution Exploring Operation: 81+123=204, Resulting Numbers: [204] 204,95 unequal: No Solution Exploring Operation: 81*123=9963, Resulting Numbers: [9963] 9963,95 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
[ 30, 22, 11, 37 ]
26
[ "30+22=52", "37-11=26", "52-26=26" ]
Current State: 26:[30, 22, 11, 37], Operations: [] Exploring Operation: 30+22=52, Resulting Numbers: [11, 37, 52] Generated Node #2: [11, 37, 52] from Operation: 30+22=52 Current State: 26:[11, 37, 52], Operations: ['30+22=52'] Exploring Operation: 37-11=26, Resulting Numbers: [52, 26] Generated Node #3: [52, 26] from Operation: 37-11=26 Current State: 26:[52, 26], Operations: ['30+22=52', '37-11=26'] Exploring Operation: 52-26=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[30, 22, 11, 37], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [30, 22, 26] Generated Node #0,0: 26:[30, 22, 26] Operation: 37-11=26 Exploring Operation: 37-22=15, Resulting Numbers: [30, 11, 15] Generated Node #0,1: 26:[30, 11, 15] Operation: 37-22=15 Exploring Operation: 37-30=7, Resulting Numbers: [22, 11, 7] Generated Node #0,2: 26:[22, 11, 7] Operation: 37-30=7 Moving to Node #0,0 Current State: 26:[30, 22, 26], Operations: ['37-11=26'] Exploring Operation: 30-26=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 26:[22, 4] Operation: 30-26=4 Exploring Operation: 26-22=4, Resulting Numbers: [30, 4] Generated Node #0,0,1: 26:[30, 4] Operation: 26-22=4 Exploring Operation: 30-22=8, Resulting Numbers: [26, 8] Generated Node #0,0,2: 26:[26, 8] Operation: 30-22=8 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 26:[26, 8], Operations: ['37-11=26', '30-22=8'] Exploring Operation: 26+8=34, Resulting Numbers: [34] 34,26 unequal: No Solution Exploring Operation: 26-8=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 26*8=208, Resulting Numbers: [208] 208,26 unequal: No Solution No 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: 26:[22, 4], Operations: ['37-11=26', '30-26=4'] Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 22*4=88, Resulting Numbers: [88] 88,26 unequal: No Solution Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[30, 22, 11, 37], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [30, 22, 26] Generated Node #0,0: 26:[30, 22, 26] Operation: 37-11=26 Moving to Node #0,0 Current State: 26:[30, 22, 26], Operations: ['37-11=26'] Exploring Operation: 30-26=4, Resulting Numbers: [22, 4] Generated Node #0,0,0: 26:[22, 4] Operation: 30-26=4 Moving to Node #0,0,0 Current State: 26:[22, 4], Operations: ['37-11=26', '30-26=4'] Exploring Operation: 22+4=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 51, 7, 34, 59 ]
90
[ "59-51=8", "7*8=56", "34+56=90" ]
Current State: 90:[51, 7, 34, 59], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [7, 34, 8] Generated Node #2: [7, 34, 8] from Operation: 59-51=8 Current State: 90:[7, 34, 8], Operations: ['59-51=8'] Exploring Operation: 7*8=56, Resulting Numbers: [34, 56] Generated Node #3: [34, 56] from Operation: 7*8=56 Current State: 90:[34, 56], Operations: ['59-51=8', '7*8=56'] Exploring Operation: 34+56=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[51, 7, 34, 59], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [7, 34, 8] Generated Node #0,0: 90:[7, 34, 8] Operation: 59-51=8 Exploring Operation: 34+59=93, Resulting Numbers: [51, 7, 93] Generated Node #0,1: 90:[51, 7, 93] Operation: 34+59=93 Exploring Operation: 59-7=52, Resulting Numbers: [51, 34, 52] Generated Node #0,2: 90:[51, 34, 52] Operation: 59-7=52 Exploring Operation: 51-34=17, Resulting Numbers: [7, 59, 17] Generated Node #0,3: 90:[7, 59, 17] Operation: 51-34=17 Exploring Operation: 59-34=25, Resulting Numbers: [51, 7, 25] Generated Node #0,4: 90:[51, 7, 25] Operation: 59-34=25 Moving to Node #0,0 Current State: 90:[7, 34, 8], Operations: ['59-51=8'] Exploring Operation: 34+8=42, Resulting Numbers: [7, 42] Generated Node #0,0,0: 90:[7, 42] Operation: 34+8=42 Exploring Operation: 7+34=41, Resulting Numbers: [8, 41] Generated Node #0,0,1: 90:[8, 41] Operation: 7+34=41 Exploring Operation: 8-7=1, Resulting Numbers: [34, 1] Generated Node #0,0,2: 90:[34, 1] Operation: 8-7=1 Exploring Operation: 7+8=15, Resulting Numbers: [34, 15] Generated Node #0,0,3: 90:[34, 15] Operation: 7+8=15 Exploring Operation: 34-7=27, Resulting Numbers: [8, 27] Generated Node #0,0,4: 90:[8, 27] Operation: 34-7=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 90:[7, 42], Operations: ['59-51=8', '34+8=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 90:[34, 15], Operations: ['59-51=8', '7+8=15'] Exploring Operation: 34-15=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 34*15=510, Resulting Numbers: [510] 510,90 unequal: No Solution Exploring Operation: 34+15=49, Resulting Numbers: [49] 49,90 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 #0,0,4 Current State: 90:[8, 27], Operations: ['59-51=8', '34-7=27'] Exploring Operation: 8*27=216, Resulting Numbers: [216] 216,90 unequal: No Solution Exploring Operation: 27-8=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 8+27=35, Resulting Numbers: [35] 35,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 90:[8, 41], Operations: ['59-51=8', '7+34=41'] Exploring Operation: 41-8=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 8+41=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 8*41=328, Resulting Numbers: [328] 328,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 90:[34, 1], Operations: ['59-51=8', '8-7=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 90:[51, 7, 93], Operations: ['34+59=93'] Exploring Operation: 93-7=86, Resulting Numbers: [51, 86] Generated Node #0,1,0: 90:[51, 86] Operation: 93-7=86 Exploring Operation: 7+93=100, Resulting Numbers: [51, 100] Generated Node #0,1,1: 90:[51, 100] Operation: 7+93=100 Exploring Operation: 51+7=58, Resulting Numbers: [93, 58] Generated Node #0,1,2: 90:[93, 58] Operation: 51+7=58 Exploring Operation: 51-7=44, Resulting Numbers: [93, 44] Generated Node #0,1,3: 90:[93, 44] Operation: 51-7=44 Exploring Operation: 93-51=42, Resulting Numbers: [7, 42] Generated Node #0,1,4: 90:[7, 42] Operation: 93-51=42 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 90:[93, 44], Operations: ['34+59=93', '51-7=44'] Exploring Operation: 93*44=4092, Resulting Numbers: [4092] 4092,90 unequal: No Solution Exploring Operation: 93-44=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 93+44=137, Resulting Numbers: [137] 137,90 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 #0,1,4 Current State: 90:[7, 42], Operations: ['34+59=93', '93-51=42'] Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,90 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 #0,1,0 Current State: 90:[51, 86], Operations: ['34+59=93', '93-7=86'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,90 unequal: No Solution Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,90 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 #0,1,1 Current State: 90:[51, 100], Operations: ['34+59=93', '7+93=100'] Exploring Operation: 100-51=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 51*100=5100, Resulting Numbers: [5100] 5100,90 unequal: No Solution Exploring Operation: 51+100=151, Resulting Numbers: [151] 151,90 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 #0,1,2 Current State: 90:[93, 58], Operations: ['34+59=93', '51+7=58'] Exploring Operation: 93-58=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 93*58=5394, Resulting Numbers: [5394] 5394,90 unequal: No Solution Exploring Operation: 93+58=151, Resulting Numbers: [151] 151,90 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: 90:[51, 7, 25], Operations: ['59-34=25'] Exploring Operation: 51+25=76, Resulting Numbers: [7, 76] Generated Node #0,4,0: 90:[7, 76] Operation: 51+25=76 Exploring Operation: 51-25=26, Resulting Numbers: [7, 26] Generated Node #0,4,1: 90:[7, 26] Operation: 51-25=26 Exploring Operation: 51-7=44, Resulting Numbers: [25, 44] Generated Node #0,4,2: 90:[25, 44] Operation: 51-7=44 Exploring Operation: 7+25=32, Resulting Numbers: [51, 32] Generated Node #0,4,3: 90:[51, 32] Operation: 7+25=32 Exploring Operation: 25-7=18, Resulting Numbers: [51, 18] Generated Node #0,4,4: 90:[51, 18] Operation: 25-7=18 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 90:[7, 26], Operations: ['59-34=25', '51-25=26'] Exploring Operation: 7+26=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 7*26=182, Resulting Numbers: [182] 182,90 unequal: No Solution Exploring Operation: 26-7=19, Resulting Numbers: [19] 19,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 90:[25, 44], Operations: ['59-34=25', '51-7=44'] Exploring Operation: 25*44=1100, Resulting Numbers: [1100] 1100,90 unequal: No Solution Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 90:[51, 18], Operations: ['59-34=25', '25-7=18'] Exploring Operation: 51*18=918, Resulting Numbers: [918] 918,90 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 51+18=69, Resulting Numbers: [69] 69,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 90:[51, 32], Operations: ['59-34=25', '7+25=32'] Exploring Operation: 51-32=19, Resulting Numbers: [19] 19,90 unequal: No Solution Exploring Operation: 51+32=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 51*32=1632, Resulting Numbers: [1632] 1632,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 90:[7, 76], Operations: ['59-34=25', '51+25=76'] Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,90 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: 90:[7, 59, 17], Operations: ['51-34=17'] Exploring Operation: 59-7=52, Resulting Numbers: [17, 52] Generated Node #0,3,0: 90:[17, 52] Operation: 59-7=52 Exploring Operation: 17-7=10, Resulting Numbers: [59, 10] Generated Node #0,3,1: 90:[59, 10] Operation: 17-7=10 Exploring Operation: 59-17=42, Resulting Numbers: [7, 42] Generated Node #0,3,2: 90:[7, 42] Operation: 59-17=42 Exploring Operation: 59+17=76, Resulting Numbers: [7, 76] Generated Node #0,3,3: 90:[7, 76] Operation: 59+17=76 Exploring Operation: 7+17=24, Resulting Numbers: [59, 24] Generated Node #0,3,4: 90:[59, 24] Operation: 7+17=24 Moving to Node #0,2 Current State: 90:[51, 34, 52], Operations: ['59-7=52'] Exploring Operation: 51+34=85, Resulting Numbers: [52, 85] Generated Node #0,2,0: 90:[52, 85] Operation: 51+34=85 Exploring Operation: 34+52=86, Resulting Numbers: [51, 86] Generated Node #0,2,1: 90:[51, 86] Operation: 34+52=86 Exploring Operation: 52-51=1, Resulting Numbers: [34, 1] Generated Node #0,2,2: 90:[34, 1] Operation: 52-51=1 Exploring Operation: 52-34=18, Resulting Numbers: [51, 18] Generated Node #0,2,3: 90:[51, 18] Operation: 52-34=18 Exploring Operation: 51-34=17, Resulting Numbers: [52, 17] Generated Node #0,2,4: 90:[52, 17] Operation: 51-34=17 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 90:[34, 1], Operations: ['59-7=52', '52-51=1'] Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,90 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,90 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 #0,2,3 Current State: 90:[51, 18], Operations: ['59-7=52', '52-34=18'] Exploring Operation: 51+18=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 51*18=918, Resulting Numbers: [918] 918,90 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 #0,2,4 Current State: 90:[52, 17], Operations: ['59-7=52', '51-34=17'] Exploring Operation: 52*17=884, Resulting Numbers: [884] 884,90 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,90 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 #0,2,1 Current State: 90:[51, 86], Operations: ['59-7=52', '34+52=86'] Exploring Operation: 86-51=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 51+86=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 51*86=4386, Resulting Numbers: [4386] 4386,90 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 #0,2,0 Current State: 90:[52, 85], Operations: ['59-7=52', '51+34=85'] Exploring Operation: 85-52=33, Resulting Numbers: [33] 33,90 unequal: No Solution Exploring Operation: 52+85=137, Resulting Numbers: [137] 137,90 unequal: No Solution Exploring Operation: 52*85=4420, Resulting Numbers: [4420] 4420,90 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: 90:[7, 42], Operations: ['51-34=17', '59-17=42'] Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 7+42=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 7*42=294, Resulting Numbers: [294] 294,90 unequal: No Solution Moving to Node #0,3,0 Current State: 90:[17, 52], Operations: ['51-34=17', '59-7=52'] Exploring Operation: 17+52=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 17*52=884, Resulting Numbers: [884] 884,90 unequal: No Solution Moving to Node #0,3,1 Current State: 90:[59, 10], Operations: ['51-34=17', '17-7=10'] Exploring Operation: 59*10=590, Resulting Numbers: [590] 590,90 unequal: No Solution Exploring Operation: 59-10=49, Resulting Numbers: [49] 49,90 unequal: No Solution Exploring Operation: 59+10=69, Resulting Numbers: [69] 69,90 unequal: No Solution Moving to Node #0,3,3 Current State: 90:[7, 76], Operations: ['51-34=17', '59+17=76'] Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,90 unequal: No Solution Exploring Operation: 7*76=532, Resulting Numbers: [532] 532,90 unequal: No Solution Moving to Node #0,3,4 Current State: 90:[59, 24], Operations: ['51-34=17', '7+17=24'] Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,90 unequal: No Solution Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,90 unequal: No Solution Exploring Operation: 59*24=1416, Resulting Numbers: [1416] 1416,90 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 35, 86, 13, 80 ]
54
[ "35+86=121", "80-13=67", "121-67=54" ]
Current State: 54:[35, 86, 13, 80], Operations: [] Exploring Operation: 35+86=121, Resulting Numbers: [13, 80, 121] Generated Node #2: [13, 80, 121] from Operation: 35+86=121 Current State: 54:[13, 80, 121], Operations: ['35+86=121'] Exploring Operation: 80-13=67, Resulting Numbers: [121, 67] Generated Node #3: [121, 67] from Operation: 80-13=67 Current State: 54:[121, 67], Operations: ['35+86=121', '80-13=67'] Exploring Operation: 121-67=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[35, 86, 13, 80], Operations: [] Exploring Operation: 86-35=51, Resulting Numbers: [13, 80, 51] Generated Node #0,0: 54:[13, 80, 51] Operation: 86-35=51 Exploring Operation: 86-80=6, Resulting Numbers: [35, 13, 6] Generated Node #0,1: 54:[35, 13, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 54:[35, 13, 6], Operations: ['86-80=6'] Exploring Operation: 35+13=48, Resulting Numbers: [6, 48] Generated Node #0,1,0: 54:[6, 48] Operation: 35+13=48 Exploring Operation: 35-13=22, Resulting Numbers: [6, 22] Generated Node #0,1,1: 54:[6, 22] Operation: 35-13=22 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[6, 22], Operations: ['86-80=6', '35-13=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,54 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,54 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 #0,1,0 Current State: 54:[6, 48], Operations: ['86-80=6', '35+13=48'] Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[35, 86, 13, 80], Operations: [] Exploring Operation: 86-80=6, Resulting Numbers: [35, 13, 6] Generated Node #0,1: 54:[35, 13, 6] Operation: 86-80=6 Moving to Node #0,1 Current State: 54:[35, 13, 6], Operations: ['86-80=6'] Exploring Operation: 35+13=48, Resulting Numbers: [6, 48] Generated Node #0,1,0: 54:[6, 48] Operation: 35+13=48 Moving to Node #0,1,0 Current State: 54:[6, 48], Operations: ['86-80=6', '35+13=48'] Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 72, 80, 67, 30 ]
10
[ "72-67=5", "80-30=50", "50/5=10" ]
Current State: 10:[72, 80, 67, 30], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [80, 30, 5] Generated Node #2: [80, 30, 5] from Operation: 72-67=5 Current State: 10:[80, 30, 5], Operations: ['72-67=5'] Exploring Operation: 80-30=50, Resulting Numbers: [5, 50] Generated Node #3: [5, 50] from Operation: 80-30=50 Current State: 10:[5, 50], Operations: ['72-67=5', '80-30=50'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[72, 80, 67, 30], Operations: [] Exploring Operation: 80-67=13, Resulting Numbers: [72, 30, 13] Generated Node #0,0: 10:[72, 30, 13] Operation: 80-67=13 Exploring Operation: 80-30=50, Resulting Numbers: [72, 67, 50] Generated Node #0,1: 10:[72, 67, 50] Operation: 80-30=50 Exploring Operation: 72-67=5, Resulting Numbers: [80, 30, 5] Generated Node #0,2: 10:[80, 30, 5] Operation: 72-67=5 Exploring Operation: 80-72=8, Resulting Numbers: [67, 30, 8] Generated Node #0,3: 10:[67, 30, 8] Operation: 80-72=8 Exploring Operation: 72-30=42, Resulting Numbers: [80, 67, 42] Generated Node #0,4: 10:[80, 67, 42] Operation: 72-30=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 10:[67, 30, 8], Operations: ['80-72=8'] Exploring Operation: 30-8=22, Resulting Numbers: [67, 22] Generated Node #0,3,0: 10:[67, 22] Operation: 30-8=22 Exploring Operation: 67-30=37, Resulting Numbers: [8, 37] Generated Node #0,3,1: 10:[8, 37] Operation: 67-30=37 Exploring Operation: 67-8=59, Resulting Numbers: [30, 59] Generated Node #0,3,2: 10:[30, 59] Operation: 67-8=59 Exploring Operation: 30+8=38, Resulting Numbers: [67, 38] Generated Node #0,3,3: 10:[67, 38] Operation: 30+8=38 Exploring Operation: 67+8=75, Resulting Numbers: [30, 75] Generated Node #0,3,4: 10:[30, 75] Operation: 67+8=75 Moving to Node #0,3,1 Current State: 10:[8, 37], Operations: ['80-72=8', '67-30=37'] Exploring Operation: 8*37=296, Resulting Numbers: [296] 296,10 unequal: No Solution Exploring Operation: 37-8=29, Resulting Numbers: [29] 29,10 unequal: No Solution Exploring Operation: 8+37=45, Resulting Numbers: [45] 45,10 unequal: No Solution Moving to Node #0,3,2 Current State: 10:[30, 59], Operations: ['80-72=8', '67-8=59'] Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,10 unequal: No Solution Exploring Operation: 30*59=1770, Resulting Numbers: [1770] 1770,10 unequal: No Solution Exploring Operation: 30+59=89, Resulting Numbers: [89] 89,10 unequal: No Solution Moving to Node #0,3,0 Current State: 10:[67, 22], Operations: ['80-72=8', '30-8=22'] Exploring Operation: 67*22=1474, Resulting Numbers: [1474] 1474,10 unequal: No Solution Exploring Operation: 67+22=89, Resulting Numbers: [89] 89,10 unequal: No Solution Exploring Operation: 67-22=45, Resulting Numbers: [45] 45,10 unequal: No Solution Moving to Node #0,3,3 Current State: 10:[67, 38], Operations: ['80-72=8', '30+8=38'] Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,10 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,10 unequal: No Solution Exploring Operation: 67*38=2546, Resulting Numbers: [2546] 2546,10 unequal: No Solution Moving to Node #0,3,4 Current State: 10:[30, 75], Operations: ['80-72=8', '67+8=75'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,10 unequal: No Solution Exploring Operation: 30+75=105, Resulting Numbers: [105] 105,10 unequal: No Solution Exploring Operation: 30*75=2250, Resulting Numbers: [2250] 2250,10 unequal: No Solution No 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: 10:[72, 30, 13], Operations: ['80-67=13'] Exploring Operation: 72-13=59, Resulting Numbers: [30, 59] Generated Node #0,0,0: 10:[30, 59] Operation: 72-13=59 Exploring Operation: 72-30=42, Resulting Numbers: [13, 42] Generated Node #0,0,1: 10:[13, 42] Operation: 72-30=42 Exploring Operation: 30-13=17, Resulting Numbers: [72, 17] Generated Node #0,0,2: 10:[72, 17] Operation: 30-13=17 Exploring Operation: 72+30=102, Resulting Numbers: [13, 102] Generated Node #0,0,3: 10:[13, 102] Operation: 72+30=102 Exploring Operation: 72+13=85, Resulting Numbers: [30, 85] Generated Node #0,0,4: 10:[30, 85] Operation: 72+13=85 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[13, 42], Operations: ['80-67=13', '72-30=42'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,10 unequal: No Solution Exploring Operation: 13*42=546, Resulting Numbers: [546] 546,10 unequal: No Solution Exploring Operation: 13+42=55, Resulting Numbers: [55] 55,10 unequal: No Solution No 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: 10:[30, 59], Operations: ['80-67=13', '72-13=59'] Exploring Operation: 59-30=29, Resulting Numbers: [29] 29,10 unequal: No Solution Exploring Operation: 30+59=89, Resulting Numbers: [89] 89,10 unequal: No Solution Exploring Operation: 30*59=1770, Resulting Numbers: [1770] 1770,10 unequal: No Solution No 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: 10:[72, 17], Operations: ['80-67=13', '30-13=17'] Exploring Operation: 72-17=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 72+17=89, Resulting Numbers: [89] 89,10 unequal: No Solution Exploring Operation: 72*17=1224, Resulting Numbers: [1224] 1224,10 unequal: No Solution No 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: 10:[13, 102], Operations: ['80-67=13', '72+30=102'] Exploring Operation: 13+102=115, Resulting Numbers: [115] 115,10 unequal: No Solution Exploring Operation: 13*102=1326, Resulting Numbers: [1326] 1326,10 unequal: No Solution Exploring Operation: 102-13=89, Resulting Numbers: [89] 89,10 unequal: No Solution No 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: 10:[30, 85], Operations: ['80-67=13', '72+13=85'] Exploring Operation: 30*85=2550, Resulting Numbers: [2550] 2550,10 unequal: No Solution Exploring Operation: 85-30=55, Resulting Numbers: [55] 55,10 unequal: No Solution Exploring Operation: 30+85=115, Resulting Numbers: [115] 115,10 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: 10:[80, 30, 5], Operations: ['72-67=5'] Exploring Operation: 30-5=25, Resulting Numbers: [80, 25] Generated Node #0,2,0: 10:[80, 25] Operation: 30-5=25 Exploring Operation: 80-30=50, Resulting Numbers: [5, 50] Generated Node #0,2,1: 10:[5, 50] Operation: 80-30=50 Exploring Operation: 80-5=75, Resulting Numbers: [30, 75] Generated Node #0,2,2: 10:[30, 75] Operation: 80-5=75 Exploring Operation: 80/5=16, Resulting Numbers: [30, 16] Generated Node #0,2,3: 10:[30, 16] Operation: 80/5=16 Exploring Operation: 30/5=6, Resulting Numbers: [80, 6] Generated Node #0,2,4: 10:[80, 6] Operation: 30/5=6 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 10:[30, 16], Operations: ['72-67=5', '80/5=16'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,10 unequal: No Solution Exploring Operation: 30*16=480, Resulting Numbers: [480] 480,10 unequal: No Solution Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,10 unequal: No Solution No 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: 10:[5, 50], Operations: ['72-67=5', '80-30=50'] Exploring Operation: 5*50=250, Resulting Numbers: [250] 250,10 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[72, 80, 67, 30], Operations: [] Exploring Operation: 72-67=5, Resulting Numbers: [80, 30, 5] Generated Node #0,2: 10:[80, 30, 5] Operation: 72-67=5 Moving to Node #0,2 Current State: 10:[80, 30, 5], Operations: ['72-67=5'] Exploring Operation: 80-30=50, Resulting Numbers: [5, 50] Generated Node #0,2,1: 10:[5, 50] Operation: 80-30=50 Moving to Node #0,2,1 Current State: 10:[5, 50], Operations: ['72-67=5', '80-30=50'] Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.948785
hs_5
sum_heuristic
[ 79, 1, 72, 64 ]
72
[ "79+1=80", "72-64=8", "80-8=72" ]
Current State: 72:[79, 1, 72, 64], Operations: [] Exploring Operation: 79+1=80, Resulting Numbers: [72, 64, 80] Generated Node #2: [72, 64, 80] from Operation: 79+1=80 Current State: 72:[72, 64, 80], Operations: ['79+1=80'] Exploring Operation: 72-64=8, Resulting Numbers: [80, 8] Generated Node #3: [80, 8] from Operation: 72-64=8 Current State: 72:[80, 8], Operations: ['79+1=80', '72-64=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[79, 1, 72, 64], Operations: [] Exploring Operation: 1+64=65, Resulting Numbers: [79, 72, 65] Generated Node #0,0: 72:[79, 72, 65] Operation: 1+64=65 Exploring Operation: 79-72=7, Resulting Numbers: [1, 64, 7] Generated Node #0,1: 72:[1, 64, 7] Operation: 79-72=7 Exploring Operation: 72-64=8, Resulting Numbers: [79, 1, 8] Generated Node #0,2: 72:[79, 1, 8] Operation: 72-64=8 Exploring Operation: 79-64=15, Resulting Numbers: [1, 72, 15] Generated Node #0,3: 72:[1, 72, 15] Operation: 79-64=15 Exploring Operation: 79-1=78, Resulting Numbers: [72, 64, 78] Generated Node #0,4: 72:[72, 64, 78] Operation: 79-1=78 Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[1, 72, 15], Operations: ['79-64=15'] Exploring Operation: 72/1=72, Resulting Numbers: [15, 72] Generated Node #0,3,0: 72:[15, 72] Operation: 72/1=72 Exploring Operation: 1*72=72, Resulting Numbers: [15, 72] Generated Node #0,3,1: 72:[15, 72] Operation: 1*72=72 Exploring Operation: 1*15=15, Resulting Numbers: [72, 15] Generated Node #0,3,2: 72:[72, 15] Operation: 1*15=15 Exploring Operation: 15-1=14, Resulting Numbers: [72, 14] Generated Node #0,3,3: 72:[72, 14] Operation: 15-1=14 Exploring Operation: 1+15=16, Resulting Numbers: [72, 16] Generated Node #0,3,4: 72:[72, 16] Operation: 1+15=16 Moving to Node #0,3,3 Current State: 72:[72, 14], Operations: ['79-64=15', '15-1=14'] Exploring Operation: 72-14=58, Resulting Numbers: [58] 58,72 unequal: No Solution Exploring Operation: 72*14=1008, Resulting Numbers: [1008] 1008,72 unequal: No Solution Exploring Operation: 72+14=86, Resulting Numbers: [86] 86,72 unequal: No Solution Moving to Node #0,3,4 Current State: 72:[72, 16], Operations: ['79-64=15', '1+15=16'] Exploring Operation: 72+16=88, Resulting Numbers: [88] 88,72 unequal: No Solution Exploring Operation: 72*16=1152, Resulting Numbers: [1152] 1152,72 unequal: No Solution Exploring Operation: 72-16=56, Resulting Numbers: [56] 56,72 unequal: No Solution Moving to Node #0,3,0 Current State: 72:[15, 72], Operations: ['79-64=15', '72/1=72'] Exploring Operation: 15+72=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 15*72=1080, Resulting Numbers: [1080] 1080,72 unequal: No Solution Moving to Node #0,3,1 Current State: 72:[15, 72], Operations: ['79-64=15', '1*72=72'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 15+72=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 15*72=1080, Resulting Numbers: [1080] 1080,72 unequal: No Solution Moving to Node #0,3,2 Current State: 72:[72, 15], Operations: ['79-64=15', '1*15=15'] Exploring Operation: 72-15=57, Resulting Numbers: [57] 57,72 unequal: No Solution Exploring Operation: 72+15=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 72*15=1080, Resulting Numbers: [1080] 1080,72 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 #0,2 Current State: 72:[79, 1, 8], Operations: ['72-64=8'] Exploring Operation: 79-1=78, Resulting Numbers: [8, 78] Generated Node #0,2,0: 72:[8, 78] Operation: 79-1=78 Exploring Operation: 1+8=9, Resulting Numbers: [79, 9] Generated Node #0,2,1: 72:[79, 9] Operation: 1+8=9 Exploring Operation: 79*1=79, Resulting Numbers: [8, 79] Generated Node #0,2,2: 72:[8, 79] Operation: 79*1=79 Exploring Operation: 79/1=79, Resulting Numbers: [8, 79] Generated Node #0,2,3: 72:[8, 79] Operation: 79/1=79 Exploring Operation: 79-8=71, Resulting Numbers: [1, 71] Generated Node #0,2,4: 72:[1, 71] Operation: 79-8=71 Moving to Node #0,2,4 Current State: 72:[1, 71], Operations: ['72-64=8', '79-8=71'] Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[79, 1, 72, 64], Operations: [] Exploring Operation: 72-64=8, Resulting Numbers: [79, 1, 8] Generated Node #0,2: 72:[79, 1, 8] Operation: 72-64=8 Moving to Node #0,2 Current State: 72:[79, 1, 8], Operations: ['72-64=8'] Exploring Operation: 79-8=71, Resulting Numbers: [1, 71] Generated Node #0,2,4: 72:[1, 71] Operation: 79-8=71 Moving to Node #0,2,4 Current State: 72:[1, 71], Operations: ['72-64=8', '79-8=71'] Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 48, 78, 18, 94 ]
87
[ "48+78=126", "126/18=7", "94-7=87" ]
Current State: 87:[48, 78, 18, 94], Operations: [] Exploring Operation: 48+78=126, Resulting Numbers: [18, 94, 126] Generated Node #2: [18, 94, 126] from Operation: 48+78=126 Current State: 87:[18, 94, 126], Operations: ['48+78=126'] Exploring Operation: 126/18=7, Resulting Numbers: [94, 7] Generated Node #3: [94, 7] from Operation: 126/18=7 Current State: 87:[94, 7], Operations: ['48+78=126', '126/18=7'] Exploring Operation: 94-7=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[48, 78, 18, 94], Operations: [] Exploring Operation: 78-48=30, Resulting Numbers: [18, 94, 30] Generated Node #0,0: 87:[18, 94, 30] Operation: 78-48=30 Exploring Operation: 48-18=30, Resulting Numbers: [78, 94, 30] Generated Node #0,1: 87:[78, 94, 30] Operation: 48-18=30 Moving to Node #0,1 Current State: 87:[78, 94, 30], Operations: ['48-18=30'] Exploring Operation: 78-30=48, Resulting Numbers: [94, 48] Generated Node #0,1,0: 87:[94, 48] Operation: 78-30=48 Exploring Operation: 94-78=16, Resulting Numbers: [30, 16] Generated Node #0,1,1: 87:[30, 16] Operation: 94-78=16 Moving to Node #0,0 Current State: 87:[18, 94, 30], Operations: ['78-48=30'] Exploring Operation: 94-18=76, Resulting Numbers: [30, 76] Generated Node #0,0,0: 87:[30, 76] Operation: 94-18=76 Exploring Operation: 30-18=12, Resulting Numbers: [94, 12] Generated Node #0,0,1: 87:[94, 12] Operation: 30-18=12 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[30, 76], Operations: ['78-48=30', '94-18=76'] Exploring Operation: 30+76=106, Resulting Numbers: [106] 106,87 unequal: No Solution Exploring Operation: 76-30=46, Resulting Numbers: [46] 46,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[94, 12], Operations: ['78-48=30', '30-18=12'] Exploring Operation: 94-12=82, Resulting Numbers: [82] 82,87 unequal: No Solution Exploring Operation: 94+12=106, Resulting Numbers: [106] 106,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,1 Current State: 87:[30, 16], Operations: ['48-18=30', '94-78=16'] Exploring Operation: 30+16=46, Resulting Numbers: [46] 46,87 unequal: No Solution Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,87 unequal: No Solution Moving to Node #0,1,0 Current State: 87:[94, 48], Operations: ['48-18=30', '78-30=48'] Exploring Operation: 94-48=46, Resulting Numbers: [46] 46,87 unequal: No Solution Exploring Operation: 94+48=142, Resulting Numbers: [142] 142,87 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 7, 14, 14, 12 ]
86
[ "14-7=7", "14*7=98", "98-12=86" ]
Current State: 86:[7, 14, 14, 12], Operations: [] Exploring Operation: 14-7=7, Resulting Numbers: [12, 7] Generated Node #2: [12, 7] from Operation: 14-7=7 Current State: 86:[12, 7], Operations: ['14-7=7'] Exploring Operation: 14*7=98, Resulting Numbers: [12, 98] Generated Node #3: [12, 98] from Operation: 14*7=98 Current State: 86:[12, 98], Operations: ['14-7=7', '14*7=98'] Exploring Operation: 98-12=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[7, 14, 14, 12], Operations: [] Exploring Operation: 14-14=0, Resulting Numbers: [7, 12, 0] Generated Node #0,0: 86:[7, 12, 0] Operation: 14-14=0 Exploring Operation: 14/7=2, Resulting Numbers: [14, 12, 2] Generated Node #0,1: 86:[14, 12, 2] Operation: 14/7=2 Exploring Operation: 14-12=2, Resulting Numbers: [7, 14, 2] Generated Node #0,2: 86:[7, 14, 2] Operation: 14-12=2 Exploring Operation: 14/14=1, Resulting Numbers: [7, 12, 1] Generated Node #0,3: 86:[7, 12, 1] Operation: 14/14=1 Exploring Operation: 14-12=2, Resulting Numbers: [7, 14, 2] Generated Node #0,4: 86:[7, 14, 2] Operation: 14-12=2 Start Sub Search at level 1: Moving to Node #0,3 Current State: 86:[7, 12, 1], Operations: ['14/14=1'] Exploring Operation: 7-1=6, Resulting Numbers: [12, 6] Generated Node #0,3,0: 86:[12, 6] Operation: 7-1=6 Exploring Operation: 7*1=7, Resulting Numbers: [12, 7] Generated Node #0,3,1: 86:[12, 7] Operation: 7*1=7 Exploring Operation: 12-1=11, Resulting Numbers: [7, 11] Generated Node #0,3,2: 86:[7, 11] Operation: 12-1=11 Exploring Operation: 12-7=5, Resulting Numbers: [1, 5] Generated Node #0,3,3: 86:[1, 5] Operation: 12-7=5 Exploring Operation: 7*12=84, Resulting Numbers: [1, 84] Generated Node #0,3,4: 86:[1, 84] Operation: 7*12=84 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 86:[1, 84], Operations: ['14/14=1', '7*12=84'] Exploring Operation: 1*84=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 84-1=83, Resulting Numbers: [83] 83,86 unequal: No Solution Exploring Operation: 1+84=85, Resulting Numbers: [85] 85,86 unequal: No Solution Exploring Operation: 84/1=84, Resulting Numbers: [84] 84,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 86:[1, 5], Operations: ['14/14=1', '12-7=5'] Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 5/1=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 86:[12, 6], Operations: ['14/14=1', '7-1=6'] Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,86 unequal: No Solution Exploring Operation: 12*6=72, Resulting Numbers: [72] 72,86 unequal: No Solution Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,86 unequal: No Solution Exploring Operation: 12+6=18, Resulting Numbers: [18] 18,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 86:[7, 11], Operations: ['14/14=1', '12-1=11'] Exploring Operation: 7*11=77, Resulting Numbers: [77] 77,86 unequal: No Solution Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 7+11=18, Resulting Numbers: [18] 18,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 86:[12, 7], Operations: ['14/14=1', '7*1=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 86:[7, 12, 0], Operations: ['14-14=0'] Exploring Operation: 12*0=0, Resulting Numbers: [7, 0] Generated Node #0,0,0: 86:[7, 0] Operation: 12*0=0 Exploring Operation: 7+0=7, Resulting Numbers: [12, 7] Generated Node #0,0,1: 86:[12, 7] Operation: 7+0=7 Exploring Operation: 7*12=84, Resulting Numbers: [0, 84] Generated Node #0,0,2: 86:[0, 84] Operation: 7*12=84 Exploring Operation: 12-7=5, Resulting Numbers: [0, 5] Generated Node #0,0,3: 86:[0, 5] Operation: 12-7=5 Exploring Operation: 7*0=0, Resulting Numbers: [12, 0] Generated Node #0,0,4: 86:[12, 0] Operation: 7*0=0 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 86:[0, 84], Operations: ['14-14=0', '7*12=84'] Exploring Operation: 84-0=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 0*84=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 0+84=84, Resulting Numbers: [84] 84,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 86:[0, 5], Operations: ['14-14=0', '12-7=5'] Exploring Operation: 0+5=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 5-0=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 0*5=0, Resulting Numbers: [0] 0,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 86:[7, 0], Operations: ['14-14=0', '12*0=0'] Exploring Operation: 7*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 7-0=7, Resulting Numbers: [7] 7,86 unequal: No Solution Exploring Operation: 7+0=7, Resulting Numbers: [7] 7,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 86:[12, 0], Operations: ['14-14=0', '7*0=0'] Exploring Operation: 12+0=12, Resulting Numbers: [12] 12,86 unequal: No Solution Exploring Operation: 12*0=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 12-0=12, Resulting Numbers: [12] 12,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 86:[12, 7], Operations: ['14-14=0', '7+0=7'] Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,86 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 86:[7, 14, 2], Operations: ['14-12=2'] Exploring Operation: 7-2=5, Resulting Numbers: [14, 5] Generated Node #0,2,0: 86:[14, 5] Operation: 7-2=5 Exploring Operation: 14/7=2, Resulting Numbers: [2, 2] Generated Node #0,2,1: 86:[2, 2] Operation: 14/7=2 Exploring Operation: 14/2=7, Resulting Numbers: [7, 7] Generated Node #0,2,2: 86:[7, 7] Operation: 14/2=7 Exploring Operation: 7*14=98, Resulting Numbers: [2, 98] Generated Node #0,2,3: 86:[2, 98] Operation: 7*14=98 Exploring Operation: 14-7=7, Resulting Numbers: [2, 7] Generated Node #0,2,4: 86:[2, 7] Operation: 14-7=7 Moving to Node #0,2,1 Current State: 86:[2, 2], Operations: ['14-12=2', '14/7=2'] Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,2,4 Current State: 86:[2, 7], Operations: ['14-12=2', '14-7=7'] Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,86 unequal: No Solution Moving to Node #0,2,2 Current State: 86:[7, 7], Operations: ['14-12=2', '14/2=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,86 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,2,3 Current State: 86:[2, 98], Operations: ['14-12=2', '7*14=98'] Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,86 unequal: No Solution Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,86 unequal: No Solution Exploring Operation: 2*98=196, Resulting Numbers: [196] 196,86 unequal: No Solution Moving to Node #0,2,0 Current State: 86:[14, 5], Operations: ['14-12=2', '7-2=5'] Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 86:[7, 14, 2], Operations: ['14-12=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7, 7] Generated Node #0,4,0: 86:[7, 7] Operation: 14/2=7 Exploring Operation: 14/7=2, Resulting Numbers: [2, 2] Generated Node #0,4,1: 86:[2, 2] Operation: 14/7=2 Exploring Operation: 14-7=7, Resulting Numbers: [2, 7] Generated Node #0,4,2: 86:[2, 7] Operation: 14-7=7 Exploring Operation: 7*14=98, Resulting Numbers: [2, 98] Generated Node #0,4,3: 86:[2, 98] Operation: 7*14=98 Exploring Operation: 7-2=5, Resulting Numbers: [14, 5] Generated Node #0,4,4: 86:[14, 5] Operation: 7-2=5 Moving to Node #0,4,1 Current State: 86:[2, 2], Operations: ['14-12=2', '14/7=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,4,2 Current State: 86:[2, 7], Operations: ['14-12=2', '14-7=7'] Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,86 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,86 unequal: No Solution Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,86 unequal: No Solution Moving to Node #0,4,0 Current State: 86:[7, 7], Operations: ['14-12=2', '14/2=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,86 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,4,3 Current State: 86:[2, 98], Operations: ['14-12=2', '7*14=98'] Exploring Operation: 98/2=49, Resulting Numbers: [49] 49,86 unequal: No Solution Exploring Operation: 2*98=196, Resulting Numbers: [196] 196,86 unequal: No Solution Exploring Operation: 2+98=100, Resulting Numbers: [100] 100,86 unequal: No Solution Exploring Operation: 98-2=96, Resulting Numbers: [96] 96,86 unequal: No Solution Moving to Node #0,4,4 Current State: 86:[14, 5], Operations: ['14-12=2', '7-2=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,86 unequal: No Solution Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[14, 12, 2], Operations: ['14/7=2'] Exploring Operation: 12/2=6, Resulting Numbers: [14, 6] Generated Node #0,1,0: 86:[14, 6] Operation: 12/2=6 Exploring Operation: 14/2=7, Resulting Numbers: [12, 7] Generated Node #0,1,1: 86:[12, 7] Operation: 14/2=7 Exploring Operation: 14-12=2, Resulting Numbers: [2, 2] Generated Node #0,1,2: 86:[2, 2] Operation: 14-12=2 Exploring Operation: 14+12=26, Resulting Numbers: [2, 26] Generated Node #0,1,3: 86:[2, 26] Operation: 14+12=26 Exploring Operation: 14-2=12, Resulting Numbers: [12, 12] Generated Node #0,1,4: 86:[12, 12] Operation: 14-2=12 Moving to Node #0,1,2 Current State: 86:[2, 2], Operations: ['14/7=2', '14-12=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,86 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[12, 7], Operations: ['14/7=2', '14/2=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19] 19,86 unequal: No Solution Exploring Operation: 12-7=5, Resulting Numbers: [5] 5,86 unequal: No Solution Exploring Operation: 12*7=84, Resulting Numbers: [84] 84,86 unequal: No Solution Moving to Node #0,1,0 Current State: 86:[14, 6], Operations: ['14/7=2', '12/2=6'] Exploring Operation: 14*6=84, Resulting Numbers: [84] 84,86 unequal: No Solution Exploring Operation: 14+6=20, Resulting Numbers: [20] 20,86 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,86 unequal: No Solution Moving to Node #0,1,3 Current State: 86:[2, 26], Operations: ['14/7=2', '14+12=26'] Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,86 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,86 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,86 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,86 unequal: No Solution Moving to Node #0,1,4 Current State: 86:[12, 12], Operations: ['14/7=2', '14-2=12'] Exploring Operation: 12+12=24, Resulting Numbers: [24] 24,86 unequal: No Solution Exploring Operation: 12/12=1, Resulting Numbers: [1] 1,86 unequal: No Solution Exploring Operation: 12-12=0, Resulting Numbers: [0] 0,86 unequal: No Solution Exploring Operation: 12*12=144, Resulting Numbers: [144] 144,86 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
[ 35, 19, 15, 55 ]
86
[ "35-19=16", "15+55=70", "16+70=86" ]
Current State: 86:[35, 19, 15, 55], Operations: [] Exploring Operation: 35-19=16, Resulting Numbers: [15, 55, 16] Generated Node #2: [15, 55, 16] from Operation: 35-19=16 Current State: 86:[15, 55, 16], Operations: ['35-19=16'] Exploring Operation: 15+55=70, Resulting Numbers: [16, 70] Generated Node #3: [16, 70] from Operation: 15+55=70 Current State: 86:[16, 70], Operations: ['35-19=16', '15+55=70'] Exploring Operation: 16+70=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[35, 19, 15, 55], Operations: [] Exploring Operation: 55-19=36, Resulting Numbers: [35, 15, 36] Generated Node #0,0: 86:[35, 15, 36] Operation: 55-19=36 Exploring Operation: 19-15=4, Resulting Numbers: [35, 55, 4] Generated Node #0,1: 86:[35, 55, 4] Operation: 19-15=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 86:[35, 55, 4], Operations: ['19-15=4'] Exploring Operation: 35+55=90, Resulting Numbers: [4, 90] Generated Node #0,1,0: 86:[4, 90] Operation: 35+55=90 Exploring Operation: 35+4=39, Resulting Numbers: [55, 39] Generated Node #0,1,1: 86:[55, 39] Operation: 35+4=39 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 86:[4, 90], Operations: ['19-15=4', '35+55=90'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Moving to Node #0 Current State: 86:[35, 19, 15, 55], Operations: [] Exploring Operation: 19-15=4, Resulting Numbers: [35, 55, 4] Generated Node #0,1: 86:[35, 55, 4] Operation: 19-15=4 Moving to Node #0,1 Current State: 86:[35, 55, 4], Operations: ['19-15=4'] Exploring Operation: 35+55=90, Resulting Numbers: [4, 90] Generated Node #0,1,0: 86:[4, 90] Operation: 35+55=90 Moving to Node #0,1,0 Current State: 86:[4, 90], Operations: ['19-15=4', '35+55=90'] Exploring Operation: 90-4=86, Resulting Numbers: [86] 86,86 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 44, 9, 30, 22 ]
37
[ "44/22=2", "9+30=39", "39-2=37" ]
Current State: 37:[44, 9, 30, 22], Operations: [] Exploring Operation: 44/22=2, Resulting Numbers: [9, 30, 2] Generated Node #2: [9, 30, 2] from Operation: 44/22=2 Current State: 37:[9, 30, 2], Operations: ['44/22=2'] Exploring Operation: 9+30=39, Resulting Numbers: [2, 39] Generated Node #3: [2, 39] from Operation: 9+30=39 Current State: 37:[2, 39], Operations: ['44/22=2', '9+30=39'] Exploring Operation: 39-2=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[44, 9, 30, 22], Operations: [] Exploring Operation: 9+22=31, Resulting Numbers: [44, 30, 31] Generated Node #0,0: 37:[44, 30, 31] Operation: 9+22=31 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[44, 30, 31], Operations: ['9+22=31'] Exploring Operation: 44-30=14, Resulting Numbers: [31, 14] Generated Node #0,0,0: 37:[31, 14] Operation: 44-30=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[31, 14], Operations: ['9+22=31', '44-30=14'] Exploring Operation: 31+14=45, Resulting Numbers: [45] 45,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 61, 52, 15, 2 ]
20
[ "61-15=46", "52/2=26", "46-26=20" ]
Current State: 20:[61, 52, 15, 2], Operations: [] Exploring Operation: 61-15=46, Resulting Numbers: [52, 2, 46] Generated Node #2: [52, 2, 46] from Operation: 61-15=46 Current State: 20:[52, 2, 46], Operations: ['61-15=46'] Exploring Operation: 52/2=26, Resulting Numbers: [46, 26] Generated Node #3: [46, 26] from Operation: 52/2=26 Current State: 20:[46, 26], Operations: ['61-15=46', '52/2=26'] Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[61, 52, 15, 2], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [61, 15, 26] Generated Node #0,0: 20:[61, 15, 26] Operation: 52/2=26 Exploring Operation: 61-15=46, Resulting Numbers: [52, 2, 46] Generated Node #0,1: 20:[52, 2, 46] Operation: 61-15=46 Exploring Operation: 61-2=59, Resulting Numbers: [52, 15, 59] Generated Node #0,2: 20:[52, 15, 59] Operation: 61-2=59 Exploring Operation: 52-15=37, Resulting Numbers: [61, 2, 37] Generated Node #0,3: 20:[61, 2, 37] Operation: 52-15=37 Exploring Operation: 61-52=9, Resulting Numbers: [15, 2, 9] Generated Node #0,4: 20:[15, 2, 9] Operation: 61-52=9 Moving to Node #0,4 Current State: 20:[15, 2, 9], Operations: ['61-52=9'] Exploring Operation: 15-9=6, Resulting Numbers: [2, 6] Generated Node #0,4,0: 20:[2, 6] Operation: 15-9=6 Exploring Operation: 15-2=13, Resulting Numbers: [9, 13] Generated Node #0,4,1: 20:[9, 13] Operation: 15-2=13 Exploring Operation: 15+2=17, Resulting Numbers: [9, 17] Generated Node #0,4,2: 20:[9, 17] Operation: 15+2=17 Exploring Operation: 15+9=24, Resulting Numbers: [2, 24] Generated Node #0,4,3: 20:[2, 24] Operation: 15+9=24 Exploring Operation: 2+9=11, Resulting Numbers: [15, 11] Generated Node #0,4,4: 20:[15, 11] Operation: 2+9=11 Moving to Node #0,0 Current State: 20:[61, 15, 26], Operations: ['52/2=26'] Exploring Operation: 26-15=11, Resulting Numbers: [61, 11] Generated Node #0,0,0: 20:[61, 11] Operation: 26-15=11 Exploring Operation: 15+26=41, Resulting Numbers: [61, 41] Generated Node #0,0,1: 20:[61, 41] Operation: 15+26=41 Exploring Operation: 61+15=76, Resulting Numbers: [26, 76] Generated Node #0,0,2: 20:[26, 76] Operation: 61+15=76 Exploring Operation: 61-26=35, Resulting Numbers: [15, 35] Generated Node #0,0,3: 20:[15, 35] Operation: 61-26=35 Exploring Operation: 61-15=46, Resulting Numbers: [26, 46] Generated Node #0,0,4: 20:[26, 46] Operation: 61-15=46 Moving to Node #0,1 Current State: 20:[52, 2, 46], Operations: ['61-15=46'] Exploring Operation: 52/2=26, Resulting Numbers: [46, 26] Generated Node #0,1,0: 20:[46, 26] Operation: 52/2=26 Exploring Operation: 46/2=23, Resulting Numbers: [52, 23] Generated Node #0,1,1: 20:[52, 23] Operation: 46/2=23 Exploring Operation: 52-2=50, Resulting Numbers: [46, 50] Generated Node #0,1,2: 20:[46, 50] Operation: 52-2=50 Exploring Operation: 46-2=44, Resulting Numbers: [52, 44] Generated Node #0,1,3: 20:[52, 44] Operation: 46-2=44 Exploring Operation: 52-46=6, Resulting Numbers: [2, 6] Generated Node #0,1,4: 20:[2, 6] Operation: 52-46=6 Moving to Node #0,3 Current State: 20:[61, 2, 37], Operations: ['52-15=37'] Exploring Operation: 37-2=35, Resulting Numbers: [61, 35] Generated Node #0,3,0: 20:[61, 35] Operation: 37-2=35 Exploring Operation: 61-2=59, Resulting Numbers: [37, 59] Generated Node #0,3,1: 20:[37, 59] Operation: 61-2=59 Exploring Operation: 61+2=63, Resulting Numbers: [37, 63] Generated Node #0,3,2: 20:[37, 63] Operation: 61+2=63 Exploring Operation: 61-37=24, Resulting Numbers: [2, 24] Generated Node #0,3,3: 20:[2, 24] Operation: 61-37=24 Exploring Operation: 2+37=39, Resulting Numbers: [61, 39] Generated Node #0,3,4: 20:[61, 39] Operation: 2+37=39 Moving to Node #0,2 Current State: 20:[52, 15, 59], Operations: ['61-2=59'] Exploring Operation: 15+59=74, Resulting Numbers: [52, 74] Generated Node #0,2,0: 20:[52, 74] Operation: 15+59=74 Exploring Operation: 59-15=44, Resulting Numbers: [52, 44] Generated Node #0,2,1: 20:[52, 44] Operation: 59-15=44 Exploring Operation: 52+15=67, Resulting Numbers: [59, 67] Generated Node #0,2,2: 20:[59, 67] Operation: 52+15=67 Exploring Operation: 52-15=37, Resulting Numbers: [59, 37] Generated Node #0,2,3: 20:[59, 37] Operation: 52-15=37 Exploring Operation: 59-52=7, Resulting Numbers: [15, 7] Generated Node #0,2,4: 20:[15, 7] Operation: 59-52=7 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 20:[15, 7], Operations: ['61-2=59', '59-52=7'] Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 15*7=105, Resulting Numbers: [105] 105,20 unequal: No Solution Exploring Operation: 15+7=22, Resulting Numbers: [22] 22,20 unequal: No Solution No 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: 20:[52, 44], Operations: ['61-2=59', '59-15=44'] Exploring Operation: 52*44=2288, Resulting Numbers: [2288] 2288,20 unequal: No Solution Exploring Operation: 52-44=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 52+44=96, Resulting Numbers: [96] 96,20 unequal: No Solution No 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: 20:[59, 37], Operations: ['61-2=59', '52-15=37'] Exploring Operation: 59*37=2183, Resulting Numbers: [2183] 2183,20 unequal: No Solution Exploring Operation: 59+37=96, Resulting Numbers: [96] 96,20 unequal: No Solution Exploring Operation: 59-37=22, Resulting Numbers: [22] 22,20 unequal: No Solution No 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: 20:[52, 74], Operations: ['61-2=59', '15+59=74'] Exploring Operation: 52+74=126, Resulting Numbers: [126] 126,20 unequal: No Solution Exploring Operation: 52*74=3848, Resulting Numbers: [3848] 3848,20 unequal: No Solution Exploring Operation: 74-52=22, Resulting Numbers: [22] 22,20 unequal: No Solution No 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: 20:[59, 67], Operations: ['61-2=59', '52+15=67'] Exploring Operation: 59+67=126, Resulting Numbers: [126] 126,20 unequal: No Solution Exploring Operation: 67-59=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 59*67=3953, Resulting Numbers: [3953] 3953,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 20:[2, 6], Operations: ['61-52=9', '15-9=6'] Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,20 unequal: No Solution Moving to Node #0,1,4 Current State: 20:[2, 6], Operations: ['61-15=46', '52-46=6'] Exploring Operation: 2*6=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 2+6=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,20 unequal: No Solution Moving to Node #0,4,2 Current State: 20:[9, 17], Operations: ['61-52=9', '15+2=17'] Exploring Operation: 17-9=8, Resulting Numbers: [8] 8,20 unequal: No Solution Exploring Operation: 9+17=26, Resulting Numbers: [26] 26,20 unequal: No Solution Exploring Operation: 9*17=153, Resulting Numbers: [153] 153,20 unequal: No Solution Moving to Node #0,4,1 Current State: 20:[9, 13], Operations: ['61-52=9', '15-2=13'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,20 unequal: No Solution Exploring Operation: 9+13=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 9*13=117, Resulting Numbers: [117] 117,20 unequal: No Solution Moving to Node #0,4,3 Current State: 20:[2, 24], Operations: ['61-52=9', '15+9=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,20 unequal: No Solution Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,20 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,20 unequal: No Solution Moving to Node #0,3,3 Current State: 20:[2, 24], Operations: ['52-15=37', '61-37=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,20 unequal: No Solution Exploring Operation: 2*24=48, Resulting Numbers: [48] 48,20 unequal: No Solution Exploring Operation: 24/2=12, Resulting Numbers: [12] 12,20 unequal: No Solution Moving to Node #0,4,4 Current State: 20:[15, 11], Operations: ['61-52=9', '2+9=11'] Exploring Operation: 15*11=165, Resulting Numbers: [165] 165,20 unequal: No Solution Exploring Operation: 15+11=26, Resulting Numbers: [26] 26,20 unequal: No Solution Exploring Operation: 15-11=4, Resulting Numbers: [4] 4,20 unequal: No Solution Moving to Node #0,0,3 Current State: 20:[15, 35], Operations: ['52/2=26', '61-26=35'] Exploring Operation: 15*35=525, Resulting Numbers: [525] 525,20 unequal: No Solution Exploring Operation: 15+35=50, Resulting Numbers: [50] 50,20 unequal: No Solution Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[61, 52, 15, 2], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [61, 15, 26] Generated Node #0,0: 20:[61, 15, 26] Operation: 52/2=26 Moving to Node #0,0 Current State: 20:[61, 15, 26], Operations: ['52/2=26'] Exploring Operation: 61-26=35, Resulting Numbers: [15, 35] Generated Node #0,0,3: 20:[15, 35] Operation: 61-26=35 Moving to Node #0,0,3 Current State: 20:[15, 35], Operations: ['52/2=26', '61-26=35'] Exploring Operation: 35-15=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.93316
hs_5
mult_heuristic
[ 48, 1, 51, 31 ]
29
[ "48+1=49", "51-31=20", "49-20=29" ]
Current State: 29:[48, 1, 51, 31], Operations: [] Exploring Operation: 48+1=49, Resulting Numbers: [51, 31, 49] Generated Node #2: [51, 31, 49] from Operation: 48+1=49 Current State: 29:[51, 31, 49], Operations: ['48+1=49'] Exploring Operation: 51-31=20, Resulting Numbers: [49, 20] Generated Node #3: [49, 20] from Operation: 51-31=20 Current State: 29:[49, 20], Operations: ['48+1=49', '51-31=20'] Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[48, 1, 51, 31], Operations: [] Exploring Operation: 51-1=50, Resulting Numbers: [48, 31, 50] Generated Node #0,0: 29:[48, 31, 50] Operation: 51-1=50 Exploring Operation: 48-1=47, Resulting Numbers: [51, 31, 47] Generated Node #0,1: 29:[51, 31, 47] Operation: 48-1=47 Exploring Operation: 31-1=30, Resulting Numbers: [48, 51, 30] Generated Node #0,2: 29:[48, 51, 30] Operation: 31-1=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[48, 31, 50], Operations: ['51-1=50'] Exploring Operation: 48-31=17, Resulting Numbers: [50, 17] Generated Node #0,0,0: 29:[50, 17] Operation: 48-31=17 Exploring Operation: 50-31=19, Resulting Numbers: [48, 19] Generated Node #0,0,1: 29:[48, 19] Operation: 50-31=19 Exploring Operation: 50-48=2, Resulting Numbers: [31, 2] Generated Node #0,0,2: 29:[31, 2] Operation: 50-48=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[48, 19], Operations: ['51-1=50', '50-31=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[48, 1, 51, 31], Operations: [] Exploring Operation: 51-1=50, Resulting Numbers: [48, 31, 50] Generated Node #0,0: 29:[48, 31, 50] Operation: 51-1=50 Moving to Node #0,0 Current State: 29:[48, 31, 50], Operations: ['51-1=50'] Exploring Operation: 50-31=19, Resulting Numbers: [48, 19] Generated Node #0,0,1: 29:[48, 19] Operation: 50-31=19 Moving to Node #0,0,1 Current State: 29:[48, 19], Operations: ['51-1=50', '50-31=19'] Exploring Operation: 48-19=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 57, 14, 24, 77 ]
18
[ "57+14=71", "77-24=53", "71-53=18" ]
Current State: 18:[57, 14, 24, 77], Operations: [] Exploring Operation: 57+14=71, Resulting Numbers: [24, 77, 71] Generated Node #2: [24, 77, 71] from Operation: 57+14=71 Current State: 18:[24, 77, 71], Operations: ['57+14=71'] Exploring Operation: 77-24=53, Resulting Numbers: [71, 53] Generated Node #3: [71, 53] from Operation: 77-24=53 Current State: 18:[71, 53], Operations: ['57+14=71', '77-24=53'] Exploring Operation: 71-53=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[57, 14, 24, 77], Operations: [] Exploring Operation: 77-24=53, Resulting Numbers: [57, 14, 53] Generated Node #0,0: 18:[57, 14, 53] Operation: 77-24=53 Exploring Operation: 57-14=43, Resulting Numbers: [24, 77, 43] Generated Node #0,1: 18:[24, 77, 43] Operation: 57-14=43 Exploring Operation: 77-57=20, Resulting Numbers: [14, 24, 20] Generated Node #0,2: 18:[14, 24, 20] Operation: 77-57=20 Exploring Operation: 57-24=33, Resulting Numbers: [14, 77, 33] Generated Node #0,3: 18:[14, 77, 33] Operation: 57-24=33 Exploring Operation: 77-14=63, Resulting Numbers: [57, 24, 63] Generated Node #0,4: 18:[57, 24, 63] Operation: 77-14=63 Moving to Node #0,2 Current State: 18:[14, 24, 20], Operations: ['77-57=20'] Exploring Operation: 20-14=6, Resulting Numbers: [24, 6] Generated Node #0,2,0: 18:[24, 6] Operation: 20-14=6 Exploring Operation: 24-20=4, Resulting Numbers: [14, 4] Generated Node #0,2,1: 18:[14, 4] Operation: 24-20=4 Exploring Operation: 14+24=38, Resulting Numbers: [20, 38] Generated Node #0,2,2: 18:[20, 38] Operation: 14+24=38 Exploring Operation: 14+20=34, Resulting Numbers: [24, 34] Generated Node #0,2,3: 18:[24, 34] Operation: 14+20=34 Exploring Operation: 24-14=10, Resulting Numbers: [20, 10] Generated Node #0,2,4: 18:[20, 10] Operation: 24-14=10 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 18:[20, 10], Operations: ['77-57=20', '24-14=10'] Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,18 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,18 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,18 unequal: No Solution Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[14, 4], Operations: ['77-57=20', '24-20=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[57, 14, 24, 77], Operations: [] Exploring Operation: 77-57=20, Resulting Numbers: [14, 24, 20] Generated Node #0,2: 18:[14, 24, 20] Operation: 77-57=20 Moving to Node #0,2 Current State: 18:[14, 24, 20], Operations: ['77-57=20'] Exploring Operation: 24-20=4, Resulting Numbers: [14, 4] Generated Node #0,2,1: 18:[14, 4] Operation: 24-20=4 Moving to Node #0,2,1 Current State: 18:[14, 4], Operations: ['77-57=20', '24-20=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_5
sum_heuristic
[ 65, 30, 49, 62 ]
22
[ "65-30=35", "62-49=13", "35-13=22" ]
Current State: 22:[65, 30, 49, 62], Operations: [] Exploring Operation: 65-30=35, Resulting Numbers: [49, 62, 35] Generated Node #2: [49, 62, 35] from Operation: 65-30=35 Current State: 22:[49, 62, 35], Operations: ['65-30=35'] Exploring Operation: 62-49=13, Resulting Numbers: [35, 13] Generated Node #3: [35, 13] from Operation: 62-49=13 Current State: 22:[35, 13], Operations: ['65-30=35', '62-49=13'] Exploring Operation: 35-13=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[65, 30, 49, 62], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [30, 49, 3] Generated Node #0,0: 22:[30, 49, 3] Operation: 65-62=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[30, 49, 3], Operations: ['65-62=3'] Exploring Operation: 49-30=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 22:[3, 19] Operation: 49-30=19 Moving to Node #0,0,0 Current State: 22:[3, 19], Operations: ['65-62=3', '49-30=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[65, 30, 49, 62], Operations: [] Exploring Operation: 65-62=3, Resulting Numbers: [30, 49, 3] Generated Node #0,0: 22:[30, 49, 3] Operation: 65-62=3 Moving to Node #0,0 Current State: 22:[30, 49, 3], Operations: ['65-62=3'] Exploring Operation: 49-30=19, Resulting Numbers: [3, 19] Generated Node #0,0,0: 22:[3, 19] Operation: 49-30=19 Moving to Node #0,0,0 Current State: 22:[3, 19], Operations: ['65-62=3', '49-30=19'] Exploring Operation: 3+19=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 49, 77, 77 ]
21
[ "77-49=28", "2*28=56", "77-56=21" ]
Current State: 21:[2, 49, 77, 77], Operations: [] Exploring Operation: 77-49=28, Resulting Numbers: [2, 28] Generated Node #2: [2, 28] from Operation: 77-49=28 Current State: 21:[2, 28], Operations: ['77-49=28'] Exploring Operation: 2*28=56, Resulting Numbers: [56] 56,21 equal: Goal Reached Exploring Operation: 77-56=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[2, 49, 77, 77], Operations: [] Exploring Operation: 77/77=1, Resulting Numbers: [2, 49, 1] Generated Node #0,0: 21:[2, 49, 1] Operation: 77/77=1 Exploring Operation: 77-49=28, Resulting Numbers: [2, 77, 28] Generated Node #0,1: 21:[2, 77, 28] Operation: 77-49=28 Exploring Operation: 77-77=0, Resulting Numbers: [2, 49, 0] Generated Node #0,2: 21:[2, 49, 0] Operation: 77-77=0 Exploring Operation: 77-49=28, Resulting Numbers: [2, 77, 28] Generated Node #0,3: 21:[2, 77, 28] Operation: 77-49=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[2, 49, 1], Operations: ['77/77=1'] Exploring Operation: 49-2=47, Resulting Numbers: [1, 47] Generated Node #0,0,0: 21:[1, 47] Operation: 49-2=47 Exploring Operation: 49-1=48, Resulting Numbers: [2, 48] Generated Node #0,0,1: 21:[2, 48] Operation: 49-1=48 Exploring Operation: 2+1=3, Resulting Numbers: [49, 3] Generated Node #0,0,2: 21:[49, 3] Operation: 2+1=3 Exploring Operation: 2*1=2, Resulting Numbers: [49, 2] Generated Node #0,0,3: 21:[49, 2] Operation: 2*1=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[1, 47], Operations: ['77/77=1', '49-2=47'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,21 unequal: No Solution Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 21:[2, 48], Operations: ['77/77=1', '49-1=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,21 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,21 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 21:[49, 3], Operations: ['77/77=1', '2+1=3'] Exploring Operation: 49*3=147, Resulting Numbers: [147] 147,21 unequal: No Solution Exploring Operation: 49+3=52, Resulting Numbers: [52] 52,21 unequal: No Solution Exploring Operation: 49-3=46, Resulting Numbers: [46] 46,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 21:[49, 2], Operations: ['77/77=1', '2*1=2'] Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,21 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 21:[2, 49, 0], Operations: ['77-77=0'] Exploring Operation: 2+0=2, Resulting Numbers: [49, 2] Generated Node #0,2,0: 21:[49, 2] Operation: 2+0=2 Exploring Operation: 49*0=0, Resulting Numbers: [2, 0] Generated Node #0,2,1: 21:[2, 0] Operation: 49*0=0 Exploring Operation: 2-0=2, Resulting Numbers: [49, 2] Generated Node #0,2,2: 21:[49, 2] Operation: 2-0=2 Exploring Operation: 49-2=47, Resulting Numbers: [0, 47] Generated Node #0,2,3: 21:[0, 47] Operation: 49-2=47 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 21:[2, 0], Operations: ['77-77=0', '49*0=0'] Exploring Operation: 2-0=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 2+0=2, Resulting Numbers: [2] 2,21 unequal: No Solution Exploring Operation: 2*0=0, Resulting Numbers: [0] 0,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 21:[49, 2], Operations: ['77-77=0', '2+0=2'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 21:[49, 2], Operations: ['77-77=0', '2-0=2'] Exploring Operation: 49+2=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 49*2=98, Resulting Numbers: [98] 98,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 21:[0, 47], Operations: ['77-77=0', '49-2=47'] Exploring Operation: 0+47=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 0*47=0, Resulting Numbers: [0] 0,21 unequal: No Solution Exploring Operation: 47-0=47, Resulting Numbers: [47] 47,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 21:[2, 77, 28], Operations: ['77-49=28'] Exploring Operation: 77-2=75, Resulting Numbers: [28, 75] Generated Node #0,1,0: 21:[28, 75] Operation: 77-2=75 Exploring Operation: 28-2=26, Resulting Numbers: [77, 26] Generated Node #0,1,1: 21:[77, 26] Operation: 28-2=26 Exploring Operation: 77-28=49, Resulting Numbers: [2, 49] Generated Node #0,1,2: 21:[2, 49] Operation: 77-28=49 Exploring Operation: 28/2=14, Resulting Numbers: [77, 14] Generated Node #0,1,3: 21:[77, 14] Operation: 28/2=14 Moving to Node #0,1,2 Current State: 21:[2, 49], Operations: ['77-49=28', '77-28=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,21 unequal: No Solution Moving to Node #0,1,1 Current State: 21:[77, 26], Operations: ['77-49=28', '28-2=26'] Exploring Operation: 77*26=2002, Resulting Numbers: [2002] 2002,21 unequal: No Solution Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,21 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,21 unequal: No Solution Moving to Node #0,1,0 Current State: 21:[28, 75], Operations: ['77-49=28', '77-2=75'] Exploring Operation: 28*75=2100, Resulting Numbers: [2100] 2100,21 unequal: No Solution Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 28+75=103, Resulting Numbers: [103] 103,21 unequal: No Solution Moving to Node #0,1,3 Current State: 21:[77, 14], Operations: ['77-49=28', '28/2=14'] Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,21 unequal: No Solution Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,21 unequal: No Solution Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,21 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 #0,3 Current State: 21:[2, 77, 28], Operations: ['77-49=28'] Exploring Operation: 77-2=75, Resulting Numbers: [28, 75] Generated Node #0,3,0: 21:[28, 75] Operation: 77-2=75 Exploring Operation: 28/2=14, Resulting Numbers: [77, 14] Generated Node #0,3,1: 21:[77, 14] Operation: 28/2=14 Exploring Operation: 77-28=49, Resulting Numbers: [2, 49] Generated Node #0,3,2: 21:[2, 49] Operation: 77-28=49 Exploring Operation: 28-2=26, Resulting Numbers: [77, 26] Generated Node #0,3,3: 21:[77, 26] Operation: 28-2=26 Moving to Node #0,3,2 Current State: 21:[2, 49], Operations: ['77-49=28', '77-28=49'] Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,21 unequal: No Solution Moving to Node #0,3,3 Current State: 21:[77, 26], Operations: ['77-49=28', '28-2=26'] Exploring Operation: 77*26=2002, Resulting Numbers: [2002] 2002,21 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,21 unequal: No Solution Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,21 unequal: No Solution Moving to Node #0,3,0 Current State: 21:[28, 75], Operations: ['77-49=28', '77-2=75'] Exploring Operation: 28*75=2100, Resulting Numbers: [2100] 2100,21 unequal: No Solution Exploring Operation: 75-28=47, Resulting Numbers: [47] 47,21 unequal: No Solution Exploring Operation: 28+75=103, Resulting Numbers: [103] 103,21 unequal: No Solution Moving to Node #0,3,1 Current State: 21:[77, 14], Operations: ['77-49=28', '28/2=14'] Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,21 unequal: No Solution Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,21 unequal: No Solution Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,21 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
[ 40, 69, 61, 66 ]
59
[ "69-66=3", "40*3=120", "120-61=59" ]
Current State: 59:[40, 69, 61, 66], Operations: [] Exploring Operation: 69-66=3, Resulting Numbers: [40, 61, 3] Generated Node #2: [40, 61, 3] from Operation: 69-66=3 Current State: 59:[40, 61, 3], Operations: ['69-66=3'] Exploring Operation: 40*3=120, Resulting Numbers: [61, 120] Generated Node #3: [61, 120] from Operation: 40*3=120 Current State: 59:[61, 120], Operations: ['69-66=3', '40*3=120'] Exploring Operation: 120-61=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[40, 69, 61, 66], Operations: [] Exploring Operation: 69-40=29, Resulting Numbers: [61, 66, 29] Generated Node #0,0: 59:[61, 66, 29] Operation: 69-40=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 59:[61, 66, 29], Operations: ['69-40=29'] Exploring Operation: 66-29=37, Resulting Numbers: [61, 37] Generated Node #0,0,0: 59:[61, 37] Operation: 66-29=37 Moving to Node #0,0,0 Current State: 59:[61, 37], Operations: ['69-40=29', '66-29=37'] Exploring Operation: 61-37=24, Resulting Numbers: [24] 24,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 27, 2, 78, 39 ]
13
[ "39-27=12", "2*78=156", "156/12=13" ]
Current State: 13:[27, 2, 78, 39], Operations: [] Exploring Operation: 39-27=12, Resulting Numbers: [2, 78, 12] Generated Node #2: [2, 78, 12] from Operation: 39-27=12 Current State: 13:[2, 78, 12], Operations: ['39-27=12'] Exploring Operation: 2*78=156, Resulting Numbers: [12, 156] Generated Node #3: [12, 156] from Operation: 2*78=156 Current State: 13:[12, 156], Operations: ['39-27=12', '2*78=156'] Exploring Operation: 156/12=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[27, 2, 78, 39], Operations: [] Exploring Operation: 78/39=2, Resulting Numbers: [27, 2, 2] Generated Node #0,0: 13:[27, 2, 2] Operation: 78/39=2 Moving to Node #0,0 Current State: 13:[27, 2, 2], Operations: ['78/39=2'] Exploring Operation: 27-2=25, Resulting Numbers: [2, 25] Generated Node #0,0,0: 13:[2, 25] Operation: 27-2=25 Moving to Node #0,0,0 Current State: 13:[2, 25], Operations: ['78/39=2', '27-2=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,13 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 20, 14, 6, 1 ]
65
[ "20-1=19", "14*6=84", "84-19=65" ]
Current State: 65:[20, 14, 6, 1], Operations: [] Exploring Operation: 20-1=19, Resulting Numbers: [14, 6, 19] Generated Node #2: [14, 6, 19] from Operation: 20-1=19 Current State: 65:[14, 6, 19], Operations: ['20-1=19'] Exploring Operation: 14*6=84, Resulting Numbers: [19, 84] Generated Node #3: [19, 84] from Operation: 14*6=84 Current State: 65:[19, 84], Operations: ['20-1=19', '14*6=84'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[20, 14, 6, 1], Operations: [] Exploring Operation: 20-6=14, Resulting Numbers: [14, 1, 14] Generated Node #0,0: 65:[14, 1, 14] Operation: 20-6=14 Exploring Operation: 20-1=19, Resulting Numbers: [14, 6, 19] Generated Node #0,1: 65:[14, 6, 19] Operation: 20-1=19 Exploring Operation: 20-14=6, Resulting Numbers: [6, 1, 6] Generated Node #0,2: 65:[6, 1, 6] Operation: 20-14=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[14, 1, 14], Operations: ['20-6=14'] Exploring Operation: 14*1=14, Resulting Numbers: [14, 14] Generated Node #0,0,0: 65:[14, 14] Operation: 14*1=14 Exploring Operation: 14-1=13, Resulting Numbers: [14, 13] Generated Node #0,0,1: 65:[14, 13] Operation: 14-1=13 Exploring Operation: 14-1=13, Resulting Numbers: [14, 13] Generated Node #0,0,2: 65:[14, 13] Operation: 14-1=13 Moving to Node #0,0,1 Current State: 65:[14, 13], Operations: ['20-6=14', '14-1=13'] Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[14, 13], Operations: ['20-6=14', '14-1=13'] Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,65 unequal: No Solution Moving to Node #0,0,0 Current State: 65:[14, 14], Operations: ['20-6=14', '14*1=14'] Exploring Operation: 14+14=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 14/14=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 14-14=0, Resulting Numbers: [0] 0,65 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 #0,2 Current State: 65:[6, 1, 6], Operations: ['20-14=6'] Exploring Operation: 6-1=5, Resulting Numbers: [6, 5] Generated Node #0,2,0: 65:[6, 5] Operation: 6-1=5 Exploring Operation: 6*1=6, Resulting Numbers: [6, 6] Generated Node #0,2,1: 65:[6, 6] Operation: 6*1=6 Exploring Operation: 6-1=5, Resulting Numbers: [6, 5] Generated Node #0,2,2: 65:[6, 5] Operation: 6-1=5 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 65:[6, 5], Operations: ['20-14=6', '6-1=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,65 unequal: No Solution No 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: 65:[6, 5], Operations: ['20-14=6', '6-1=5'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,65 unequal: No Solution No 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: 65:[6, 6], Operations: ['20-14=6', '6*1=6'] Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 6-6=0, Resulting Numbers: [0] 0,65 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: 65:[14, 6, 19], Operations: ['20-1=19'] Exploring Operation: 19-14=5, Resulting Numbers: [6, 5] Generated Node #0,1,0: 65:[6, 5] Operation: 19-14=5 Exploring Operation: 19-6=13, Resulting Numbers: [14, 13] Generated Node #0,1,1: 65:[14, 13] Operation: 19-6=13 Exploring Operation: 14-6=8, Resulting Numbers: [19, 8] Generated Node #0,1,2: 65:[19, 8] Operation: 14-6=8 Moving to Node #0,1,0 Current State: 65:[6, 5], Operations: ['20-1=19', '19-14=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 6+5=11, Resulting Numbers: [11] 11,65 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,65 unequal: No Solution Moving to Node #0,1,1 Current State: 65:[14, 13], Operations: ['20-1=19', '19-6=13'] Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,65 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,65 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,65 unequal: No Solution Moving to Node #0,1,2 Current State: 65:[19, 8], Operations: ['20-1=19', '14-6=8'] Exploring Operation: 19*8=152, Resulting Numbers: [152] 152,65 unequal: No Solution Exploring Operation: 19+8=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 19-8=11, Resulting Numbers: [11] 11,65 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
[ 60, 51, 46, 58 ]
99
[ "60+51=111", "58-46=12", "111-12=99" ]
Current State: 99:[60, 51, 46, 58], Operations: [] Exploring Operation: 60+51=111, Resulting Numbers: [46, 58, 111] Generated Node #2: [46, 58, 111] from Operation: 60+51=111 Current State: 99:[46, 58, 111], Operations: ['60+51=111'] Exploring Operation: 58-46=12, Resulting Numbers: [111, 12] Generated Node #3: [111, 12] from Operation: 58-46=12 Current State: 99:[111, 12], Operations: ['60+51=111', '58-46=12'] Exploring Operation: 111-12=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[60, 51, 46, 58], Operations: [] Exploring Operation: 60-51=9, Resulting Numbers: [46, 58, 9] Generated Node #0,0: 99:[46, 58, 9] Operation: 60-51=9 Exploring Operation: 60-46=14, Resulting Numbers: [51, 58, 14] Generated Node #0,1: 99:[51, 58, 14] Operation: 60-46=14 Exploring Operation: 58-51=7, Resulting Numbers: [60, 46, 7] Generated Node #0,2: 99:[60, 46, 7] Operation: 58-51=7 Exploring Operation: 58-46=12, Resulting Numbers: [60, 51, 12] Generated Node #0,3: 99:[60, 51, 12] Operation: 58-46=12 Exploring Operation: 60-58=2, Resulting Numbers: [51, 46, 2] Generated Node #0,4: 99:[51, 46, 2] Operation: 60-58=2 Start Sub Search at level 1: Moving to Node #0,4 Current State: 99:[51, 46, 2], Operations: ['60-58=2'] Exploring Operation: 46/2=23, Resulting Numbers: [51, 23] Generated Node #0,4,0: 99:[51, 23] Operation: 46/2=23 Exploring Operation: 51*2=102, Resulting Numbers: [46, 102] Generated Node #0,4,1: 99:[46, 102] Operation: 51*2=102 Exploring Operation: 46*2=92, Resulting Numbers: [51, 92] Generated Node #0,4,2: 99:[51, 92] Operation: 46*2=92 Exploring Operation: 51-46=5, Resulting Numbers: [2, 5] Generated Node #0,4,3: 99:[2, 5] Operation: 51-46=5 Exploring Operation: 51+46=97, Resulting Numbers: [2, 97] Generated Node #0,4,4: 99:[2, 97] Operation: 51+46=97 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 99:[2, 5], Operations: ['60-58=2', '51-46=5'] Exploring Operation: 2+5=7, Resulting Numbers: [7] 7,99 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,99 unequal: No Solution Exploring Operation: 2*5=10, Resulting Numbers: [10] 10,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 99:[2, 97], Operations: ['60-58=2', '51+46=97'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,99 unequal: No Solution Exploring Operation: 2*97=194, Resulting Numbers: [194] 194,99 unequal: No Solution Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Moving to Node #0 Current State: 99:[60, 51, 46, 58], Operations: [] Exploring Operation: 60-58=2, Resulting Numbers: [51, 46, 2] Generated Node #0,4: 99:[51, 46, 2] Operation: 60-58=2 Moving to Node #0,4 Current State: 99:[51, 46, 2], Operations: ['60-58=2'] Exploring Operation: 51+46=97, Resulting Numbers: [2, 97] Generated Node #0,4,4: 99:[2, 97] Operation: 51+46=97 Moving to Node #0,4,4 Current State: 99:[2, 97], Operations: ['60-58=2', '51+46=97'] Exploring Operation: 2+97=99, Resulting Numbers: [99] 99,99 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 45, 41, 41, 10 ]
10
[ "41-41=0", "45*0=0", "10+0=10" ]
Current State: 10:[45, 41, 41, 10], Operations: [] Exploring Operation: 41-41=0, Resulting Numbers: [45, 10, 0] Generated Node #2: [45, 10, 0] from Operation: 41-41=0 Current State: 10:[45, 10, 0], Operations: ['41-41=0'] Exploring Operation: 45*0=0, Resulting Numbers: [10, 0] Generated Node #3: [10, 0] from Operation: 45*0=0 Current State: 10:[10, 0], Operations: ['41-41=0', '45*0=0'] Exploring Operation: 10+0=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[45, 41, 41, 10], Operations: [] Exploring Operation: 45-41=4, Resulting Numbers: [41, 10, 4] Generated Node #0,0: 10:[41, 10, 4] Operation: 45-41=4 Moving to Node #0,0 Current State: 10:[41, 10, 4], Operations: ['45-41=4'] Exploring Operation: 41-10=31, Resulting Numbers: [4, 31] Generated Node #0,0,0: 10:[4, 31] Operation: 41-10=31 Moving to Node #0,0,0 Current State: 10:[4, 31], Operations: ['45-41=4', '41-10=31'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,10 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 10, 95, 20, 62 ]
43
[ "95-10=85", "62-20=42", "85-42=43" ]
Current State: 43:[10, 95, 20, 62], Operations: [] Exploring Operation: 95-10=85, Resulting Numbers: [20, 62, 85] Generated Node #2: [20, 62, 85] from Operation: 95-10=85 Current State: 43:[20, 62, 85], Operations: ['95-10=85'] Exploring Operation: 62-20=42, Resulting Numbers: [85, 42] Generated Node #3: [85, 42] from Operation: 62-20=42 Current State: 43:[85, 42], Operations: ['95-10=85', '62-20=42'] Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[10, 95, 20, 62], Operations: [] Exploring Operation: 95-10=85, Resulting Numbers: [20, 62, 85] Generated Node #0,0: 43:[20, 62, 85] Operation: 95-10=85 Exploring Operation: 95-62=33, Resulting Numbers: [10, 20, 33] Generated Node #0,1: 43:[10, 20, 33] Operation: 95-62=33 Exploring Operation: 62-10=52, Resulting Numbers: [95, 20, 52] Generated Node #0,2: 43:[95, 20, 52] Operation: 62-10=52 Exploring Operation: 95-20=75, Resulting Numbers: [10, 62, 75] Generated Node #0,3: 43:[10, 62, 75] Operation: 95-20=75 Exploring Operation: 10+20=30, Resulting Numbers: [95, 62, 30] Generated Node #0,4: 43:[95, 62, 30] Operation: 10+20=30 Moving to Node #0,1 Current State: 43:[10, 20, 33], Operations: ['95-62=33'] Exploring Operation: 33-10=23, Resulting Numbers: [20, 23] Generated Node #0,1,0: 43:[20, 23] Operation: 33-10=23 Exploring Operation: 20-10=10, Resulting Numbers: [33, 10] Generated Node #0,1,1: 43:[33, 10] Operation: 20-10=10 Exploring Operation: 20+33=53, Resulting Numbers: [10, 53] Generated Node #0,1,2: 43:[10, 53] Operation: 20+33=53 Exploring Operation: 10+33=43, Resulting Numbers: [20, 43] Generated Node #0,1,3: 43:[20, 43] Operation: 10+33=43 Exploring Operation: 10+20=30, Resulting Numbers: [33, 30] Generated Node #0,1,4: 43:[33, 30] Operation: 10+20=30 Moving to Node #0,2 Current State: 43:[95, 20, 52], Operations: ['62-10=52'] Exploring Operation: 95-20=75, Resulting Numbers: [52, 75] Generated Node #0,2,0: 43:[52, 75] Operation: 95-20=75 Exploring Operation: 52-20=32, Resulting Numbers: [95, 32] Generated Node #0,2,1: 43:[95, 32] Operation: 52-20=32 Exploring Operation: 20+52=72, Resulting Numbers: [95, 72] Generated Node #0,2,2: 43:[95, 72] Operation: 20+52=72 Exploring Operation: 95+20=115, Resulting Numbers: [52, 115] Generated Node #0,2,3: 43:[52, 115] Operation: 95+20=115 Exploring Operation: 95-52=43, Resulting Numbers: [20, 43] Generated Node #0,2,4: 43:[20, 43] Operation: 95-52=43 Moving to Node #0,4 Current State: 43:[95, 62, 30], Operations: ['10+20=30'] Exploring Operation: 95+30=125, Resulting Numbers: [62, 125] Generated Node #0,4,0: 43:[62, 125] Operation: 95+30=125 Exploring Operation: 62+30=92, Resulting Numbers: [95, 92] Generated Node #0,4,1: 43:[95, 92] Operation: 62+30=92 Exploring Operation: 62-30=32, Resulting Numbers: [95, 32] Generated Node #0,4,2: 43:[95, 32] Operation: 62-30=32 Exploring Operation: 95-30=65, Resulting Numbers: [62, 65] Generated Node #0,4,3: 43:[62, 65] Operation: 95-30=65 Exploring Operation: 95-62=33, Resulting Numbers: [30, 33] Generated Node #0,4,4: 43:[30, 33] Operation: 95-62=33 Moving to Node #0,0 Current State: 43:[20, 62, 85], Operations: ['95-10=85'] Exploring Operation: 62-20=42, Resulting Numbers: [85, 42] Generated Node #0,0,0: 43:[85, 42] Operation: 62-20=42 Exploring Operation: 85-62=23, Resulting Numbers: [20, 23] Generated Node #0,0,1: 43:[20, 23] Operation: 85-62=23 Exploring Operation: 20+62=82, Resulting Numbers: [85, 82] Generated Node #0,0,2: 43:[85, 82] Operation: 20+62=82 Exploring Operation: 85-20=65, Resulting Numbers: [62, 65] Generated Node #0,0,3: 43:[62, 65] Operation: 85-20=65 Exploring Operation: 20+85=105, Resulting Numbers: [62, 105] Generated Node #0,0,4: 43:[62, 105] Operation: 20+85=105 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 43:[62, 65], Operations: ['95-10=85', '85-20=65'] Exploring Operation: 62+65=127, Resulting Numbers: [127] 127,43 unequal: No Solution Exploring Operation: 62*65=4030, Resulting Numbers: [4030] 4030,43 unequal: No Solution Exploring Operation: 65-62=3, Resulting Numbers: [3] 3,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 43:[85, 42], Operations: ['95-10=85', '62-20=42'] Exploring Operation: 85+42=127, Resulting Numbers: [127] 127,43 unequal: No Solution Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[10, 95, 20, 62], Operations: [] Exploring Operation: 95-10=85, Resulting Numbers: [20, 62, 85] Generated Node #0,0: 43:[20, 62, 85] Operation: 95-10=85 Moving to Node #0,0 Current State: 43:[20, 62, 85], Operations: ['95-10=85'] Exploring Operation: 62-20=42, Resulting Numbers: [85, 42] Generated Node #0,0,0: 43:[85, 42] Operation: 62-20=42 Moving to Node #0,0,0 Current State: 43:[85, 42], Operations: ['95-10=85', '62-20=42'] Exploring Operation: 85-42=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 1
0.970486
hs_5
sum_heuristic
[ 4, 15, 40, 61 ]
69
[ "61-40=21", "4*21=84", "84-15=69" ]
Current State: 69:[4, 15, 40, 61], Operations: [] Exploring Operation: 61-40=21, Resulting Numbers: [4, 15, 21] Generated Node #2: [4, 15, 21] from Operation: 61-40=21 Current State: 69:[4, 15, 21], Operations: ['61-40=21'] Exploring Operation: 4*21=84, Resulting Numbers: [15, 84] Generated Node #3: [15, 84] from Operation: 4*21=84 Current State: 69:[15, 84], Operations: ['61-40=21', '4*21=84'] Exploring Operation: 84-15=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[4, 15, 40, 61], Operations: [] Exploring Operation: 40-15=25, Resulting Numbers: [4, 61, 25] Generated Node #0,0: 69:[4, 61, 25] Operation: 40-15=25 Exploring Operation: 61-40=21, Resulting Numbers: [4, 15, 21] Generated Node #0,1: 69:[4, 15, 21] Operation: 61-40=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[4, 61, 25], Operations: ['40-15=25'] Exploring Operation: 25-4=21, Resulting Numbers: [61, 21] Generated Node #0,0,0: 69:[61, 21] Operation: 25-4=21 Exploring Operation: 4+61=65, Resulting Numbers: [25, 65] Generated Node #0,0,1: 69:[25, 65] Operation: 4+61=65 Moving to Node #0,0,1 Current State: 69:[25, 65], Operations: ['40-15=25', '4+61=65'] Exploring Operation: 25+65=90, Resulting Numbers: [90] 90,69 unequal: No Solution Exploring Operation: 65-25=40, Resulting Numbers: [40] 40,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[61, 21], Operations: ['40-15=25', '25-4=21'] Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,69 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 Current State: 69:[4, 15, 21], Operations: ['61-40=21'] Exploring Operation: 4+15=19, Resulting Numbers: [21, 19] Generated Node #0,1,0: 69:[21, 19] Operation: 4+15=19 Exploring Operation: 21-15=6, Resulting Numbers: [4, 6] Generated Node #0,1,1: 69:[4, 6] Operation: 21-15=6 Moving to Node #0,1,1 Current State: 69:[4, 6], Operations: ['61-40=21', '21-15=6'] Exploring Operation: 4*6=24, Resulting Numbers: [24] 24,69 unequal: No Solution Exploring Operation: 6-4=2, Resulting Numbers: [2] 2,69 unequal: No Solution Moving to Node #0,1,0 Current State: 69:[21, 19], Operations: ['61-40=21', '4+15=19'] Exploring Operation: 21+19=40, Resulting Numbers: [40] 40,69 unequal: No Solution Exploring Operation: 21-19=2, Resulting Numbers: [2] 2,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 37, 12, 37, 47 ]
74
[ "37+12=49", "49-47=2", "37*2=74" ]
Current State: 74:[37, 12, 37, 47], Operations: [] Exploring Operation: 37+12=49, Resulting Numbers: [47, 49] Generated Node #2: [47, 49] from Operation: 37+12=49 Current State: 74:[47, 49], Operations: ['37+12=49'] Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,74 equal: Goal Reached Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[37, 12, 37, 47], Operations: [] Exploring Operation: 47-37=10, Resulting Numbers: [12, 37, 10] Generated Node #0,0: 74:[12, 37, 10] Operation: 47-37=10 Exploring Operation: 47-12=35, Resulting Numbers: [37, 37, 35] Generated Node #0,1: 74:[37, 37, 35] Operation: 47-12=35 Exploring Operation: 12+47=59, Resulting Numbers: [37, 37, 59] Generated Node #0,2: 74:[37, 37, 59] Operation: 12+47=59 Moving to Node #0,1 Current State: 74:[37, 37, 35], Operations: ['47-12=35'] Exploring Operation: 37-35=2, Resulting Numbers: [37, 2] Generated Node #0,1,0: 74:[37, 2] Operation: 37-35=2 Exploring Operation: 37+37=74, Resulting Numbers: [35, 74] Generated Node #0,1,1: 74:[35, 74] Operation: 37+37=74 Exploring Operation: 37-35=2, Resulting Numbers: [37, 2] Generated Node #0,1,2: 74:[37, 2] Operation: 37-35=2 Moving to Node #0,2 Current State: 74:[37, 37, 59], Operations: ['12+47=59'] Exploring Operation: 37+37=74, Resulting Numbers: [59, 74] Generated Node #0,2,0: 74:[59, 74] Operation: 37+37=74 Exploring Operation: 59-37=22, Resulting Numbers: [37, 22] Generated Node #0,2,1: 74:[37, 22] Operation: 59-37=22 Exploring Operation: 59-37=22, Resulting Numbers: [37, 22] Generated Node #0,2,2: 74:[37, 22] Operation: 59-37=22 Moving to Node #0,0 Current State: 74:[12, 37, 10], Operations: ['47-37=10'] Exploring Operation: 12+10=22, Resulting Numbers: [37, 22] Generated Node #0,0,0: 74:[37, 22] Operation: 12+10=22 Exploring Operation: 12-10=2, Resulting Numbers: [37, 2] Generated Node #0,0,1: 74:[37, 2] Operation: 12-10=2 Exploring Operation: 12+37=49, Resulting Numbers: [10, 49] Generated Node #0,0,2: 74:[10, 49] Operation: 12+37=49 Moving to Node #0,1,0 Current State: 74:[37, 2], Operations: ['47-12=35', '37-35=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[37, 12, 37, 47], Operations: [] Exploring Operation: 47-12=35, Resulting Numbers: [37, 37, 35] Generated Node #0,1: 74:[37, 37, 35] Operation: 47-12=35 Moving to Node #0,1 Current State: 74:[37, 37, 35], Operations: ['47-12=35'] Exploring Operation: 37-35=2, Resulting Numbers: [37, 2] Generated Node #0,1,0: 74:[37, 2] Operation: 37-35=2 Moving to Node #0,1,0 Current State: 74:[37, 2], Operations: ['47-12=35', '37-35=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
0.985243
hs_3
mult_heuristic
[ 75, 16, 10, 2 ]
96
[ "75+16=91", "10/2=5", "91+5=96" ]
Current State: 96:[75, 16, 10, 2], Operations: [] Exploring Operation: 75+16=91, Resulting Numbers: [10, 2, 91] Generated Node #2: [10, 2, 91] from Operation: 75+16=91 Current State: 96:[10, 2, 91], Operations: ['75+16=91'] Exploring Operation: 10/2=5, Resulting Numbers: [91, 5] Generated Node #3: [91, 5] from Operation: 10/2=5 Current State: 96:[91, 5], Operations: ['75+16=91', '10/2=5'] Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[75, 16, 10, 2], Operations: [] Exploring Operation: 75+10=85, Resulting Numbers: [16, 2, 85] Generated Node #0,0: 96:[16, 2, 85] Operation: 75+10=85 Exploring Operation: 75+2=77, Resulting Numbers: [16, 10, 77] Generated Node #0,1: 96:[16, 10, 77] Operation: 75+2=77 Exploring Operation: 75+16=91, Resulting Numbers: [10, 2, 91] Generated Node #0,2: 96:[10, 2, 91] Operation: 75+16=91 Exploring Operation: 75-10=65, Resulting Numbers: [16, 2, 65] Generated Node #0,3: 96:[16, 2, 65] Operation: 75-10=65 Exploring Operation: 75-16=59, Resulting Numbers: [10, 2, 59] Generated Node #0,4: 96:[10, 2, 59] Operation: 75-16=59 Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[10, 2, 91], Operations: ['75+16=91'] Exploring Operation: 10/2=5, Resulting Numbers: [91, 5] Generated Node #0,2,0: 96:[91, 5] Operation: 10/2=5 Exploring Operation: 10+91=101, Resulting Numbers: [2, 101] Generated Node #0,2,1: 96:[2, 101] Operation: 10+91=101 Exploring Operation: 10-2=8, Resulting Numbers: [91, 8] Generated Node #0,2,2: 96:[91, 8] Operation: 10-2=8 Exploring Operation: 2+91=93, Resulting Numbers: [10, 93] Generated Node #0,2,3: 96:[10, 93] Operation: 2+91=93 Exploring Operation: 10+2=12, Resulting Numbers: [91, 12] Generated Node #0,2,4: 96:[91, 12] Operation: 10+2=12 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 96:[2, 101], Operations: ['75+16=91', '10+91=101'] Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,96 unequal: No Solution Exploring Operation: 2+101=103, Resulting Numbers: [103] 103,96 unequal: No Solution Exploring Operation: 2*101=202, Resulting Numbers: [202] 202,96 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 #0,2,2 Current State: 96:[91, 8], Operations: ['75+16=91', '10-2=8'] Exploring Operation: 91+8=99, Resulting Numbers: [99] 99,96 unequal: No Solution Exploring Operation: 91-8=83, Resulting Numbers: [83] 83,96 unequal: No Solution Exploring Operation: 91*8=728, Resulting Numbers: [728] 728,96 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 #0,2,3 Current State: 96:[10, 93], Operations: ['75+16=91', '2+91=93'] Exploring Operation: 10*93=930, Resulting Numbers: [930] 930,96 unequal: No Solution Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,96 unequal: No Solution Exploring Operation: 10+93=103, Resulting Numbers: [103] 103,96 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 #0,2,4 Current State: 96:[91, 12], Operations: ['75+16=91', '10+2=12'] Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,96 unequal: No Solution Exploring Operation: 91+12=103, Resulting Numbers: [103] 103,96 unequal: No Solution Exploring Operation: 91*12=1092, Resulting Numbers: [1092] 1092,96 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 #0,2,0 Current State: 96:[91, 5], Operations: ['75+16=91', '10/2=5'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,96 unequal: No Solution Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[75, 16, 10, 2], Operations: [] Exploring Operation: 75+16=91, Resulting Numbers: [10, 2, 91] Generated Node #0,2: 96:[10, 2, 91] Operation: 75+16=91 Moving to Node #0,2 Current State: 96:[10, 2, 91], Operations: ['75+16=91'] Exploring Operation: 10/2=5, Resulting Numbers: [91, 5] Generated Node #0,2,0: 96:[91, 5] Operation: 10/2=5 Moving to Node #0,2,0 Current State: 96:[91, 5], Operations: ['75+16=91', '10/2=5'] Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 85, 34, 97, 60 ]
82
[ "85+34=119", "97-60=37", "119-37=82" ]
Current State: 82:[85, 34, 97, 60], Operations: [] Exploring Operation: 85+34=119, Resulting Numbers: [97, 60, 119] Generated Node #2: [97, 60, 119] from Operation: 85+34=119 Current State: 82:[97, 60, 119], Operations: ['85+34=119'] Exploring Operation: 97-60=37, Resulting Numbers: [119, 37] Generated Node #3: [119, 37] from Operation: 97-60=37 Current State: 82:[119, 37], Operations: ['85+34=119', '97-60=37'] Exploring Operation: 119-37=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[85, 34, 97, 60], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [85, 34, 37] Generated Node #0,0: 82:[85, 34, 37] Operation: 97-60=37 Exploring Operation: 60-34=26, Resulting Numbers: [85, 97, 26] Generated Node #0,1: 82:[85, 97, 26] Operation: 60-34=26 Exploring Operation: 34+60=94, Resulting Numbers: [85, 97, 94] Generated Node #0,2: 82:[85, 97, 94] Operation: 34+60=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[85, 34, 37], Operations: ['97-60=37'] Exploring Operation: 85-37=48, Resulting Numbers: [34, 48] Generated Node #0,0,0: 82:[34, 48] Operation: 85-37=48 Exploring Operation: 85-34=51, Resulting Numbers: [37, 51] Generated Node #0,0,1: 82:[37, 51] Operation: 85-34=51 Exploring Operation: 37-34=3, Resulting Numbers: [85, 3] Generated Node #0,0,2: 82:[85, 3] Operation: 37-34=3 Moving to Node #0,0,2 Current State: 82:[85, 3], Operations: ['97-60=37', '37-34=3'] Exploring Operation: 85*3=255, Resulting Numbers: [255] 255,82 unequal: No Solution Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,82 unequal: No Solution Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[85, 34, 97, 60], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [85, 34, 37] Generated Node #0,0: 82:[85, 34, 37] Operation: 97-60=37 Moving to Node #0,0 Current State: 82:[85, 34, 37], Operations: ['97-60=37'] Exploring Operation: 37-34=3, Resulting Numbers: [85, 3] Generated Node #0,0,2: 82:[85, 3] Operation: 37-34=3 Moving to Node #0,0,2 Current State: 82:[85, 3], Operations: ['97-60=37', '37-34=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 6, 87, 6, 41 ]
41
[ "6-6=0", "87*0=0", "41+0=41" ]
Current State: 41:[6, 87, 6, 41], Operations: [] Exploring Operation: 6-6=0, Resulting Numbers: [87, 41, 0] Generated Node #2: [87, 41, 0] from Operation: 6-6=0 Current State: 41:[87, 41, 0], Operations: ['6-6=0'] Exploring Operation: 87*0=0, Resulting Numbers: [41, 0] Generated Node #3: [41, 0] from Operation: 87*0=0 Current State: 41:[41, 0], Operations: ['6-6=0', '87*0=0'] Exploring Operation: 41+0=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[6, 87, 6, 41], Operations: [] Exploring Operation: 6*6=36, Resulting Numbers: [87, 41, 36] Generated Node #0,0: 41:[87, 41, 36] Operation: 6*6=36 Exploring Operation: 87-6=81, Resulting Numbers: [6, 41, 81] Generated Node #0,1: 41:[6, 41, 81] Operation: 87-6=81 Exploring Operation: 6+6=12, Resulting Numbers: [87, 41, 12] Generated Node #0,2: 41:[87, 41, 12] Operation: 6+6=12 Exploring Operation: 87-6=81, Resulting Numbers: [6, 41, 81] Generated Node #0,3: 41:[6, 41, 81] Operation: 87-6=81 Moving to Node #0,0 Current State: 41:[87, 41, 36], Operations: ['6*6=36'] Exploring Operation: 87-36=51, Resulting Numbers: [41, 51] Generated Node #0,0,0: 41:[41, 51] Operation: 87-36=51 Exploring Operation: 87-41=46, Resulting Numbers: [36, 46] Generated Node #0,0,1: 41:[36, 46] Operation: 87-41=46 Exploring Operation: 41+36=77, Resulting Numbers: [87, 77] Generated Node #0,0,2: 41:[87, 77] Operation: 41+36=77 Exploring Operation: 87+36=123, Resulting Numbers: [41, 123] Generated Node #0,0,3: 41:[41, 123] Operation: 87+36=123 Moving to Node #0,2 Current State: 41:[87, 41, 12], Operations: ['6+6=12'] Exploring Operation: 87-41=46, Resulting Numbers: [12, 46] Generated Node #0,2,0: 41:[12, 46] Operation: 87-41=46 Exploring Operation: 41+12=53, Resulting Numbers: [87, 53] Generated Node #0,2,1: 41:[87, 53] Operation: 41+12=53 Exploring Operation: 87+12=99, Resulting Numbers: [41, 99] Generated Node #0,2,2: 41:[41, 99] Operation: 87+12=99 Exploring Operation: 87-12=75, Resulting Numbers: [41, 75] Generated Node #0,2,3: 41:[41, 75] Operation: 87-12=75 Moving to Node #0,1 Current State: 41:[6, 41, 81], Operations: ['87-6=81'] Exploring Operation: 6+41=47, Resulting Numbers: [81, 47] Generated Node #0,1,0: 41:[81, 47] Operation: 6+41=47 Exploring Operation: 41-6=35, Resulting Numbers: [81, 35] Generated Node #0,1,1: 41:[81, 35] Operation: 41-6=35 Exploring Operation: 81-6=75, Resulting Numbers: [41, 75] Generated Node #0,1,2: 41:[41, 75] Operation: 81-6=75 Exploring Operation: 81-41=40, Resulting Numbers: [6, 40] Generated Node #0,1,3: 41:[6, 40] Operation: 81-41=40 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[41, 75], Operations: ['87-6=81', '81-6=75'] Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,41 unequal: No Solution Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[6, 40], Operations: ['87-6=81', '81-41=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,41 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[81, 47], Operations: ['87-6=81', '6+41=47'] Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 81*47=3807, Resulting Numbers: [3807] 3807,41 unequal: No Solution Exploring Operation: 81+47=128, Resulting Numbers: [128] 128,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[81, 35], Operations: ['87-6=81', '41-6=35'] Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,41 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,41 unequal: No Solution Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,41 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: 41:[6, 41, 81], Operations: ['87-6=81'] Exploring Operation: 81-41=40, Resulting Numbers: [6, 40] Generated Node #0,3,0: 41:[6, 40] Operation: 81-41=40 Exploring Operation: 6+41=47, Resulting Numbers: [81, 47] Generated Node #0,3,1: 41:[81, 47] Operation: 6+41=47 Exploring Operation: 41-6=35, Resulting Numbers: [81, 35] Generated Node #0,3,2: 41:[81, 35] Operation: 41-6=35 Exploring Operation: 81-6=75, Resulting Numbers: [41, 75] Generated Node #0,3,3: 41:[41, 75] Operation: 81-6=75 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 41:[41, 75], Operations: ['87-6=81', '81-6=75'] Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,41 unequal: No Solution Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,41 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 41:[6, 40], Operations: ['87-6=81', '81-41=40'] Exploring Operation: 40-6=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 6*40=240, Resulting Numbers: [240] 240,41 unequal: No Solution Exploring Operation: 6+40=46, Resulting Numbers: [46] 46,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 41:[81, 47], Operations: ['87-6=81', '6+41=47'] Exploring Operation: 81+47=128, Resulting Numbers: [128] 128,41 unequal: No Solution Exploring Operation: 81*47=3807, Resulting Numbers: [3807] 3807,41 unequal: No Solution Exploring Operation: 81-47=34, Resulting Numbers: [34] 34,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 41:[81, 35], Operations: ['87-6=81', '41-6=35'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,41 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,41 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: 41:[41, 51], Operations: ['6*6=36', '87-36=51'] Exploring Operation: 51-41=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 41+51=92, Resulting Numbers: [92] 92,41 unequal: No Solution Exploring Operation: 41*51=2091, Resulting Numbers: [2091] 2091,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[36, 46], Operations: ['6*6=36', '87-41=46'] Exploring Operation: 36+46=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 46-36=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 36*46=1656, Resulting Numbers: [1656] 1656,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[41, 75], Operations: ['6+6=12', '87-12=75'] Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,41 unequal: No Solution Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,41 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,41 unequal: No Solution Moving to Node #0,2,0 Current State: 41:[12, 46], Operations: ['6+6=12', '87-41=46'] Exploring Operation: 12+46=58, Resulting Numbers: [58] 58,41 unequal: No Solution Exploring Operation: 12*46=552, Resulting Numbers: [552] 552,41 unequal: No Solution Exploring Operation: 46-12=34, Resulting Numbers: [34] 34,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[87, 53], Operations: ['6+6=12', '41+12=53'] Exploring Operation: 87-53=34, Resulting Numbers: [34] 34,41 unequal: No Solution Exploring Operation: 87*53=4611, Resulting Numbers: [4611] 4611,41 unequal: No Solution Exploring Operation: 87+53=140, Resulting Numbers: [140] 140,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[41, 99], Operations: ['6+6=12', '87+12=99'] Exploring Operation: 99-41=58, Resulting Numbers: [58] 58,41 unequal: No Solution Exploring Operation: 41+99=140, Resulting Numbers: [140] 140,41 unequal: No Solution Exploring Operation: 41*99=4059, Resulting Numbers: [4059] 4059,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[87, 77], Operations: ['6*6=36', '41+36=77'] Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,41 unequal: No Solution Exploring Operation: 87*77=6699, Resulting Numbers: [6699] 6699,41 unequal: No Solution Exploring Operation: 87+77=164, Resulting Numbers: [164] 164,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[41, 123], Operations: ['6*6=36', '87+36=123'] Exploring Operation: 123/41=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 41+123=164, Resulting Numbers: [164] 164,41 unequal: No Solution Exploring Operation: 123-41=82, Resulting Numbers: [82] 82,41 unequal: No Solution Exploring Operation: 41*123=5043, Resulting Numbers: [5043] 5043,41 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 50, 48, 38, 75 ]
34
[ "48*75=3600", "3600/50=72", "72-38=34" ]
Current State: 34:[50, 48, 38, 75], Operations: [] Exploring Operation: 48*75=3600, Resulting Numbers: [50, 38, 3600] Generated Node #2: [50, 38, 3600] from Operation: 48*75=3600 Current State: 34:[50, 38, 3600], Operations: ['48*75=3600'] Exploring Operation: 3600/50=72, Resulting Numbers: [38, 72] Generated Node #3: [38, 72] from Operation: 3600/50=72 Current State: 34:[38, 72], Operations: ['48*75=3600', '3600/50=72'] Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[50, 48, 38, 75], Operations: [] Exploring Operation: 75-48=27, Resulting Numbers: [50, 38, 27] Generated Node #0,0: 34:[50, 38, 27] Operation: 75-48=27 Exploring Operation: 75-50=25, Resulting Numbers: [48, 38, 25] Generated Node #0,1: 34:[48, 38, 25] Operation: 75-50=25 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[48, 38, 25], Operations: ['75-50=25'] Exploring Operation: 48-38=10, Resulting Numbers: [25, 10] Generated Node #0,1,0: 34:[25, 10] Operation: 48-38=10 Exploring Operation: 48-25=23, Resulting Numbers: [38, 23] Generated Node #0,1,1: 34:[38, 23] Operation: 48-25=23 Moving to Node #0,1,1 Current State: 34:[38, 23], Operations: ['75-50=25', '48-25=23'] Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,34 unequal: No Solution Moving to Node #0,1,0 Current State: 34:[25, 10], Operations: ['75-50=25', '48-38=10'] Exploring Operation: 25-10=15, Resulting Numbers: [15] 15,34 unequal: No Solution Exploring Operation: 25+10=35, Resulting Numbers: [35] 35,34 unequal: No Solution No 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: 34:[50, 38, 27], Operations: ['75-48=27'] Exploring Operation: 50-27=23, Resulting Numbers: [38, 23] Generated Node #0,0,0: 34:[38, 23] Operation: 50-27=23 Exploring Operation: 50-38=12, Resulting Numbers: [27, 12] Generated Node #0,0,1: 34:[27, 12] Operation: 50-38=12 Moving to Node #0,0,0 Current State: 34:[38, 23], Operations: ['75-48=27', '50-27=23'] Exploring Operation: 38+23=61, Resulting Numbers: [61] 61,34 unequal: No Solution Exploring Operation: 38-23=15, Resulting Numbers: [15] 15,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[27, 12], Operations: ['75-48=27', '50-38=12'] Exploring Operation: 27+12=39, Resulting Numbers: [39] 39,34 unequal: No Solution Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,34 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
[ 87, 24, 73, 10 ]
100
[ "87-24=63", "73-63=10", "10*10=100" ]
Current State: 100:[87, 24, 73, 10], Operations: [] Exploring Operation: 87-24=63, Resulting Numbers: [73, 10, 63] Generated Node #2: [73, 10, 63] from Operation: 87-24=63 Current State: 100:[73, 10, 63], Operations: ['87-24=63'] Exploring Operation: 73-63=10, Resulting Numbers: [10, 10] Generated Node #3: [10, 10] from Operation: 73-63=10 Current State: 100:[10, 10], Operations: ['87-24=63', '73-63=10'] Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[87, 24, 73, 10], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [24, 10, 14] Generated Node #0,0: 100:[24, 10, 14] Operation: 87-73=14 Exploring Operation: 24+73=97, Resulting Numbers: [87, 10, 97] Generated Node #0,1: 100:[87, 10, 97] Operation: 24+73=97 Exploring Operation: 73-24=49, Resulting Numbers: [87, 10, 49] Generated Node #0,2: 100:[87, 10, 49] Operation: 73-24=49 Moving to Node #0,0 Current State: 100:[24, 10, 14], Operations: ['87-73=14'] Exploring Operation: 14-10=4, Resulting Numbers: [24, 4] Generated Node #0,0,0: 100:[24, 4] Operation: 14-10=4 Exploring Operation: 24-14=10, Resulting Numbers: [10, 10] Generated Node #0,0,1: 100:[10, 10] Operation: 24-14=10 Exploring Operation: 10+14=24, Resulting Numbers: [24, 24] Generated Node #0,0,2: 100:[24, 24] Operation: 10+14=24 Moving to Node #0,2 Current State: 100:[87, 10, 49], Operations: ['73-24=49'] Exploring Operation: 87-49=38, Resulting Numbers: [10, 38] Generated Node #0,2,0: 100:[10, 38] Operation: 87-49=38 Exploring Operation: 10+49=59, Resulting Numbers: [87, 59] Generated Node #0,2,1: 100:[87, 59] Operation: 10+49=59 Exploring Operation: 87+10=97, Resulting Numbers: [49, 97] Generated Node #0,2,2: 100:[49, 97] Operation: 87+10=97 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[49, 97], Operations: ['73-24=49', '87+10=97'] Exploring Operation: 97-49=48, Resulting Numbers: [48] 48,100 unequal: No Solution Exploring Operation: 49+97=146, Resulting Numbers: [146] 146,100 unequal: No Solution Exploring Operation: 49*97=4753, Resulting Numbers: [4753] 4753,100 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 #0,2,0 Current State: 100:[10, 38], Operations: ['73-24=49', '87-49=38'] Exploring Operation: 10*38=380, Resulting Numbers: [380] 380,100 unequal: No Solution Exploring Operation: 38-10=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 10+38=48, Resulting Numbers: [48] 48,100 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 #0,2,1 Current State: 100:[87, 59], Operations: ['73-24=49', '10+49=59'] Exploring Operation: 87-59=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 87*59=5133, Resulting Numbers: [5133] 5133,100 unequal: No Solution Exploring Operation: 87+59=146, Resulting Numbers: [146] 146,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 100:[87, 10, 97], Operations: ['24+73=97'] Exploring Operation: 10+97=107, Resulting Numbers: [87, 107] Generated Node #0,1,0: 100:[87, 107] Operation: 10+97=107 Exploring Operation: 87+10=97, Resulting Numbers: [97, 97] Generated Node #0,1,1: 100:[97, 97] Operation: 87+10=97 Exploring Operation: 97-87=10, Resulting Numbers: [10, 10] Generated Node #0,1,2: 100:[10, 10] Operation: 97-87=10 Moving to Node #0,0,1 Current State: 100:[10, 10], Operations: ['87-73=14', '24-14=10'] Exploring Operation: 10/10=1, Resulting Numbers: [1] 1,100 unequal: No Solution Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[87, 24, 73, 10], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [24, 10, 14] Generated Node #0,0: 100:[24, 10, 14] Operation: 87-73=14 Moving to Node #0,0 Current State: 100:[24, 10, 14], Operations: ['87-73=14'] Exploring Operation: 24-14=10, Resulting Numbers: [10, 10] Generated Node #0,0,1: 100:[10, 10] Operation: 24-14=10 Moving to Node #0,0,1 Current State: 100:[10, 10], Operations: ['87-73=14', '24-14=10'] Exploring Operation: 10*10=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 95, 3, 10, 33 ]
94
[ "95+10=105", "33/3=11", "105-11=94" ]
Current State: 94:[95, 3, 10, 33], Operations: [] Exploring Operation: 95+10=105, Resulting Numbers: [3, 33, 105] Generated Node #2: [3, 33, 105] from Operation: 95+10=105 Current State: 94:[3, 33, 105], Operations: ['95+10=105'] Exploring Operation: 33/3=11, Resulting Numbers: [105, 11] Generated Node #3: [105, 11] from Operation: 33/3=11 Current State: 94:[105, 11], Operations: ['95+10=105', '33/3=11'] Exploring Operation: 105-11=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[95, 3, 10, 33], Operations: [] Exploring Operation: 10+33=43, Resulting Numbers: [95, 3, 43] Generated Node #0,0: 94:[95, 3, 43] Operation: 10+33=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[95, 3, 43], Operations: ['10+33=43'] Exploring Operation: 3+43=46, Resulting Numbers: [95, 46] Generated Node #0,0,0: 94:[95, 46] Operation: 3+43=46 Moving to Node #0,0,0 Current State: 94:[95, 46], Operations: ['10+33=43', '3+43=46'] Exploring Operation: 95-46=49, Resulting Numbers: [49] 49,94 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
[ 54, 6, 29, 47 ]
12
[ "54-29=25", "47+25=72", "72/6=12" ]
Current State: 12:[54, 6, 29, 47], Operations: [] Exploring Operation: 54-29=25, Resulting Numbers: [6, 47, 25] Generated Node #2: [6, 47, 25] from Operation: 54-29=25 Current State: 12:[6, 47, 25], Operations: ['54-29=25'] Exploring Operation: 47+25=72, Resulting Numbers: [6, 72] Generated Node #3: [6, 72] from Operation: 47+25=72 Current State: 12:[6, 72], Operations: ['54-29=25', '47+25=72'] Exploring Operation: 72/6=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[54, 6, 29, 47], Operations: [] Exploring Operation: 47-29=18, Resulting Numbers: [54, 6, 18] Generated Node #0,0: 12:[54, 6, 18] Operation: 47-29=18 Exploring Operation: 54/6=9, Resulting Numbers: [29, 47, 9] Generated Node #0,1: 12:[29, 47, 9] Operation: 54/6=9 Exploring Operation: 54-47=7, Resulting Numbers: [6, 29, 7] Generated Node #0,2: 12:[6, 29, 7] Operation: 54-47=7 Exploring Operation: 54-29=25, Resulting Numbers: [6, 47, 25] Generated Node #0,3: 12:[6, 47, 25] Operation: 54-29=25 Moving to Node #0,2 Current State: 12:[6, 29, 7], Operations: ['54-47=7'] Exploring Operation: 6+7=13, Resulting Numbers: [29, 13] Generated Node #0,2,0: 12:[29, 13] Operation: 6+7=13 Exploring Operation: 29-7=22, Resulting Numbers: [6, 22] Generated Node #0,2,1: 12:[6, 22] Operation: 29-7=22 Exploring Operation: 7-6=1, Resulting Numbers: [29, 1] Generated Node #0,2,2: 12:[29, 1] Operation: 7-6=1 Exploring Operation: 29-6=23, Resulting Numbers: [7, 23] Generated Node #0,2,3: 12:[7, 23] Operation: 29-6=23 Moving to Node #0,3 Current State: 12:[6, 47, 25], Operations: ['54-29=25'] Exploring Operation: 47-6=41, Resulting Numbers: [25, 41] Generated Node #0,3,0: 12:[25, 41] Operation: 47-6=41 Exploring Operation: 47-25=22, Resulting Numbers: [6, 22] Generated Node #0,3,1: 12:[6, 22] Operation: 47-25=22 Exploring Operation: 25-6=19, Resulting Numbers: [47, 19] Generated Node #0,3,2: 12:[47, 19] Operation: 25-6=19 Exploring Operation: 6+47=53, Resulting Numbers: [25, 53] Generated Node #0,3,3: 12:[25, 53] Operation: 6+47=53 Moving to Node #0,0 Current State: 12:[54, 6, 18], Operations: ['47-29=18'] Exploring Operation: 54-6=48, Resulting Numbers: [18, 48] Generated Node #0,0,0: 12:[18, 48] Operation: 54-6=48 Exploring Operation: 54-18=36, Resulting Numbers: [6, 36] Generated Node #0,0,1: 12:[6, 36] Operation: 54-18=36 Exploring Operation: 54/6=9, Resulting Numbers: [18, 9] Generated Node #0,0,2: 12:[18, 9] Operation: 54/6=9 Exploring Operation: 54/18=3, Resulting Numbers: [6, 3] Generated Node #0,0,3: 12:[6, 3] Operation: 54/18=3 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 12:[6, 3], Operations: ['47-29=18', '54/18=3'] Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 6+3=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 6*3=18, Resulting Numbers: [18] 18,12 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 12:[18, 9], Operations: ['47-29=18', '54/6=9'] Exploring Operation: 18*9=162, Resulting Numbers: [162] 162,12 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 18+9=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 12:[6, 36], Operations: ['47-29=18', '54-18=36'] Exploring Operation: 6+36=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,12 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 6*36=216, Resulting Numbers: [216] 216,12 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 12:[18, 48], Operations: ['47-29=18', '54-6=48'] Exploring Operation: 18*48=864, Resulting Numbers: [864] 864,12 unequal: No Solution Exploring Operation: 48-18=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 18+48=66, Resulting Numbers: [66] 66,12 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: 12:[29, 47, 9], Operations: ['54/6=9'] Exploring Operation: 47-9=38, Resulting Numbers: [29, 38] Generated Node #0,1,0: 12:[29, 38] Operation: 47-9=38 Exploring Operation: 29-9=20, Resulting Numbers: [47, 20] Generated Node #0,1,1: 12:[47, 20] Operation: 29-9=20 Exploring Operation: 47-29=18, Resulting Numbers: [9, 18] Generated Node #0,1,2: 12:[9, 18] Operation: 47-29=18 Exploring Operation: 29+9=38, Resulting Numbers: [47, 38] Generated Node #0,1,3: 12:[47, 38] Operation: 29+9=38 Moving to Node #0,1,2 Current State: 12:[9, 18], Operations: ['54/6=9', '47-29=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,12 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,12 unequal: No Solution Moving to Node #0,2,1 Current State: 12:[6, 22], Operations: ['54-47=7', '29-7=22'] Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,12 unequal: No Solution Moving to Node #0,3,1 Current State: 12:[6, 22], Operations: ['54-29=25', '47-25=22'] Exploring Operation: 6*22=132, Resulting Numbers: [132] 132,12 unequal: No Solution Exploring Operation: 22-6=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 6+22=28, Resulting Numbers: [28] 28,12 unequal: No Solution Moving to Node #0,2,3 Current State: 12:[7, 23], Operations: ['54-47=7', '29-6=23'] Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 7+23=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 7*23=161, Resulting Numbers: [161] 161,12 unequal: No Solution Moving to Node #0,2,0 Current State: 12:[29, 13], Operations: ['54-47=7', '6+7=13'] Exploring Operation: 29*13=377, Resulting Numbers: [377] 377,12 unequal: No Solution Exploring Operation: 29+13=42, Resulting Numbers: [42] 42,12 unequal: No Solution Exploring Operation: 29-13=16, Resulting Numbers: [16] 16,12 unequal: No Solution Moving to Node #0,2,2 Current State: 12:[29, 1], Operations: ['54-47=7', '7-6=1'] Exploring Operation: 29+1=30, Resulting Numbers: [30] 30,12 unequal: No Solution Exploring Operation: 29*1=29, Resulting Numbers: [29] 29,12 unequal: No Solution Exploring Operation: 29/1=29, Resulting Numbers: [29] 29,12 unequal: No Solution Exploring Operation: 29-1=28, Resulting Numbers: [28] 28,12 unequal: No Solution Moving to Node #0,3,2 Current State: 12:[47, 19], Operations: ['54-29=25', '25-6=19'] Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,12 unequal: No Solution Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,12 unequal: No Solution Exploring Operation: 47*19=893, Resulting Numbers: [893] 893,12 unequal: No Solution Moving to Node #0,3,0 Current State: 12:[25, 41], Operations: ['54-29=25', '47-6=41'] Exploring Operation: 25*41=1025, Resulting Numbers: [1025] 1025,12 unequal: No Solution Exploring Operation: 41-25=16, Resulting Numbers: [16] 16,12 unequal: No Solution Exploring Operation: 25+41=66, Resulting Numbers: [66] 66,12 unequal: No Solution Moving to Node #0,1,0 Current State: 12:[29, 38], Operations: ['54/6=9', '47-9=38'] Exploring Operation: 38-29=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 29*38=1102, Resulting Numbers: [1102] 1102,12 unequal: No Solution Exploring Operation: 29+38=67, Resulting Numbers: [67] 67,12 unequal: No Solution Moving to Node #0,1,1 Current State: 12:[47, 20], Operations: ['54/6=9', '29-9=20'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,12 unequal: No Solution Exploring Operation: 47*20=940, Resulting Numbers: [940] 940,12 unequal: No Solution Exploring Operation: 47+20=67, Resulting Numbers: [67] 67,12 unequal: No Solution Moving to Node #0,3,3 Current State: 12:[25, 53], Operations: ['54-29=25', '6+47=53'] Exploring Operation: 25+53=78, Resulting Numbers: [78] 78,12 unequal: No Solution Exploring Operation: 25*53=1325, Resulting Numbers: [1325] 1325,12 unequal: No Solution Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[47, 38], Operations: ['54/6=9', '29+9=38'] Exploring Operation: 47+38=85, Resulting Numbers: [85] 85,12 unequal: No Solution Exploring Operation: 47-38=9, Resulting Numbers: [9] 9,12 unequal: No Solution Exploring Operation: 47*38=1786, Resulting Numbers: [1786] 1786,12 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 3, 24, 63 ]
92
[ "15/3=5", "24+63=87", "5+87=92" ]
Current State: 92:[15, 3, 24, 63], Operations: [] Exploring Operation: 15/3=5, Resulting Numbers: [24, 63, 5] Generated Node #2: [24, 63, 5] from Operation: 15/3=5 Current State: 92:[24, 63, 5], Operations: ['15/3=5'] Exploring Operation: 24+63=87, Resulting Numbers: [5, 87] Generated Node #3: [5, 87] from Operation: 24+63=87 Current State: 92:[5, 87], Operations: ['15/3=5', '24+63=87'] Exploring Operation: 5+87=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[15, 3, 24, 63], Operations: [] Exploring Operation: 63/3=21, Resulting Numbers: [15, 24, 21] Generated Node #0,0: 92:[15, 24, 21] Operation: 63/3=21 Exploring Operation: 15+63=78, Resulting Numbers: [3, 24, 78] Generated Node #0,1: 92:[3, 24, 78] Operation: 15+63=78 Exploring Operation: 63-24=39, Resulting Numbers: [15, 3, 39] Generated Node #0,2: 92:[15, 3, 39] Operation: 63-24=39 Exploring Operation: 63-15=48, Resulting Numbers: [3, 24, 48] Generated Node #0,3: 92:[3, 24, 48] Operation: 63-15=48 Exploring Operation: 24+63=87, Resulting Numbers: [15, 3, 87] Generated Node #0,4: 92:[15, 3, 87] Operation: 24+63=87 Moving to Node #0,3 Current State: 92:[3, 24, 48], Operations: ['63-15=48'] Exploring Operation: 24-3=21, Resulting Numbers: [48, 21] Generated Node #0,3,0: 92:[48, 21] Operation: 24-3=21 Exploring Operation: 48/24=2, Resulting Numbers: [3, 2] Generated Node #0,3,1: 92:[3, 2] Operation: 48/24=2 Exploring Operation: 48-3=45, Resulting Numbers: [24, 45] Generated Node #0,3,2: 92:[24, 45] Operation: 48-3=45 Exploring Operation: 3+24=27, Resulting Numbers: [48, 27] Generated Node #0,3,3: 92:[48, 27] Operation: 3+24=27 Exploring Operation: 48-24=24, Resulting Numbers: [3, 24] Generated Node #0,3,4: 92:[3, 24] Operation: 48-24=24 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 92:[3, 2], Operations: ['63-15=48', '48/24=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,92 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,92 unequal: No Solution Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 92:[24, 45], Operations: ['63-15=48', '48-3=45'] Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,92 unequal: No Solution Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,92 unequal: No Solution Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 92:[3, 24], Operations: ['63-15=48', '48-24=24'] Exploring Operation: 24/3=8, Resulting Numbers: [8] 8,92 unequal: No Solution Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,92 unequal: No Solution Exploring Operation: 3+24=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 24-3=21, Resulting Numbers: [21] 21,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 92:[48, 21], Operations: ['63-15=48', '24-3=21'] Exploring Operation: 48-21=27, Resulting Numbers: [27] 27,92 unequal: No Solution Exploring Operation: 48*21=1008, Resulting Numbers: [1008] 1008,92 unequal: No Solution Exploring Operation: 48+21=69, Resulting Numbers: [69] 69,92 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 92:[48, 27], Operations: ['63-15=48', '3+24=27'] Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,92 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,92 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,92 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: 92:[15, 24, 21], Operations: ['63/3=21'] Exploring Operation: 24+21=45, Resulting Numbers: [15, 45] Generated Node #0,0,0: 92:[15, 45] Operation: 24+21=45 Exploring Operation: 24-15=9, Resulting Numbers: [21, 9] Generated Node #0,0,1: 92:[21, 9] Operation: 24-15=9 Exploring Operation: 21-15=6, Resulting Numbers: [24, 6] Generated Node #0,0,2: 92:[24, 6] Operation: 21-15=6 Exploring Operation: 15+24=39, Resulting Numbers: [21, 39] Generated Node #0,0,3: 92:[21, 39] Operation: 15+24=39 Exploring Operation: 24-21=3, Resulting Numbers: [15, 3] Generated Node #0,0,4: 92:[15, 3] Operation: 24-21=3 Moving to Node #0,4 Current State: 92:[15, 3, 87], Operations: ['24+63=87'] Exploring Operation: 15/3=5, Resulting Numbers: [87, 5] Generated Node #0,4,0: 92:[87, 5] Operation: 15/3=5 Exploring Operation: 15+3=18, Resulting Numbers: [87, 18] Generated Node #0,4,1: 92:[87, 18] Operation: 15+3=18 Exploring Operation: 3+87=90, Resulting Numbers: [15, 90] Generated Node #0,4,2: 92:[15, 90] Operation: 3+87=90 Exploring Operation: 15+87=102, Resulting Numbers: [3, 102] Generated Node #0,4,3: 92:[3, 102] Operation: 15+87=102 Exploring Operation: 15*3=45, Resulting Numbers: [87, 45] Generated Node #0,4,4: 92:[87, 45] Operation: 15*3=45 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 92:[87, 5], Operations: ['24+63=87', '15/3=5'] Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,92 unequal: No Solution Exploring Operation: 87+5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[15, 3, 24, 63], Operations: [] Exploring Operation: 24+63=87, Resulting Numbers: [15, 3, 87] Generated Node #0,4: 92:[15, 3, 87] Operation: 24+63=87 Moving to Node #0,4 Current State: 92:[15, 3, 87], Operations: ['24+63=87'] Exploring Operation: 15/3=5, Resulting Numbers: [87, 5] Generated Node #0,4,0: 92:[87, 5] Operation: 15/3=5 Moving to Node #0,4,0 Current State: 92:[87, 5], Operations: ['24+63=87', '15/3=5'] Exploring Operation: 87+5=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.963542
hs_5
sum_heuristic
[ 17, 14, 84, 85 ]
62
[ "85-17=68", "84/14=6", "68-6=62" ]
Current State: 62:[17, 14, 84, 85], Operations: [] Exploring Operation: 85-17=68, Resulting Numbers: [14, 84, 68] Generated Node #2: [14, 84, 68] from Operation: 85-17=68 Current State: 62:[14, 84, 68], Operations: ['85-17=68'] Exploring Operation: 84/14=6, Resulting Numbers: [68, 6] Generated Node #3: [68, 6] from Operation: 84/14=6 Current State: 62:[68, 6], Operations: ['85-17=68', '84/14=6'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[17, 14, 84, 85], Operations: [] Exploring Operation: 85-84=1, Resulting Numbers: [17, 14, 1] Generated Node #0,0: 62:[17, 14, 1] Operation: 85-84=1 Exploring Operation: 84-17=67, Resulting Numbers: [14, 85, 67] Generated Node #0,1: 62:[14, 85, 67] Operation: 84-17=67 Exploring Operation: 85/17=5, Resulting Numbers: [14, 84, 5] Generated Node #0,2: 62:[14, 84, 5] Operation: 85/17=5 Exploring Operation: 85-17=68, Resulting Numbers: [14, 84, 68] Generated Node #0,3: 62:[14, 84, 68] Operation: 85-17=68 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[17, 14, 1], Operations: ['85-84=1'] Exploring Operation: 17+1=18, Resulting Numbers: [14, 18] Generated Node #0,0,0: 62:[14, 18] Operation: 17+1=18 Exploring Operation: 17-14=3, Resulting Numbers: [1, 3] Generated Node #0,0,1: 62:[1, 3] Operation: 17-14=3 Exploring Operation: 14-1=13, Resulting Numbers: [17, 13] Generated Node #0,0,2: 62:[17, 13] Operation: 14-1=13 Exploring Operation: 17+14=31, Resulting Numbers: [1, 31] Generated Node #0,0,3: 62:[1, 31] Operation: 17+14=31 Moving to Node #0,0,3 Current State: 62:[1, 31], Operations: ['85-84=1', '17+14=31'] Exploring Operation: 1*31=31, Resulting Numbers: [31] 31,62 unequal: No Solution Exploring Operation: 31-1=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 1+31=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 31/1=31, Resulting Numbers: [31] 31,62 unequal: No Solution Moving to Node #0,0,1 Current State: 62:[1, 3], Operations: ['85-84=1', '17-14=3'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,62 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,62 unequal: No Solution Moving to Node #0,0,2 Current State: 62:[17, 13], Operations: ['85-84=1', '14-1=13'] Exploring Operation: 17-13=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 17*13=221, Resulting Numbers: [221] 221,62 unequal: No Solution Exploring Operation: 17+13=30, Resulting Numbers: [30] 30,62 unequal: No Solution Moving to Node #0,0,0 Current State: 62:[14, 18], Operations: ['85-84=1', '17+1=18'] Exploring Operation: 14*18=252, Resulting Numbers: [252] 252,62 unequal: No Solution Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 62:[14, 84, 5], Operations: ['85/17=5'] Exploring Operation: 84/14=6, Resulting Numbers: [5, 6] Generated Node #0,2,0: 62:[5, 6] Operation: 84/14=6 Exploring Operation: 14-5=9, Resulting Numbers: [84, 9] Generated Node #0,2,1: 62:[84, 9] Operation: 14-5=9 Exploring Operation: 84-14=70, Resulting Numbers: [5, 70] Generated Node #0,2,2: 62:[5, 70] Operation: 84-14=70 Exploring Operation: 84-5=79, Resulting Numbers: [14, 79] Generated Node #0,2,3: 62:[14, 79] Operation: 84-5=79 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 62:[5, 6], Operations: ['85/17=5', '84/14=6'] Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,62 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,62 unequal: No Solution Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,62 unequal: No Solution No 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: 62:[5, 70], Operations: ['85/17=5', '84-14=70'] Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,62 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,62 unequal: No Solution Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,62 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,62 unequal: No Solution No 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: 62:[84, 9], Operations: ['85/17=5', '14-5=9'] Exploring Operation: 84*9=756, Resulting Numbers: [756] 756,62 unequal: No Solution Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 84-9=75, Resulting Numbers: [75] 75,62 unequal: No Solution No 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: 62:[14, 79], Operations: ['85/17=5', '84-5=79'] Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,62 unequal: No Solution Exploring Operation: 14+79=93, Resulting Numbers: [93] 93,62 unequal: No Solution Exploring Operation: 14*79=1106, Resulting Numbers: [1106] 1106,62 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: 62:[14, 85, 67], Operations: ['84-17=67'] Exploring Operation: 85-14=71, Resulting Numbers: [67, 71] Generated Node #0,1,0: 62:[67, 71] Operation: 85-14=71 Exploring Operation: 14+85=99, Resulting Numbers: [67, 99] Generated Node #0,1,1: 62:[67, 99] Operation: 14+85=99 Exploring Operation: 85-67=18, Resulting Numbers: [14, 18] Generated Node #0,1,2: 62:[14, 18] Operation: 85-67=18 Exploring Operation: 67-14=53, Resulting Numbers: [85, 53] Generated Node #0,1,3: 62:[85, 53] Operation: 67-14=53 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 62:[67, 71], Operations: ['84-17=67', '85-14=71'] Exploring Operation: 67+71=138, Resulting Numbers: [138] 138,62 unequal: No Solution Exploring Operation: 67*71=4757, Resulting Numbers: [4757] 4757,62 unequal: No Solution Exploring Operation: 71-67=4, Resulting Numbers: [4] 4,62 unequal: No Solution No 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: 62:[14, 18], Operations: ['84-17=67', '85-67=18'] Exploring Operation: 18-14=4, Resulting Numbers: [4] 4,62 unequal: No Solution Exploring Operation: 14+18=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 14*18=252, Resulting Numbers: [252] 252,62 unequal: No Solution No 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: 62:[85, 53], Operations: ['84-17=67', '67-14=53'] Exploring Operation: 85-53=32, Resulting Numbers: [32] 32,62 unequal: No Solution Exploring Operation: 85+53=138, Resulting Numbers: [138] 138,62 unequal: No Solution Exploring Operation: 85*53=4505, Resulting Numbers: [4505] 4505,62 unequal: No Solution No 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: 62:[67, 99], Operations: ['84-17=67', '14+85=99'] Exploring Operation: 67+99=166, Resulting Numbers: [166] 166,62 unequal: No Solution Exploring Operation: 67*99=6633, Resulting Numbers: [6633] 6633,62 unequal: No Solution Exploring Operation: 99-67=32, Resulting Numbers: [32] 32,62 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: 62:[14, 84, 68], Operations: ['85-17=68'] Exploring Operation: 84/14=6, Resulting Numbers: [68, 6] Generated Node #0,3,0: 62:[68, 6] Operation: 84/14=6 Exploring Operation: 84-68=16, Resulting Numbers: [14, 16] Generated Node #0,3,1: 62:[14, 16] Operation: 84-68=16 Exploring Operation: 68-14=54, Resulting Numbers: [84, 54] Generated Node #0,3,2: 62:[84, 54] Operation: 68-14=54 Exploring Operation: 84-14=70, Resulting Numbers: [68, 70] Generated Node #0,3,3: 62:[68, 70] Operation: 84-14=70 Moving to Node #0,3,0 Current State: 62:[68, 6], Operations: ['85-17=68', '84/14=6'] Exploring Operation: 68+6=74, Resulting Numbers: [74] 74,62 unequal: No Solution Exploring Operation: 68*6=408, Resulting Numbers: [408] 408,62 unequal: No Solution Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[17, 14, 84, 85], Operations: [] Exploring Operation: 85-17=68, Resulting Numbers: [14, 84, 68] Generated Node #0,3: 62:[14, 84, 68] Operation: 85-17=68 Moving to Node #0,3 Current State: 62:[14, 84, 68], Operations: ['85-17=68'] Exploring Operation: 84/14=6, Resulting Numbers: [68, 6] Generated Node #0,3,0: 62:[68, 6] Operation: 84/14=6 Moving to Node #0,3,0 Current State: 62:[68, 6], Operations: ['85-17=68', '84/14=6'] Exploring Operation: 68-6=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.942708
hs_4
mult_heuristic
[ 8, 98, 75, 26 ]
24
[ "98-75=23", "26-23=3", "8*3=24" ]
Current State: 24:[8, 98, 75, 26], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [8, 26, 23] Generated Node #2: [8, 26, 23] from Operation: 98-75=23 Current State: 24:[8, 26, 23], Operations: ['98-75=23'] Exploring Operation: 26-23=3, Resulting Numbers: [8, 3] Generated Node #3: [8, 3] from Operation: 26-23=3 Current State: 24:[8, 3], Operations: ['98-75=23', '26-23=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[8, 98, 75, 26], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [8, 26, 23] Generated Node #0,0: 24:[8, 26, 23] Operation: 98-75=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 24:[8, 26, 23], Operations: ['98-75=23'] Exploring Operation: 26-23=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 24:[8, 3] Operation: 26-23=3 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 24:[8, 3], Operations: ['98-75=23', '26-23=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[8, 98, 75, 26], Operations: [] Exploring Operation: 98-75=23, Resulting Numbers: [8, 26, 23] Generated Node #0,0: 24:[8, 26, 23] Operation: 98-75=23 Moving to Node #0,0 Current State: 24:[8, 26, 23], Operations: ['98-75=23'] Exploring Operation: 26-23=3, Resulting Numbers: [8, 3] Generated Node #0,0,0: 24:[8, 3] Operation: 26-23=3 Moving to Node #0,0,0 Current State: 24:[8, 3], Operations: ['98-75=23', '26-23=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 13, 55, 60, 67 ]
18
[ "67-55=12", "60/12=5", "13+5=18" ]
Current State: 18:[13, 55, 60, 67], Operations: [] Exploring Operation: 67-55=12, Resulting Numbers: [13, 60, 12] Generated Node #2: [13, 60, 12] from Operation: 67-55=12 Current State: 18:[13, 60, 12], Operations: ['67-55=12'] Exploring Operation: 60/12=5, Resulting Numbers: [13, 5] Generated Node #3: [13, 5] from Operation: 60/12=5 Current State: 18:[13, 5], Operations: ['67-55=12', '60/12=5'] Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[13, 55, 60, 67], Operations: [] Exploring Operation: 67-60=7, Resulting Numbers: [13, 55, 7] Generated Node #0,0: 18:[13, 55, 7] Operation: 67-60=7 Moving to Node #0,0 Current State: 18:[13, 55, 7], Operations: ['67-60=7'] Exploring Operation: 55-13=42, Resulting Numbers: [7, 42] Generated Node #0,0,0: 18:[7, 42] Operation: 55-13=42 Moving to Node #0,0,0 Current State: 18:[7, 42], Operations: ['67-60=7', '55-13=42'] Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,18 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 48, 63, 31, 2 ]
23
[ "63-48=15", "31+15=46", "46/2=23" ]
Current State: 23:[48, 63, 31, 2], Operations: [] Exploring Operation: 63-48=15, Resulting Numbers: [31, 2, 15] Generated Node #2: [31, 2, 15] from Operation: 63-48=15 Current State: 23:[31, 2, 15], Operations: ['63-48=15'] Exploring Operation: 31+15=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 31+15=46 Current State: 23:[2, 46], Operations: ['63-48=15', '31+15=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[48, 63, 31, 2], Operations: [] Exploring Operation: 63-48=15, Resulting Numbers: [31, 2, 15] Generated Node #0,0: 23:[31, 2, 15] Operation: 63-48=15 Exploring Operation: 48-31=17, Resulting Numbers: [63, 2, 17] Generated Node #0,1: 23:[63, 2, 17] Operation: 48-31=17 Exploring Operation: 48/2=24, Resulting Numbers: [63, 31, 24] Generated Node #0,2: 23:[63, 31, 24] Operation: 48/2=24 Exploring Operation: 63-31=32, Resulting Numbers: [48, 2, 32] Generated Node #0,3: 23:[48, 2, 32] Operation: 63-31=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[31, 2, 15], Operations: ['63-48=15'] Exploring Operation: 2+15=17, Resulting Numbers: [31, 17] Generated Node #0,0,0: 23:[31, 17] Operation: 2+15=17 Exploring Operation: 31+2=33, Resulting Numbers: [15, 33] Generated Node #0,0,1: 23:[15, 33] Operation: 31+2=33 Exploring Operation: 31-2=29, Resulting Numbers: [15, 29] Generated Node #0,0,2: 23:[15, 29] Operation: 31-2=29 Exploring Operation: 2*15=30, Resulting Numbers: [31, 30] Generated Node #0,0,3: 23:[31, 30] Operation: 2*15=30 Moving to Node #0,0,0 Current State: 23:[31, 17], Operations: ['63-48=15', '2+15=17'] Exploring Operation: 31+17=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 31*17=527, Resulting Numbers: [527] 527,23 unequal: No Solution Exploring Operation: 31-17=14, Resulting Numbers: [14] 14,23 unequal: No Solution Moving to Node #0,0,2 Current State: 23:[15, 29], Operations: ['63-48=15', '31-2=29'] Exploring Operation: 15+29=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 29-15=14, Resulting Numbers: [14] 14,23 unequal: No Solution Exploring Operation: 15*29=435, Resulting Numbers: [435] 435,23 unequal: No Solution Moving to Node #0,0,3 Current State: 23:[31, 30], Operations: ['63-48=15', '2*15=30'] Exploring Operation: 31-30=1, Resulting Numbers: [1] 1,23 unequal: No Solution Exploring Operation: 31+30=61, Resulting Numbers: [61] 61,23 unequal: No Solution Exploring Operation: 31*30=930, Resulting Numbers: [930] 930,23 unequal: No Solution Moving to Node #0,0,1 Current State: 23:[15, 33], Operations: ['63-48=15', '31+2=33'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,23 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[63, 31, 24], Operations: ['48/2=24'] Exploring Operation: 63+31=94, Resulting Numbers: [24, 94] Generated Node #0,2,0: 23:[24, 94] Operation: 63+31=94 Exploring Operation: 63-31=32, Resulting Numbers: [24, 32] Generated Node #0,2,1: 23:[24, 32] Operation: 63-31=32 Exploring Operation: 31-24=7, Resulting Numbers: [63, 7] Generated Node #0,2,2: 23:[63, 7] Operation: 31-24=7 Exploring Operation: 63-24=39, Resulting Numbers: [31, 39] Generated Node #0,2,3: 23:[31, 39] Operation: 63-24=39 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 23:[24, 32], Operations: ['48/2=24', '63-31=32'] Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,23 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 23:[31, 39], Operations: ['48/2=24', '63-24=39'] Exploring Operation: 31+39=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 31*39=1209, Resulting Numbers: [1209] 1209,23 unequal: No Solution Exploring Operation: 39-31=8, Resulting Numbers: [8] 8,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 23:[63, 7], Operations: ['48/2=24', '31-24=7'] Exploring Operation: 63*7=441, Resulting Numbers: [441] 441,23 unequal: No Solution Exploring Operation: 63+7=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 63-7=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 63/7=9, Resulting Numbers: [9] 9,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 23:[24, 94], Operations: ['48/2=24', '63+31=94'] Exploring Operation: 24*94=2256, Resulting Numbers: [2256] 2256,23 unequal: No Solution Exploring Operation: 94-24=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 24+94=118, Resulting Numbers: [118] 118,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 23:[48, 2, 32], Operations: ['63-31=32'] Exploring Operation: 48-32=16, Resulting Numbers: [2, 16] Generated Node #0,3,0: 23:[2, 16] Operation: 48-32=16 Exploring Operation: 48-2=46, Resulting Numbers: [32, 46] Generated Node #0,3,1: 23:[32, 46] Operation: 48-2=46 Exploring Operation: 48/2=24, Resulting Numbers: [32, 24] Generated Node #0,3,2: 23:[32, 24] Operation: 48/2=24 Exploring Operation: 32-2=30, Resulting Numbers: [48, 30] Generated Node #0,3,3: 23:[48, 30] Operation: 32-2=30 Moving to Node #0,3,2 Current State: 23:[32, 24], Operations: ['63-31=32', '48/2=24'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 32*24=768, Resulting Numbers: [768] 768,23 unequal: No Solution Exploring Operation: 32+24=56, Resulting Numbers: [56] 56,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[2, 16], Operations: ['63-31=32', '48-32=16'] Exploring Operation: 2+16=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,23 unequal: No Solution Exploring Operation: 2*16=32, Resulting Numbers: [32] 32,23 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[48, 30], Operations: ['63-31=32', '32-2=30'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,23 unequal: No Solution Exploring Operation: 48*30=1440, Resulting Numbers: [1440] 1440,23 unequal: No Solution Exploring Operation: 48+30=78, Resulting Numbers: [78] 78,23 unequal: No Solution Moving to Node #0,3,1 Current State: 23:[32, 46], Operations: ['63-31=32', '48-2=46'] Exploring Operation: 32*46=1472, Resulting Numbers: [1472] 1472,23 unequal: No Solution Exploring Operation: 32+46=78, Resulting Numbers: [78] 78,23 unequal: No Solution Exploring Operation: 46-32=14, Resulting Numbers: [14] 14,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[63, 2, 17], Operations: ['48-31=17'] Exploring Operation: 2+17=19, Resulting Numbers: [63, 19] Generated Node #0,1,0: 23:[63, 19] Operation: 2+17=19 Exploring Operation: 63-17=46, Resulting Numbers: [2, 46] Generated Node #0,1,1: 23:[2, 46] Operation: 63-17=46 Exploring Operation: 63+2=65, Resulting Numbers: [17, 65] Generated Node #0,1,2: 23:[17, 65] Operation: 63+2=65 Exploring Operation: 63-2=61, Resulting Numbers: [17, 61] Generated Node #0,1,3: 23:[17, 61] Operation: 63-2=61 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 23:[63, 19], Operations: ['48-31=17', '2+17=19'] Exploring Operation: 63+19=82, Resulting Numbers: [82] 82,23 unequal: No Solution Exploring Operation: 63*19=1197, Resulting Numbers: [1197] 1197,23 unequal: No Solution Exploring Operation: 63-19=44, Resulting Numbers: [44] 44,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 23:[2, 46], Operations: ['48-31=17', '63-17=46'] Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[48, 63, 31, 2], Operations: [] Exploring Operation: 48-31=17, Resulting Numbers: [63, 2, 17] Generated Node #0,1: 23:[63, 2, 17] Operation: 48-31=17 Moving to Node #0,1 Current State: 23:[63, 2, 17], Operations: ['48-31=17'] Exploring Operation: 63-17=46, Resulting Numbers: [2, 46] Generated Node #0,1,1: 23:[2, 46] Operation: 63-17=46 Moving to Node #0,1,1 Current State: 23:[2, 46], Operations: ['48-31=17', '63-17=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.940104
hs_4
sum_heuristic
[ 29, 92, 91, 3 ]
94
[ "91-29=62", "3*62=186", "186-92=94" ]
Current State: 94:[29, 92, 91, 3], Operations: [] Exploring Operation: 91-29=62, Resulting Numbers: [92, 3, 62] Generated Node #2: [92, 3, 62] from Operation: 91-29=62 Current State: 94:[92, 3, 62], Operations: ['91-29=62'] Exploring Operation: 3*62=186, Resulting Numbers: [92, 186] Generated Node #3: [92, 186] from Operation: 3*62=186 Current State: 94:[92, 186], Operations: ['91-29=62', '3*62=186'] Exploring Operation: 186-92=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[29, 92, 91, 3], Operations: [] Exploring Operation: 29*3=87, Resulting Numbers: [92, 91, 87] Generated Node #0,0: 94:[92, 91, 87] Operation: 29*3=87 Exploring Operation: 91-29=62, Resulting Numbers: [92, 3, 62] Generated Node #0,1: 94:[92, 3, 62] Operation: 91-29=62 Moving to Node #0,0 Current State: 94:[92, 91, 87], Operations: ['29*3=87'] Exploring Operation: 91-87=4, Resulting Numbers: [92, 4] Generated Node #0,0,0: 94:[92, 4] Operation: 91-87=4 Exploring Operation: 92-87=5, Resulting Numbers: [91, 5] Generated Node #0,0,1: 94:[91, 5] Operation: 92-87=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 94:[92, 4], Operations: ['29*3=87', '91-87=4'] Exploring Operation: 92-4=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 94:[91, 5], Operations: ['29*3=87', '92-87=5'] Exploring Operation: 91-5=86, Resulting Numbers: [86] 86,94 unequal: No Solution Exploring Operation: 91+5=96, Resulting Numbers: [96] 96,94 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: 94:[92, 3, 62], Operations: ['91-29=62'] Exploring Operation: 62-3=59, Resulting Numbers: [92, 59] Generated Node #0,1,0: 94:[92, 59] Operation: 62-3=59 Exploring Operation: 92+3=95, Resulting Numbers: [62, 95] Generated Node #0,1,1: 94:[62, 95] Operation: 92+3=95 Moving to Node #0,1,0 Current State: 94:[92, 59], Operations: ['91-29=62', '62-3=59'] Exploring Operation: 92-59=33, Resulting Numbers: [33] 33,94 unequal: No Solution Exploring Operation: 92+59=151, Resulting Numbers: [151] 151,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[62, 95], Operations: ['91-29=62', '92+3=95'] Exploring Operation: 62+95=157, Resulting Numbers: [157] 157,94 unequal: No Solution Exploring Operation: 95-62=33, Resulting Numbers: [33] 33,94 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 13, 2, 45, 84 ]
97
[ "84-13=71", "2*71=142", "142-45=97" ]
Current State: 97:[13, 2, 45, 84], Operations: [] Exploring Operation: 84-13=71, Resulting Numbers: [2, 45, 71] Generated Node #2: [2, 45, 71] from Operation: 84-13=71 Current State: 97:[2, 45, 71], Operations: ['84-13=71'] Exploring Operation: 2*71=142, Resulting Numbers: [45, 142] Generated Node #3: [45, 142] from Operation: 2*71=142 Current State: 97:[45, 142], Operations: ['84-13=71', '2*71=142'] Exploring Operation: 142-45=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[13, 2, 45, 84], Operations: [] Exploring Operation: 13+2=15, Resulting Numbers: [45, 84, 15] Generated Node #0,0: 97:[45, 84, 15] Operation: 13+2=15 Exploring Operation: 13*2=26, Resulting Numbers: [45, 84, 26] Generated Node #0,1: 97:[45, 84, 26] Operation: 13*2=26 Exploring Operation: 2*45=90, Resulting Numbers: [13, 84, 90] Generated Node #0,2: 97:[13, 84, 90] Operation: 2*45=90 Start Sub Search at level 1: Moving to Node #0,2 Current State: 97:[13, 84, 90], Operations: ['2*45=90'] Exploring Operation: 13+84=97, Resulting Numbers: [90, 97] Generated Node #0,2,0: 97:[90, 97] Operation: 13+84=97 Exploring Operation: 84-13=71, Resulting Numbers: [90, 71] Generated Node #0,2,1: 97:[90, 71] Operation: 84-13=71 Exploring Operation: 13+90=103, Resulting Numbers: [84, 103] Generated Node #0,2,2: 97:[84, 103] Operation: 13+90=103 Moving to Node #0,2,0 Current State: 97:[90, 97], Operations: ['2*45=90', '13+84=97'] Exploring Operation: 97-90=7, Resulting Numbers: [7] 7,97 unequal: No Solution Exploring Operation: 90+97=187, Resulting Numbers: [187] 187,97 unequal: No Solution Exploring Operation: 90*97=8730, Resulting Numbers: [8730] 8730,97 unequal: No Solution Moving to Node #0,2,2 Current State: 97:[84, 103], Operations: ['2*45=90', '13+90=103'] Exploring Operation: 84*103=8652, Resulting Numbers: [8652] 8652,97 unequal: No Solution Exploring Operation: 84+103=187, Resulting Numbers: [187] 187,97 unequal: No Solution Exploring Operation: 103-84=19, Resulting Numbers: [19] 19,97 unequal: No Solution Moving to Node #0,2,1 Current State: 97:[90, 71], Operations: ['2*45=90', '84-13=71'] Exploring Operation: 90+71=161, Resulting Numbers: [161] 161,97 unequal: No Solution Exploring Operation: 90*71=6390, Resulting Numbers: [6390] 6390,97 unequal: No Solution Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[45, 84, 26], Operations: ['13*2=26'] Exploring Operation: 45-26=19, Resulting Numbers: [84, 19] Generated Node #0,1,0: 97:[84, 19] Operation: 45-26=19 Exploring Operation: 84+26=110, Resulting Numbers: [45, 110] Generated Node #0,1,1: 97:[45, 110] Operation: 84+26=110 Exploring Operation: 45+26=71, Resulting Numbers: [84, 71] Generated Node #0,1,2: 97:[84, 71] Operation: 45+26=71 Moving to Node #0,1,2 Current State: 97:[84, 71], Operations: ['13*2=26', '45+26=71'] Exploring Operation: 84+71=155, Resulting Numbers: [155] 155,97 unequal: No Solution Exploring Operation: 84-71=13, Resulting Numbers: [13] 13,97 unequal: No Solution Exploring Operation: 84*71=5964, Resulting Numbers: [5964] 5964,97 unequal: No Solution Moving to Node #0,1,1 Current State: 97:[45, 110], Operations: ['13*2=26', '84+26=110'] Exploring Operation: 110-45=65, Resulting Numbers: [65] 65,97 unequal: No Solution Exploring Operation: 45+110=155, Resulting Numbers: [155] 155,97 unequal: No Solution Exploring Operation: 45*110=4950, Resulting Numbers: [4950] 4950,97 unequal: No Solution Moving to Node #0,1,0 Current State: 97:[84, 19], Operations: ['13*2=26', '45-26=19'] Exploring Operation: 84+19=103, Resulting Numbers: [103] 103,97 unequal: No Solution Exploring Operation: 84*19=1596, Resulting Numbers: [1596] 1596,97 unequal: No Solution Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[45, 84, 15], Operations: ['13+2=15'] Exploring Operation: 45-15=30, Resulting Numbers: [84, 30] Generated Node #0,0,0: 97:[84, 30] Operation: 45-15=30 Exploring Operation: 84+15=99, Resulting Numbers: [45, 99] Generated Node #0,0,1: 97:[45, 99] Operation: 84+15=99 Exploring Operation: 45+15=60, Resulting Numbers: [84, 60] Generated Node #0,0,2: 97:[84, 60] Operation: 45+15=60 Moving to Node #0,0,2 Current State: 97:[84, 60], Operations: ['13+2=15', '45+15=60'] Exploring Operation: 84+60=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 84-60=24, Resulting Numbers: [24] 24,97 unequal: No Solution Exploring Operation: 84*60=5040, Resulting Numbers: [5040] 5040,97 unequal: No Solution Moving to Node #0,0,1 Current State: 97:[45, 99], Operations: ['13+2=15', '84+15=99'] Exploring Operation: 45*99=4455, Resulting Numbers: [4455] 4455,97 unequal: No Solution Exploring Operation: 45+99=144, Resulting Numbers: [144] 144,97 unequal: No Solution Exploring Operation: 99-45=54, Resulting Numbers: [54] 54,97 unequal: No Solution Moving to Node #0,0,0 Current State: 97:[84, 30], Operations: ['13+2=15', '45-15=30'] Exploring Operation: 84*30=2520, Resulting Numbers: [2520] 2520,97 unequal: No Solution Exploring Operation: 84+30=114, Resulting Numbers: [114] 114,97 unequal: No Solution Exploring Operation: 84-30=54, Resulting Numbers: [54] 54,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 84, 6, 3, 1 ]
87
[ "84+6=90", "3*1=3", "90-3=87" ]
Current State: 87:[84, 6, 3, 1], Operations: [] Exploring Operation: 84+6=90, Resulting Numbers: [3, 1, 90] Generated Node #2: [3, 1, 90] from Operation: 84+6=90 Current State: 87:[3, 1, 90], Operations: ['84+6=90'] Exploring Operation: 3*1=3, Resulting Numbers: [90, 3] Generated Node #3: [90, 3] from Operation: 3*1=3 Current State: 87:[90, 3], Operations: ['84+6=90', '3*1=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[84, 6, 3, 1], Operations: [] Exploring Operation: 84+3=87, Resulting Numbers: [6, 1, 87] Generated Node #0,0: 87:[6, 1, 87] Operation: 84+3=87 Exploring Operation: 84+1=85, Resulting Numbers: [6, 3, 85] Generated Node #0,1: 87:[6, 3, 85] Operation: 84+1=85 Exploring Operation: 6-1=5, Resulting Numbers: [84, 3, 5] Generated Node #0,2: 87:[84, 3, 5] Operation: 6-1=5 Exploring Operation: 6-3=3, Resulting Numbers: [84, 1, 3] Generated Node #0,3: 87:[84, 1, 3] Operation: 6-3=3 Exploring Operation: 84+6=90, Resulting Numbers: [3, 1, 90] Generated Node #0,4: 87:[3, 1, 90] Operation: 84+6=90 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[6, 1, 87], Operations: ['84+3=87'] Exploring Operation: 6-1=5, Resulting Numbers: [87, 5] Generated Node #0,0,0: 87:[87, 5] Operation: 6-1=5 Exploring Operation: 87/1=87, Resulting Numbers: [6, 87] Generated Node #0,0,1: 87:[6, 87] Operation: 87/1=87 Exploring Operation: 1*87=87, Resulting Numbers: [6, 87] Generated Node #0,0,2: 87:[6, 87] Operation: 1*87=87 Exploring Operation: 6/1=6, Resulting Numbers: [87, 6] Generated Node #0,0,3: 87:[87, 6] Operation: 6/1=6 Exploring Operation: 6*1=6, Resulting Numbers: [87, 6] Generated Node #0,0,4: 87:[87, 6] Operation: 6*1=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 87:[87, 5], Operations: ['84+3=87', '6-1=5'] Exploring Operation: 87*5=435, Resulting Numbers: [435] 435,87 unequal: No Solution Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,87 unequal: No Solution Exploring Operation: 87+5=92, Resulting Numbers: [92] 92,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 87:[6, 87], Operations: ['84+3=87', '87/1=87'] Exploring Operation: 6*87=522, Resulting Numbers: [522] 522,87 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 87:[6, 87], Operations: ['84+3=87', '1*87=87'] Exploring Operation: 6*87=522, Resulting Numbers: [522] 522,87 unequal: No Solution Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 6+87=93, Resulting Numbers: [93] 93,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 87:[87, 6], Operations: ['84+3=87', '6/1=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,87 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 87:[87, 6], Operations: ['84+3=87', '6*1=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,87 unequal: No Solution Exploring Operation: 87+6=93, Resulting Numbers: [93] 93,87 unequal: No Solution Exploring Operation: 87*6=522, Resulting Numbers: [522] 522,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[6, 3, 85], Operations: ['84+1=85'] Exploring Operation: 3+85=88, Resulting Numbers: [6, 88] Generated Node #0,1,0: 87:[6, 88] Operation: 3+85=88 Exploring Operation: 6/3=2, Resulting Numbers: [85, 2] Generated Node #0,1,1: 87:[85, 2] Operation: 6/3=2 Exploring Operation: 6-3=3, Resulting Numbers: [85, 3] Generated Node #0,1,2: 87:[85, 3] Operation: 6-3=3 Exploring Operation: 6+85=91, Resulting Numbers: [3, 91] Generated Node #0,1,3: 87:[3, 91] Operation: 6+85=91 Exploring Operation: 6+3=9, Resulting Numbers: [85, 9] Generated Node #0,1,4: 87:[85, 9] Operation: 6+3=9 Moving to Node #0,1,2 Current State: 87:[85, 3], Operations: ['84+1=85', '6-3=3'] Exploring Operation: 85-3=82, Resulting Numbers: [82] 82,87 unequal: No Solution Exploring Operation: 85*3=255, Resulting Numbers: [255] 255,87 unequal: No Solution Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,87 unequal: No Solution Moving to Node #0,1,1 Current State: 87:[85, 2], Operations: ['84+1=85', '6/3=2'] Exploring Operation: 85-2=83, Resulting Numbers: [83] 83,87 unequal: No Solution Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[84, 6, 3, 1], Operations: [] Exploring Operation: 84+1=85, Resulting Numbers: [6, 3, 85] Generated Node #0,1: 87:[6, 3, 85] Operation: 84+1=85 Moving to Node #0,1 Current State: 87:[6, 3, 85], Operations: ['84+1=85'] Exploring Operation: 6/3=2, Resulting Numbers: [85, 2] Generated Node #0,1,1: 87:[85, 2] Operation: 6/3=2 Moving to Node #0,1,1 Current State: 87:[85, 2], Operations: ['84+1=85', '6/3=2'] Exploring Operation: 85+2=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
sum_heuristic
[ 61, 7, 51, 42 ]
22
[ "61+51=112", "42+112=154", "154/7=22" ]
Current State: 22:[61, 7, 51, 42], Operations: [] Exploring Operation: 61+51=112, Resulting Numbers: [7, 42, 112] Generated Node #2: [7, 42, 112] from Operation: 61+51=112 Current State: 22:[7, 42, 112], Operations: ['61+51=112'] Exploring Operation: 42+112=154, Resulting Numbers: [7, 154] Generated Node #3: [7, 154] from Operation: 42+112=154 Current State: 22:[7, 154], Operations: ['61+51=112', '42+112=154'] Exploring Operation: 154/7=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[61, 7, 51, 42], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [7, 42, 10] Generated Node #0,0: 22:[7, 42, 10] Operation: 61-51=10 Exploring Operation: 42/7=6, Resulting Numbers: [61, 51, 6] Generated Node #0,1: 22:[61, 51, 6] Operation: 42/7=6 Exploring Operation: 61-7=54, Resulting Numbers: [51, 42, 54] Generated Node #0,2: 22:[51, 42, 54] Operation: 61-7=54 Exploring Operation: 51-42=9, Resulting Numbers: [61, 7, 9] Generated Node #0,3: 22:[61, 7, 9] Operation: 51-42=9 Exploring Operation: 61-42=19, Resulting Numbers: [7, 51, 19] Generated Node #0,4: 22:[7, 51, 19] Operation: 61-42=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[7, 42, 10], Operations: ['61-51=10'] Exploring Operation: 42/7=6, Resulting Numbers: [10, 6] Generated Node #0,0,0: 22:[10, 6] Operation: 42/7=6 Exploring Operation: 42-10=32, Resulting Numbers: [7, 32] Generated Node #0,0,1: 22:[7, 32] Operation: 42-10=32 Exploring Operation: 42-7=35, Resulting Numbers: [10, 35] Generated Node #0,0,2: 22:[10, 35] Operation: 42-7=35 Exploring Operation: 7+10=17, Resulting Numbers: [42, 17] Generated Node #0,0,3: 22:[42, 17] Operation: 7+10=17 Exploring Operation: 10-7=3, Resulting Numbers: [42, 3] Generated Node #0,0,4: 22:[42, 3] Operation: 10-7=3 Moving to Node #0,0,0 Current State: 22:[10, 6], Operations: ['61-51=10', '42/7=6'] Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,22 unequal: No Solution Moving to Node #0,0,2 Current State: 22:[10, 35], Operations: ['61-51=10', '42-7=35'] Exploring Operation: 10+35=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 10*35=350, Resulting Numbers: [350] 350,22 unequal: No Solution Exploring Operation: 35-10=25, Resulting Numbers: [25] 25,22 unequal: No Solution Moving to Node #0,0,1 Current State: 22:[7, 32], Operations: ['61-51=10', '42-10=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,22 unequal: No Solution Moving to Node #0,0,4 Current State: 22:[42, 3], Operations: ['61-51=10', '10-7=3'] Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,22 unequal: No Solution Moving to Node #0,0,3 Current State: 22:[42, 17], Operations: ['61-51=10', '7+10=17'] Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,22 unequal: No Solution Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,22 unequal: No Solution No 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: 22:[7, 51, 19], Operations: ['61-42=19'] Exploring Operation: 51-7=44, Resulting Numbers: [19, 44] Generated Node #0,4,0: 22:[19, 44] Operation: 51-7=44 Exploring Operation: 7+19=26, Resulting Numbers: [51, 26] Generated Node #0,4,1: 22:[51, 26] Operation: 7+19=26 Exploring Operation: 51-19=32, Resulting Numbers: [7, 32] Generated Node #0,4,2: 22:[7, 32] Operation: 51-19=32 Exploring Operation: 19-7=12, Resulting Numbers: [51, 12] Generated Node #0,4,3: 22:[51, 12] Operation: 19-7=12 Exploring Operation: 7+51=58, Resulting Numbers: [19, 58] Generated Node #0,4,4: 22:[19, 58] Operation: 7+51=58 Moving to Node #0,4,2 Current State: 22:[7, 32], Operations: ['61-42=19', '51-19=32'] Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,22 unequal: No Solution Moving to Node #0,4,0 Current State: 22:[19, 44], Operations: ['61-42=19', '51-7=44'] Exploring Operation: 19*44=836, Resulting Numbers: [836] 836,22 unequal: No Solution Exploring Operation: 19+44=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 44-19=25, Resulting Numbers: [25] 25,22 unequal: No Solution Moving to Node #0,4,3 Current State: 22:[51, 12], Operations: ['61-42=19', '19-7=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,22 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,22 unequal: No Solution Moving to Node #0,4,1 Current State: 22:[51, 26], Operations: ['61-42=19', '7+19=26'] Exploring Operation: 51+26=77, Resulting Numbers: [77] 77,22 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,22 unequal: No Solution Exploring Operation: 51*26=1326, Resulting Numbers: [1326] 1326,22 unequal: No Solution Moving to Node #0,4,4 Current State: 22:[19, 58], Operations: ['61-42=19', '7+51=58'] Exploring Operation: 58-19=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 19+58=77, Resulting Numbers: [77] 77,22 unequal: No Solution Exploring Operation: 19*58=1102, Resulting Numbers: [1102] 1102,22 unequal: No Solution No 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: 22:[61, 7, 9], Operations: ['51-42=9'] Exploring Operation: 61-9=52, Resulting Numbers: [7, 52] Generated Node #0,3,0: 22:[7, 52] Operation: 61-9=52 Exploring Operation: 9-7=2, Resulting Numbers: [61, 2] Generated Node #0,3,1: 22:[61, 2] Operation: 9-7=2 Exploring Operation: 61+7=68, Resulting Numbers: [9, 68] Generated Node #0,3,2: 22:[9, 68] Operation: 61+7=68 Exploring Operation: 7+9=16, Resulting Numbers: [61, 16] Generated Node #0,3,3: 22:[61, 16] Operation: 7+9=16 Exploring Operation: 61-7=54, Resulting Numbers: [9, 54] Generated Node #0,3,4: 22:[9, 54] Operation: 61-7=54 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 22:[7, 52], Operations: ['51-42=9', '61-9=52'] Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,22 unequal: No Solution Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 22:[9, 54], Operations: ['51-42=9', '61-7=54'] Exploring Operation: 9+54=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 9*54=486, Resulting Numbers: [486] 486,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 22:[61, 2], Operations: ['51-42=9', '9-7=2'] Exploring Operation: 61*2=122, Resulting Numbers: [122] 122,22 unequal: No Solution Exploring Operation: 61+2=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 61-2=59, Resulting Numbers: [59] 59,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 22:[61, 16], Operations: ['51-42=9', '7+9=16'] Exploring Operation: 61*16=976, Resulting Numbers: [976] 976,22 unequal: No Solution Exploring Operation: 61-16=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 61+16=77, Resulting Numbers: [77] 77,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 22:[9, 68], Operations: ['51-42=9', '61+7=68'] Exploring Operation: 68-9=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 9+68=77, Resulting Numbers: [77] 77,22 unequal: No Solution Exploring Operation: 9*68=612, Resulting Numbers: [612] 612,22 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: 22:[61, 51, 6], Operations: ['42/7=6'] Exploring Operation: 61+6=67, Resulting Numbers: [51, 67] Generated Node #0,1,0: 22:[51, 67] Operation: 61+6=67 Exploring Operation: 61-6=55, Resulting Numbers: [51, 55] Generated Node #0,1,1: 22:[51, 55] Operation: 61-6=55 Exploring Operation: 51+6=57, Resulting Numbers: [61, 57] Generated Node #0,1,2: 22:[61, 57] Operation: 51+6=57 Exploring Operation: 51-6=45, Resulting Numbers: [61, 45] Generated Node #0,1,3: 22:[61, 45] Operation: 51-6=45 Exploring Operation: 61-51=10, Resulting Numbers: [6, 10] Generated Node #0,1,4: 22:[6, 10] Operation: 61-51=10 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 22:[6, 10], Operations: ['42/7=6', '61-51=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 22:[51, 55], Operations: ['42/7=6', '61-6=55'] Exploring Operation: 55-51=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 51*55=2805, Resulting Numbers: [2805] 2805,22 unequal: No Solution Exploring Operation: 51+55=106, Resulting Numbers: [106] 106,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 22:[61, 45], Operations: ['42/7=6', '51-6=45'] Exploring Operation: 61-45=16, Resulting Numbers: [16] 16,22 unequal: No Solution Exploring Operation: 61+45=106, Resulting Numbers: [106] 106,22 unequal: No Solution Exploring Operation: 61*45=2745, Resulting Numbers: [2745] 2745,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 22:[51, 67], Operations: ['42/7=6', '61+6=67'] Exploring Operation: 51*67=3417, Resulting Numbers: [3417] 3417,22 unequal: No Solution Exploring Operation: 51+67=118, Resulting Numbers: [118] 118,22 unequal: No Solution Exploring Operation: 67-51=16, Resulting Numbers: [16] 16,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 22:[61, 57], Operations: ['42/7=6', '51+6=57'] Exploring Operation: 61*57=3477, Resulting Numbers: [3477] 3477,22 unequal: No Solution Exploring Operation: 61-57=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 61+57=118, Resulting Numbers: [118] 118,22 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: 22:[51, 42, 54], Operations: ['61-7=54'] Exploring Operation: 54-42=12, Resulting Numbers: [51, 12] Generated Node #0,2,0: 22:[51, 12] Operation: 54-42=12 Exploring Operation: 51+54=105, Resulting Numbers: [42, 105] Generated Node #0,2,1: 22:[42, 105] Operation: 51+54=105 Exploring Operation: 54-51=3, Resulting Numbers: [42, 3] Generated Node #0,2,2: 22:[42, 3] Operation: 54-51=3 Exploring Operation: 51+42=93, Resulting Numbers: [54, 93] Generated Node #0,2,3: 22:[54, 93] Operation: 51+42=93 Exploring Operation: 51-42=9, Resulting Numbers: [54, 9] Generated Node #0,2,4: 22:[54, 9] Operation: 51-42=9 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 22:[42, 3], Operations: ['61-7=54', '54-51=3'] Exploring Operation: 42-3=39, Resulting Numbers: [39] 39,22 unequal: No Solution Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 42*3=126, Resulting Numbers: [126] 126,22 unequal: No Solution Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 22:[51, 12], Operations: ['61-7=54', '54-42=12'] Exploring Operation: 51+12=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 51*12=612, Resulting Numbers: [612] 612,22 unequal: No Solution Exploring Operation: 51-12=39, Resulting Numbers: [39] 39,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 22:[54, 9], Operations: ['61-7=54', '51-42=9'] Exploring Operation: 54-9=45, Resulting Numbers: [45] 45,22 unequal: No Solution Exploring Operation: 54+9=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,22 unequal: No Solution Exploring Operation: 54*9=486, Resulting Numbers: [486] 486,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 22:[42, 105], Operations: ['61-7=54', '51+54=105'] Exploring Operation: 42+105=147, Resulting Numbers: [147] 147,22 unequal: No Solution Exploring Operation: 105-42=63, Resulting Numbers: [63] 63,22 unequal: No Solution Exploring Operation: 42*105=4410, Resulting Numbers: [4410] 4410,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 22:[54, 93], Operations: ['61-7=54', '51+42=93'] Exploring Operation: 54+93=147, Resulting Numbers: [147] 147,22 unequal: No Solution Exploring Operation: 54*93=5022, Resulting Numbers: [5022] 5022,22 unequal: No Solution Exploring Operation: 93-54=39, Resulting Numbers: [39] 39,22 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 9, 16, 97, 10 ]
94
[ "16-9=7", "97-10=87", "7+87=94" ]
Current State: 94:[9, 16, 97, 10], Operations: [] Exploring Operation: 16-9=7, Resulting Numbers: [97, 10, 7] Generated Node #2: [97, 10, 7] from Operation: 16-9=7 Current State: 94:[97, 10, 7], Operations: ['16-9=7'] Exploring Operation: 97-10=87, Resulting Numbers: [7, 87] Generated Node #3: [7, 87] from Operation: 97-10=87 Current State: 94:[7, 87], Operations: ['16-9=7', '97-10=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[9, 16, 97, 10], Operations: [] Exploring Operation: 16-10=6, Resulting Numbers: [9, 97, 6] Generated Node #0,0: 94:[9, 97, 6] Operation: 16-10=6 Exploring Operation: 16-9=7, Resulting Numbers: [97, 10, 7] Generated Node #0,1: 94:[97, 10, 7] Operation: 16-9=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[9, 97, 6], Operations: ['16-10=6'] Exploring Operation: 97-9=88, Resulting Numbers: [6, 88] Generated Node #0,0,0: 94:[6, 88] Operation: 97-9=88 Exploring Operation: 9-6=3, Resulting Numbers: [97, 3] Generated Node #0,0,1: 94:[97, 3] Operation: 9-6=3 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 94:[97, 3], Operations: ['16-10=6', '9-6=3'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[9, 16, 97, 10], Operations: [] Exploring Operation: 16-10=6, Resulting Numbers: [9, 97, 6] Generated Node #0,0: 94:[9, 97, 6] Operation: 16-10=6 Moving to Node #0,0 Current State: 94:[9, 97, 6], Operations: ['16-10=6'] Exploring Operation: 9-6=3, Resulting Numbers: [97, 3] Generated Node #0,0,1: 94:[97, 3] Operation: 9-6=3 Moving to Node #0,0,1 Current State: 94:[97, 3], Operations: ['16-10=6', '9-6=3'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 34, 31, 96, 10 ]
27
[ "34-10=24", "96/24=4", "31-4=27" ]
Current State: 27:[34, 31, 96, 10], Operations: [] Exploring Operation: 34-10=24, Resulting Numbers: [31, 96, 24] Generated Node #2: [31, 96, 24] from Operation: 34-10=24 Current State: 27:[31, 96, 24], Operations: ['34-10=24'] Exploring Operation: 96/24=4, Resulting Numbers: [31, 4] Generated Node #3: [31, 4] from Operation: 96/24=4 Current State: 27:[31, 4], Operations: ['34-10=24', '96/24=4'] Exploring Operation: 31-4=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[34, 31, 96, 10], Operations: [] Exploring Operation: 96-31=65, Resulting Numbers: [34, 10, 65] Generated Node #0,0: 27:[34, 10, 65] Operation: 96-31=65 Exploring Operation: 96-10=86, Resulting Numbers: [34, 31, 86] Generated Node #0,1: 27:[34, 31, 86] Operation: 96-10=86 Exploring Operation: 96-34=62, Resulting Numbers: [31, 10, 62] Generated Node #0,2: 27:[31, 10, 62] Operation: 96-34=62 Exploring Operation: 34-31=3, Resulting Numbers: [96, 10, 3] Generated Node #0,3: 27:[96, 10, 3] Operation: 34-31=3 Moving to Node #0,2 Current State: 27:[31, 10, 62], Operations: ['96-34=62'] Exploring Operation: 31-10=21, Resulting Numbers: [62, 21] Generated Node #0,2,0: 27:[62, 21] Operation: 31-10=21 Exploring Operation: 62-31=31, Resulting Numbers: [10, 31] Generated Node #0,2,1: 27:[10, 31] Operation: 62-31=31 Exploring Operation: 62-10=52, Resulting Numbers: [31, 52] Generated Node #0,2,2: 27:[31, 52] Operation: 62-10=52 Exploring Operation: 62/31=2, Resulting Numbers: [10, 2] Generated Node #0,2,3: 27:[10, 2] Operation: 62/31=2 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[10, 2], Operations: ['96-34=62', '62/31=2'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,27 unequal: No Solution Exploring Operation: 10*2=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 10-2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 10+2=12, Resulting Numbers: [12] 12,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[10, 31], Operations: ['96-34=62', '62-31=31'] Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,27 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[31, 52], Operations: ['96-34=62', '62-10=52'] Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,27 unequal: No Solution Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[62, 21], Operations: ['96-34=62', '31-10=21'] Exploring Operation: 62-21=41, Resulting Numbers: [41] 41,27 unequal: No Solution Exploring Operation: 62+21=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 62*21=1302, Resulting Numbers: [1302] 1302,27 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: 27:[34, 10, 65], Operations: ['96-31=65'] Exploring Operation: 65-34=31, Resulting Numbers: [10, 31] Generated Node #0,0,0: 27:[10, 31] Operation: 65-34=31 Exploring Operation: 65-10=55, Resulting Numbers: [34, 55] Generated Node #0,0,1: 27:[34, 55] Operation: 65-10=55 Exploring Operation: 34-10=24, Resulting Numbers: [65, 24] Generated Node #0,0,2: 27:[65, 24] Operation: 34-10=24 Exploring Operation: 34+10=44, Resulting Numbers: [65, 44] Generated Node #0,0,3: 27:[65, 44] Operation: 34+10=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[10, 31], Operations: ['96-31=65', '65-34=31'] Exploring Operation: 10+31=41, Resulting Numbers: [41] 41,27 unequal: No Solution Exploring Operation: 10*31=310, Resulting Numbers: [310] 310,27 unequal: No Solution Exploring Operation: 31-10=21, Resulting Numbers: [21] 21,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[34, 55], Operations: ['96-31=65', '65-10=55'] Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,27 unequal: No Solution Exploring Operation: 34*55=1870, Resulting Numbers: [1870] 1870,27 unequal: No Solution Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 27:[65, 24], Operations: ['96-31=65', '34-10=24'] Exploring Operation: 65+24=89, Resulting Numbers: [89] 89,27 unequal: No Solution Exploring Operation: 65*24=1560, Resulting Numbers: [1560] 1560,27 unequal: No Solution Exploring Operation: 65-24=41, Resulting Numbers: [41] 41,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 27:[65, 44], Operations: ['96-31=65', '34+10=44'] Exploring Operation: 65+44=109, Resulting Numbers: [109] 109,27 unequal: No Solution Exploring Operation: 65-44=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 65*44=2860, Resulting Numbers: [2860] 2860,27 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: 27:[96, 10, 3], Operations: ['34-31=3'] Exploring Operation: 96-10=86, Resulting Numbers: [3, 86] Generated Node #0,3,0: 27:[3, 86] Operation: 96-10=86 Exploring Operation: 96/3=32, Resulting Numbers: [10, 32] Generated Node #0,3,1: 27:[10, 32] Operation: 96/3=32 Exploring Operation: 96-3=93, Resulting Numbers: [10, 93] Generated Node #0,3,2: 27:[10, 93] Operation: 96-3=93 Exploring Operation: 10-3=7, Resulting Numbers: [96, 7] Generated Node #0,3,3: 27:[96, 7] Operation: 10-3=7 Moving to Node #0,1 Current State: 27:[34, 31, 86], Operations: ['96-10=86'] Exploring Operation: 86-31=55, Resulting Numbers: [34, 55] Generated Node #0,1,0: 27:[34, 55] Operation: 86-31=55 Exploring Operation: 86-34=52, Resulting Numbers: [31, 52] Generated Node #0,1,1: 27:[31, 52] Operation: 86-34=52 Exploring Operation: 34-31=3, Resulting Numbers: [86, 3] Generated Node #0,1,2: 27:[86, 3] Operation: 34-31=3 Exploring Operation: 34+31=65, Resulting Numbers: [86, 65] Generated Node #0,1,3: 27:[86, 65] Operation: 34+31=65 Moving to Node #0,3,1 Current State: 27:[10, 32], Operations: ['34-31=3', '96/3=32'] Exploring Operation: 10+32=42, Resulting Numbers: [42] 42,27 unequal: No Solution Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 10*32=320, Resulting Numbers: [320] 320,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[31, 52], Operations: ['96-10=86', '86-34=52'] Exploring Operation: 52-31=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 31+52=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 31*52=1612, Resulting Numbers: [1612] 1612,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[34, 55], Operations: ['96-10=86', '86-31=55'] Exploring Operation: 55-34=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 34*55=1870, Resulting Numbers: [1870] 1870,27 unequal: No Solution Exploring Operation: 34+55=89, Resulting Numbers: [89] 89,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[86, 3], Operations: ['96-10=86', '34-31=3'] Exploring Operation: 86*3=258, Resulting Numbers: [258] 258,27 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 86+3=89, Resulting Numbers: [89] 89,27 unequal: No Solution Moving to Node #0,3,0 Current State: 27:[3, 86], Operations: ['34-31=3', '96-10=86'] Exploring Operation: 3+86=89, Resulting Numbers: [89] 89,27 unequal: No Solution Exploring Operation: 86-3=83, Resulting Numbers: [83] 83,27 unequal: No Solution Exploring Operation: 3*86=258, Resulting Numbers: [258] 258,27 unequal: No Solution Moving to Node #0,3,2 Current State: 27:[10, 93], Operations: ['34-31=3', '96-3=93'] Exploring Operation: 10+93=103, Resulting Numbers: [103] 103,27 unequal: No Solution Exploring Operation: 10*93=930, Resulting Numbers: [930] 930,27 unequal: No Solution Exploring Operation: 93-10=83, Resulting Numbers: [83] 83,27 unequal: No Solution Moving to Node #0,3,3 Current State: 27:[96, 7], Operations: ['34-31=3', '10-3=7'] Exploring Operation: 96+7=103, Resulting Numbers: [103] 103,27 unequal: No Solution Exploring Operation: 96-7=89, Resulting Numbers: [89] 89,27 unequal: No Solution Exploring Operation: 96*7=672, Resulting Numbers: [672] 672,27 unequal: No Solution Moving to Node #0,1,3 Current State: 27:[86, 65], Operations: ['96-10=86', '34+31=65'] Exploring Operation: 86*65=5590, Resulting Numbers: [5590] 5590,27 unequal: No Solution Exploring Operation: 86-65=21, Resulting Numbers: [21] 21,27 unequal: No Solution Exploring Operation: 86+65=151, Resulting Numbers: [151] 151,27 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 79, 58, 98, 1 ]
77
[ "79-58=21", "98*1=98", "98-21=77" ]
Current State: 77:[79, 58, 98, 1], Operations: [] Exploring Operation: 79-58=21, Resulting Numbers: [98, 1, 21] Generated Node #2: [98, 1, 21] from Operation: 79-58=21 Current State: 77:[98, 1, 21], Operations: ['79-58=21'] Exploring Operation: 98*1=98, Resulting Numbers: [21, 98] Generated Node #3: [21, 98] from Operation: 98*1=98 Current State: 77:[21, 98], Operations: ['79-58=21', '98*1=98'] Exploring Operation: 98-21=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[79, 58, 98, 1], Operations: [] Exploring Operation: 58+1=59, Resulting Numbers: [79, 98, 59] Generated Node #0,0: 77:[79, 98, 59] Operation: 58+1=59 Exploring Operation: 79-1=78, Resulting Numbers: [58, 98, 78] Generated Node #0,1: 77:[58, 98, 78] Operation: 79-1=78 Exploring Operation: 98-79=19, Resulting Numbers: [58, 1, 19] Generated Node #0,2: 77:[58, 1, 19] Operation: 98-79=19 Exploring Operation: 98-58=40, Resulting Numbers: [79, 1, 40] Generated Node #0,3: 77:[79, 1, 40] Operation: 98-58=40 Exploring Operation: 79-58=21, Resulting Numbers: [98, 1, 21] Generated Node #0,4: 77:[98, 1, 21] Operation: 79-58=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[58, 1, 19], Operations: ['98-79=19'] Exploring Operation: 58/1=58, Resulting Numbers: [19, 58] Generated Node #0,2,0: 77:[19, 58] Operation: 58/1=58 Exploring Operation: 58+19=77, Resulting Numbers: [1, 77] Generated Node #0,2,1: 77:[1, 77] Operation: 58+19=77 Exploring Operation: 58+1=59, Resulting Numbers: [19, 59] Generated Node #0,2,2: 77:[19, 59] Operation: 58+1=59 Exploring Operation: 19-1=18, Resulting Numbers: [58, 18] Generated Node #0,2,3: 77:[58, 18] Operation: 19-1=18 Exploring Operation: 58*1=58, Resulting Numbers: [19, 58] Generated Node #0,2,4: 77:[19, 58] Operation: 58*1=58 Moving to Node #0,2,1 Current State: 77:[1, 77], Operations: ['98-79=19', '58+19=77'] Exploring Operation: 1+77=78, Resulting Numbers: [78] 78,77 unequal: No Solution Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[79, 58, 98, 1], Operations: [] Exploring Operation: 98-79=19, Resulting Numbers: [58, 1, 19] Generated Node #0,2: 77:[58, 1, 19] Operation: 98-79=19 Moving to Node #0,2 Current State: 77:[58, 1, 19], Operations: ['98-79=19'] Exploring Operation: 58+19=77, Resulting Numbers: [1, 77] Generated Node #0,2,1: 77:[1, 77] Operation: 58+19=77 Moving to Node #0,2,1 Current State: 77:[1, 77], Operations: ['98-79=19', '58+19=77'] Exploring Operation: 1*77=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 63, 6, 20, 23 ]
26
[ "63+6=69", "20+23=43", "69-43=26" ]
Current State: 26:[63, 6, 20, 23], Operations: [] Exploring Operation: 63+6=69, Resulting Numbers: [20, 23, 69] Generated Node #2: [20, 23, 69] from Operation: 63+6=69 Current State: 26:[20, 23, 69], Operations: ['63+6=69'] Exploring Operation: 20+23=43, Resulting Numbers: [69, 43] Generated Node #3: [69, 43] from Operation: 20+23=43 Current State: 26:[69, 43], Operations: ['63+6=69', '20+23=43'] Exploring Operation: 69-43=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[63, 6, 20, 23], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [6, 20, 40] Generated Node #0,0: 26:[6, 20, 40] Operation: 63-23=40 Exploring Operation: 63-6=57, Resulting Numbers: [20, 23, 57] Generated Node #0,1: 26:[20, 23, 57] Operation: 63-6=57 Exploring Operation: 63-20=43, Resulting Numbers: [6, 23, 43] Generated Node #0,2: 26:[6, 23, 43] Operation: 63-20=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 26:[6, 20, 40], Operations: ['63-23=40'] Exploring Operation: 40/20=2, Resulting Numbers: [6, 2] Generated Node #0,0,0: 26:[6, 2] Operation: 40/20=2 Exploring Operation: 6+20=26, Resulting Numbers: [40, 26] Generated Node #0,0,1: 26:[40, 26] Operation: 6+20=26 Exploring Operation: 40-20=20, Resulting Numbers: [6, 20] Generated Node #0,0,2: 26:[6, 20] Operation: 40-20=20 Moving to Node #0,0,0 Current State: 26:[6, 2], Operations: ['63-23=40', '40/20=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,26 unequal: No Solution Exploring Operation: 6*2=12, Resulting Numbers: [12] 12,26 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,26 unequal: No Solution Moving to Node #0,0,2 Current State: 26:[6, 20], Operations: ['63-23=40', '40-20=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[63, 6, 20, 23], Operations: [] Exploring Operation: 63-23=40, Resulting Numbers: [6, 20, 40] Generated Node #0,0: 26:[6, 20, 40] Operation: 63-23=40 Moving to Node #0,0 Current State: 26:[6, 20, 40], Operations: ['63-23=40'] Exploring Operation: 40-20=20, Resulting Numbers: [6, 20] Generated Node #0,0,2: 26:[6, 20] Operation: 40-20=20 Moving to Node #0,0,2 Current State: 26:[6, 20], Operations: ['63-23=40', '40-20=20'] Exploring Operation: 6+20=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_3
mult_heuristic
[ 15, 61, 43, 88 ]
55
[ "15+61=76", "43+88=131", "131-76=55" ]
Current State: 55:[15, 61, 43, 88], Operations: [] Exploring Operation: 15+61=76, Resulting Numbers: [43, 88, 76] Generated Node #2: [43, 88, 76] from Operation: 15+61=76 Current State: 55:[43, 88, 76], Operations: ['15+61=76'] Exploring Operation: 43+88=131, Resulting Numbers: [76, 131] Generated Node #3: [76, 131] from Operation: 43+88=131 Current State: 55:[76, 131], Operations: ['15+61=76', '43+88=131'] Exploring Operation: 131-76=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[15, 61, 43, 88], Operations: [] Exploring Operation: 88-61=27, Resulting Numbers: [15, 43, 27] Generated Node #0,0: 55:[15, 43, 27] Operation: 88-61=27 Exploring Operation: 61-43=18, Resulting Numbers: [15, 88, 18] Generated Node #0,1: 55:[15, 88, 18] Operation: 61-43=18 Exploring Operation: 88-15=73, Resulting Numbers: [61, 43, 73] Generated Node #0,2: 55:[61, 43, 73] Operation: 88-15=73 Exploring Operation: 15+43=58, Resulting Numbers: [61, 88, 58] Generated Node #0,3: 55:[61, 88, 58] Operation: 15+43=58 Exploring Operation: 88-43=45, Resulting Numbers: [15, 61, 45] Generated Node #0,4: 55:[15, 61, 45] Operation: 88-43=45 Moving to Node #0,4 Current State: 55:[15, 61, 45], Operations: ['88-43=45'] Exploring Operation: 15+45=60, Resulting Numbers: [61, 60] Generated Node #0,4,0: 55:[61, 60] Operation: 15+45=60 Exploring Operation: 45/15=3, Resulting Numbers: [61, 3] Generated Node #0,4,1: 55:[61, 3] Operation: 45/15=3 Exploring Operation: 61-45=16, Resulting Numbers: [15, 16] Generated Node #0,4,2: 55:[15, 16] Operation: 61-45=16 Exploring Operation: 45-15=30, Resulting Numbers: [61, 30] Generated Node #0,4,3: 55:[61, 30] Operation: 45-15=30 Exploring Operation: 61-15=46, Resulting Numbers: [45, 46] Generated Node #0,4,4: 55:[45, 46] Operation: 61-15=46 Moving to Node #0,0 Current State: 55:[15, 43, 27], Operations: ['88-61=27'] Exploring Operation: 15+43=58, Resulting Numbers: [27, 58] Generated Node #0,0,0: 55:[27, 58] Operation: 15+43=58 Exploring Operation: 27-15=12, Resulting Numbers: [43, 12] Generated Node #0,0,1: 55:[43, 12] Operation: 27-15=12 Exploring Operation: 43+27=70, Resulting Numbers: [15, 70] Generated Node #0,0,2: 55:[15, 70] Operation: 43+27=70 Exploring Operation: 15+27=42, Resulting Numbers: [43, 42] Generated Node #0,0,3: 55:[43, 42] Operation: 15+27=42 Exploring Operation: 43-27=16, Resulting Numbers: [15, 16] Generated Node #0,0,4: 55:[15, 16] Operation: 43-27=16 Moving to Node #0,2 Current State: 55:[61, 43, 73], Operations: ['88-15=73'] Exploring Operation: 61-43=18, Resulting Numbers: [73, 18] Generated Node #0,2,0: 55:[73, 18] Operation: 61-43=18 Exploring Operation: 61+43=104, Resulting Numbers: [73, 104] Generated Node #0,2,1: 55:[73, 104] Operation: 61+43=104 Exploring Operation: 43+73=116, Resulting Numbers: [61, 116] Generated Node #0,2,2: 55:[61, 116] Operation: 43+73=116 Exploring Operation: 73-43=30, Resulting Numbers: [61, 30] Generated Node #0,2,3: 55:[61, 30] Operation: 73-43=30 Exploring Operation: 73-61=12, Resulting Numbers: [43, 12] Generated Node #0,2,4: 55:[43, 12] Operation: 73-61=12 Moving to Node #0,3 Current State: 55:[61, 88, 58], Operations: ['15+43=58'] Exploring Operation: 61+58=119, Resulting Numbers: [88, 119] Generated Node #0,3,0: 55:[88, 119] Operation: 61+58=119 Exploring Operation: 61+88=149, Resulting Numbers: [58, 149] Generated Node #0,3,1: 55:[58, 149] Operation: 61+88=149 Exploring Operation: 88-58=30, Resulting Numbers: [61, 30] Generated Node #0,3,2: 55:[61, 30] Operation: 88-58=30 Exploring Operation: 61-58=3, Resulting Numbers: [88, 3] Generated Node #0,3,3: 55:[88, 3] Operation: 61-58=3 Exploring Operation: 88-61=27, Resulting Numbers: [58, 27] Generated Node #0,3,4: 55:[58, 27] Operation: 88-61=27 Moving to Node #0,1 Current State: 55:[15, 88, 18], Operations: ['61-43=18'] Exploring Operation: 88-18=70, Resulting Numbers: [15, 70] Generated Node #0,1,0: 55:[15, 70] Operation: 88-18=70 Exploring Operation: 18-15=3, Resulting Numbers: [88, 3] Generated Node #0,1,1: 55:[88, 3] Operation: 18-15=3 Exploring Operation: 15+18=33, Resulting Numbers: [88, 33] Generated Node #0,1,2: 55:[88, 33] Operation: 15+18=33 Exploring Operation: 15+88=103, Resulting Numbers: [18, 103] Generated Node #0,1,3: 55:[18, 103] Operation: 15+88=103 Exploring Operation: 88-15=73, Resulting Numbers: [18, 73] Generated Node #0,1,4: 55:[18, 73] Operation: 88-15=73 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 55:[15, 70], Operations: ['61-43=18', '88-18=70'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[15, 61, 43, 88], Operations: [] Exploring Operation: 61-43=18, Resulting Numbers: [15, 88, 18] Generated Node #0,1: 55:[15, 88, 18] Operation: 61-43=18 Moving to Node #0,1 Current State: 55:[15, 88, 18], Operations: ['61-43=18'] Exploring Operation: 88-18=70, Resulting Numbers: [15, 70] Generated Node #0,1,0: 55:[15, 70] Operation: 88-18=70 Moving to Node #0,1,0 Current State: 55:[15, 70], Operations: ['61-43=18', '88-18=70'] Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
sum_heuristic
[ 28, 31, 79, 94 ]
74
[ "28+31=59", "94-79=15", "59+15=74" ]
Current State: 74:[28, 31, 79, 94], Operations: [] Exploring Operation: 28+31=59, Resulting Numbers: [79, 94, 59] Generated Node #2: [79, 94, 59] from Operation: 28+31=59 Current State: 74:[79, 94, 59], Operations: ['28+31=59'] Exploring Operation: 94-79=15, Resulting Numbers: [59, 15] Generated Node #3: [59, 15] from Operation: 94-79=15 Current State: 74:[59, 15], Operations: ['28+31=59', '94-79=15'] Exploring Operation: 59+15=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[28, 31, 79, 94], Operations: [] Exploring Operation: 94-31=63, Resulting Numbers: [28, 79, 63] Generated Node #0,0: 74:[28, 79, 63] Operation: 94-31=63 Exploring Operation: 94-28=66, Resulting Numbers: [31, 79, 66] Generated Node #0,1: 74:[31, 79, 66] Operation: 94-28=66 Exploring Operation: 94-79=15, Resulting Numbers: [28, 31, 15] Generated Node #0,2: 74:[28, 31, 15] Operation: 94-79=15 Exploring Operation: 31-28=3, Resulting Numbers: [79, 94, 3] Generated Node #0,3: 74:[79, 94, 3] Operation: 31-28=3 Moving to Node #0,1 Current State: 74:[31, 79, 66], Operations: ['94-28=66'] Exploring Operation: 79-31=48, Resulting Numbers: [66, 48] Generated Node #0,1,0: 74:[66, 48] Operation: 79-31=48 Exploring Operation: 79-66=13, Resulting Numbers: [31, 13] Generated Node #0,1,1: 74:[31, 13] Operation: 79-66=13 Exploring Operation: 66-31=35, Resulting Numbers: [79, 35] Generated Node #0,1,2: 74:[79, 35] Operation: 66-31=35 Exploring Operation: 31+66=97, Resulting Numbers: [79, 97] Generated Node #0,1,3: 74:[79, 97] Operation: 31+66=97 Moving to Node #0,0 Current State: 74:[28, 79, 63], Operations: ['94-31=63'] Exploring Operation: 28+63=91, Resulting Numbers: [79, 91] Generated Node #0,0,0: 74:[79, 91] Operation: 28+63=91 Exploring Operation: 63-28=35, Resulting Numbers: [79, 35] Generated Node #0,0,1: 74:[79, 35] Operation: 63-28=35 Exploring Operation: 79-28=51, Resulting Numbers: [63, 51] Generated Node #0,0,2: 74:[63, 51] Operation: 79-28=51 Exploring Operation: 79-63=16, Resulting Numbers: [28, 16] Generated Node #0,0,3: 74:[28, 16] Operation: 79-63=16 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[79, 35], Operations: ['94-31=63', '63-28=35'] Exploring Operation: 79+35=114, Resulting Numbers: [114] 114,74 unequal: No Solution Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,74 unequal: No Solution Exploring Operation: 79*35=2765, Resulting Numbers: [2765] 2765,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[79, 91], Operations: ['94-31=63', '28+63=91'] Exploring Operation: 79*91=7189, Resulting Numbers: [7189] 7189,74 unequal: No Solution Exploring Operation: 79+91=170, Resulting Numbers: [170] 170,74 unequal: No Solution Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[28, 16], Operations: ['94-31=63', '79-63=16'] Exploring Operation: 28*16=448, Resulting Numbers: [448] 448,74 unequal: No Solution Exploring Operation: 28-16=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 28+16=44, Resulting Numbers: [44] 44,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[63, 51], Operations: ['94-31=63', '79-28=51'] Exploring Operation: 63-51=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 63+51=114, Resulting Numbers: [114] 114,74 unequal: No Solution Exploring Operation: 63*51=3213, Resulting Numbers: [3213] 3213,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 74:[79, 94, 3], Operations: ['31-28=3'] Exploring Operation: 94-3=91, Resulting Numbers: [79, 91] Generated Node #0,3,0: 74:[79, 91] Operation: 94-3=91 Exploring Operation: 94-79=15, Resulting Numbers: [3, 15] Generated Node #0,3,1: 74:[3, 15] Operation: 94-79=15 Exploring Operation: 79+3=82, Resulting Numbers: [94, 82] Generated Node #0,3,2: 74:[94, 82] Operation: 79+3=82 Exploring Operation: 79-3=76, Resulting Numbers: [94, 76] Generated Node #0,3,3: 74:[94, 76] Operation: 79-3=76 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[3, 15], Operations: ['31-28=3', '94-79=15'] Exploring Operation: 3+15=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 3*15=45, Resulting Numbers: [45] 45,74 unequal: No Solution Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[79, 91], Operations: ['31-28=3', '94-3=91'] Exploring Operation: 91-79=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 79*91=7189, Resulting Numbers: [7189] 7189,74 unequal: No Solution Exploring Operation: 79+91=170, Resulting Numbers: [170] 170,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[94, 76], Operations: ['31-28=3', '79-3=76'] Exploring Operation: 94-76=18, Resulting Numbers: [18] 18,74 unequal: No Solution Exploring Operation: 94*76=7144, Resulting Numbers: [7144] 7144,74 unequal: No Solution Exploring Operation: 94+76=170, Resulting Numbers: [170] 170,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[94, 82], Operations: ['31-28=3', '79+3=82'] Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,74 unequal: No Solution Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,74 unequal: No Solution Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,74 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: 74:[28, 31, 15], Operations: ['94-79=15'] Exploring Operation: 28+15=43, Resulting Numbers: [31, 43] Generated Node #0,2,0: 74:[31, 43] Operation: 28+15=43 Exploring Operation: 28-15=13, Resulting Numbers: [31, 13] Generated Node #0,2,1: 74:[31, 13] Operation: 28-15=13 Exploring Operation: 31+15=46, Resulting Numbers: [28, 46] Generated Node #0,2,2: 74:[28, 46] Operation: 31+15=46 Exploring Operation: 31-28=3, Resulting Numbers: [15, 3] Generated Node #0,2,3: 74:[15, 3] Operation: 31-28=3 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 74:[31, 43], Operations: ['94-79=15', '28+15=43'] Exploring Operation: 31*43=1333, Resulting Numbers: [1333] 1333,74 unequal: No Solution Exploring Operation: 31+43=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[28, 31, 79, 94], Operations: [] Exploring Operation: 94-79=15, Resulting Numbers: [28, 31, 15] Generated Node #0,2: 74:[28, 31, 15] Operation: 94-79=15 Moving to Node #0,2 Current State: 74:[28, 31, 15], Operations: ['94-79=15'] Exploring Operation: 28+15=43, Resulting Numbers: [31, 43] Generated Node #0,2,0: 74:[31, 43] Operation: 28+15=43 Moving to Node #0,2,0 Current State: 74:[31, 43], Operations: ['94-79=15', '28+15=43'] Exploring Operation: 31+43=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.955729
hs_4
sum_heuristic
[ 14, 54, 2, 19 ]
75
[ "14+19=33", "54*2=108", "108-33=75" ]
Current State: 75:[14, 54, 2, 19], Operations: [] Exploring Operation: 14+19=33, Resulting Numbers: [54, 2, 33] Generated Node #2: [54, 2, 33] from Operation: 14+19=33 Current State: 75:[54, 2, 33], Operations: ['14+19=33'] Exploring Operation: 54*2=108, Resulting Numbers: [33, 108] Generated Node #3: [33, 108] from Operation: 54*2=108 Current State: 75:[33, 108], Operations: ['14+19=33', '54*2=108'] Exploring Operation: 108-33=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[14, 54, 2, 19], Operations: [] Exploring Operation: 54/2=27, Resulting Numbers: [14, 19, 27] Generated Node #0,0: 75:[14, 19, 27] Operation: 54/2=27 Exploring Operation: 54+19=73, Resulting Numbers: [14, 2, 73] Generated Node #0,1: 75:[14, 2, 73] Operation: 54+19=73 Exploring Operation: 54-19=35, Resulting Numbers: [14, 2, 35] Generated Node #0,2: 75:[14, 2, 35] Operation: 54-19=35 Exploring Operation: 14+54=68, Resulting Numbers: [2, 19, 68] Generated Node #0,3: 75:[2, 19, 68] Operation: 14+54=68 Moving to Node #0,1 Current State: 75:[14, 2, 73], Operations: ['54+19=73'] Exploring Operation: 14/2=7, Resulting Numbers: [73, 7] Generated Node #0,1,0: 75:[73, 7] Operation: 14/2=7 Exploring Operation: 2+73=75, Resulting Numbers: [14, 75] Generated Node #0,1,1: 75:[14, 75] Operation: 2+73=75 Exploring Operation: 14+2=16, Resulting Numbers: [73, 16] Generated Node #0,1,2: 75:[73, 16] Operation: 14+2=16 Exploring Operation: 14*2=28, Resulting Numbers: [73, 28] Generated Node #0,1,3: 75:[73, 28] Operation: 14*2=28 Moving to Node #0,0 Current State: 75:[14, 19, 27], Operations: ['54/2=27'] Exploring Operation: 19-14=5, Resulting Numbers: [27, 5] Generated Node #0,0,0: 75:[27, 5] Operation: 19-14=5 Exploring Operation: 27-19=8, Resulting Numbers: [14, 8] Generated Node #0,0,1: 75:[14, 8] Operation: 27-19=8 Exploring Operation: 27-14=13, Resulting Numbers: [19, 13] Generated Node #0,0,2: 75:[19, 13] Operation: 27-14=13 Exploring Operation: 14+19=33, Resulting Numbers: [27, 33] Generated Node #0,0,3: 75:[27, 33] Operation: 14+19=33 Moving to Node #0,3 Current State: 75:[2, 19, 68], Operations: ['14+54=68'] Exploring Operation: 2+68=70, Resulting Numbers: [19, 70] Generated Node #0,3,0: 75:[19, 70] Operation: 2+68=70 Exploring Operation: 19-2=17, Resulting Numbers: [68, 17] Generated Node #0,3,1: 75:[68, 17] Operation: 19-2=17 Exploring Operation: 68-2=66, Resulting Numbers: [19, 66] Generated Node #0,3,2: 75:[19, 66] Operation: 68-2=66 Exploring Operation: 2+19=21, Resulting Numbers: [68, 21] Generated Node #0,3,3: 75:[68, 21] Operation: 2+19=21 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 75:[19, 70], Operations: ['14+54=68', '2+68=70'] Exploring Operation: 70-19=51, Resulting Numbers: [51] 51,75 unequal: No Solution Exploring Operation: 19*70=1330, Resulting Numbers: [1330] 1330,75 unequal: No Solution Exploring Operation: 19+70=89, Resulting Numbers: [89] 89,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 75:[68, 17], Operations: ['14+54=68', '19-2=17'] Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,75 unequal: No Solution Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,75 unequal: No Solution Exploring Operation: 68*17=1156, Resulting Numbers: [1156] 1156,75 unequal: No Solution Exploring Operation: 68+17=85, Resulting Numbers: [85] 85,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 75:[68, 21], Operations: ['14+54=68', '2+19=21'] Exploring Operation: 68-21=47, Resulting Numbers: [47] 47,75 unequal: No Solution Exploring Operation: 68+21=89, Resulting Numbers: [89] 89,75 unequal: No Solution Exploring Operation: 68*21=1428, Resulting Numbers: [1428] 1428,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 75:[19, 66], Operations: ['14+54=68', '68-2=66'] Exploring Operation: 19*66=1254, Resulting Numbers: [1254] 1254,75 unequal: No Solution Exploring Operation: 66-19=47, Resulting Numbers: [47] 47,75 unequal: No Solution Exploring Operation: 19+66=85, Resulting Numbers: [85] 85,75 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: 75:[14, 2, 35], Operations: ['54-19=35'] Exploring Operation: 35-14=21, Resulting Numbers: [2, 21] Generated Node #0,2,0: 75:[2, 21] Operation: 35-14=21 Exploring Operation: 35-2=33, Resulting Numbers: [14, 33] Generated Node #0,2,1: 75:[14, 33] Operation: 35-2=33 Exploring Operation: 14+2=16, Resulting Numbers: [35, 16] Generated Node #0,2,2: 75:[35, 16] Operation: 14+2=16 Exploring Operation: 2*35=70, Resulting Numbers: [14, 70] Generated Node #0,2,3: 75:[14, 70] Operation: 2*35=70 Moving to Node #0,1,1 Current State: 75:[14, 75], Operations: ['54+19=73', '2+73=75'] Exploring Operation: 14*75=1050, Resulting Numbers: [1050] 1050,75 unequal: No Solution Exploring Operation: 75-14=61, Resulting Numbers: [61] 61,75 unequal: No Solution Exploring Operation: 14+75=89, Resulting Numbers: [89] 89,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[27, 5], Operations: ['54/2=27', '19-14=5'] Exploring Operation: 27*5=135, Resulting Numbers: [135] 135,75 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,75 unequal: No Solution Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[73, 16], Operations: ['54+19=73', '14+2=16'] Exploring Operation: 73-16=57, Resulting Numbers: [57] 57,75 unequal: No Solution Exploring Operation: 73*16=1168, Resulting Numbers: [1168] 1168,75 unequal: No Solution Exploring Operation: 73+16=89, Resulting Numbers: [89] 89,75 unequal: No Solution Moving to Node #0,1,0 Current State: 75:[73, 7], Operations: ['54+19=73', '14/2=7'] Exploring Operation: 73*7=511, Resulting Numbers: [511] 511,75 unequal: No Solution Exploring Operation: 73-7=66, Resulting Numbers: [66] 66,75 unequal: No Solution Exploring Operation: 73+7=80, Resulting Numbers: [80] 80,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[14, 8], Operations: ['54/2=27', '27-19=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,75 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[73, 28], Operations: ['54+19=73', '14*2=28'] Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,75 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,75 unequal: No Solution Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[2, 21], Operations: ['54-19=35', '35-14=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,75 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[19, 13], Operations: ['54/2=27', '27-14=13'] Exploring Operation: 19*13=247, Resulting Numbers: [247] 247,75 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 19+13=32, Resulting Numbers: [32] 32,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[14, 70], Operations: ['54-19=35', '2*35=70'] Exploring Operation: 70/14=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 14*70=980, Resulting Numbers: [980] 980,75 unequal: No Solution Exploring Operation: 14+70=84, Resulting Numbers: [84] 84,75 unequal: No Solution Exploring Operation: 70-14=56, Resulting Numbers: [56] 56,75 unequal: No Solution Moving to Node #0,2,1 Current State: 75:[14, 33], Operations: ['54-19=35', '35-2=33'] Exploring Operation: 14*33=462, Resulting Numbers: [462] 462,75 unequal: No Solution Exploring Operation: 33-14=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 14+33=47, Resulting Numbers: [47] 47,75 unequal: No Solution Moving to Node #0,0,3 Current State: 75:[27, 33], Operations: ['54/2=27', '14+19=33'] Exploring Operation: 27*33=891, Resulting Numbers: [891] 891,75 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 27+33=60, Resulting Numbers: [60] 60,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[35, 16], Operations: ['54-19=35', '14+2=16'] Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,75 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,75 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,75 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 23, 17, 55, 18 ]
79
[ "23-17=6", "55+18=73", "6+73=79" ]
Current State: 79:[23, 17, 55, 18], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [55, 18, 6] Generated Node #2: [55, 18, 6] from Operation: 23-17=6 Current State: 79:[55, 18, 6], Operations: ['23-17=6'] Exploring Operation: 55+18=73, Resulting Numbers: [6, 73] Generated Node #3: [6, 73] from Operation: 55+18=73 Current State: 79:[6, 73], Operations: ['23-17=6', '55+18=73'] Exploring Operation: 6+73=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[23, 17, 55, 18], Operations: [] Exploring Operation: 17+55=72, Resulting Numbers: [23, 18, 72] Generated Node #0,0: 79:[23, 18, 72] Operation: 17+55=72 Exploring Operation: 23+17=40, Resulting Numbers: [55, 18, 40] Generated Node #0,1: 79:[55, 18, 40] Operation: 23+17=40 Exploring Operation: 23+18=41, Resulting Numbers: [17, 55, 41] Generated Node #0,2: 79:[17, 55, 41] Operation: 23+18=41 Exploring Operation: 17+18=35, Resulting Numbers: [23, 55, 35] Generated Node #0,3: 79:[23, 55, 35] Operation: 17+18=35 Exploring Operation: 23+55=78, Resulting Numbers: [17, 18, 78] Generated Node #0,4: 79:[17, 18, 78] Operation: 23+55=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[23, 18, 72], Operations: ['17+55=72'] Exploring Operation: 23-18=5, Resulting Numbers: [72, 5] Generated Node #0,0,0: 79:[72, 5] Operation: 23-18=5 Exploring Operation: 18+72=90, Resulting Numbers: [23, 90] Generated Node #0,0,1: 79:[23, 90] Operation: 18+72=90 Exploring Operation: 23+18=41, Resulting Numbers: [72, 41] Generated Node #0,0,2: 79:[72, 41] Operation: 23+18=41 Exploring Operation: 23+72=95, Resulting Numbers: [18, 95] Generated Node #0,0,3: 79:[18, 95] Operation: 23+72=95 Exploring Operation: 72-18=54, Resulting Numbers: [23, 54] Generated Node #0,0,4: 79:[23, 54] Operation: 72-18=54 Moving to Node #0,0,2 Current State: 79:[72, 41], Operations: ['17+55=72', '23+18=41'] Exploring Operation: 72-41=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 72*41=2952, Resulting Numbers: [2952] 2952,79 unequal: No Solution Exploring Operation: 72+41=113, Resulting Numbers: [113] 113,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[23, 90], Operations: ['17+55=72', '18+72=90'] Exploring Operation: 23+90=113, Resulting Numbers: [113] 113,79 unequal: No Solution Exploring Operation: 90-23=67, Resulting Numbers: [67] 67,79 unequal: No Solution Exploring Operation: 23*90=2070, Resulting Numbers: [2070] 2070,79 unequal: No Solution Moving to Node #0,0,3 Current State: 79:[18, 95], Operations: ['17+55=72', '23+72=95'] Exploring Operation: 18*95=1710, Resulting Numbers: [1710] 1710,79 unequal: No Solution Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 18+95=113, Resulting Numbers: [113] 113,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[72, 5], Operations: ['17+55=72', '23-18=5'] Exploring Operation: 72*5=360, Resulting Numbers: [360] 360,79 unequal: No Solution Exploring Operation: 72+5=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,79 unequal: No Solution Moving to Node #0,0,4 Current State: 79:[23, 54], Operations: ['17+55=72', '72-18=54'] Exploring Operation: 54-23=31, Resulting Numbers: [31] 31,79 unequal: No Solution Exploring Operation: 23*54=1242, Resulting Numbers: [1242] 1242,79 unequal: No Solution Exploring Operation: 23+54=77, Resulting Numbers: [77] 77,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 79:[55, 18, 40], Operations: ['23+17=40'] Exploring Operation: 18+40=58, Resulting Numbers: [55, 58] Generated Node #0,1,0: 79:[55, 58] Operation: 18+40=58 Exploring Operation: 55-18=37, Resulting Numbers: [40, 37] Generated Node #0,1,1: 79:[40, 37] Operation: 55-18=37 Exploring Operation: 40-18=22, Resulting Numbers: [55, 22] Generated Node #0,1,2: 79:[55, 22] Operation: 40-18=22 Exploring Operation: 55+40=95, Resulting Numbers: [18, 95] Generated Node #0,1,3: 79:[18, 95] Operation: 55+40=95 Exploring Operation: 55+18=73, Resulting Numbers: [40, 73] Generated Node #0,1,4: 79:[40, 73] Operation: 55+18=73 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 79:[55, 58], Operations: ['23+17=40', '18+40=58'] Exploring Operation: 55+58=113, Resulting Numbers: [113] 113,79 unequal: No Solution Exploring Operation: 55*58=3190, Resulting Numbers: [3190] 3190,79 unequal: No Solution Exploring Operation: 58-55=3, Resulting Numbers: [3] 3,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 79:[40, 73], Operations: ['23+17=40', '55+18=73'] Exploring Operation: 40+73=113, Resulting Numbers: [113] 113,79 unequal: No Solution Exploring Operation: 73-40=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 40*73=2920, Resulting Numbers: [2920] 2920,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 79:[18, 95], Operations: ['23+17=40', '55+40=95'] Exploring Operation: 18*95=1710, Resulting Numbers: [1710] 1710,79 unequal: No Solution Exploring Operation: 18+95=113, Resulting Numbers: [113] 113,79 unequal: No Solution Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 79:[40, 37], Operations: ['23+17=40', '55-18=37'] Exploring Operation: 40-37=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 40+37=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 40*37=1480, Resulting Numbers: [1480] 1480,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 79:[55, 22], Operations: ['23+17=40', '40-18=22'] Exploring Operation: 55+22=77, Resulting Numbers: [77] 77,79 unequal: No Solution Exploring Operation: 55-22=33, Resulting Numbers: [33] 33,79 unequal: No Solution Exploring Operation: 55*22=1210, Resulting Numbers: [1210] 1210,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 79:[17, 55, 41], Operations: ['23+18=41'] Exploring Operation: 55-17=38, Resulting Numbers: [41, 38] Generated Node #0,2,0: 79:[41, 38] Operation: 55-17=38 Exploring Operation: 41-17=24, Resulting Numbers: [55, 24] Generated Node #0,2,1: 79:[55, 24] Operation: 41-17=24 Exploring Operation: 55+41=96, Resulting Numbers: [17, 96] Generated Node #0,2,2: 79:[17, 96] Operation: 55+41=96 Exploring Operation: 17+41=58, Resulting Numbers: [55, 58] Generated Node #0,2,3: 79:[55, 58] Operation: 17+41=58 Exploring Operation: 17+55=72, Resulting Numbers: [41, 72] Generated Node #0,2,4: 79:[41, 72] Operation: 17+55=72 Moving to Node #0,2,3 Current State: 79:[55, 58], Operations: ['23+18=41', '17+41=58'] Exploring Operation: 58-55=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 55*58=3190, Resulting Numbers: [3190] 3190,79 unequal: No Solution Exploring Operation: 55+58=113, Resulting Numbers: [113] 113,79 unequal: No Solution Moving to Node #0,2,4 Current State: 79:[41, 72], Operations: ['23+18=41', '17+55=72'] Exploring Operation: 41*72=2952, Resulting Numbers: [2952] 2952,79 unequal: No Solution Exploring Operation: 41+72=113, Resulting Numbers: [113] 113,79 unequal: No Solution Exploring Operation: 72-41=31, Resulting Numbers: [31] 31,79 unequal: No Solution Moving to Node #0,2,0 Current State: 79:[41, 38], Operations: ['23+18=41', '55-17=38'] Exploring Operation: 41-38=3, Resulting Numbers: [3] 3,79 unequal: No Solution Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[23, 17, 55, 18], Operations: [] Exploring Operation: 23+18=41, Resulting Numbers: [17, 55, 41] Generated Node #0,2: 79:[17, 55, 41] Operation: 23+18=41 Moving to Node #0,2 Current State: 79:[17, 55, 41], Operations: ['23+18=41'] Exploring Operation: 55-17=38, Resulting Numbers: [41, 38] Generated Node #0,2,0: 79:[41, 38] Operation: 55-17=38 Moving to Node #0,2,0 Current State: 79:[41, 38], Operations: ['23+18=41', '55-17=38'] Exploring Operation: 41+38=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 1
0.946181
hs_5
mult_heuristic
[ 57, 43, 12, 77 ]
91
[ "57-43=14", "12*14=168", "168-77=91" ]
Current State: 91:[57, 43, 12, 77], Operations: [] Exploring Operation: 57-43=14, Resulting Numbers: [12, 77, 14] Generated Node #2: [12, 77, 14] from Operation: 57-43=14 Current State: 91:[12, 77, 14], Operations: ['57-43=14'] Exploring Operation: 12*14=168, Resulting Numbers: [77, 168] Generated Node #3: [77, 168] from Operation: 12*14=168 Current State: 91:[77, 168], Operations: ['57-43=14', '12*14=168'] Exploring Operation: 168-77=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[57, 43, 12, 77], Operations: [] Exploring Operation: 57+43=100, Resulting Numbers: [12, 77, 100] Generated Node #0,0: 91:[12, 77, 100] Operation: 57+43=100 Exploring Operation: 77-43=34, Resulting Numbers: [57, 12, 34] Generated Node #0,1: 91:[57, 12, 34] Operation: 77-43=34 Exploring Operation: 57-43=14, Resulting Numbers: [12, 77, 14] Generated Node #0,2: 91:[12, 77, 14] Operation: 57-43=14 Exploring Operation: 43+77=120, Resulting Numbers: [57, 12, 120] Generated Node #0,3: 91:[57, 12, 120] Operation: 43+77=120 Exploring Operation: 77-57=20, Resulting Numbers: [43, 12, 20] Generated Node #0,4: 91:[43, 12, 20] Operation: 77-57=20 Start Sub Search at level 1: Moving to Node #0,2 Current State: 91:[12, 77, 14], Operations: ['57-43=14'] Exploring Operation: 12+77=89, Resulting Numbers: [14, 89] Generated Node #0,2,0: 91:[14, 89] Operation: 12+77=89 Exploring Operation: 77+14=91, Resulting Numbers: [12, 91] Generated Node #0,2,1: 91:[12, 91] Operation: 77+14=91 Exploring Operation: 14-12=2, Resulting Numbers: [77, 2] Generated Node #0,2,2: 91:[77, 2] Operation: 14-12=2 Exploring Operation: 77-12=65, Resulting Numbers: [14, 65] Generated Node #0,2,3: 91:[14, 65] Operation: 77-12=65 Exploring Operation: 12+14=26, Resulting Numbers: [77, 26] Generated Node #0,2,4: 91:[77, 26] Operation: 12+14=26 Moving to Node #0,2,1 Current State: 91:[12, 91], Operations: ['57-43=14', '77+14=91'] Exploring Operation: 12+91=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,91 unequal: No Solution Exploring Operation: 12*91=1092, Resulting Numbers: [1092] 1092,91 unequal: No Solution Moving to Node #0,2,0 Current State: 91:[14, 89], Operations: ['57-43=14', '12+77=89'] Exploring Operation: 14+89=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 14*89=1246, Resulting Numbers: [1246] 1246,91 unequal: No Solution Exploring Operation: 89-14=75, Resulting Numbers: [75] 75,91 unequal: No Solution Moving to Node #0,2,2 Current State: 91:[77, 2], Operations: ['57-43=14', '14-12=2'] Exploring Operation: 77*2=154, Resulting Numbers: [154] 154,91 unequal: No Solution Exploring Operation: 77-2=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 77+2=79, Resulting Numbers: [79] 79,91 unequal: No Solution Moving to Node #0,2,3 Current State: 91:[14, 65], Operations: ['57-43=14', '77-12=65'] Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,91 unequal: No Solution Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,91 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,91 unequal: No Solution Moving to Node #0,2,4 Current State: 91:[77, 26], Operations: ['57-43=14', '12+14=26'] Exploring Operation: 77+26=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 77*26=2002, Resulting Numbers: [2002] 2002,91 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 Current State: 91:[12, 77, 100], Operations: ['57+43=100'] Exploring Operation: 12+100=112, Resulting Numbers: [77, 112] Generated Node #0,0,0: 91:[77, 112] Operation: 12+100=112 Exploring Operation: 100-12=88, Resulting Numbers: [77, 88] Generated Node #0,0,1: 91:[77, 88] Operation: 100-12=88 Exploring Operation: 77-12=65, Resulting Numbers: [100, 65] Generated Node #0,0,2: 91:[100, 65] Operation: 77-12=65 Exploring Operation: 12+77=89, Resulting Numbers: [100, 89] Generated Node #0,0,3: 91:[100, 89] Operation: 12+77=89 Exploring Operation: 100-77=23, Resulting Numbers: [12, 23] Generated Node #0,0,4: 91:[12, 23] Operation: 100-77=23 Moving to Node #0,0,3 Current State: 91:[100, 89], Operations: ['57+43=100', '12+77=89'] Exploring Operation: 100-89=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 100+89=189, Resulting Numbers: [189] 189,91 unequal: No Solution Exploring Operation: 100*89=8900, Resulting Numbers: [8900] 8900,91 unequal: No Solution Moving to Node #0,0,4 Current State: 91:[12, 23], Operations: ['57+43=100', '100-77=23'] Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,91 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,91 unequal: No Solution Moving to Node #0,0,1 Current State: 91:[77, 88], Operations: ['57+43=100', '100-12=88'] Exploring Operation: 77+88=165, Resulting Numbers: [165] 165,91 unequal: No Solution Exploring Operation: 88-77=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 77*88=6776, Resulting Numbers: [6776] 6776,91 unequal: No Solution Moving to Node #0,0,0 Current State: 91:[77, 112], Operations: ['57+43=100', '12+100=112'] Exploring Operation: 112-77=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 77+112=189, Resulting Numbers: [189] 189,91 unequal: No Solution Exploring Operation: 77*112=8624, Resulting Numbers: [8624] 8624,91 unequal: No Solution Moving to Node #0,0,2 Current State: 91:[100, 65], Operations: ['57+43=100', '77-12=65'] Exploring Operation: 100+65=165, Resulting Numbers: [165] 165,91 unequal: No Solution Exploring Operation: 100*65=6500, Resulting Numbers: [6500] 6500,91 unequal: No Solution Exploring Operation: 100-65=35, Resulting Numbers: [35] 35,91 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 #0,4 Current State: 91:[43, 12, 20], Operations: ['77-57=20'] Exploring Operation: 43+12=55, Resulting Numbers: [20, 55] Generated Node #0,4,0: 91:[20, 55] Operation: 43+12=55 Exploring Operation: 43+20=63, Resulting Numbers: [12, 63] Generated Node #0,4,1: 91:[12, 63] Operation: 43+20=63 Exploring Operation: 20-12=8, Resulting Numbers: [43, 8] Generated Node #0,4,2: 91:[43, 8] Operation: 20-12=8 Exploring Operation: 43-20=23, Resulting Numbers: [12, 23] Generated Node #0,4,3: 91:[12, 23] Operation: 43-20=23 Exploring Operation: 43-12=31, Resulting Numbers: [20, 31] Generated Node #0,4,4: 91:[20, 31] Operation: 43-12=31 Moving to Node #0,4,3 Current State: 91:[12, 23], Operations: ['77-57=20', '43-20=23'] Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,91 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,91 unequal: No Solution Moving to Node #0,4,4 Current State: 91:[20, 31], Operations: ['77-57=20', '43-12=31'] Exploring Operation: 20+31=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 20*31=620, Resulting Numbers: [620] 620,91 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,91 unequal: No Solution Moving to Node #0,4,1 Current State: 91:[12, 63], Operations: ['77-57=20', '43+20=63'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 12*63=756, Resulting Numbers: [756] 756,91 unequal: No Solution Exploring Operation: 12+63=75, Resulting Numbers: [75] 75,91 unequal: No Solution Moving to Node #0,4,2 Current State: 91:[43, 8], Operations: ['77-57=20', '20-12=8'] Exploring Operation: 43+8=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 43*8=344, Resulting Numbers: [344] 344,91 unequal: No Solution Exploring Operation: 43-8=35, Resulting Numbers: [35] 35,91 unequal: No Solution Moving to Node #0,4,0 Current State: 91:[20, 55], Operations: ['77-57=20', '43+12=55'] Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,91 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,91 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 #0,1 Current State: 91:[57, 12, 34], Operations: ['77-43=34'] Exploring Operation: 57-12=45, Resulting Numbers: [34, 45] Generated Node #0,1,0: 91:[34, 45] Operation: 57-12=45 Exploring Operation: 57+12=69, Resulting Numbers: [34, 69] Generated Node #0,1,1: 91:[34, 69] Operation: 57+12=69 Exploring Operation: 34-12=22, Resulting Numbers: [57, 22] Generated Node #0,1,2: 91:[57, 22] Operation: 34-12=22 Exploring Operation: 57-34=23, Resulting Numbers: [12, 23] Generated Node #0,1,3: 91:[12, 23] Operation: 57-34=23 Exploring Operation: 57+34=91, Resulting Numbers: [12, 91] Generated Node #0,1,4: 91:[12, 91] Operation: 57+34=91 Moving to Node #0,1,4 Current State: 91:[12, 91], Operations: ['77-43=34', '57+34=91'] Exploring Operation: 12+91=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,91 unequal: No Solution Exploring Operation: 12*91=1092, Resulting Numbers: [1092] 1092,91 unequal: No Solution Moving to Node #0,1,3 Current State: 91:[12, 23], Operations: ['77-43=34', '57-34=23'] Exploring Operation: 12*23=276, Resulting Numbers: [276] 276,91 unequal: No Solution Exploring Operation: 12+23=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 23-12=11, Resulting Numbers: [11] 11,91 unequal: No Solution Moving to Node #0,1,1 Current State: 91:[34, 69], Operations: ['77-43=34', '57+12=69'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 34+69=103, Resulting Numbers: [103] 103,91 unequal: No Solution Exploring Operation: 34*69=2346, Resulting Numbers: [2346] 2346,91 unequal: No Solution Moving to Node #0,1,2 Current State: 91:[57, 22], Operations: ['77-43=34', '34-12=22'] Exploring Operation: 57+22=79, Resulting Numbers: [79] 79,91 unequal: No Solution Exploring Operation: 57-22=35, Resulting Numbers: [35] 35,91 unequal: No Solution Exploring Operation: 57*22=1254, Resulting Numbers: [1254] 1254,91 unequal: No Solution Moving to Node #0,1,0 Current State: 91:[34, 45], Operations: ['77-43=34', '57-12=45'] Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,91 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,91 unequal: No Solution Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,91 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 #0,3 Current State: 91:[57, 12, 120], Operations: ['43+77=120'] Exploring Operation: 120/12=10, Resulting Numbers: [57, 10] Generated Node #0,3,0: 91:[57, 10] Operation: 120/12=10 Exploring Operation: 57-12=45, Resulting Numbers: [120, 45] Generated Node #0,3,1: 91:[120, 45] Operation: 57-12=45 Exploring Operation: 57+12=69, Resulting Numbers: [120, 69] Generated Node #0,3,2: 91:[120, 69] Operation: 57+12=69 Exploring Operation: 120-12=108, Resulting Numbers: [57, 108] Generated Node #0,3,3: 91:[57, 108] Operation: 120-12=108 Exploring Operation: 120-57=63, Resulting Numbers: [12, 63] Generated Node #0,3,4: 91:[12, 63] Operation: 120-57=63 Moving to Node #0,3,4 Current State: 91:[12, 63], Operations: ['43+77=120', '120-57=63'] Exploring Operation: 12+63=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 12*63=756, Resulting Numbers: [756] 756,91 unequal: No Solution Moving to Node #0,3,0 Current State: 91:[57, 10], Operations: ['43+77=120', '120/12=10'] Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,91 unequal: No Solution Exploring Operation: 57*10=570, Resulting Numbers: [570] 570,91 unequal: No Solution Exploring Operation: 57+10=67, Resulting Numbers: [67] 67,91 unequal: No Solution Moving to Node #0,3,2 Current State: 91:[120, 69], Operations: ['43+77=120', '57+12=69'] Exploring Operation: 120+69=189, Resulting Numbers: [189] 189,91 unequal: No Solution Exploring Operation: 120-69=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 120*69=8280, Resulting Numbers: [8280] 8280,91 unequal: No Solution Moving to Node #0,3,3 Current State: 91:[57, 108], Operations: ['43+77=120', '120-12=108'] Exploring Operation: 57+108=165, Resulting Numbers: [165] 165,91 unequal: No Solution Exploring Operation: 108-57=51, Resulting Numbers: [51] 51,91 unequal: No Solution Exploring Operation: 57*108=6156, Resulting Numbers: [6156] 6156,91 unequal: No Solution Moving to Node #0,3,1 Current State: 91:[120, 45], Operations: ['43+77=120', '57-12=45'] Exploring Operation: 120-45=75, Resulting Numbers: [75] 75,91 unequal: No Solution Exploring Operation: 120*45=5400, Resulting Numbers: [5400] 5400,91 unequal: No Solution Exploring Operation: 120+45=165, Resulting Numbers: [165] 165,91 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 32, 98, 18, 16 ]
40
[ "32/16=2", "98-18=80", "80/2=40" ]
Current State: 40:[32, 98, 18, 16], Operations: [] Exploring Operation: 32/16=2, Resulting Numbers: [98, 18, 2] Generated Node #2: [98, 18, 2] from Operation: 32/16=2 Current State: 40:[98, 18, 2], Operations: ['32/16=2'] Exploring Operation: 98-18=80, Resulting Numbers: [2, 80] Generated Node #3: [2, 80] from Operation: 98-18=80 Current State: 40:[2, 80], Operations: ['32/16=2', '98-18=80'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[32, 98, 18, 16], Operations: [] Exploring Operation: 98-32=66, Resulting Numbers: [18, 16, 66] Generated Node #0,0: 40:[18, 16, 66] Operation: 98-32=66 Exploring Operation: 98-16=82, Resulting Numbers: [32, 18, 82] Generated Node #0,1: 40:[32, 18, 82] Operation: 98-16=82 Exploring Operation: 98-18=80, Resulting Numbers: [32, 16, 80] Generated Node #0,2: 40:[32, 16, 80] Operation: 98-18=80 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[18, 16, 66], Operations: ['98-32=66'] Exploring Operation: 66-16=50, Resulting Numbers: [18, 50] Generated Node #0,0,0: 40:[18, 50] Operation: 66-16=50 Exploring Operation: 18-16=2, Resulting Numbers: [66, 2] Generated Node #0,0,1: 40:[66, 2] Operation: 18-16=2 Exploring Operation: 66-18=48, Resulting Numbers: [16, 48] Generated Node #0,0,2: 40:[16, 48] Operation: 66-18=48 Moving to Node #0,0,0 Current State: 40:[18, 50], Operations: ['98-32=66', '66-16=50'] Exploring Operation: 18*50=900, Resulting Numbers: [900] 900,40 unequal: No Solution Exploring Operation: 18+50=68, Resulting Numbers: [68] 68,40 unequal: No Solution Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,40 unequal: No Solution Moving to Node #0,0,2 Current State: 40:[16, 48], Operations: ['98-32=66', '66-18=48'] Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,40 unequal: No Solution Moving to Node #0,0,1 Current State: 40:[66, 2], Operations: ['98-32=66', '18-16=2'] Exploring Operation: 66+2=68, Resulting Numbers: [68] 68,40 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,40 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[32, 18, 82], Operations: ['98-16=82'] Exploring Operation: 32-18=14, Resulting Numbers: [82, 14] Generated Node #0,1,0: 40:[82, 14] Operation: 32-18=14 Exploring Operation: 82-18=64, Resulting Numbers: [32, 64] Generated Node #0,1,1: 40:[32, 64] Operation: 82-18=64 Exploring Operation: 82-32=50, Resulting Numbers: [18, 50] Generated Node #0,1,2: 40:[18, 50] Operation: 82-32=50 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 40:[18, 50], Operations: ['98-16=82', '82-32=50'] Exploring Operation: 50-18=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 18+50=68, Resulting Numbers: [68] 68,40 unequal: No Solution Exploring Operation: 18*50=900, Resulting Numbers: [900] 900,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[32, 64], Operations: ['98-16=82', '82-18=64'] Exploring Operation: 32+64=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,40 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[82, 14], Operations: ['98-16=82', '32-18=14'] Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 82*14=1148, Resulting Numbers: [1148] 1148,40 unequal: No Solution Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[32, 16, 80], Operations: ['98-18=80'] Exploring Operation: 80-32=48, Resulting Numbers: [16, 48] Generated Node #0,2,0: 40:[16, 48] Operation: 80-32=48 Exploring Operation: 80/16=5, Resulting Numbers: [32, 5] Generated Node #0,2,1: 40:[32, 5] Operation: 80/16=5 Exploring Operation: 80-16=64, Resulting Numbers: [32, 64] Generated Node #0,2,2: 40:[32, 64] Operation: 80-16=64 Moving to Node #0,2,1 Current State: 40:[32, 5], Operations: ['98-18=80', '80/16=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,40 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,40 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,40 unequal: No Solution Moving to Node #0,2,0 Current State: 40:[16, 48], Operations: ['98-18=80', '80-32=48'] Exploring Operation: 16+48=64, Resulting Numbers: [64] 64,40 unequal: No Solution Exploring Operation: 48/16=3, Resulting Numbers: [3] 3,40 unequal: No Solution Exploring Operation: 48-16=32, Resulting Numbers: [32] 32,40 unequal: No Solution Moving to Node #0,2,2 Current State: 40:[32, 64], Operations: ['98-18=80', '80-16=64'] Exploring Operation: 32+64=96, Resulting Numbers: [96] 96,40 unequal: No Solution Exploring Operation: 64-32=32, Resulting Numbers: [32] 32,40 unequal: No Solution Exploring Operation: 64/32=2, Resulting Numbers: [2] 2,40 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
[ 61, 29, 18, 7 ]
94
[ "61-29=32", "18*7=126", "126-32=94" ]
Current State: 94:[61, 29, 18, 7], Operations: [] Exploring Operation: 61-29=32, Resulting Numbers: [18, 7, 32] Generated Node #2: [18, 7, 32] from Operation: 61-29=32 Current State: 94:[18, 7, 32], Operations: ['61-29=32'] Exploring Operation: 18*7=126, Resulting Numbers: [32, 126] Generated Node #3: [32, 126] from Operation: 18*7=126 Current State: 94:[32, 126], Operations: ['61-29=32', '18*7=126'] Exploring Operation: 126-32=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[61, 29, 18, 7], Operations: [] Exploring Operation: 29+18=47, Resulting Numbers: [61, 7, 47] Generated Node #0,0: 94:[61, 7, 47] Operation: 29+18=47 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[61, 7, 47], Operations: ['29+18=47'] Exploring Operation: 61-7=54, Resulting Numbers: [47, 54] Generated Node #0,0,0: 94:[47, 54] Operation: 61-7=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[47, 54], Operations: ['29+18=47', '61-7=54'] Exploring Operation: 54-47=7, Resulting Numbers: [7] 7,94 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 No solution found.
0
hs_1
mult_heuristic
[ 88, 6, 28, 79 ]
69
[ "88-28=60", "60/6=10", "79-10=69" ]
Current State: 69:[88, 6, 28, 79], Operations: [] Exploring Operation: 88-28=60, Resulting Numbers: [6, 79, 60] Generated Node #2: [6, 79, 60] from Operation: 88-28=60 Current State: 69:[6, 79, 60], Operations: ['88-28=60'] Exploring Operation: 60/6=10, Resulting Numbers: [79, 10] Generated Node #3: [79, 10] from Operation: 60/6=10 Current State: 69:[79, 10], Operations: ['88-28=60', '60/6=10'] Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[88, 6, 28, 79], Operations: [] Exploring Operation: 88-28=60, Resulting Numbers: [6, 79, 60] Generated Node #0,0: 69:[6, 79, 60] Operation: 88-28=60 Exploring Operation: 88-6=82, Resulting Numbers: [28, 79, 82] Generated Node #0,1: 69:[28, 79, 82] Operation: 88-6=82 Exploring Operation: 88-79=9, Resulting Numbers: [6, 28, 9] Generated Node #0,2: 69:[6, 28, 9] Operation: 88-79=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[6, 28, 9], Operations: ['88-79=9'] Exploring Operation: 9-6=3, Resulting Numbers: [28, 3] Generated Node #0,2,0: 69:[28, 3] Operation: 9-6=3 Exploring Operation: 28-9=19, Resulting Numbers: [6, 19] Generated Node #0,2,1: 69:[6, 19] Operation: 28-9=19 Exploring Operation: 28-6=22, Resulting Numbers: [9, 22] Generated Node #0,2,2: 69:[9, 22] Operation: 28-6=22 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 69:[28, 3], Operations: ['88-79=9', '9-6=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,69 unequal: No Solution No 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: 69:[6, 19], Operations: ['88-79=9', '28-9=19'] Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,69 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,69 unequal: No Solution No 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: 69:[9, 22], Operations: ['88-79=9', '28-6=22'] Exploring Operation: 9*22=198, Resulting Numbers: [198] 198,69 unequal: No Solution Exploring Operation: 9+22=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 22-9=13, Resulting Numbers: [13] 13,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 69:[6, 79, 60], Operations: ['88-28=60'] Exploring Operation: 79-60=19, Resulting Numbers: [6, 19] Generated Node #0,0,0: 69:[6, 19] Operation: 79-60=19 Exploring Operation: 79-6=73, Resulting Numbers: [60, 73] Generated Node #0,0,1: 69:[60, 73] Operation: 79-6=73 Exploring Operation: 6+60=66, Resulting Numbers: [79, 66] Generated Node #0,0,2: 69:[79, 66] Operation: 6+60=66 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[6, 19], Operations: ['88-28=60', '79-60=19'] Exploring Operation: 6+19=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 19-6=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 6*19=114, Resulting Numbers: [114] 114,69 unequal: No Solution No 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: 69:[60, 73], Operations: ['88-28=60', '79-6=73'] Exploring Operation: 60*73=4380, Resulting Numbers: [4380] 4380,69 unequal: No Solution Exploring Operation: 73-60=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 60+73=133, Resulting Numbers: [133] 133,69 unequal: No Solution No 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: 69:[79, 66], Operations: ['88-28=60', '6+60=66'] Exploring Operation: 79+66=145, Resulting Numbers: [145] 145,69 unequal: No Solution Exploring Operation: 79-66=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 79*66=5214, Resulting Numbers: [5214] 5214,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[28, 79, 82], Operations: ['88-6=82'] Exploring Operation: 82-79=3, Resulting Numbers: [28, 3] Generated Node #0,1,0: 69:[28, 3] Operation: 82-79=3 Exploring Operation: 82-28=54, Resulting Numbers: [79, 54] Generated Node #0,1,1: 69:[79, 54] Operation: 82-28=54 Exploring Operation: 79-28=51, Resulting Numbers: [82, 51] Generated Node #0,1,2: 69:[82, 51] Operation: 79-28=51 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 69:[28, 3], Operations: ['88-6=82', '82-79=3'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,69 unequal: No Solution Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,69 unequal: No Solution No 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: 69:[79, 54], Operations: ['88-6=82', '82-28=54'] Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,69 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,69 unequal: No Solution No 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: 69:[82, 51], Operations: ['88-6=82', '79-28=51'] Exploring Operation: 82-51=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 82*51=4182, Resulting Numbers: [4182] 4182,69 unequal: No Solution Exploring Operation: 82+51=133, Resulting Numbers: [133] 133,69 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 41, 17, 81, 96 ]
39
[ "41-17=24", "96-81=15", "24+15=39" ]
Current State: 39:[41, 17, 81, 96], Operations: [] Exploring Operation: 41-17=24, Resulting Numbers: [81, 96, 24] Generated Node #2: [81, 96, 24] from Operation: 41-17=24 Current State: 39:[81, 96, 24], Operations: ['41-17=24'] Exploring Operation: 96-81=15, Resulting Numbers: [24, 15] Generated Node #3: [24, 15] from Operation: 96-81=15 Current State: 39:[24, 15], Operations: ['41-17=24', '96-81=15'] Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[41, 17, 81, 96], Operations: [] Exploring Operation: 96-81=15, Resulting Numbers: [41, 17, 15] Generated Node #0,0: 39:[41, 17, 15] Operation: 96-81=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[41, 17, 15], Operations: ['96-81=15'] Exploring Operation: 17-15=2, Resulting Numbers: [41, 2] Generated Node #0,0,0: 39:[41, 2] Operation: 17-15=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 39:[41, 2], Operations: ['96-81=15', '17-15=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[41, 17, 81, 96], Operations: [] Exploring Operation: 96-81=15, Resulting Numbers: [41, 17, 15] Generated Node #0,0: 39:[41, 17, 15] Operation: 96-81=15 Moving to Node #0,0 Current State: 39:[41, 17, 15], Operations: ['96-81=15'] Exploring Operation: 17-15=2, Resulting Numbers: [41, 2] Generated Node #0,0,0: 39:[41, 2] Operation: 17-15=2 Moving to Node #0,0,0 Current State: 39:[41, 2], Operations: ['96-81=15', '17-15=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 27, 1, 13, 34 ]
75
[ "27+1=28", "13+34=47", "28+47=75" ]
Current State: 75:[27, 1, 13, 34], Operations: [] Exploring Operation: 27+1=28, Resulting Numbers: [13, 34, 28] Generated Node #2: [13, 34, 28] from Operation: 27+1=28 Current State: 75:[13, 34, 28], Operations: ['27+1=28'] Exploring Operation: 13+34=47, Resulting Numbers: [28, 47] Generated Node #3: [28, 47] from Operation: 13+34=47 Current State: 75:[28, 47], Operations: ['27+1=28', '13+34=47'] Exploring Operation: 28+47=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[27, 1, 13, 34], Operations: [] Exploring Operation: 1+13=14, Resulting Numbers: [27, 34, 14] Generated Node #0,0: 75:[27, 34, 14] Operation: 1+13=14 Exploring Operation: 34-13=21, Resulting Numbers: [27, 1, 21] Generated Node #0,1: 75:[27, 1, 21] Operation: 34-13=21 Exploring Operation: 34-27=7, Resulting Numbers: [1, 13, 7] Generated Node #0,2: 75:[1, 13, 7] Operation: 34-27=7 Exploring Operation: 27-1=26, Resulting Numbers: [13, 34, 26] Generated Node #0,3: 75:[13, 34, 26] Operation: 27-1=26 Exploring Operation: 27-13=14, Resulting Numbers: [1, 34, 14] Generated Node #0,4: 75:[1, 34, 14] Operation: 27-13=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 75:[1, 13, 7], Operations: ['34-27=7'] Exploring Operation: 13/1=13, Resulting Numbers: [7, 13] Generated Node #0,2,0: 75:[7, 13] Operation: 13/1=13 Exploring Operation: 1+13=14, Resulting Numbers: [7, 14] Generated Node #0,2,1: 75:[7, 14] Operation: 1+13=14 Exploring Operation: 7-1=6, Resulting Numbers: [13, 6] Generated Node #0,2,2: 75:[13, 6] Operation: 7-1=6 Exploring Operation: 1*13=13, Resulting Numbers: [7, 13] Generated Node #0,2,3: 75:[7, 13] Operation: 1*13=13 Exploring Operation: 13-7=6, Resulting Numbers: [1, 6] Generated Node #0,2,4: 75:[1, 6] Operation: 13-7=6 Moving to Node #0,2,1 Current State: 75:[7, 14], Operations: ['34-27=7', '1+13=14'] Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,75 unequal: No Solution Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,75 unequal: No Solution Moving to Node #0,2,4 Current State: 75:[1, 6], Operations: ['34-27=7', '13-7=6'] Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,75 unequal: No Solution Moving to Node #0,2,2 Current State: 75:[13, 6], Operations: ['34-27=7', '7-1=6'] Exploring Operation: 13-6=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 13+6=19, Resulting Numbers: [19] 19,75 unequal: No Solution Exploring Operation: 13*6=78, Resulting Numbers: [78] 78,75 unequal: No Solution Moving to Node #0,2,0 Current State: 75:[7, 13], Operations: ['34-27=7', '13/1=13'] Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,75 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,75 unequal: No Solution Moving to Node #0,2,3 Current State: 75:[7, 13], Operations: ['34-27=7', '1*13=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,75 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 75:[27, 1, 21], Operations: ['34-13=21'] Exploring Operation: 27-21=6, Resulting Numbers: [1, 6] Generated Node #0,1,0: 75:[1, 6] Operation: 27-21=6 Exploring Operation: 27-1=26, Resulting Numbers: [21, 26] Generated Node #0,1,1: 75:[21, 26] Operation: 27-1=26 Exploring Operation: 27/1=27, Resulting Numbers: [21, 27] Generated Node #0,1,2: 75:[21, 27] Operation: 27/1=27 Exploring Operation: 27*1=27, Resulting Numbers: [21, 27] Generated Node #0,1,3: 75:[21, 27] Operation: 27*1=27 Exploring Operation: 1+21=22, Resulting Numbers: [27, 22] Generated Node #0,1,4: 75:[27, 22] Operation: 1+21=22 Moving to Node #0,1,0 Current State: 75:[1, 6], Operations: ['34-13=21', '27-21=6'] Exploring Operation: 6/1=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 6-1=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 1+6=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 1*6=6, Resulting Numbers: [6] 6,75 unequal: No Solution Moving to Node #0,1,4 Current State: 75:[27, 22], Operations: ['34-13=21', '1+21=22'] Exploring Operation: 27+22=49, Resulting Numbers: [49] 49,75 unequal: No Solution Exploring Operation: 27-22=5, Resulting Numbers: [5] 5,75 unequal: No Solution Exploring Operation: 27*22=594, Resulting Numbers: [594] 594,75 unequal: No Solution Moving to Node #0,1,1 Current State: 75:[21, 26], Operations: ['34-13=21', '27-1=26'] Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,75 unequal: No Solution Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,75 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,75 unequal: No Solution Moving to Node #0,1,2 Current State: 75:[21, 27], Operations: ['34-13=21', '27/1=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,75 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,75 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,75 unequal: No Solution Moving to Node #0,1,3 Current State: 75:[21, 27], Operations: ['34-13=21', '27*1=27'] Exploring Operation: 21*27=567, Resulting Numbers: [567] 567,75 unequal: No Solution Exploring Operation: 27-21=6, Resulting Numbers: [6] 6,75 unequal: No Solution Exploring Operation: 21+27=48, Resulting Numbers: [48] 48,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[27, 34, 14], Operations: ['1+13=14'] Exploring Operation: 34-14=20, Resulting Numbers: [27, 20] Generated Node #0,0,0: 75:[27, 20] Operation: 34-14=20 Exploring Operation: 34-27=7, Resulting Numbers: [14, 7] Generated Node #0,0,1: 75:[14, 7] Operation: 34-27=7 Exploring Operation: 27+34=61, Resulting Numbers: [14, 61] Generated Node #0,0,2: 75:[14, 61] Operation: 27+34=61 Exploring Operation: 27+14=41, Resulting Numbers: [34, 41] Generated Node #0,0,3: 75:[34, 41] Operation: 27+14=41 Exploring Operation: 27-14=13, Resulting Numbers: [34, 13] Generated Node #0,0,4: 75:[34, 13] Operation: 27-14=13 Moving to Node #0,0,1 Current State: 75:[14, 7], Operations: ['1+13=14', '34-27=7'] Exploring Operation: 14*7=98, Resulting Numbers: [98] 98,75 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,75 unequal: No Solution Moving to Node #0,0,0 Current State: 75:[27, 20], Operations: ['1+13=14', '34-14=20'] Exploring Operation: 27-20=7, Resulting Numbers: [7] 7,75 unequal: No Solution Exploring Operation: 27*20=540, Resulting Numbers: [540] 540,75 unequal: No Solution Exploring Operation: 27+20=47, Resulting Numbers: [47] 47,75 unequal: No Solution Moving to Node #0,0,4 Current State: 75:[34, 13], Operations: ['1+13=14', '27-14=13'] Exploring Operation: 34+13=47, Resulting Numbers: [47] 47,75 unequal: No Solution Exploring Operation: 34*13=442, Resulting Numbers: [442] 442,75 unequal: No Solution Exploring Operation: 34-13=21, Resulting Numbers: [21] 21,75 unequal: No Solution Moving to Node #0,0,2 Current State: 75:[14, 61], Operations: ['1+13=14', '27+34=61'] Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[27, 1, 13, 34], Operations: [] Exploring Operation: 1+13=14, Resulting Numbers: [27, 34, 14] Generated Node #0,0: 75:[27, 34, 14] Operation: 1+13=14 Moving to Node #0,0 Current State: 75:[27, 34, 14], Operations: ['1+13=14'] Exploring Operation: 27+34=61, Resulting Numbers: [14, 61] Generated Node #0,0,2: 75:[14, 61] Operation: 27+34=61 Moving to Node #0,0,2 Current State: 75:[14, 61], Operations: ['1+13=14', '27+34=61'] Exploring Operation: 14+61=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.940972
hs_5
sum_heuristic
[ 7, 80, 76, 78 ]
81
[ "80-7=73", "76+78=154", "154-73=81" ]
Current State: 81:[7, 80, 76, 78], Operations: [] Exploring Operation: 80-7=73, Resulting Numbers: [76, 78, 73] Generated Node #2: [76, 78, 73] from Operation: 80-7=73 Current State: 81:[76, 78, 73], Operations: ['80-7=73'] Exploring Operation: 76+78=154, Resulting Numbers: [73, 154] Generated Node #3: [73, 154] from Operation: 76+78=154 Current State: 81:[73, 154], Operations: ['80-7=73', '76+78=154'] Exploring Operation: 154-73=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[7, 80, 76, 78], Operations: [] Exploring Operation: 7+76=83, Resulting Numbers: [80, 78, 83] Generated Node #0,0: 81:[80, 78, 83] Operation: 7+76=83 Exploring Operation: 80-76=4, Resulting Numbers: [7, 78, 4] Generated Node #0,1: 81:[7, 78, 4] Operation: 80-76=4 Exploring Operation: 78-76=2, Resulting Numbers: [7, 80, 2] Generated Node #0,2: 81:[7, 80, 2] Operation: 78-76=2 Moving to Node #0,2 Current State: 81:[7, 80, 2], Operations: ['78-76=2'] Exploring Operation: 7-2=5, Resulting Numbers: [80, 5] Generated Node #0,2,0: 81:[80, 5] Operation: 7-2=5 Exploring Operation: 7+2=9, Resulting Numbers: [80, 9] Generated Node #0,2,1: 81:[80, 9] Operation: 7+2=9 Exploring Operation: 80+2=82, Resulting Numbers: [7, 82] Generated Node #0,2,2: 81:[7, 82] Operation: 80+2=82 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[80, 9], Operations: ['78-76=2', '7+2=9'] Exploring Operation: 80*9=720, Resulting Numbers: [720] 720,81 unequal: No Solution Exploring Operation: 80-9=71, Resulting Numbers: [71] 71,81 unequal: No Solution Exploring Operation: 80+9=89, Resulting Numbers: [89] 89,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[80, 5], Operations: ['78-76=2', '7-2=5'] Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,81 unequal: No Solution Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,81 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,81 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 #0,2,2 Current State: 81:[7, 82], Operations: ['78-76=2', '80+2=82'] Exploring Operation: 7+82=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 7*82=574, Resulting Numbers: [574] 574,81 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,81 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:[80, 78, 83], Operations: ['7+76=83'] Exploring Operation: 83-78=5, Resulting Numbers: [80, 5] Generated Node #0,0,0: 81:[80, 5] Operation: 83-78=5 Exploring Operation: 80-78=2, Resulting Numbers: [83, 2] Generated Node #0,0,1: 81:[83, 2] Operation: 80-78=2 Exploring Operation: 83-80=3, Resulting Numbers: [78, 3] Generated Node #0,0,2: 81:[78, 3] Operation: 83-80=3 Moving to Node #0,1 Current State: 81:[7, 78, 4], Operations: ['80-76=4'] Exploring Operation: 7*4=28, Resulting Numbers: [78, 28] Generated Node #0,1,0: 81:[78, 28] Operation: 7*4=28 Exploring Operation: 7-4=3, Resulting Numbers: [78, 3] Generated Node #0,1,1: 81:[78, 3] Operation: 7-4=3 Exploring Operation: 78+4=82, Resulting Numbers: [7, 82] Generated Node #0,1,2: 81:[7, 82] Operation: 78+4=82 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[78, 3], Operations: ['80-76=4', '7-4=3'] Exploring Operation: 78/3=26, Resulting Numbers: [26] 26,81 unequal: No Solution Exploring Operation: 78-3=75, Resulting Numbers: [75] 75,81 unequal: No Solution Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[7, 80, 76, 78], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [7, 78, 4] Generated Node #0,1: 81:[7, 78, 4] Operation: 80-76=4 Moving to Node #0,1 Current State: 81:[7, 78, 4], Operations: ['80-76=4'] Exploring Operation: 7-4=3, Resulting Numbers: [78, 3] Generated Node #0,1,1: 81:[78, 3] Operation: 7-4=3 Moving to Node #0,1,1 Current State: 81:[78, 3], Operations: ['80-76=4', '7-4=3'] Exploring Operation: 78+3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_3
sum_heuristic
[ 15, 5, 2, 25 ]
65
[ "15+5=20", "2*20=40", "25+40=65" ]
Current State: 65:[15, 5, 2, 25], Operations: [] Exploring Operation: 15+5=20, Resulting Numbers: [2, 25, 20] Generated Node #2: [2, 25, 20] from Operation: 15+5=20 Current State: 65:[2, 25, 20], Operations: ['15+5=20'] Exploring Operation: 2*20=40, Resulting Numbers: [25, 40] Generated Node #3: [25, 40] from Operation: 2*20=40 Current State: 65:[25, 40], Operations: ['15+5=20', '2*20=40'] Exploring Operation: 25+40=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[15, 5, 2, 25], Operations: [] Exploring Operation: 25-5=20, Resulting Numbers: [15, 2, 20] Generated Node #0,0: 65:[15, 2, 20] Operation: 25-5=20 Exploring Operation: 25-15=10, Resulting Numbers: [5, 2, 10] Generated Node #0,1: 65:[5, 2, 10] Operation: 25-15=10 Exploring Operation: 15-2=13, Resulting Numbers: [5, 25, 13] Generated Node #0,2: 65:[5, 25, 13] Operation: 15-2=13 Exploring Operation: 25/5=5, Resulting Numbers: [15, 2, 5] Generated Node #0,3: 65:[15, 2, 5] Operation: 25/5=5 Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[15, 2, 5], Operations: ['25/5=5'] Exploring Operation: 5-2=3, Resulting Numbers: [15, 3] Generated Node #0,3,0: 65:[15, 3] Operation: 5-2=3 Exploring Operation: 15+2=17, Resulting Numbers: [5, 17] Generated Node #0,3,1: 65:[5, 17] Operation: 15+2=17 Exploring Operation: 15-2=13, Resulting Numbers: [5, 13] Generated Node #0,3,2: 65:[5, 13] Operation: 15-2=13 Exploring Operation: 2+5=7, Resulting Numbers: [15, 7] Generated Node #0,3,3: 65:[15, 7] Operation: 2+5=7 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 65:[5, 13], Operations: ['25/5=5', '15-2=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[15, 5, 2, 25], Operations: [] Exploring Operation: 25/5=5, Resulting Numbers: [15, 2, 5] Generated Node #0,3: 65:[15, 2, 5] Operation: 25/5=5 Moving to Node #0,3 Current State: 65:[15, 2, 5], Operations: ['25/5=5'] Exploring Operation: 15-2=13, Resulting Numbers: [5, 13] Generated Node #0,3,2: 65:[5, 13] Operation: 15-2=13 Moving to Node #0,3,2 Current State: 65:[5, 13], Operations: ['25/5=5', '15-2=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.988715
hs_4
sum_heuristic
[ 31, 62, 26, 42 ]
70
[ "62/31=2", "26+42=68", "2+68=70" ]
Current State: 70:[31, 62, 26, 42], Operations: [] Exploring Operation: 62/31=2, Resulting Numbers: [26, 42, 2] Generated Node #2: [26, 42, 2] from Operation: 62/31=2 Current State: 70:[26, 42, 2], Operations: ['62/31=2'] Exploring Operation: 26+42=68, Resulting Numbers: [2, 68] Generated Node #3: [2, 68] from Operation: 26+42=68 Current State: 70:[2, 68], Operations: ['62/31=2', '26+42=68'] Exploring Operation: 2+68=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[31, 62, 26, 42], Operations: [] Exploring Operation: 62-26=36, Resulting Numbers: [31, 42, 36] Generated Node #0,0: 70:[31, 42, 36] Operation: 62-26=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[31, 42, 36], Operations: ['62-26=36'] Exploring Operation: 42-31=11, Resulting Numbers: [36, 11] Generated Node #0,0,0: 70:[36, 11] Operation: 42-31=11 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 70:[36, 11], Operations: ['62-26=36', '42-31=11'] Exploring Operation: 36-11=25, Resulting Numbers: [25] 25,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 40, 31, 19, 20 ]
70
[ "40+31=71", "20-19=1", "71-1=70" ]
Current State: 70:[40, 31, 19, 20], Operations: [] Exploring Operation: 40+31=71, Resulting Numbers: [19, 20, 71] Generated Node #2: [19, 20, 71] from Operation: 40+31=71 Current State: 70:[19, 20, 71], Operations: ['40+31=71'] Exploring Operation: 20-19=1, Resulting Numbers: [71, 1] Generated Node #3: [71, 1] from Operation: 20-19=1 Current State: 70:[71, 1], Operations: ['40+31=71', '20-19=1'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[40, 31, 19, 20], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [31, 19, 2] Generated Node #0,0: 70:[31, 19, 2] Operation: 40/20=2 Exploring Operation: 31-20=11, Resulting Numbers: [40, 19, 11] Generated Node #0,1: 70:[40, 19, 11] Operation: 31-20=11 Exploring Operation: 20-19=1, Resulting Numbers: [40, 31, 1] Generated Node #0,2: 70:[40, 31, 1] Operation: 20-19=1 Moving to Node #0,0 Current State: 70:[31, 19, 2], Operations: ['40/20=2'] Exploring Operation: 31+2=33, Resulting Numbers: [19, 33] Generated Node #0,0,0: 70:[19, 33] Operation: 31+2=33 Exploring Operation: 19*2=38, Resulting Numbers: [31, 38] Generated Node #0,0,1: 70:[31, 38] Operation: 19*2=38 Exploring Operation: 31-19=12, Resulting Numbers: [2, 12] Generated Node #0,0,2: 70:[2, 12] Operation: 31-19=12 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 70:[2, 12], Operations: ['40/20=2', '31-19=12'] Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[19, 33], Operations: ['40/20=2', '31+2=33'] Exploring Operation: 19*33=627, Resulting Numbers: [627] 627,70 unequal: No Solution Exploring Operation: 19+33=52, Resulting Numbers: [52] 52,70 unequal: No Solution Exploring Operation: 33-19=14, Resulting Numbers: [14] 14,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[31, 38], Operations: ['40/20=2', '19*2=38'] Exploring Operation: 31+38=69, Resulting Numbers: [69] 69,70 unequal: No Solution Exploring Operation: 38-31=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 31*38=1178, Resulting Numbers: [1178] 1178,70 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: 70:[40, 31, 1], Operations: ['20-19=1'] Exploring Operation: 40-1=39, Resulting Numbers: [31, 39] Generated Node #0,2,0: 70:[31, 39] Operation: 40-1=39 Exploring Operation: 40-31=9, Resulting Numbers: [1, 9] Generated Node #0,2,1: 70:[1, 9] Operation: 40-31=9 Exploring Operation: 40+31=71, Resulting Numbers: [1, 71] Generated Node #0,2,2: 70:[1, 71] Operation: 40+31=71 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[1, 9], Operations: ['20-19=1', '40-31=9'] Exploring Operation: 9-1=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 1*9=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 1+9=10, Resulting Numbers: [10] 10,70 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 #0,2,2 Current State: 70:[1, 71], Operations: ['20-19=1', '40+31=71'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[40, 31, 19, 20], Operations: [] Exploring Operation: 20-19=1, Resulting Numbers: [40, 31, 1] Generated Node #0,2: 70:[40, 31, 1] Operation: 20-19=1 Moving to Node #0,2 Current State: 70:[40, 31, 1], Operations: ['20-19=1'] Exploring Operation: 40+31=71, Resulting Numbers: [1, 71] Generated Node #0,2,2: 70:[1, 71] Operation: 40+31=71 Moving to Node #0,2,2 Current State: 70:[1, 71], Operations: ['20-19=1', '40+31=71'] Exploring Operation: 71-1=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 90, 54, 15, 2 ]
18
[ "90/15=6", "54*2=108", "108/6=18" ]
Current State: 18:[90, 54, 15, 2], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [54, 2, 6] Generated Node #2: [54, 2, 6] from Operation: 90/15=6 Current State: 18:[54, 2, 6], Operations: ['90/15=6'] Exploring Operation: 54*2=108, Resulting Numbers: [6, 108] Generated Node #3: [6, 108] from Operation: 54*2=108 Current State: 18:[6, 108], Operations: ['90/15=6', '54*2=108'] Exploring Operation: 108/6=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[90, 54, 15, 2], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [54, 2, 6] Generated Node #0,0: 18:[54, 2, 6] Operation: 90/15=6 Exploring Operation: 90/2=45, Resulting Numbers: [54, 15, 45] Generated Node #0,1: 18:[54, 15, 45] Operation: 90/2=45 Exploring Operation: 90-54=36, Resulting Numbers: [15, 2, 36] Generated Node #0,2: 18:[15, 2, 36] Operation: 90-54=36 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[15, 2, 36], Operations: ['90-54=36'] Exploring Operation: 15+2=17, Resulting Numbers: [36, 17] Generated Node #0,2,0: 18:[36, 17] Operation: 15+2=17 Exploring Operation: 36-15=21, Resulting Numbers: [2, 21] Generated Node #0,2,1: 18:[2, 21] Operation: 36-15=21 Exploring Operation: 36/2=18, Resulting Numbers: [15, 18] Generated Node #0,2,2: 18:[15, 18] Operation: 36/2=18 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 18:[2, 21], Operations: ['90-54=36', '36-15=21'] Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 18:[15, 18], Operations: ['90-54=36', '36/2=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,18 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,18 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 18:[36, 17], Operations: ['90-54=36', '15+2=17'] Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,18 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[54, 2, 6], Operations: ['90/15=6'] Exploring Operation: 54/2=27, Resulting Numbers: [6, 27] Generated Node #0,0,0: 18:[6, 27] Operation: 54/2=27 Exploring Operation: 54-6=48, Resulting Numbers: [2, 48] Generated Node #0,0,1: 18:[2, 48] Operation: 54-6=48 Exploring Operation: 54/6=9, Resulting Numbers: [2, 9] Generated Node #0,0,2: 18:[2, 9] Operation: 54/6=9 Moving to Node #0,0,2 Current State: 18:[2, 9], Operations: ['90/15=6', '54/6=9'] Exploring Operation: 2+9=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[90, 54, 15, 2], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [54, 2, 6] Generated Node #0,0: 18:[54, 2, 6] Operation: 90/15=6 Moving to Node #0,0 Current State: 18:[54, 2, 6], Operations: ['90/15=6'] Exploring Operation: 54/6=9, Resulting Numbers: [2, 9] Generated Node #0,0,2: 18:[2, 9] Operation: 54/6=9 Moving to Node #0,0,2 Current State: 18:[2, 9], Operations: ['90/15=6', '54/6=9'] Exploring Operation: 2*9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
sum_heuristic
[ 6, 70, 56, 68 ]
35
[ "6*70=420", "68-56=12", "420/12=35" ]
Current State: 35:[6, 70, 56, 68], Operations: [] Exploring Operation: 6*70=420, Resulting Numbers: [56, 68, 420] Generated Node #2: [56, 68, 420] from Operation: 6*70=420 Current State: 35:[56, 68, 420], Operations: ['6*70=420'] Exploring Operation: 68-56=12, Resulting Numbers: [420, 12] Generated Node #3: [420, 12] from Operation: 68-56=12 Current State: 35:[420, 12], Operations: ['6*70=420', '68-56=12'] Exploring Operation: 420/12=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 70, 56, 68], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [6, 56, 2] Generated Node #0,0: 35:[6, 56, 2] Operation: 70-68=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 35:[6, 56, 2], Operations: ['70-68=2'] Exploring Operation: 56/2=28, Resulting Numbers: [6, 28] Generated Node #0,0,0: 35:[6, 28] Operation: 56/2=28 Moving to Node #0,0,0 Current State: 35:[6, 28], Operations: ['70-68=2', '56/2=28'] Exploring Operation: 6+28=34, Resulting Numbers: [34] 34,35 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
[ 51, 50, 35, 69 ]
84
[ "51+69=120", "35*120=4200", "4200/50=84" ]
Current State: 84:[51, 50, 35, 69], Operations: [] Exploring Operation: 51+69=120, Resulting Numbers: [50, 35, 120] Generated Node #2: [50, 35, 120] from Operation: 51+69=120 Current State: 84:[50, 35, 120], Operations: ['51+69=120'] Exploring Operation: 35*120=4200, Resulting Numbers: [50, 4200] Generated Node #3: [50, 4200] from Operation: 35*120=4200 Current State: 84:[50, 4200], Operations: ['51+69=120', '35*120=4200'] Exploring Operation: 4200/50=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[51, 50, 35, 69], Operations: [] Exploring Operation: 51-50=1, Resulting Numbers: [35, 69, 1] Generated Node #0,0: 84:[35, 69, 1] Operation: 51-50=1 Exploring Operation: 51+35=86, Resulting Numbers: [50, 69, 86] Generated Node #0,1: 84:[50, 69, 86] Operation: 51+35=86 Exploring Operation: 69-35=34, Resulting Numbers: [51, 50, 34] Generated Node #0,2: 84:[51, 50, 34] Operation: 69-35=34 Exploring Operation: 69-50=19, Resulting Numbers: [51, 35, 19] Generated Node #0,3: 84:[51, 35, 19] Operation: 69-50=19 Exploring Operation: 69-51=18, Resulting Numbers: [50, 35, 18] Generated Node #0,4: 84:[50, 35, 18] Operation: 69-51=18 Moving to Node #0,3 Current State: 84:[51, 35, 19], Operations: ['69-50=19'] Exploring Operation: 51+19=70, Resulting Numbers: [35, 70] Generated Node #0,3,0: 84:[35, 70] Operation: 51+19=70 Exploring Operation: 51-35=16, Resulting Numbers: [19, 16] Generated Node #0,3,1: 84:[19, 16] Operation: 51-35=16 Exploring Operation: 51+35=86, Resulting Numbers: [19, 86] Generated Node #0,3,2: 84:[19, 86] Operation: 51+35=86 Exploring Operation: 35-19=16, Resulting Numbers: [51, 16] Generated Node #0,3,3: 84:[51, 16] Operation: 35-19=16 Exploring Operation: 51-19=32, Resulting Numbers: [35, 32] Generated Node #0,3,4: 84:[35, 32] Operation: 51-19=32 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 84:[19, 16], Operations: ['69-50=19', '51-35=16'] Exploring Operation: 19-16=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 19+16=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 19*16=304, Resulting Numbers: [304] 304,84 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:[19, 86], Operations: ['69-50=19', '51+35=86'] Exploring Operation: 19*86=1634, Resulting Numbers: [1634] 1634,84 unequal: No Solution Exploring Operation: 19+86=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,84 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 #0,3,3 Current State: 84:[51, 16], Operations: ['69-50=19', '35-19=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,84 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 #0,3,4 Current State: 84:[35, 32], Operations: ['69-50=19', '51-19=32'] Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,84 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 84:[35, 70], Operations: ['69-50=19', '51+19=70'] Exploring Operation: 35*70=2450, Resulting Numbers: [2450] 2450,84 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,84 unequal: No Solution Exploring Operation: 35+70=105, Resulting Numbers: [105] 105,84 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: 84:[50, 35, 18], Operations: ['69-51=18'] Exploring Operation: 50-18=32, Resulting Numbers: [35, 32] Generated Node #0,4,0: 84:[35, 32] Operation: 50-18=32 Exploring Operation: 50+35=85, Resulting Numbers: [18, 85] Generated Node #0,4,1: 84:[18, 85] Operation: 50+35=85 Exploring Operation: 35-18=17, Resulting Numbers: [50, 17] Generated Node #0,4,2: 84:[50, 17] Operation: 35-18=17 Exploring Operation: 35+18=53, Resulting Numbers: [50, 53] Generated Node #0,4,3: 84:[50, 53] Operation: 35+18=53 Exploring Operation: 50-35=15, Resulting Numbers: [18, 15] Generated Node #0,4,4: 84:[18, 15] Operation: 50-35=15 Moving to Node #0,0 Current State: 84:[35, 69, 1], Operations: ['51-50=1'] Exploring Operation: 35+1=36, Resulting Numbers: [69, 36] Generated Node #0,0,0: 84:[69, 36] Operation: 35+1=36 Exploring Operation: 35+69=104, Resulting Numbers: [1, 104] Generated Node #0,0,1: 84:[1, 104] Operation: 35+69=104 Exploring Operation: 69+1=70, Resulting Numbers: [35, 70] Generated Node #0,0,2: 84:[35, 70] Operation: 69+1=70 Exploring Operation: 35-1=34, Resulting Numbers: [69, 34] Generated Node #0,0,3: 84:[69, 34] Operation: 35-1=34 Exploring Operation: 69-35=34, Resulting Numbers: [1, 34] Generated Node #0,0,4: 84:[1, 34] Operation: 69-35=34 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 84:[1, 34], Operations: ['51-50=1', '69-35=34'] Exploring Operation: 1*34=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 1+34=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[69, 36], Operations: ['51-50=1', '35+1=36'] Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,84 unequal: No Solution Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[1, 104], Operations: ['51-50=1', '35+69=104'] Exploring Operation: 1+104=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 104-1=103, Resulting Numbers: [103] 103,84 unequal: No Solution Exploring Operation: 1*104=104, Resulting Numbers: [104] 104,84 unequal: No Solution Exploring Operation: 104/1=104, Resulting Numbers: [104] 104,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[35, 70], Operations: ['51-50=1', '69+1=70'] Exploring Operation: 35*70=2450, Resulting Numbers: [2450] 2450,84 unequal: No Solution Exploring Operation: 35+70=105, Resulting Numbers: [105] 105,84 unequal: No Solution Exploring Operation: 70-35=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 70/35=2, Resulting Numbers: [2] 2,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[69, 34], Operations: ['51-50=1', '35-1=34'] Exploring Operation: 69-34=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 69+34=103, Resulting Numbers: [103] 103,84 unequal: No Solution Exploring Operation: 69*34=2346, Resulting Numbers: [2346] 2346,84 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:[51, 50, 34], Operations: ['69-35=34'] Exploring Operation: 50+34=84, Resulting Numbers: [51, 84] Generated Node #0,2,0: 84:[51, 84] Operation: 50+34=84 Exploring Operation: 51+34=85, Resulting Numbers: [50, 85] Generated Node #0,2,1: 84:[50, 85] Operation: 51+34=85 Exploring Operation: 50-34=16, Resulting Numbers: [51, 16] Generated Node #0,2,2: 84:[51, 16] Operation: 50-34=16 Exploring Operation: 51-34=17, Resulting Numbers: [50, 17] Generated Node #0,2,3: 84:[50, 17] Operation: 51-34=17 Exploring Operation: 51-50=1, Resulting Numbers: [34, 1] Generated Node #0,2,4: 84:[34, 1] Operation: 51-50=1 Moving to Node #0,1 Current State: 84:[50, 69, 86], Operations: ['51+35=86'] Exploring Operation: 69-50=19, Resulting Numbers: [86, 19] Generated Node #0,1,0: 84:[86, 19] Operation: 69-50=19 Exploring Operation: 86-69=17, Resulting Numbers: [50, 17] Generated Node #0,1,1: 84:[50, 17] Operation: 86-69=17 Exploring Operation: 50+69=119, Resulting Numbers: [86, 119] Generated Node #0,1,2: 84:[86, 119] Operation: 50+69=119 Exploring Operation: 50+86=136, Resulting Numbers: [69, 136] Generated Node #0,1,3: 84:[69, 136] Operation: 50+86=136 Exploring Operation: 86-50=36, Resulting Numbers: [69, 36] Generated Node #0,1,4: 84:[69, 36] Operation: 86-50=36 Moving to Node #0,4,1 Current State: 84:[18, 85], Operations: ['69-51=18', '50+35=85'] Exploring Operation: 18+85=103, Resulting Numbers: [103] 103,84 unequal: No Solution Exploring Operation: 85-18=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 18*85=1530, Resulting Numbers: [1530] 1530,84 unequal: No Solution Moving to Node #0,4,4 Current State: 84:[18, 15], Operations: ['69-51=18', '50-35=15'] Exploring Operation: 18*15=270, Resulting Numbers: [270] 270,84 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 18+15=33, Resulting Numbers: [33] 33,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[86, 19], Operations: ['51+35=86', '69-50=19'] Exploring Operation: 86*19=1634, Resulting Numbers: [1634] 1634,84 unequal: No Solution Exploring Operation: 86-19=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 86+19=105, Resulting Numbers: [105] 105,84 unequal: No Solution Moving to Node #0,2,4 Current State: 84:[34, 1], Operations: ['69-35=34', '51-50=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,84 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,84 unequal: No Solution Moving to Node #0,2,0 Current State: 84:[51, 84], Operations: ['69-35=34', '50+34=84'] Exploring Operation: 51+84=135, Resulting Numbers: [135] 135,84 unequal: No Solution Exploring Operation: 84-51=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 51*84=4284, Resulting Numbers: [4284] 4284,84 unequal: No Solution Moving to Node #0,2,1 Current State: 84:[50, 85], Operations: ['69-35=34', '51+34=85'] Exploring Operation: 50+85=135, Resulting Numbers: [135] 135,84 unequal: No Solution Exploring Operation: 85-50=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 50*85=4250, Resulting Numbers: [4250] 4250,84 unequal: No Solution Moving to Node #0,4,0 Current State: 84:[35, 32], Operations: ['69-51=18', '50-18=32'] Exploring Operation: 35-32=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 35+32=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 35*32=1120, Resulting Numbers: [1120] 1120,84 unequal: No Solution Moving to Node #0,1,1 Current State: 84:[50, 17], Operations: ['51+35=86', '86-69=17'] Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,84 unequal: No Solution Moving to Node #0,2,3 Current State: 84:[50, 17], Operations: ['69-35=34', '51-34=17'] Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,84 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,2,2 Current State: 84:[51, 16], Operations: ['69-35=34', '50-34=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,84 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,84 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,84 unequal: No Solution Moving to Node #0,4,2 Current State: 84:[50, 17], Operations: ['69-51=18', '35-18=17'] Exploring Operation: 50*17=850, Resulting Numbers: [850] 850,84 unequal: No Solution Exploring Operation: 50-17=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 50+17=67, Resulting Numbers: [67] 67,84 unequal: No Solution Moving to Node #0,4,3 Current State: 84:[50, 53], Operations: ['69-51=18', '35+18=53'] Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,84 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,84 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,84 unequal: No Solution Moving to Node #0,1,4 Current State: 84:[69, 36], Operations: ['51+35=86', '86-50=36'] Exploring Operation: 69*36=2484, Resulting Numbers: [2484] 2484,84 unequal: No Solution Exploring Operation: 69-36=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 69+36=105, Resulting Numbers: [105] 105,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[86, 119], Operations: ['51+35=86', '50+69=119'] Exploring Operation: 86*119=10234, Resulting Numbers: [10234] 10234,84 unequal: No Solution Exploring Operation: 119-86=33, Resulting Numbers: [33] 33,84 unequal: No Solution Exploring Operation: 86+119=205, Resulting Numbers: [205] 205,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[69, 136], Operations: ['51+35=86', '50+86=136'] Exploring Operation: 69*136=9384, Resulting Numbers: [9384] 9384,84 unequal: No Solution Exploring Operation: 69+136=205, Resulting Numbers: [205] 205,84 unequal: No Solution Exploring Operation: 136-69=67, Resulting Numbers: [67] 67,84 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 38, 33, 72, 75 ]
15
[ "38-33=5", "75-72=3", "5*3=15" ]
Current State: 15:[38, 33, 72, 75], Operations: [] Exploring Operation: 38-33=5, Resulting Numbers: [72, 75, 5] Generated Node #2: [72, 75, 5] from Operation: 38-33=5 Current State: 15:[72, 75, 5], Operations: ['38-33=5'] Exploring Operation: 75-72=3, Resulting Numbers: [5, 3] Generated Node #3: [5, 3] from Operation: 75-72=3 Current State: 15:[5, 3], Operations: ['38-33=5', '75-72=3'] Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[38, 33, 72, 75], Operations: [] Exploring Operation: 75-33=42, Resulting Numbers: [38, 72, 42] Generated Node #0,0: 15:[38, 72, 42] Operation: 75-33=42 Exploring Operation: 75-72=3, Resulting Numbers: [38, 33, 3] Generated Node #0,1: 15:[38, 33, 3] Operation: 75-72=3 Exploring Operation: 72-33=39, Resulting Numbers: [38, 75, 39] Generated Node #0,2: 15:[38, 75, 39] Operation: 72-33=39 Exploring Operation: 75-38=37, Resulting Numbers: [33, 72, 37] Generated Node #0,3: 15:[33, 72, 37] Operation: 75-38=37 Exploring Operation: 72-38=34, Resulting Numbers: [33, 75, 34] Generated Node #0,4: 15:[33, 75, 34] Operation: 72-38=34 Moving to Node #0,1 Current State: 15:[38, 33, 3], Operations: ['75-72=3'] Exploring Operation: 33/3=11, Resulting Numbers: [38, 11] Generated Node #0,1,0: 15:[38, 11] Operation: 33/3=11 Exploring Operation: 38+3=41, Resulting Numbers: [33, 41] Generated Node #0,1,1: 15:[33, 41] Operation: 38+3=41 Exploring Operation: 38-33=5, Resulting Numbers: [3, 5] Generated Node #0,1,2: 15:[3, 5] Operation: 38-33=5 Exploring Operation: 33-3=30, Resulting Numbers: [38, 30] Generated Node #0,1,3: 15:[38, 30] Operation: 33-3=30 Exploring Operation: 38-3=35, Resulting Numbers: [33, 35] Generated Node #0,1,4: 15:[33, 35] Operation: 38-3=35 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[3, 5], Operations: ['75-72=3', '38-33=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,15 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,15 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[38, 33, 72, 75], Operations: [] Exploring Operation: 75-72=3, Resulting Numbers: [38, 33, 3] Generated Node #0,1: 15:[38, 33, 3] Operation: 75-72=3 Moving to Node #0,1 Current State: 15:[38, 33, 3], Operations: ['75-72=3'] Exploring Operation: 38-33=5, Resulting Numbers: [3, 5] Generated Node #0,1,2: 15:[3, 5] Operation: 38-33=5 Moving to Node #0,1,2 Current State: 15:[3, 5], Operations: ['75-72=3', '38-33=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 6, 18, 81, 11 ]
81
[ "18-6=12", "12-11=1", "81*1=81" ]
Current State: 81:[6, 18, 81, 11], Operations: [] Exploring Operation: 18-6=12, Resulting Numbers: [81, 11, 12] Generated Node #2: [81, 11, 12] from Operation: 18-6=12 Current State: 81:[81, 11, 12], Operations: ['18-6=12'] Exploring Operation: 12-11=1, Resulting Numbers: [81, 1] Generated Node #3: [81, 1] from Operation: 12-11=1 Current State: 81:[81, 1], Operations: ['18-6=12', '12-11=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[6, 18, 81, 11], Operations: [] Exploring Operation: 18/6=3, Resulting Numbers: [81, 11, 3] Generated Node #0,0: 81:[81, 11, 3] Operation: 18/6=3 Exploring Operation: 18-6=12, Resulting Numbers: [81, 11, 12] Generated Node #0,1: 81:[81, 11, 12] Operation: 18-6=12 Exploring Operation: 18+11=29, Resulting Numbers: [6, 81, 29] Generated Node #0,2: 81:[6, 81, 29] Operation: 18+11=29 Exploring Operation: 6+18=24, Resulting Numbers: [81, 11, 24] Generated Node #0,3: 81:[81, 11, 24] Operation: 6+18=24 Exploring Operation: 18-11=7, Resulting Numbers: [6, 81, 7] Generated Node #0,4: 81:[6, 81, 7] Operation: 18-11=7 Moving to Node #0,0 Current State: 81:[81, 11, 3], Operations: ['18/6=3'] Exploring Operation: 81+3=84, Resulting Numbers: [11, 84] Generated Node #0,0,0: 81:[11, 84] Operation: 81+3=84 Exploring Operation: 81/3=27, Resulting Numbers: [11, 27] Generated Node #0,0,1: 81:[11, 27] Operation: 81/3=27 Exploring Operation: 11-3=8, Resulting Numbers: [81, 8] Generated Node #0,0,2: 81:[81, 8] Operation: 11-3=8 Exploring Operation: 81-3=78, Resulting Numbers: [11, 78] Generated Node #0,0,3: 81:[11, 78] Operation: 81-3=78 Exploring Operation: 11+3=14, Resulting Numbers: [81, 14] Generated Node #0,0,4: 81:[81, 14] Operation: 11+3=14 Moving to Node #0,2 Current State: 81:[6, 81, 29], Operations: ['18+11=29'] Exploring Operation: 6+29=35, Resulting Numbers: [81, 35] Generated Node #0,2,0: 81:[81, 35] Operation: 6+29=35 Exploring Operation: 6+81=87, Resulting Numbers: [29, 87] Generated Node #0,2,1: 81:[29, 87] Operation: 6+81=87 Exploring Operation: 29-6=23, Resulting Numbers: [81, 23] Generated Node #0,2,2: 81:[81, 23] Operation: 29-6=23 Exploring Operation: 81-29=52, Resulting Numbers: [6, 52] Generated Node #0,2,3: 81:[6, 52] Operation: 81-29=52 Exploring Operation: 81-6=75, Resulting Numbers: [29, 75] Generated Node #0,2,4: 81:[29, 75] Operation: 81-6=75 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[81, 23], Operations: ['18+11=29', '29-6=23'] Exploring Operation: 81*23=1863, Resulting Numbers: [1863] 1863,81 unequal: No Solution Exploring Operation: 81-23=58, Resulting Numbers: [58] 58,81 unequal: No Solution Exploring Operation: 81+23=104, Resulting Numbers: [104] 104,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[81, 35], Operations: ['18+11=29', '6+29=35'] Exploring Operation: 81-35=46, Resulting Numbers: [46] 46,81 unequal: No Solution Exploring Operation: 81+35=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 81*35=2835, Resulting Numbers: [2835] 2835,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[29, 87], Operations: ['18+11=29', '6+81=87'] Exploring Operation: 87-29=58, Resulting Numbers: [58] 58,81 unequal: No Solution Exploring Operation: 87/29=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 29+87=116, Resulting Numbers: [116] 116,81 unequal: No Solution Exploring Operation: 29*87=2523, Resulting Numbers: [2523] 2523,81 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 #0,2,4 Current State: 81:[29, 75], Operations: ['18+11=29', '81-6=75'] Exploring Operation: 29*75=2175, Resulting Numbers: [2175] 2175,81 unequal: No Solution Exploring Operation: 29+75=104, Resulting Numbers: [104] 104,81 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,81 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 #0,2,3 Current State: 81:[6, 52], Operations: ['18+11=29', '81-29=52'] Exploring Operation: 6+52=58, Resulting Numbers: [58] 58,81 unequal: No Solution Exploring Operation: 6*52=312, Resulting Numbers: [312] 312,81 unequal: No Solution Exploring Operation: 52-6=46, Resulting Numbers: [46] 46,81 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: 81:[6, 81, 7], Operations: ['18-11=7'] Exploring Operation: 81+7=88, Resulting Numbers: [6, 88] Generated Node #0,4,0: 81:[6, 88] Operation: 81+7=88 Exploring Operation: 81-6=75, Resulting Numbers: [7, 75] Generated Node #0,4,1: 81:[7, 75] Operation: 81-6=75 Exploring Operation: 7-6=1, Resulting Numbers: [81, 1] Generated Node #0,4,2: 81:[81, 1] Operation: 7-6=1 Exploring Operation: 6+7=13, Resulting Numbers: [81, 13] Generated Node #0,4,3: 81:[81, 13] Operation: 6+7=13 Exploring Operation: 6+81=87, Resulting Numbers: [7, 87] Generated Node #0,4,4: 81:[7, 87] Operation: 6+81=87 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 81:[81, 1], Operations: ['18-11=7', '7-6=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[6, 18, 81, 11], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [6, 81, 7] Generated Node #0,4: 81:[6, 81, 7] Operation: 18-11=7 Moving to Node #0,4 Current State: 81:[6, 81, 7], Operations: ['18-11=7'] Exploring Operation: 7-6=1, Resulting Numbers: [81, 1] Generated Node #0,4,2: 81:[81, 1] Operation: 7-6=1 Moving to Node #0,4,2 Current State: 81:[81, 1], Operations: ['18-11=7', '7-6=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
sum_heuristic
[ 84, 14, 56, 27 ]
23
[ "84/14=6", "56-27=29", "29-6=23" ]
Current State: 23:[84, 14, 56, 27], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [56, 27, 6] Generated Node #2: [56, 27, 6] from Operation: 84/14=6 Current State: 23:[56, 27, 6], Operations: ['84/14=6'] Exploring Operation: 56-27=29, Resulting Numbers: [6, 29] Generated Node #3: [6, 29] from Operation: 56-27=29 Current State: 23:[6, 29], Operations: ['84/14=6', '56-27=29'] Exploring Operation: 29-6=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[84, 14, 56, 27], Operations: [] Exploring Operation: 84-56=28, Resulting Numbers: [14, 27, 28] Generated Node #0,0: 23:[14, 27, 28] Operation: 84-56=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[14, 27, 28], Operations: ['84-56=28'] Exploring Operation: 28-14=14, Resulting Numbers: [27, 14] Generated Node #0,0,0: 23:[27, 14] Operation: 28-14=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 23:[27, 14], Operations: ['84-56=28', '28-14=14'] Exploring Operation: 27-14=13, Resulting Numbers: [13] 13,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 10, 36, 47, 62 ]
45
[ "10+62=72", "72/36=2", "47-2=45" ]
Current State: 45:[10, 36, 47, 62], Operations: [] Exploring Operation: 10+62=72, Resulting Numbers: [36, 47, 72] Generated Node #2: [36, 47, 72] from Operation: 10+62=72 Current State: 45:[36, 47, 72], Operations: ['10+62=72'] Exploring Operation: 72/36=2, Resulting Numbers: [47, 2] Generated Node #3: [47, 2] from Operation: 72/36=2 Current State: 45:[47, 2], Operations: ['10+62=72', '72/36=2'] Exploring Operation: 47-2=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[10, 36, 47, 62], Operations: [] Exploring Operation: 62-47=15, Resulting Numbers: [10, 36, 15] Generated Node #0,0: 45:[10, 36, 15] Operation: 62-47=15 Moving to Node #0,0 Current State: 45:[10, 36, 15], Operations: ['62-47=15'] Exploring Operation: 10+36=46, Resulting Numbers: [15, 46] Generated Node #0,0,0: 45:[15, 46] Operation: 10+36=46 Moving to Node #0,0,0 Current State: 45:[15, 46], Operations: ['62-47=15', '10+36=46'] Exploring Operation: 46-15=31, Resulting Numbers: [31] 31,45 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 11, 13, 37, 91 ]
93
[ "37-11=26", "26/13=2", "91+2=93" ]
Current State: 93:[11, 13, 37, 91], Operations: [] Exploring Operation: 37-11=26, Resulting Numbers: [13, 91, 26] Generated Node #2: [13, 91, 26] from Operation: 37-11=26 Current State: 93:[13, 91, 26], Operations: ['37-11=26'] Exploring Operation: 26/13=2, Resulting Numbers: [91, 2] Generated Node #3: [91, 2] from Operation: 26/13=2 Current State: 93:[91, 2], Operations: ['37-11=26', '26/13=2'] Exploring Operation: 91+2=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[11, 13, 37, 91], Operations: [] Exploring Operation: 13-11=2, Resulting Numbers: [37, 91, 2] Generated Node #0,0: 93:[37, 91, 2] Operation: 13-11=2 Moving to Node #0,0 Current State: 93:[37, 91, 2], Operations: ['13-11=2'] Exploring Operation: 37-2=35, Resulting Numbers: [91, 35] Generated Node #0,0,0: 93:[91, 35] Operation: 37-2=35 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 93:[91, 35], Operations: ['13-11=2', '37-2=35'] Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,93 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 39, 34, 63, 74 ]
16
[ "39-34=5", "74-63=11", "5+11=16" ]
Current State: 16:[39, 34, 63, 74], Operations: [] Exploring Operation: 39-34=5, Resulting Numbers: [63, 74, 5] Generated Node #2: [63, 74, 5] from Operation: 39-34=5 Current State: 16:[63, 74, 5], Operations: ['39-34=5'] Exploring Operation: 74-63=11, Resulting Numbers: [5, 11] Generated Node #3: [5, 11] from Operation: 74-63=11 Current State: 16:[5, 11], Operations: ['39-34=5', '74-63=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[39, 34, 63, 74], Operations: [] Exploring Operation: 74-63=11, Resulting Numbers: [39, 34, 11] Generated Node #0,0: 16:[39, 34, 11] Operation: 74-63=11 Exploring Operation: 63-39=24, Resulting Numbers: [34, 74, 24] Generated Node #0,1: 16:[34, 74, 24] Operation: 63-39=24 Moving to Node #0,0 Current State: 16:[39, 34, 11], Operations: ['74-63=11'] Exploring Operation: 39-34=5, Resulting Numbers: [11, 5] Generated Node #0,0,0: 16:[11, 5] Operation: 39-34=5 Exploring Operation: 39-11=28, Resulting Numbers: [34, 28] Generated Node #0,0,1: 16:[34, 28] Operation: 39-11=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[11, 5], Operations: ['74-63=11', '39-34=5'] Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[39, 34, 63, 74], Operations: [] Exploring Operation: 74-63=11, Resulting Numbers: [39, 34, 11] Generated Node #0,0: 16:[39, 34, 11] Operation: 74-63=11 Moving to Node #0,0 Current State: 16:[39, 34, 11], Operations: ['74-63=11'] Exploring Operation: 39-34=5, Resulting Numbers: [11, 5] Generated Node #0,0,0: 16:[11, 5] Operation: 39-34=5 Moving to Node #0,0,0 Current State: 16:[11, 5], Operations: ['74-63=11', '39-34=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 53, 77, 38, 37 ]
99
[ "77-53=24", "38+37=75", "24+75=99" ]
Current State: 99:[53, 77, 38, 37], Operations: [] Exploring Operation: 77-53=24, Resulting Numbers: [38, 37, 24] Generated Node #2: [38, 37, 24] from Operation: 77-53=24 Current State: 99:[38, 37, 24], Operations: ['77-53=24'] Exploring Operation: 38+37=75, Resulting Numbers: [24, 75] Generated Node #3: [24, 75] from Operation: 38+37=75 Current State: 99:[24, 75], Operations: ['77-53=24', '38+37=75'] Exploring Operation: 24+75=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[53, 77, 38, 37], Operations: [] Exploring Operation: 77-53=24, Resulting Numbers: [38, 37, 24] Generated Node #0,0: 99:[38, 37, 24] Operation: 77-53=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[38, 37, 24], Operations: ['77-53=24'] Exploring Operation: 38-24=14, Resulting Numbers: [37, 14] Generated Node #0,0,0: 99:[37, 14] Operation: 38-24=14 Moving to Node #0,0,0 Current State: 99:[37, 14], Operations: ['77-53=24', '38-24=14'] Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,99 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
[ 12, 51, 84, 68 ]
93
[ "12*51=612", "612/68=9", "84+9=93" ]
Current State: 93:[12, 51, 84, 68], Operations: [] Exploring Operation: 12*51=612, Resulting Numbers: [84, 68, 612] Generated Node #2: [84, 68, 612] from Operation: 12*51=612 Current State: 93:[84, 68, 612], Operations: ['12*51=612'] Exploring Operation: 612/68=9, Resulting Numbers: [84, 9] Generated Node #3: [84, 9] from Operation: 612/68=9 Current State: 93:[84, 9], Operations: ['12*51=612', '612/68=9'] Exploring Operation: 84+9=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[12, 51, 84, 68], Operations: [] Exploring Operation: 68-51=17, Resulting Numbers: [12, 84, 17] Generated Node #0,0: 93:[12, 84, 17] Operation: 68-51=17 Exploring Operation: 84-51=33, Resulting Numbers: [12, 68, 33] Generated Node #0,1: 93:[12, 68, 33] Operation: 84-51=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[12, 84, 17], Operations: ['68-51=17'] Exploring Operation: 17-12=5, Resulting Numbers: [84, 5] Generated Node #0,0,0: 93:[84, 5] Operation: 17-12=5 Exploring Operation: 12+17=29, Resulting Numbers: [84, 29] Generated Node #0,0,1: 93:[84, 29] Operation: 12+17=29 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 93:[84, 5], Operations: ['68-51=17', '17-12=5'] Exploring Operation: 84+5=89, Resulting Numbers: [89] 89,93 unequal: No Solution Exploring Operation: 84-5=79, Resulting Numbers: [79] 79,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 93:[84, 29], Operations: ['68-51=17', '12+17=29'] Exploring Operation: 84+29=113, Resulting Numbers: [113] 113,93 unequal: No Solution Exploring Operation: 84-29=55, Resulting Numbers: [55] 55,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 93:[12, 68, 33], Operations: ['84-51=33'] Exploring Operation: 12+68=80, Resulting Numbers: [33, 80] Generated Node #0,1,0: 93:[33, 80] Operation: 12+68=80 Exploring Operation: 68-33=35, Resulting Numbers: [12, 35] Generated Node #0,1,1: 93:[12, 35] Operation: 68-33=35 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 93:[12, 35], Operations: ['84-51=33', '68-33=35'] Exploring Operation: 12+35=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 35-12=23, Resulting Numbers: [23] 23,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 93:[33, 80], Operations: ['84-51=33', '12+68=80'] Exploring Operation: 80-33=47, Resulting Numbers: [47] 47,93 unequal: No Solution Exploring Operation: 33+80=113, Resulting Numbers: [113] 113,93 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 68, 39, 78, 22 ]
74
[ "39-22=17", "68/17=4", "78-4=74" ]
Current State: 74:[68, 39, 78, 22], Operations: [] Exploring Operation: 39-22=17, Resulting Numbers: [68, 78, 17] Generated Node #2: [68, 78, 17] from Operation: 39-22=17 Current State: 74:[68, 78, 17], Operations: ['39-22=17'] Exploring Operation: 68/17=4, Resulting Numbers: [78, 4] Generated Node #3: [78, 4] from Operation: 68/17=4 Current State: 74:[78, 4], Operations: ['39-22=17', '68/17=4'] Exploring Operation: 78-4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[68, 39, 78, 22], Operations: [] Exploring Operation: 68-22=46, Resulting Numbers: [39, 78, 46] Generated Node #0,0: 74:[39, 78, 46] Operation: 68-22=46 Moving to Node #0,0 Current State: 74:[39, 78, 46], Operations: ['68-22=46'] Exploring Operation: 78-46=32, Resulting Numbers: [39, 32] Generated Node #0,0,0: 74:[39, 32] Operation: 78-46=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[39, 32], Operations: ['68-22=46', '78-46=32'] Exploring Operation: 39+32=71, Resulting Numbers: [71] 71,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 32, 81, 9, 24 ]
34
[ "81-32=49", "24-9=15", "49-15=34" ]
Current State: 34:[32, 81, 9, 24], Operations: [] Exploring Operation: 81-32=49, Resulting Numbers: [9, 24, 49] Generated Node #2: [9, 24, 49] from Operation: 81-32=49 Current State: 34:[9, 24, 49], Operations: ['81-32=49'] Exploring Operation: 24-9=15, Resulting Numbers: [49, 15] Generated Node #3: [49, 15] from Operation: 24-9=15 Current State: 34:[49, 15], Operations: ['81-32=49', '24-9=15'] Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[32, 81, 9, 24], Operations: [] Exploring Operation: 81-32=49, Resulting Numbers: [9, 24, 49] Generated Node #0,0: 34:[9, 24, 49] Operation: 81-32=49 Exploring Operation: 81/9=9, Resulting Numbers: [32, 24, 9] Generated Node #0,1: 34:[32, 24, 9] Operation: 81/9=9 Exploring Operation: 81-24=57, Resulting Numbers: [32, 9, 57] Generated Node #0,2: 34:[32, 9, 57] Operation: 81-24=57 Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[32, 24, 9], Operations: ['81/9=9'] Exploring Operation: 24-9=15, Resulting Numbers: [32, 15] Generated Node #0,1,0: 34:[32, 15] Operation: 24-9=15 Exploring Operation: 24+9=33, Resulting Numbers: [32, 33] Generated Node #0,1,1: 34:[32, 33] Operation: 24+9=33 Exploring Operation: 32-24=8, Resulting Numbers: [9, 8] Generated Node #0,1,2: 34:[9, 8] Operation: 32-24=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 34:[32, 33], Operations: ['81/9=9', '24+9=33'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,34 unequal: No Solution Exploring Operation: 32+33=65, Resulting Numbers: [65] 65,34 unequal: No Solution Exploring Operation: 32*33=1056, Resulting Numbers: [1056] 1056,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 34:[32, 15], Operations: ['81/9=9', '24-9=15'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,34 unequal: No Solution Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 34:[9, 8], Operations: ['81/9=9', '32-24=8'] Exploring Operation: 9+8=17, Resulting Numbers: [17] 17,34 unequal: No Solution Exploring Operation: 9*8=72, Resulting Numbers: [72] 72,34 unequal: No Solution Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[9, 24, 49], Operations: ['81-32=49'] Exploring Operation: 49-9=40, Resulting Numbers: [24, 40] Generated Node #0,0,0: 34:[24, 40] Operation: 49-9=40 Exploring Operation: 9+24=33, Resulting Numbers: [49, 33] Generated Node #0,0,1: 34:[49, 33] Operation: 9+24=33 Exploring Operation: 49-24=25, Resulting Numbers: [9, 25] Generated Node #0,0,2: 34:[9, 25] Operation: 49-24=25 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 34:[24, 40], Operations: ['81-32=49', '49-9=40'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,34 unequal: No Solution Exploring Operation: 24*40=960, Resulting Numbers: [960] 960,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 34:[9, 25], Operations: ['81-32=49', '49-24=25'] Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[32, 81, 9, 24], Operations: [] Exploring Operation: 81-32=49, Resulting Numbers: [9, 24, 49] Generated Node #0,0: 34:[9, 24, 49] Operation: 81-32=49 Moving to Node #0,0 Current State: 34:[9, 24, 49], Operations: ['81-32=49'] Exploring Operation: 49-24=25, Resulting Numbers: [9, 25] Generated Node #0,0,2: 34:[9, 25] Operation: 49-24=25 Moving to Node #0,0,2 Current State: 34:[9, 25], Operations: ['81-32=49', '49-24=25'] Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.976563
hs_3
sum_heuristic
[ 63, 48, 87, 68 ]
66
[ "87-63=24", "48/24=2", "68-2=66" ]
Current State: 66:[63, 48, 87, 68], Operations: [] Exploring Operation: 87-63=24, Resulting Numbers: [48, 68, 24] Generated Node #2: [48, 68, 24] from Operation: 87-63=24 Current State: 66:[48, 68, 24], Operations: ['87-63=24'] Exploring Operation: 48/24=2, Resulting Numbers: [68, 2] Generated Node #3: [68, 2] from Operation: 48/24=2 Current State: 66:[68, 2], Operations: ['87-63=24', '48/24=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[63, 48, 87, 68], Operations: [] Exploring Operation: 87-48=39, Resulting Numbers: [63, 68, 39] Generated Node #0,0: 66:[63, 68, 39] Operation: 87-48=39 Exploring Operation: 87-63=24, Resulting Numbers: [48, 68, 24] Generated Node #0,1: 66:[48, 68, 24] Operation: 87-63=24 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[63, 68, 39], Operations: ['87-48=39'] Exploring Operation: 63-39=24, Resulting Numbers: [68, 24] Generated Node #0,0,0: 66:[68, 24] Operation: 63-39=24 Exploring Operation: 68-63=5, Resulting Numbers: [39, 5] Generated Node #0,0,1: 66:[39, 5] Operation: 68-63=5 Moving to Node #0,0,0 Current State: 66:[68, 24], Operations: ['87-48=39', '63-39=24'] Exploring Operation: 68+24=92, Resulting Numbers: [92] 92,66 unequal: No Solution Exploring Operation: 68-24=44, Resulting Numbers: [44] 44,66 unequal: No Solution Moving to Node #0,0,1 Current State: 66:[39, 5], Operations: ['87-48=39', '68-63=5'] Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,66 unequal: No Solution Exploring Operation: 39+5=44, Resulting Numbers: [44] 44,66 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 66:[48, 68, 24], Operations: ['87-63=24'] Exploring Operation: 68-48=20, Resulting Numbers: [24, 20] Generated Node #0,1,0: 66:[24, 20] Operation: 68-48=20 Exploring Operation: 48/24=2, Resulting Numbers: [68, 2] Generated Node #0,1,1: 66:[68, 2] Operation: 48/24=2 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 66:[68, 2], Operations: ['87-63=24', '48/24=2'] Exploring Operation: 68/2=34, Resulting Numbers: [34] 34,66 unequal: No Solution Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[63, 48, 87, 68], Operations: [] Exploring Operation: 87-63=24, Resulting Numbers: [48, 68, 24] Generated Node #0,1: 66:[48, 68, 24] Operation: 87-63=24 Moving to Node #0,1 Current State: 66:[48, 68, 24], Operations: ['87-63=24'] Exploring Operation: 48/24=2, Resulting Numbers: [68, 2] Generated Node #0,1,1: 66:[68, 2] Operation: 48/24=2 Moving to Node #0,1,1 Current State: 66:[68, 2], Operations: ['87-63=24', '48/24=2'] Exploring Operation: 68-2=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 70, 32, 25, 94 ]
31
[ "70-32=38", "94-25=69", "69-38=31" ]
Current State: 31:[70, 32, 25, 94], Operations: [] Exploring Operation: 70-32=38, Resulting Numbers: [25, 94, 38] Generated Node #2: [25, 94, 38] from Operation: 70-32=38 Current State: 31:[25, 94, 38], Operations: ['70-32=38'] Exploring Operation: 94-25=69, Resulting Numbers: [38, 69] Generated Node #3: [38, 69] from Operation: 94-25=69 Current State: 31:[38, 69], Operations: ['70-32=38', '94-25=69'] Exploring Operation: 69-38=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[70, 32, 25, 94], Operations: [] Exploring Operation: 94-70=24, Resulting Numbers: [32, 25, 24] Generated Node #0,0: 31:[32, 25, 24] Operation: 94-70=24 Exploring Operation: 70-32=38, Resulting Numbers: [25, 94, 38] Generated Node #0,1: 31:[25, 94, 38] Operation: 70-32=38 Exploring Operation: 94-32=62, Resulting Numbers: [70, 25, 62] Generated Node #0,2: 31:[70, 25, 62] Operation: 94-32=62 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[32, 25, 24], Operations: ['94-70=24'] Exploring Operation: 32-24=8, Resulting Numbers: [25, 8] Generated Node #0,0,0: 31:[25, 8] Operation: 32-24=8 Exploring Operation: 25+24=49, Resulting Numbers: [32, 49] Generated Node #0,0,1: 31:[32, 49] Operation: 25+24=49 Exploring Operation: 32-25=7, Resulting Numbers: [24, 7] Generated Node #0,0,2: 31:[24, 7] Operation: 32-25=7 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[32, 49], Operations: ['94-70=24', '25+24=49'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,31 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,31 unequal: No Solution No 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: 31:[25, 8], Operations: ['94-70=24', '32-24=8'] Exploring Operation: 25-8=17, Resulting Numbers: [17] 17,31 unequal: No Solution Exploring Operation: 25*8=200, Resulting Numbers: [200] 200,31 unequal: No Solution Exploring Operation: 25+8=33, Resulting Numbers: [33] 33,31 unequal: No Solution No 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: 31:[24, 7], Operations: ['94-70=24', '32-25=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[70, 32, 25, 94], Operations: [] Exploring Operation: 94-70=24, Resulting Numbers: [32, 25, 24] Generated Node #0,0: 31:[32, 25, 24] Operation: 94-70=24 Moving to Node #0,0 Current State: 31:[32, 25, 24], Operations: ['94-70=24'] Exploring Operation: 32-25=7, Resulting Numbers: [24, 7] Generated Node #0,0,2: 31:[24, 7] Operation: 32-25=7 Moving to Node #0,0,2 Current State: 31:[24, 7], Operations: ['94-70=24', '32-25=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 15, 14, 51, 5 ]
57
[ "15-14=1", "51+5=56", "1+56=57" ]
Current State: 57:[15, 14, 51, 5], Operations: [] Exploring Operation: 15-14=1, Resulting Numbers: [51, 5, 1] Generated Node #2: [51, 5, 1] from Operation: 15-14=1 Current State: 57:[51, 5, 1], Operations: ['15-14=1'] Exploring Operation: 51+5=56, Resulting Numbers: [1, 56] Generated Node #3: [1, 56] from Operation: 51+5=56 Current State: 57:[1, 56], Operations: ['15-14=1', '51+5=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[15, 14, 51, 5], Operations: [] Exploring Operation: 51+5=56, Resulting Numbers: [15, 14, 56] Generated Node #0,0: 57:[15, 14, 56] Operation: 51+5=56 Exploring Operation: 15-14=1, Resulting Numbers: [51, 5, 1] Generated Node #0,1: 57:[51, 5, 1] Operation: 15-14=1 Exploring Operation: 14+5=19, Resulting Numbers: [15, 51, 19] Generated Node #0,2: 57:[15, 51, 19] Operation: 14+5=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[15, 14, 56], Operations: ['51+5=56'] Exploring Operation: 15-14=1, Resulting Numbers: [56, 1] Generated Node #0,0,0: 57:[56, 1] Operation: 15-14=1 Exploring Operation: 15+14=29, Resulting Numbers: [56, 29] Generated Node #0,0,1: 57:[56, 29] Operation: 15+14=29 Exploring Operation: 56/14=4, Resulting Numbers: [15, 4] Generated Node #0,0,2: 57:[15, 4] Operation: 56/14=4 Moving to Node #0,0,0 Current State: 57:[56, 1], Operations: ['51+5=56', '15-14=1'] Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,57 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[15, 14, 51, 5], Operations: [] Exploring Operation: 51+5=56, Resulting Numbers: [15, 14, 56] Generated Node #0,0: 57:[15, 14, 56] Operation: 51+5=56 Moving to Node #0,0 Current State: 57:[15, 14, 56], Operations: ['51+5=56'] Exploring Operation: 15-14=1, Resulting Numbers: [56, 1] Generated Node #0,0,0: 57:[56, 1] Operation: 15-14=1 Moving to Node #0,0,0 Current State: 57:[56, 1], Operations: ['51+5=56', '15-14=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 31, 32, 21, 11 ]
10
[ "32-31=1", "21-11=10", "1*10=10" ]
Current State: 10:[31, 32, 21, 11], Operations: [] Exploring Operation: 32-31=1, Resulting Numbers: [21, 11, 1] Generated Node #2: [21, 11, 1] from Operation: 32-31=1 Current State: 10:[21, 11, 1], Operations: ['32-31=1'] Exploring Operation: 21-11=10, Resulting Numbers: [1, 10] Generated Node #3: [1, 10] from Operation: 21-11=10 Current State: 10:[1, 10], Operations: ['32-31=1', '21-11=10'] Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[31, 32, 21, 11], Operations: [] Exploring Operation: 32-21=11, Resulting Numbers: [31, 11, 11] Generated Node #0,0: 10:[31, 11, 11] Operation: 32-21=11 Exploring Operation: 31-21=10, Resulting Numbers: [32, 11, 10] Generated Node #0,1: 10:[32, 11, 10] Operation: 31-21=10 Exploring Operation: 32-31=1, Resulting Numbers: [21, 11, 1] Generated Node #0,2: 10:[21, 11, 1] Operation: 32-31=1 Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[21, 11, 1], Operations: ['32-31=1'] Exploring Operation: 21-11=10, Resulting Numbers: [1, 10] Generated Node #0,2,0: 10:[1, 10] Operation: 21-11=10 Exploring Operation: 21-1=20, Resulting Numbers: [11, 20] Generated Node #0,2,1: 10:[11, 20] Operation: 21-1=20 Exploring Operation: 11-1=10, Resulting Numbers: [21, 10] Generated Node #0,2,2: 10:[21, 10] Operation: 11-1=10 Moving to Node #0,2,0 Current State: 10:[1, 10], Operations: ['32-31=1', '21-11=10'] Exploring Operation: 1+10=11, Resulting Numbers: [11] 11,10 unequal: No Solution Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[31, 32, 21, 11], Operations: [] Exploring Operation: 32-31=1, Resulting Numbers: [21, 11, 1] Generated Node #0,2: 10:[21, 11, 1] Operation: 32-31=1 Moving to Node #0,2 Current State: 10:[21, 11, 1], Operations: ['32-31=1'] Exploring Operation: 21-11=10, Resulting Numbers: [1, 10] Generated Node #0,2,0: 10:[1, 10] Operation: 21-11=10 Moving to Node #0,2,0 Current State: 10:[1, 10], Operations: ['32-31=1', '21-11=10'] Exploring Operation: 1*10=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 19, 26, 55, 3 ]
51
[ "26-19=7", "55+3=58", "58-7=51" ]
Current State: 51:[19, 26, 55, 3], Operations: [] Exploring Operation: 26-19=7, Resulting Numbers: [55, 3, 7] Generated Node #2: [55, 3, 7] from Operation: 26-19=7 Current State: 51:[55, 3, 7], Operations: ['26-19=7'] Exploring Operation: 55+3=58, Resulting Numbers: [7, 58] Generated Node #3: [7, 58] from Operation: 55+3=58 Current State: 51:[7, 58], Operations: ['26-19=7', '55+3=58'] Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[19, 26, 55, 3], Operations: [] Exploring Operation: 26-19=7, Resulting Numbers: [55, 3, 7] Generated Node #0,0: 51:[55, 3, 7] Operation: 26-19=7 Exploring Operation: 19+26=45, Resulting Numbers: [55, 3, 45] Generated Node #0,1: 51:[55, 3, 45] Operation: 19+26=45 Moving to Node #0,0 Current State: 51:[55, 3, 7], Operations: ['26-19=7'] Exploring Operation: 55-7=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 51:[3, 48] Operation: 55-7=48 Exploring Operation: 55-3=52, Resulting Numbers: [7, 52] Generated Node #0,0,1: 51:[7, 52] Operation: 55-3=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 51:[3, 48], Operations: ['26-19=7', '55-7=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[19, 26, 55, 3], Operations: [] Exploring Operation: 26-19=7, Resulting Numbers: [55, 3, 7] Generated Node #0,0: 51:[55, 3, 7] Operation: 26-19=7 Moving to Node #0,0 Current State: 51:[55, 3, 7], Operations: ['26-19=7'] Exploring Operation: 55-7=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 51:[3, 48] Operation: 55-7=48 Moving to Node #0,0,0 Current State: 51:[3, 48], Operations: ['26-19=7', '55-7=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 32, 19, 96, 54 ]
55
[ "32-19=13", "96-54=42", "13+42=55" ]
Current State: 55:[32, 19, 96, 54], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [96, 54, 13] Generated Node #2: [96, 54, 13] from Operation: 32-19=13 Current State: 55:[96, 54, 13], Operations: ['32-19=13'] Exploring Operation: 96-54=42, Resulting Numbers: [13, 42] Generated Node #3: [13, 42] from Operation: 96-54=42 Current State: 55:[13, 42], Operations: ['32-19=13', '96-54=42'] Exploring Operation: 13+42=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[32, 19, 96, 54], Operations: [] Exploring Operation: 32-19=13, Resulting Numbers: [96, 54, 13] Generated Node #0,0: 55:[96, 54, 13] Operation: 32-19=13 Exploring Operation: 96/32=3, Resulting Numbers: [19, 54, 3] Generated Node #0,1: 55:[19, 54, 3] Operation: 96/32=3 Exploring Operation: 96-54=42, Resulting Numbers: [32, 19, 42] Generated Node #0,2: 55:[32, 19, 42] Operation: 96-54=42 Exploring Operation: 96-32=64, Resulting Numbers: [19, 54, 64] Generated Node #0,3: 55:[19, 54, 64] Operation: 96-32=64 Exploring Operation: 96-19=77, Resulting Numbers: [32, 54, 77] Generated Node #0,4: 55:[32, 54, 77] Operation: 96-19=77 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[19, 54, 3], Operations: ['96/32=3'] Exploring Operation: 54-3=51, Resulting Numbers: [19, 51] Generated Node #0,1,0: 55:[19, 51] Operation: 54-3=51 Exploring Operation: 19*3=57, Resulting Numbers: [54, 57] Generated Node #0,1,1: 55:[54, 57] Operation: 19*3=57 Exploring Operation: 54+3=57, Resulting Numbers: [19, 57] Generated Node #0,1,2: 55:[19, 57] Operation: 54+3=57 Exploring Operation: 19+3=22, Resulting Numbers: [54, 22] Generated Node #0,1,3: 55:[54, 22] Operation: 19+3=22 Exploring Operation: 19-3=16, Resulting Numbers: [54, 16] Generated Node #0,1,4: 55:[54, 16] Operation: 19-3=16 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[54, 57], Operations: ['96/32=3', '19*3=57'] Exploring Operation: 54+57=111, Resulting Numbers: [111] 111,55 unequal: No Solution Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 54*57=3078, Resulting Numbers: [3078] 3078,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[54, 16], Operations: ['96/32=3', '19-3=16'] Exploring Operation: 54*16=864, Resulting Numbers: [864] 864,55 unequal: No Solution Exploring Operation: 54+16=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 54-16=38, Resulting Numbers: [38] 38,55 unequal: No Solution No 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: 55:[19, 57], Operations: ['96/32=3', '54+3=57'] Exploring Operation: 19+57=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 19*57=1083, Resulting Numbers: [1083] 1083,55 unequal: No Solution Exploring Operation: 57-19=38, Resulting Numbers: [38] 38,55 unequal: No Solution Exploring Operation: 57/19=3, Resulting Numbers: [3] 3,55 unequal: No Solution No 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: 55:[19, 51], Operations: ['96/32=3', '54-3=51'] Exploring Operation: 51-19=32, Resulting Numbers: [32] 32,55 unequal: No Solution Exploring Operation: 19+51=70, Resulting Numbers: [70] 70,55 unequal: No Solution Exploring Operation: 19*51=969, Resulting Numbers: [969] 969,55 unequal: No Solution No 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: 55:[54, 22], Operations: ['96/32=3', '19+3=22'] Exploring Operation: 54*22=1188, Resulting Numbers: [1188] 1188,55 unequal: No Solution Exploring Operation: 54+22=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 54-22=32, Resulting Numbers: [32] 32,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[19, 54, 64], Operations: ['96-32=64'] Exploring Operation: 19+54=73, Resulting Numbers: [64, 73] Generated Node #0,3,0: 55:[64, 73] Operation: 19+54=73 Exploring Operation: 54-19=35, Resulting Numbers: [64, 35] Generated Node #0,3,1: 55:[64, 35] Operation: 54-19=35 Exploring Operation: 64-54=10, Resulting Numbers: [19, 10] Generated Node #0,3,2: 55:[19, 10] Operation: 64-54=10 Exploring Operation: 19+64=83, Resulting Numbers: [54, 83] Generated Node #0,3,3: 55:[54, 83] Operation: 19+64=83 Exploring Operation: 64-19=45, Resulting Numbers: [54, 45] Generated Node #0,3,4: 55:[54, 45] Operation: 64-19=45 Moving to Node #0,3,2 Current State: 55:[19, 10], Operations: ['96-32=64', '64-54=10'] Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,55 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,55 unequal: No Solution Moving to Node #0,3,4 Current State: 55:[54, 45], Operations: ['96-32=64', '64-19=45'] Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,55 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,55 unequal: No Solution Moving to Node #0,3,0 Current State: 55:[64, 73], Operations: ['96-32=64', '19+54=73'] Exploring Operation: 64*73=4672, Resulting Numbers: [4672] 4672,55 unequal: No Solution Exploring Operation: 73-64=9, Resulting Numbers: [9] 9,55 unequal: No Solution Exploring Operation: 64+73=137, Resulting Numbers: [137] 137,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[64, 35], Operations: ['96-32=64', '54-19=35'] Exploring Operation: 64+35=99, Resulting Numbers: [99] 99,55 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 64*35=2240, Resulting Numbers: [2240] 2240,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[54, 83], Operations: ['96-32=64', '19+64=83'] Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 54+83=137, Resulting Numbers: [137] 137,55 unequal: No Solution Exploring Operation: 54*83=4482, Resulting Numbers: [4482] 4482,55 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 Current State: 55:[32, 19, 42], Operations: ['96-54=42'] Exploring Operation: 32+42=74, Resulting Numbers: [19, 74] Generated Node #0,2,0: 55:[19, 74] Operation: 32+42=74 Exploring Operation: 19+42=61, Resulting Numbers: [32, 61] Generated Node #0,2,1: 55:[32, 61] Operation: 19+42=61 Exploring Operation: 32+19=51, Resulting Numbers: [42, 51] Generated Node #0,2,2: 55:[42, 51] Operation: 32+19=51 Exploring Operation: 42-32=10, Resulting Numbers: [19, 10] Generated Node #0,2,3: 55:[19, 10] Operation: 42-32=10 Exploring Operation: 32-19=13, Resulting Numbers: [42, 13] Generated Node #0,2,4: 55:[42, 13] Operation: 32-19=13 Moving to Node #0,2,3 Current State: 55:[19, 10], Operations: ['96-54=42', '42-32=10'] Exploring Operation: 19*10=190, Resulting Numbers: [190] 190,55 unequal: No Solution Exploring Operation: 19+10=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 19-10=9, Resulting Numbers: [9] 9,55 unequal: No Solution Moving to Node #0,2,4 Current State: 55:[42, 13], Operations: ['96-54=42', '32-19=13'] Exploring Operation: 42-13=29, Resulting Numbers: [29] 29,55 unequal: No Solution Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[32, 19, 96, 54], Operations: [] Exploring Operation: 96-54=42, Resulting Numbers: [32, 19, 42] Generated Node #0,2: 55:[32, 19, 42] Operation: 96-54=42 Moving to Node #0,2 Current State: 55:[32, 19, 42], Operations: ['96-54=42'] Exploring Operation: 32-19=13, Resulting Numbers: [42, 13] Generated Node #0,2,4: 55:[42, 13] Operation: 32-19=13 Moving to Node #0,2,4 Current State: 55:[42, 13], Operations: ['96-54=42', '32-19=13'] Exploring Operation: 42+13=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 63, 56, 95, 42 ]
26
[ "95-56=39", "42*39=1638", "1638/63=26" ]
Current State: 26:[63, 56, 95, 42], Operations: [] Exploring Operation: 95-56=39, Resulting Numbers: [63, 42, 39] Generated Node #2: [63, 42, 39] from Operation: 95-56=39 Current State: 26:[63, 42, 39], Operations: ['95-56=39'] Exploring Operation: 42*39=1638, Resulting Numbers: [63, 1638] Generated Node #3: [63, 1638] from Operation: 42*39=1638 Current State: 26:[63, 1638], Operations: ['95-56=39', '42*39=1638'] Exploring Operation: 1638/63=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[63, 56, 95, 42], Operations: [] Exploring Operation: 63-56=7, Resulting Numbers: [95, 42, 7] Generated Node #0,0: 26:[95, 42, 7] Operation: 63-56=7 Exploring Operation: 95-63=32, Resulting Numbers: [56, 42, 32] Generated Node #0,1: 26:[56, 42, 32] Operation: 95-63=32 Exploring Operation: 95-56=39, Resulting Numbers: [63, 42, 39] Generated Node #0,2: 26:[63, 42, 39] Operation: 95-56=39 Moving to Node #0,1 Current State: 26:[56, 42, 32], Operations: ['95-63=32'] Exploring Operation: 56-32=24, Resulting Numbers: [42, 24] Generated Node #0,1,0: 26:[42, 24] Operation: 56-32=24 Exploring Operation: 42-32=10, Resulting Numbers: [56, 10] Generated Node #0,1,1: 26:[56, 10] Operation: 42-32=10 Exploring Operation: 56-42=14, Resulting Numbers: [32, 14] Generated Node #0,1,2: 26:[32, 14] Operation: 56-42=14 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[32, 14], Operations: ['95-63=32', '56-42=14'] Exploring Operation: 32*14=448, Resulting Numbers: [448] 448,26 unequal: No Solution Exploring Operation: 32+14=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 32-14=18, Resulting Numbers: [18] 18,26 unequal: No Solution No 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: 26:[42, 24], Operations: ['95-63=32', '56-32=24'] Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,26 unequal: No Solution Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,26 unequal: No Solution Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,26 unequal: No Solution No 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: 26:[56, 10], Operations: ['95-63=32', '42-32=10'] Exploring Operation: 56*10=560, Resulting Numbers: [560] 560,26 unequal: No Solution Exploring Operation: 56+10=66, Resulting Numbers: [66] 66,26 unequal: No Solution Exploring Operation: 56-10=46, Resulting Numbers: [46] 46,26 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: 26:[63, 42, 39], Operations: ['95-56=39'] Exploring Operation: 63-42=21, Resulting Numbers: [39, 21] Generated Node #0,2,0: 26:[39, 21] Operation: 63-42=21 Exploring Operation: 63-39=24, Resulting Numbers: [42, 24] Generated Node #0,2,1: 26:[42, 24] Operation: 63-39=24 Exploring Operation: 42-39=3, Resulting Numbers: [63, 3] Generated Node #0,2,2: 26:[63, 3] Operation: 42-39=3 Moving to Node #0,0 Current State: 26:[95, 42, 7], Operations: ['63-56=7'] Exploring Operation: 95-42=53, Resulting Numbers: [7, 53] Generated Node #0,0,0: 26:[7, 53] Operation: 95-42=53 Exploring Operation: 42/7=6, Resulting Numbers: [95, 6] Generated Node #0,0,1: 26:[95, 6] Operation: 42/7=6 Exploring Operation: 95-7=88, Resulting Numbers: [42, 88] Generated Node #0,0,2: 26:[42, 88] Operation: 95-7=88 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[7, 53], Operations: ['63-56=7', '95-42=53'] Exploring Operation: 7*53=371, Resulting Numbers: [371] 371,26 unequal: No Solution Exploring Operation: 53-7=46, Resulting Numbers: [46] 46,26 unequal: No Solution Exploring Operation: 7+53=60, Resulting Numbers: [60] 60,26 unequal: No Solution No 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: 26:[95, 6], Operations: ['63-56=7', '42/7=6'] Exploring Operation: 95*6=570, Resulting Numbers: [570] 570,26 unequal: No Solution Exploring Operation: 95+6=101, Resulting Numbers: [101] 101,26 unequal: No Solution Exploring Operation: 95-6=89, Resulting Numbers: [89] 89,26 unequal: No Solution No 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: 26:[42, 88], Operations: ['63-56=7', '95-7=88'] Exploring Operation: 42+88=130, Resulting Numbers: [130] 130,26 unequal: No Solution Exploring Operation: 42*88=3696, Resulting Numbers: [3696] 3696,26 unequal: No Solution Exploring Operation: 88-42=46, Resulting Numbers: [46] 46,26 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: 26:[39, 21], Operations: ['95-56=39', '63-42=21'] Exploring Operation: 39+21=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 39*21=819, Resulting Numbers: [819] 819,26 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,26 unequal: No Solution Moving to Node #0,2,1 Current State: 26:[42, 24], Operations: ['95-56=39', '63-39=24'] Exploring Operation: 42+24=66, Resulting Numbers: [66] 66,26 unequal: No Solution Exploring Operation: 42*24=1008, Resulting Numbers: [1008] 1008,26 unequal: No Solution Exploring Operation: 42-24=18, Resulting Numbers: [18] 18,26 unequal: No Solution Moving to Node #0,2,2 Current State: 26:[63, 3], Operations: ['95-56=39', '42-39=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,26 unequal: No Solution Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,26 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,26 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 80, 82, 77, 51 ]
25
[ "82-80=2", "51*2=102", "102-77=25" ]
Current State: 25:[80, 82, 77, 51], Operations: [] Exploring Operation: 82-80=2, Resulting Numbers: [77, 51, 2] Generated Node #2: [77, 51, 2] from Operation: 82-80=2 Current State: 25:[77, 51, 2], Operations: ['82-80=2'] Exploring Operation: 51*2=102, Resulting Numbers: [77, 102] Generated Node #3: [77, 102] from Operation: 51*2=102 Current State: 25:[77, 102], Operations: ['82-80=2', '51*2=102'] Exploring Operation: 102-77=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[80, 82, 77, 51], Operations: [] Exploring Operation: 80-77=3, Resulting Numbers: [82, 51, 3] Generated Node #0,0: 25:[82, 51, 3] Operation: 80-77=3 Exploring Operation: 82-77=5, Resulting Numbers: [80, 51, 5] Generated Node #0,1: 25:[80, 51, 5] Operation: 82-77=5 Exploring Operation: 80-51=29, Resulting Numbers: [82, 77, 29] Generated Node #0,2: 25:[82, 77, 29] Operation: 80-51=29 Exploring Operation: 82-51=31, Resulting Numbers: [80, 77, 31] Generated Node #0,3: 25:[80, 77, 31] Operation: 82-51=31 Exploring Operation: 82-80=2, Resulting Numbers: [77, 51, 2] Generated Node #0,4: 25:[77, 51, 2] Operation: 82-80=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 25:[80, 51, 5], Operations: ['82-77=5'] Exploring Operation: 80+5=85, Resulting Numbers: [51, 85] Generated Node #0,1,0: 25:[51, 85] Operation: 80+5=85 Exploring Operation: 80-5=75, Resulting Numbers: [51, 75] Generated Node #0,1,1: 25:[51, 75] Operation: 80-5=75 Exploring Operation: 80/5=16, Resulting Numbers: [51, 16] Generated Node #0,1,2: 25:[51, 16] Operation: 80/5=16 Exploring Operation: 80-51=29, Resulting Numbers: [5, 29] Generated Node #0,1,3: 25:[5, 29] Operation: 80-51=29 Exploring Operation: 51-5=46, Resulting Numbers: [80, 46] Generated Node #0,1,4: 25:[80, 46] Operation: 51-5=46 Moving to Node #0,1,3 Current State: 25:[5, 29], Operations: ['82-77=5', '80-51=29'] Exploring Operation: 5+29=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 5*29=145, Resulting Numbers: [145] 145,25 unequal: No Solution Moving to Node #0,1,2 Current State: 25:[51, 16], Operations: ['82-77=5', '80/5=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,25 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,25 unequal: No Solution Moving to Node #0,1,1 Current State: 25:[51, 75], Operations: ['82-77=5', '80-5=75'] Exploring Operation: 75-51=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 51+75=126, Resulting Numbers: [126] 126,25 unequal: No Solution Exploring Operation: 51*75=3825, Resulting Numbers: [3825] 3825,25 unequal: No Solution Moving to Node #0,1,4 Current State: 25:[80, 46], Operations: ['82-77=5', '51-5=46'] Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,25 unequal: No Solution Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 80*46=3680, Resulting Numbers: [3680] 3680,25 unequal: No Solution Moving to Node #0,1,0 Current State: 25:[51, 85], Operations: ['82-77=5', '80+5=85'] Exploring Operation: 51*85=4335, Resulting Numbers: [4335] 4335,25 unequal: No Solution Exploring Operation: 51+85=136, Resulting Numbers: [136] 136,25 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 25:[77, 51, 2], Operations: ['82-80=2'] Exploring Operation: 51+2=53, Resulting Numbers: [77, 53] Generated Node #0,4,0: 25:[77, 53] Operation: 51+2=53 Exploring Operation: 77+2=79, Resulting Numbers: [51, 79] Generated Node #0,4,1: 25:[51, 79] Operation: 77+2=79 Exploring Operation: 51-2=49, Resulting Numbers: [77, 49] Generated Node #0,4,2: 25:[77, 49] Operation: 51-2=49 Exploring Operation: 77-2=75, Resulting Numbers: [51, 75] Generated Node #0,4,3: 25:[51, 75] Operation: 77-2=75 Exploring Operation: 77-51=26, Resulting Numbers: [2, 26] Generated Node #0,4,4: 25:[2, 26] Operation: 77-51=26 Moving to Node #0,4,4 Current State: 25:[2, 26], Operations: ['82-80=2', '77-51=26'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 2+26=28, Resulting Numbers: [28] 28,25 unequal: No Solution Exploring Operation: 2*26=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,25 unequal: No Solution Moving to Node #0,4,3 Current State: 25:[51, 75], Operations: ['82-80=2', '77-2=75'] Exploring Operation: 51*75=3825, Resulting Numbers: [3825] 3825,25 unequal: No Solution Exploring Operation: 75-51=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 51+75=126, Resulting Numbers: [126] 126,25 unequal: No Solution Moving to Node #0,4,2 Current State: 25:[77, 49], Operations: ['82-80=2', '51-2=49'] Exploring Operation: 77*49=3773, Resulting Numbers: [3773] 3773,25 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,25 unequal: No Solution Exploring Operation: 77+49=126, Resulting Numbers: [126] 126,25 unequal: No Solution Moving to Node #0,4,0 Current State: 25:[77, 53], Operations: ['82-80=2', '51+2=53'] Exploring Operation: 77*53=4081, Resulting Numbers: [4081] 4081,25 unequal: No Solution Exploring Operation: 77+53=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 77-53=24, Resulting Numbers: [24] 24,25 unequal: No Solution Moving to Node #0,4,1 Current State: 25:[51, 79], Operations: ['82-80=2', '77+2=79'] Exploring Operation: 51+79=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 51*79=4029, Resulting Numbers: [4029] 4029,25 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,25 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 Current State: 25:[82, 51, 3], Operations: ['80-77=3'] Exploring Operation: 51-3=48, Resulting Numbers: [82, 48] Generated Node #0,0,0: 25:[82, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [82, 17] Generated Node #0,0,1: 25:[82, 17] Operation: 51/3=17 Exploring Operation: 82-3=79, Resulting Numbers: [51, 79] Generated Node #0,0,2: 25:[51, 79] Operation: 82-3=79 Exploring Operation: 82+3=85, Resulting Numbers: [51, 85] Generated Node #0,0,3: 25:[51, 85] Operation: 82+3=85 Exploring Operation: 82-51=31, Resulting Numbers: [3, 31] Generated Node #0,0,4: 25:[3, 31] Operation: 82-51=31 Moving to Node #0,0,4 Current State: 25:[3, 31], Operations: ['80-77=3', '82-51=31'] Exploring Operation: 3+31=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 3*31=93, Resulting Numbers: [93] 93,25 unequal: No Solution Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,25 unequal: No Solution Moving to Node #0,0,1 Current State: 25:[82, 17], Operations: ['80-77=3', '51/3=17'] Exploring Operation: 82-17=65, Resulting Numbers: [65] 65,25 unequal: No Solution Exploring Operation: 82*17=1394, Resulting Numbers: [1394] 1394,25 unequal: No Solution Exploring Operation: 82+17=99, Resulting Numbers: [99] 99,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[82, 48], Operations: ['80-77=3', '51-3=48'] Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,25 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[51, 79], Operations: ['80-77=3', '82-3=79'] Exploring Operation: 51+79=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 51*79=4029, Resulting Numbers: [4029] 4029,25 unequal: No Solution Exploring Operation: 79-51=28, Resulting Numbers: [28] 28,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[51, 85], Operations: ['80-77=3', '82+3=85'] Exploring Operation: 51+85=136, Resulting Numbers: [136] 136,25 unequal: No Solution Exploring Operation: 85-51=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 51*85=4335, Resulting Numbers: [4335] 4335,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 25:[82, 77, 29], Operations: ['80-51=29'] Exploring Operation: 77-29=48, Resulting Numbers: [82, 48] Generated Node #0,2,0: 25:[82, 48] Operation: 77-29=48 Exploring Operation: 82+77=159, Resulting Numbers: [29, 159] Generated Node #0,2,1: 25:[29, 159] Operation: 82+77=159 Exploring Operation: 82-77=5, Resulting Numbers: [29, 5] Generated Node #0,2,2: 25:[29, 5] Operation: 82-77=5 Exploring Operation: 82-29=53, Resulting Numbers: [77, 53] Generated Node #0,2,3: 25:[77, 53] Operation: 82-29=53 Exploring Operation: 82+29=111, Resulting Numbers: [77, 111] Generated Node #0,2,4: 25:[77, 111] Operation: 82+29=111 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 25:[29, 5], Operations: ['80-51=29', '82-77=5'] Exploring Operation: 29*5=145, Resulting Numbers: [145] 145,25 unequal: No Solution Exploring Operation: 29-5=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 29+5=34, Resulting Numbers: [34] 34,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 25:[82, 48], Operations: ['80-51=29', '77-29=48'] Exploring Operation: 82*48=3936, Resulting Numbers: [3936] 3936,25 unequal: No Solution Exploring Operation: 82+48=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 82-48=34, Resulting Numbers: [34] 34,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 25:[77, 53], Operations: ['80-51=29', '82-29=53'] Exploring Operation: 77*53=4081, Resulting Numbers: [4081] 4081,25 unequal: No Solution Exploring Operation: 77-53=24, Resulting Numbers: [24] 24,25 unequal: No Solution Exploring Operation: 77+53=130, Resulting Numbers: [130] 130,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 25:[29, 159], Operations: ['80-51=29', '82+77=159'] Exploring Operation: 159-29=130, Resulting Numbers: [130] 130,25 unequal: No Solution Exploring Operation: 29*159=4611, Resulting Numbers: [4611] 4611,25 unequal: No Solution Exploring Operation: 29+159=188, Resulting Numbers: [188] 188,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 25:[77, 111], Operations: ['80-51=29', '82+29=111'] Exploring Operation: 77*111=8547, Resulting Numbers: [8547] 8547,25 unequal: No Solution Exploring Operation: 111-77=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 77+111=188, Resulting Numbers: [188] 188,25 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 25:[80, 77, 31], Operations: ['82-51=31'] Exploring Operation: 80+31=111, Resulting Numbers: [77, 111] Generated Node #0,3,0: 25:[77, 111] Operation: 80+31=111 Exploring Operation: 80-31=49, Resulting Numbers: [77, 49] Generated Node #0,3,1: 25:[77, 49] Operation: 80-31=49 Exploring Operation: 80+77=157, Resulting Numbers: [31, 157] Generated Node #0,3,2: 25:[31, 157] Operation: 80+77=157 Exploring Operation: 80-77=3, Resulting Numbers: [31, 3] Generated Node #0,3,3: 25:[31, 3] Operation: 80-77=3 Exploring Operation: 77-31=46, Resulting Numbers: [80, 46] Generated Node #0,3,4: 25:[80, 46] Operation: 77-31=46 Moving to Node #0,3,3 Current State: 25:[31, 3], Operations: ['82-51=31', '80-77=3'] Exploring Operation: 31-3=28, Resulting Numbers: [28] 28,25 unequal: No Solution Exploring Operation: 31*3=93, Resulting Numbers: [93] 93,25 unequal: No Solution Exploring Operation: 31+3=34, Resulting Numbers: [34] 34,25 unequal: No Solution Moving to Node #0,3,4 Current State: 25:[80, 46], Operations: ['82-51=31', '77-31=46'] Exploring Operation: 80+46=126, Resulting Numbers: [126] 126,25 unequal: No Solution Exploring Operation: 80*46=3680, Resulting Numbers: [3680] 3680,25 unequal: No Solution Exploring Operation: 80-46=34, Resulting Numbers: [34] 34,25 unequal: No Solution Moving to Node #0,3,1 Current State: 25:[77, 49], Operations: ['82-51=31', '80-31=49'] Exploring Operation: 77*49=3773, Resulting Numbers: [3773] 3773,25 unequal: No Solution Exploring Operation: 77+49=126, Resulting Numbers: [126] 126,25 unequal: No Solution Exploring Operation: 77-49=28, Resulting Numbers: [28] 28,25 unequal: No Solution Moving to Node #0,3,0 Current State: 25:[77, 111], Operations: ['82-51=31', '80+31=111'] Exploring Operation: 77*111=8547, Resulting Numbers: [8547] 8547,25 unequal: No Solution Exploring Operation: 111-77=34, Resulting Numbers: [34] 34,25 unequal: No Solution Exploring Operation: 77+111=188, Resulting Numbers: [188] 188,25 unequal: No Solution Moving to Node #0,3,2 Current State: 25:[31, 157], Operations: ['82-51=31', '80+77=157'] Exploring Operation: 31+157=188, Resulting Numbers: [188] 188,25 unequal: No Solution Exploring Operation: 157-31=126, Resulting Numbers: [126] 126,25 unequal: No Solution Exploring Operation: 31*157=4867, Resulting Numbers: [4867] 4867,25 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
[ 78, 67, 92, 2 ]
70
[ "78-67=11", "2*11=22", "92-22=70" ]
Current State: 70:[78, 67, 92, 2], Operations: [] Exploring Operation: 78-67=11, Resulting Numbers: [92, 2, 11] Generated Node #2: [92, 2, 11] from Operation: 78-67=11 Current State: 70:[92, 2, 11], Operations: ['78-67=11'] Exploring Operation: 2*11=22, Resulting Numbers: [92, 22] Generated Node #3: [92, 22] from Operation: 2*11=22 Current State: 70:[92, 22], Operations: ['78-67=11', '2*11=22'] Exploring Operation: 92-22=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[78, 67, 92, 2], Operations: [] Exploring Operation: 92-78=14, Resulting Numbers: [67, 2, 14] Generated Node #0,0: 70:[67, 2, 14] Operation: 92-78=14 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[67, 2, 14], Operations: ['92-78=14'] Exploring Operation: 67+2=69, Resulting Numbers: [14, 69] Generated Node #0,0,0: 70:[14, 69] Operation: 67+2=69 Moving to Node #0,0,0 Current State: 70:[14, 69], Operations: ['92-78=14', '67+2=69'] Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 94, 87, 9, 5 ]
11
[ "94-87=7", "9-5=4", "7+4=11" ]
Current State: 11:[94, 87, 9, 5], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [9, 5, 7] Generated Node #2: [9, 5, 7] from Operation: 94-87=7 Current State: 11:[9, 5, 7], Operations: ['94-87=7'] Exploring Operation: 9-5=4, Resulting Numbers: [7, 4] Generated Node #3: [7, 4] from Operation: 9-5=4 Current State: 11:[7, 4], Operations: ['94-87=7', '9-5=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[94, 87, 9, 5], Operations: [] Exploring Operation: 87-9=78, Resulting Numbers: [94, 5, 78] Generated Node #0,0: 11:[94, 5, 78] Operation: 87-9=78 Exploring Operation: 94-87=7, Resulting Numbers: [9, 5, 7] Generated Node #0,1: 11:[9, 5, 7] Operation: 94-87=7 Exploring Operation: 94-9=85, Resulting Numbers: [87, 5, 85] Generated Node #0,2: 11:[87, 5, 85] Operation: 94-9=85 Exploring Operation: 87-5=82, Resulting Numbers: [94, 9, 82] Generated Node #0,3: 11:[94, 9, 82] Operation: 87-5=82 Exploring Operation: 94-5=89, Resulting Numbers: [87, 9, 89] Generated Node #0,4: 11:[87, 9, 89] Operation: 94-5=89 Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[9, 5, 7], Operations: ['94-87=7'] Exploring Operation: 9+5=14, Resulting Numbers: [7, 14] Generated Node #0,1,0: 11:[7, 14] Operation: 9+5=14 Exploring Operation: 9-5=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 11:[7, 4] Operation: 9-5=4 Exploring Operation: 9+7=16, Resulting Numbers: [5, 16] Generated Node #0,1,2: 11:[5, 16] Operation: 9+7=16 Exploring Operation: 7-5=2, Resulting Numbers: [9, 2] Generated Node #0,1,3: 11:[9, 2] Operation: 7-5=2 Exploring Operation: 5+7=12, Resulting Numbers: [9, 12] Generated Node #0,1,4: 11:[9, 12] Operation: 5+7=12 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 11:[9, 12], Operations: ['94-87=7', '5+7=12'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,11 unequal: No Solution Exploring Operation: 9*12=108, Resulting Numbers: [108] 108,11 unequal: No Solution Exploring Operation: 9+12=21, Resulting Numbers: [21] 21,11 unequal: No Solution No 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: 11:[7, 14], Operations: ['94-87=7', '9+5=14'] Exploring Operation: 7+14=21, Resulting Numbers: [21] 21,11 unequal: No Solution Exploring Operation: 7*14=98, Resulting Numbers: [98] 98,11 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,11 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,11 unequal: No Solution No 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: 11:[7, 4], Operations: ['94-87=7', '9-5=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[94, 87, 9, 5], Operations: [] Exploring Operation: 94-87=7, Resulting Numbers: [9, 5, 7] Generated Node #0,1: 11:[9, 5, 7] Operation: 94-87=7 Moving to Node #0,1 Current State: 11:[9, 5, 7], Operations: ['94-87=7'] Exploring Operation: 9-5=4, Resulting Numbers: [7, 4] Generated Node #0,1,1: 11:[7, 4] Operation: 9-5=4 Moving to Node #0,1,1 Current State: 11:[7, 4], Operations: ['94-87=7', '9-5=4'] Exploring Operation: 7+4=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 40, 12, 7, 39 ]
96
[ "40+7=47", "47-39=8", "12*8=96" ]
Current State: 96:[40, 12, 7, 39], Operations: [] Exploring Operation: 40+7=47, Resulting Numbers: [12, 39, 47] Generated Node #2: [12, 39, 47] from Operation: 40+7=47 Current State: 96:[12, 39, 47], Operations: ['40+7=47'] Exploring Operation: 47-39=8, Resulting Numbers: [12, 8] Generated Node #3: [12, 8] from Operation: 47-39=8 Current State: 96:[12, 8], Operations: ['40+7=47', '47-39=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[40, 12, 7, 39], Operations: [] Exploring Operation: 40-39=1, Resulting Numbers: [12, 7, 1] Generated Node #0,0: 96:[12, 7, 1] Operation: 40-39=1 Exploring Operation: 40+7=47, Resulting Numbers: [12, 39, 47] Generated Node #0,1: 96:[12, 39, 47] Operation: 40+7=47 Moving to Node #0,0 Current State: 96:[12, 7, 1], Operations: ['40-39=1'] Exploring Operation: 7+1=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 96:[12, 8] Operation: 7+1=8 Exploring Operation: 7-1=6, Resulting Numbers: [12, 6] Generated Node #0,0,1: 96:[12, 6] Operation: 7-1=6 Moving to Node #0,1 Current State: 96:[12, 39, 47], Operations: ['40+7=47'] Exploring Operation: 47-39=8, Resulting Numbers: [12, 8] Generated Node #0,1,0: 96:[12, 8] Operation: 47-39=8 Exploring Operation: 12+39=51, Resulting Numbers: [47, 51] Generated Node #0,1,1: 96:[47, 51] Operation: 12+39=51 Moving to Node #0,0,0 Current State: 96:[12, 8], Operations: ['40-39=1', '7+1=8'] Exploring Operation: 12-8=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[40, 12, 7, 39], Operations: [] Exploring Operation: 40-39=1, Resulting Numbers: [12, 7, 1] Generated Node #0,0: 96:[12, 7, 1] Operation: 40-39=1 Moving to Node #0,0 Current State: 96:[12, 7, 1], Operations: ['40-39=1'] Exploring Operation: 7+1=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 96:[12, 8] Operation: 7+1=8 Moving to Node #0,0,0 Current State: 96:[12, 8], Operations: ['40-39=1', '7+1=8'] Exploring Operation: 12*8=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
0.989583
hs_2
mult_heuristic
[ 91, 66, 8, 40 ]
30
[ "91-66=25", "40/8=5", "25+5=30" ]
Current State: 30:[91, 66, 8, 40], Operations: [] Exploring Operation: 91-66=25, Resulting Numbers: [8, 40, 25] Generated Node #2: [8, 40, 25] from Operation: 91-66=25 Current State: 30:[8, 40, 25], Operations: ['91-66=25'] Exploring Operation: 40/8=5, Resulting Numbers: [25, 5] Generated Node #3: [25, 5] from Operation: 40/8=5 Current State: 30:[25, 5], Operations: ['91-66=25', '40/8=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[91, 66, 8, 40], Operations: [] Exploring Operation: 40/8=5, Resulting Numbers: [91, 66, 5] Generated Node #0,0: 30:[91, 66, 5] Operation: 40/8=5 Exploring Operation: 91-40=51, Resulting Numbers: [66, 8, 51] Generated Node #0,1: 30:[66, 8, 51] Operation: 91-40=51 Exploring Operation: 91-66=25, Resulting Numbers: [8, 40, 25] Generated Node #0,2: 30:[8, 40, 25] Operation: 91-66=25 Exploring Operation: 66-40=26, Resulting Numbers: [91, 8, 26] Generated Node #0,3: 30:[91, 8, 26] Operation: 66-40=26 Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[8, 40, 25], Operations: ['91-66=25'] Exploring Operation: 40/8=5, Resulting Numbers: [25, 5] Generated Node #0,2,0: 30:[25, 5] Operation: 40/8=5 Exploring Operation: 40-25=15, Resulting Numbers: [8, 15] Generated Node #0,2,1: 30:[8, 15] Operation: 40-25=15 Exploring Operation: 40-8=32, Resulting Numbers: [25, 32] Generated Node #0,2,2: 30:[25, 32] Operation: 40-8=32 Exploring Operation: 25-8=17, Resulting Numbers: [40, 17] Generated Node #0,2,3: 30:[40, 17] Operation: 25-8=17 Moving to Node #0,2,1 Current State: 30:[8, 15], Operations: ['91-66=25', '40-25=15'] Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,30 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,30 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,30 unequal: No Solution Moving to Node #0,2,0 Current State: 30:[25, 5], Operations: ['91-66=25', '40/8=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20] 20,30 unequal: No Solution Exploring Operation: 25*5=125, Resulting Numbers: [125] 125,30 unequal: No Solution Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[91, 66, 8, 40], Operations: [] Exploring Operation: 91-66=25, Resulting Numbers: [8, 40, 25] Generated Node #0,2: 30:[8, 40, 25] Operation: 91-66=25 Moving to Node #0,2 Current State: 30:[8, 40, 25], Operations: ['91-66=25'] Exploring Operation: 40/8=5, Resulting Numbers: [25, 5] Generated Node #0,2,0: 30:[25, 5] Operation: 40/8=5 Moving to Node #0,2,0 Current State: 30:[25, 5], Operations: ['91-66=25', '40/8=5'] Exploring Operation: 25+5=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 85, 87, 48, 13 ]
88
[ "87-48=39", "39/13=3", "85+3=88" ]
Current State: 88:[85, 87, 48, 13], Operations: [] Exploring Operation: 87-48=39, Resulting Numbers: [85, 13, 39] Generated Node #2: [85, 13, 39] from Operation: 87-48=39 Current State: 88:[85, 13, 39], Operations: ['87-48=39'] Exploring Operation: 39/13=3, Resulting Numbers: [85, 3] Generated Node #3: [85, 3] from Operation: 39/13=3 Current State: 88:[85, 3], Operations: ['87-48=39', '39/13=3'] Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[85, 87, 48, 13], Operations: [] Exploring Operation: 87-48=39, Resulting Numbers: [85, 13, 39] Generated Node #0,0: 88:[85, 13, 39] Operation: 87-48=39 Exploring Operation: 48-13=35, Resulting Numbers: [85, 87, 35] Generated Node #0,1: 88:[85, 87, 35] Operation: 48-13=35 Exploring Operation: 87-85=2, Resulting Numbers: [48, 13, 2] Generated Node #0,2: 88:[48, 13, 2] Operation: 87-85=2 Exploring Operation: 85-48=37, Resulting Numbers: [87, 13, 37] Generated Node #0,3: 88:[87, 13, 37] Operation: 85-48=37 Exploring Operation: 85+13=98, Resulting Numbers: [87, 48, 98] Generated Node #0,4: 88:[87, 48, 98] Operation: 85+13=98 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[48, 13, 2], Operations: ['87-85=2'] Exploring Operation: 13-2=11, Resulting Numbers: [48, 11] Generated Node #0,2,0: 88:[48, 11] Operation: 13-2=11 Exploring Operation: 48/2=24, Resulting Numbers: [13, 24] Generated Node #0,2,1: 88:[13, 24] Operation: 48/2=24 Exploring Operation: 48+2=50, Resulting Numbers: [13, 50] Generated Node #0,2,2: 88:[13, 50] Operation: 48+2=50 Exploring Operation: 48-2=46, Resulting Numbers: [13, 46] Generated Node #0,2,3: 88:[13, 46] Operation: 48-2=46 Exploring Operation: 13+2=15, Resulting Numbers: [48, 15] Generated Node #0,2,4: 88:[48, 15] Operation: 13+2=15 Moving to Node #0,2,0 Current State: 88:[48, 11], Operations: ['87-85=2', '13-2=11'] Exploring Operation: 48*11=528, Resulting Numbers: [528] 528,88 unequal: No Solution Exploring Operation: 48+11=59, Resulting Numbers: [59] 59,88 unequal: No Solution Exploring Operation: 48-11=37, Resulting Numbers: [37] 37,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[13, 46], Operations: ['87-85=2', '48-2=46'] Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,88 unequal: No Solution Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[13, 24], Operations: ['87-85=2', '48/2=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,88 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[13, 50], Operations: ['87-85=2', '48+2=50'] Exploring Operation: 50-13=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 13*50=650, Resulting Numbers: [650] 650,88 unequal: No Solution Exploring Operation: 13+50=63, Resulting Numbers: [63] 63,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[48, 15], Operations: ['87-85=2', '13+2=15'] Exploring Operation: 48-15=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 48+15=63, Resulting Numbers: [63] 63,88 unequal: No Solution Exploring Operation: 48*15=720, Resulting Numbers: [720] 720,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[85, 13, 39], Operations: ['87-48=39'] Exploring Operation: 85-39=46, Resulting Numbers: [13, 46] Generated Node #0,0,0: 88:[13, 46] Operation: 85-39=46 Exploring Operation: 39-13=26, Resulting Numbers: [85, 26] Generated Node #0,0,1: 88:[85, 26] Operation: 39-13=26 Exploring Operation: 13+39=52, Resulting Numbers: [85, 52] Generated Node #0,0,2: 88:[85, 52] Operation: 13+39=52 Exploring Operation: 85+13=98, Resulting Numbers: [39, 98] Generated Node #0,0,3: 88:[39, 98] Operation: 85+13=98 Exploring Operation: 39/13=3, Resulting Numbers: [85, 3] Generated Node #0,0,4: 88:[85, 3] Operation: 39/13=3 Moving to Node #0,0,0 Current State: 88:[13, 46], Operations: ['87-48=39', '85-39=46'] Exploring Operation: 13*46=598, Resulting Numbers: [598] 598,88 unequal: No Solution Exploring Operation: 46-13=33, Resulting Numbers: [33] 33,88 unequal: No Solution Exploring Operation: 13+46=59, Resulting Numbers: [59] 59,88 unequal: No Solution Moving to Node #0,0,4 Current State: 88:[85, 3], Operations: ['87-48=39', '39/13=3'] Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[85, 87, 48, 13], Operations: [] Exploring Operation: 87-48=39, Resulting Numbers: [85, 13, 39] Generated Node #0,0: 88:[85, 13, 39] Operation: 87-48=39 Moving to Node #0,0 Current State: 88:[85, 13, 39], Operations: ['87-48=39'] Exploring Operation: 39/13=3, Resulting Numbers: [85, 3] Generated Node #0,0,4: 88:[85, 3] Operation: 39/13=3 Moving to Node #0,0,4 Current State: 88:[85, 3], Operations: ['87-48=39', '39/13=3'] Exploring Operation: 85+3=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
sum_heuristic
[ 86, 34, 40, 69 ]
11
[ "86+34=120", "40+69=109", "120-109=11" ]
Current State: 11:[86, 34, 40, 69], Operations: [] Exploring Operation: 86+34=120, Resulting Numbers: [40, 69, 120] Generated Node #2: [40, 69, 120] from Operation: 86+34=120 Current State: 11:[40, 69, 120], Operations: ['86+34=120'] Exploring Operation: 40+69=109, Resulting Numbers: [120, 109] Generated Node #3: [120, 109] from Operation: 40+69=109 Current State: 11:[120, 109], Operations: ['86+34=120', '40+69=109'] Exploring Operation: 120-109=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[86, 34, 40, 69], Operations: [] Exploring Operation: 86-69=17, Resulting Numbers: [34, 40, 17] Generated Node #0,0: 11:[34, 40, 17] Operation: 86-69=17 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[34, 40, 17], Operations: ['86-69=17'] Exploring Operation: 40-34=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 11:[17, 6] Operation: 40-34=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[17, 6], Operations: ['86-69=17', '40-34=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[86, 34, 40, 69], Operations: [] Exploring Operation: 86-69=17, Resulting Numbers: [34, 40, 17] Generated Node #0,0: 11:[34, 40, 17] Operation: 86-69=17 Moving to Node #0,0 Current State: 11:[34, 40, 17], Operations: ['86-69=17'] Exploring Operation: 40-34=6, Resulting Numbers: [17, 6] Generated Node #0,0,0: 11:[17, 6] Operation: 40-34=6 Moving to Node #0,0,0 Current State: 11:[17, 6], Operations: ['86-69=17', '40-34=6'] Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 33, 47, 1, 68 ]
83
[ "47-33=14", "1+68=69", "14+69=83" ]
Current State: 83:[33, 47, 1, 68], Operations: [] Exploring Operation: 47-33=14, Resulting Numbers: [1, 68, 14] Generated Node #2: [1, 68, 14] from Operation: 47-33=14 Current State: 83:[1, 68, 14], Operations: ['47-33=14'] Exploring Operation: 1+68=69, Resulting Numbers: [14, 69] Generated Node #3: [14, 69] from Operation: 1+68=69 Current State: 83:[14, 69], Operations: ['47-33=14', '1+68=69'] Exploring Operation: 14+69=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[33, 47, 1, 68], Operations: [] Exploring Operation: 33+47=80, Resulting Numbers: [1, 68, 80] Generated Node #0,0: 83:[1, 68, 80] Operation: 33+47=80 Exploring Operation: 1+68=69, Resulting Numbers: [33, 47, 69] Generated Node #0,1: 83:[33, 47, 69] Operation: 1+68=69 Exploring Operation: 33+1=34, Resulting Numbers: [47, 68, 34] Generated Node #0,2: 83:[47, 68, 34] Operation: 33+1=34 Exploring Operation: 47+1=48, Resulting Numbers: [33, 68, 48] Generated Node #0,3: 83:[33, 68, 48] Operation: 47+1=48 Exploring Operation: 33*1=33, Resulting Numbers: [47, 68, 33] Generated Node #0,4: 83:[47, 68, 33] Operation: 33*1=33 Moving to Node #0,0 Current State: 83:[1, 68, 80], Operations: ['33+47=80'] Exploring Operation: 1*68=68, Resulting Numbers: [80, 68] Generated Node #0,0,0: 83:[80, 68] Operation: 1*68=68 Exploring Operation: 1+80=81, Resulting Numbers: [68, 81] Generated Node #0,0,1: 83:[68, 81] Operation: 1+80=81 Exploring Operation: 1+68=69, Resulting Numbers: [80, 69] Generated Node #0,0,2: 83:[80, 69] Operation: 1+68=69 Exploring Operation: 1*80=80, Resulting Numbers: [68, 80] Generated Node #0,0,3: 83:[68, 80] Operation: 1*80=80 Exploring Operation: 68/1=68, Resulting Numbers: [80, 68] Generated Node #0,0,4: 83:[80, 68] Operation: 68/1=68 Moving to Node #0,2 Current State: 83:[47, 68, 34], Operations: ['33+1=34'] Exploring Operation: 47+68=115, Resulting Numbers: [34, 115] Generated Node #0,2,0: 83:[34, 115] Operation: 47+68=115 Exploring Operation: 68+34=102, Resulting Numbers: [47, 102] Generated Node #0,2,1: 83:[47, 102] Operation: 68+34=102 Exploring Operation: 47-34=13, Resulting Numbers: [68, 13] Generated Node #0,2,2: 83:[68, 13] Operation: 47-34=13 Exploring Operation: 68-34=34, Resulting Numbers: [47, 34] Generated Node #0,2,3: 83:[47, 34] Operation: 68-34=34 Exploring Operation: 47+34=81, Resulting Numbers: [68, 81] Generated Node #0,2,4: 83:[68, 81] Operation: 47+34=81 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 83:[68, 81], Operations: ['33+1=34', '47+34=81'] Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 83:[47, 102], Operations: ['33+1=34', '68+34=102'] Exploring Operation: 102-47=55, Resulting Numbers: [55] 55,83 unequal: No Solution Exploring Operation: 47*102=4794, Resulting Numbers: [4794] 4794,83 unequal: No Solution Exploring Operation: 47+102=149, Resulting Numbers: [149] 149,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 83:[34, 115], Operations: ['33+1=34', '47+68=115'] Exploring Operation: 34+115=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 115-34=81, Resulting Numbers: [81] 81,83 unequal: No Solution Exploring Operation: 34*115=3910, Resulting Numbers: [3910] 3910,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 83:[68, 13], Operations: ['33+1=34', '47-34=13'] Exploring Operation: 68+13=81, Resulting Numbers: [81] 81,83 unequal: No Solution Exploring Operation: 68-13=55, Resulting Numbers: [55] 55,83 unequal: No Solution Exploring Operation: 68*13=884, Resulting Numbers: [884] 884,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 83:[47, 34], Operations: ['33+1=34', '68-34=34'] Exploring Operation: 47*34=1598, Resulting Numbers: [1598] 1598,83 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 47+34=81, Resulting Numbers: [81] 81,83 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: 83:[33, 47, 69], Operations: ['1+68=69'] Exploring Operation: 33+69=102, Resulting Numbers: [47, 102] Generated Node #0,1,0: 83:[47, 102] Operation: 33+69=102 Exploring Operation: 47+69=116, Resulting Numbers: [33, 116] Generated Node #0,1,1: 83:[33, 116] Operation: 47+69=116 Exploring Operation: 33+47=80, Resulting Numbers: [69, 80] Generated Node #0,1,2: 83:[69, 80] Operation: 33+47=80 Exploring Operation: 47-33=14, Resulting Numbers: [69, 14] Generated Node #0,1,3: 83:[69, 14] Operation: 47-33=14 Exploring Operation: 69-33=36, Resulting Numbers: [47, 36] Generated Node #0,1,4: 83:[47, 36] Operation: 69-33=36 Moving to Node #0,3 Current State: 83:[33, 68, 48], Operations: ['47+1=48'] Exploring Operation: 68-33=35, Resulting Numbers: [48, 35] Generated Node #0,3,0: 83:[48, 35] Operation: 68-33=35 Exploring Operation: 68+48=116, Resulting Numbers: [33, 116] Generated Node #0,3,1: 83:[33, 116] Operation: 68+48=116 Exploring Operation: 33+68=101, Resulting Numbers: [48, 101] Generated Node #0,3,2: 83:[48, 101] Operation: 33+68=101 Exploring Operation: 48-33=15, Resulting Numbers: [68, 15] Generated Node #0,3,3: 83:[68, 15] Operation: 48-33=15 Exploring Operation: 33+48=81, Resulting Numbers: [68, 81] Generated Node #0,3,4: 83:[68, 81] Operation: 33+48=81 Moving to Node #0,4 Current State: 83:[47, 68, 33], Operations: ['33*1=33'] Exploring Operation: 47+33=80, Resulting Numbers: [68, 80] Generated Node #0,4,0: 83:[68, 80] Operation: 47+33=80 Exploring Operation: 47-33=14, Resulting Numbers: [68, 14] Generated Node #0,4,1: 83:[68, 14] Operation: 47-33=14 Exploring Operation: 47+68=115, Resulting Numbers: [33, 115] Generated Node #0,4,2: 83:[33, 115] Operation: 47+68=115 Exploring Operation: 68-33=35, Resulting Numbers: [47, 35] Generated Node #0,4,3: 83:[47, 35] Operation: 68-33=35 Exploring Operation: 68+33=101, Resulting Numbers: [47, 101] Generated Node #0,4,4: 83:[47, 101] Operation: 68+33=101 Moving to Node #0,0,1 Current State: 83:[68, 81], Operations: ['33+47=80', '1+80=81'] Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,83 unequal: No Solution Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[69, 80], Operations: ['1+68=69', '33+47=80'] Exploring Operation: 69*80=5520, Resulting Numbers: [5520] 5520,83 unequal: No Solution Exploring Operation: 69+80=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 80-69=11, Resulting Numbers: [11] 11,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[80, 69], Operations: ['33+47=80', '1+68=69'] Exploring Operation: 80-69=11, Resulting Numbers: [11] 11,83 unequal: No Solution Exploring Operation: 80*69=5520, Resulting Numbers: [5520] 5520,83 unequal: No Solution Exploring Operation: 80+69=149, Resulting Numbers: [149] 149,83 unequal: No Solution Moving to Node #0,3,4 Current State: 83:[68, 81], Operations: ['47+1=48', '33+48=81'] Exploring Operation: 68+81=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 81-68=13, Resulting Numbers: [13] 13,83 unequal: No Solution Exploring Operation: 68*81=5508, Resulting Numbers: [5508] 5508,83 unequal: No Solution Moving to Node #0,0,0 Current State: 83:[80, 68], Operations: ['33+47=80', '1*68=68'] Exploring Operation: 80*68=5440, Resulting Numbers: [5440] 5440,83 unequal: No Solution Exploring Operation: 80+68=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,83 unequal: No Solution Moving to Node #0,0,4 Current State: 83:[80, 68], Operations: ['33+47=80', '68/1=68'] Exploring Operation: 80+68=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 80*68=5440, Resulting Numbers: [5440] 5440,83 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[68, 80], Operations: ['33+47=80', '1*80=80'] Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,83 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,83 unequal: No Solution Moving to Node #0,4,0 Current State: 83:[68, 80], Operations: ['33*1=33', '47+33=80'] Exploring Operation: 68*80=5440, Resulting Numbers: [5440] 5440,83 unequal: No Solution Exploring Operation: 68+80=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 80-68=12, Resulting Numbers: [12] 12,83 unequal: No Solution Moving to Node #0,3,2 Current State: 83:[48, 101], Operations: ['47+1=48', '33+68=101'] Exploring Operation: 48+101=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 48*101=4848, Resulting Numbers: [4848] 4848,83 unequal: No Solution Exploring Operation: 101-48=53, Resulting Numbers: [53] 53,83 unequal: No Solution Moving to Node #0,4,4 Current State: 83:[47, 101], Operations: ['33*1=33', '68+33=101'] Exploring Operation: 47+101=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 47*101=4747, Resulting Numbers: [4747] 4747,83 unequal: No Solution Exploring Operation: 101-47=54, Resulting Numbers: [54] 54,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[47, 102], Operations: ['1+68=69', '33+69=102'] Exploring Operation: 102-47=55, Resulting Numbers: [55] 55,83 unequal: No Solution Exploring Operation: 47+102=149, Resulting Numbers: [149] 149,83 unequal: No Solution Exploring Operation: 47*102=4794, Resulting Numbers: [4794] 4794,83 unequal: No Solution Moving to Node #0,4,2 Current State: 83:[33, 115], Operations: ['33*1=33', '47+68=115'] Exploring Operation: 115-33=82, Resulting Numbers: [82] 82,83 unequal: No Solution Exploring Operation: 33+115=148, Resulting Numbers: [148] 148,83 unequal: No Solution Exploring Operation: 33*115=3795, Resulting Numbers: [3795] 3795,83 unequal: No Solution Moving to Node #0,3,0 Current State: 83:[48, 35], Operations: ['47+1=48', '68-33=35'] Exploring Operation: 48*35=1680, Resulting Numbers: [1680] 1680,83 unequal: No Solution Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[33, 47, 1, 68], Operations: [] Exploring Operation: 47+1=48, Resulting Numbers: [33, 68, 48] Generated Node #0,3: 83:[33, 68, 48] Operation: 47+1=48 Moving to Node #0,3 Current State: 83:[33, 68, 48], Operations: ['47+1=48'] Exploring Operation: 68-33=35, Resulting Numbers: [48, 35] Generated Node #0,3,0: 83:[48, 35] Operation: 68-33=35 Moving to Node #0,3,0 Current State: 83:[48, 35], Operations: ['47+1=48', '68-33=35'] Exploring Operation: 48+35=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
0.924479
hs_5
sum_heuristic
[ 32, 52, 38, 61 ]
54
[ "38-32=6", "61-52=9", "6*9=54" ]
Current State: 54:[32, 52, 38, 61], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [52, 61, 6] Generated Node #2: [52, 61, 6] from Operation: 38-32=6 Current State: 54:[52, 61, 6], Operations: ['38-32=6'] Exploring Operation: 61-52=9, Resulting Numbers: [6, 9] Generated Node #3: [6, 9] from Operation: 61-52=9 Current State: 54:[6, 9], Operations: ['38-32=6', '61-52=9'] Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[32, 52, 38, 61], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [52, 61, 6] Generated Node #0,0: 54:[52, 61, 6] Operation: 38-32=6 Exploring Operation: 61-38=23, Resulting Numbers: [32, 52, 23] Generated Node #0,1: 54:[32, 52, 23] Operation: 61-38=23 Exploring Operation: 61-32=29, Resulting Numbers: [52, 38, 29] Generated Node #0,2: 54:[52, 38, 29] Operation: 61-32=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[52, 61, 6], Operations: ['38-32=6'] Exploring Operation: 52+6=58, Resulting Numbers: [61, 58] Generated Node #0,0,0: 54:[61, 58] Operation: 52+6=58 Exploring Operation: 61-52=9, Resulting Numbers: [6, 9] Generated Node #0,0,1: 54:[6, 9] Operation: 61-52=9 Exploring Operation: 61-6=55, Resulting Numbers: [52, 55] Generated Node #0,0,2: 54:[52, 55] Operation: 61-6=55 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 54:[6, 9], Operations: ['38-32=6', '61-52=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,54 unequal: No Solution Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[32, 52, 38, 61], Operations: [] Exploring Operation: 38-32=6, Resulting Numbers: [52, 61, 6] Generated Node #0,0: 54:[52, 61, 6] Operation: 38-32=6 Moving to Node #0,0 Current State: 54:[52, 61, 6], Operations: ['38-32=6'] Exploring Operation: 61-52=9, Resulting Numbers: [6, 9] Generated Node #0,0,1: 54:[6, 9] Operation: 61-52=9 Moving to Node #0,0,1 Current State: 54:[6, 9], Operations: ['38-32=6', '61-52=9'] Exploring Operation: 6*9=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
sum_heuristic
[ 54, 1, 47, 27 ]
47
[ "54/27=2", "2-1=1", "47*1=47" ]
Current State: 47:[54, 1, 47, 27], Operations: [] Exploring Operation: 54/27=2, Resulting Numbers: [1, 47, 2] Generated Node #2: [1, 47, 2] from Operation: 54/27=2 Current State: 47:[1, 47, 2], Operations: ['54/27=2'] Exploring Operation: 2-1=1, Resulting Numbers: [47, 1] Generated Node #3: [47, 1] from Operation: 2-1=1 Current State: 47:[47, 1], Operations: ['54/27=2', '2-1=1'] Exploring Operation: 47*1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[54, 1, 47, 27], Operations: [] Exploring Operation: 1+27=28, Resulting Numbers: [54, 47, 28] Generated Node #0,0: 47:[54, 47, 28] Operation: 1+27=28 Exploring Operation: 54-1=53, Resulting Numbers: [47, 27, 53] Generated Node #0,1: 47:[47, 27, 53] Operation: 54-1=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[54, 47, 28], Operations: ['1+27=28'] Exploring Operation: 54+28=82, Resulting Numbers: [47, 82] Generated Node #0,0,0: 47:[47, 82] Operation: 54+28=82 Exploring Operation: 54-28=26, Resulting Numbers: [47, 26] Generated Node #0,0,1: 47:[47, 26] Operation: 54-28=26 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 47:[47, 26], Operations: ['1+27=28', '54-28=26'] Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,47 unequal: No Solution Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 47:[47, 82], Operations: ['1+27=28', '54+28=82'] Exploring Operation: 82-47=35, Resulting Numbers: [35] 35,47 unequal: No Solution Exploring Operation: 47+82=129, Resulting Numbers: [129] 129,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 47:[47, 27, 53], Operations: ['54-1=53'] Exploring Operation: 47+27=74, Resulting Numbers: [53, 74] Generated Node #0,1,0: 47:[53, 74] Operation: 47+27=74 Exploring Operation: 53-27=26, Resulting Numbers: [47, 26] Generated Node #0,1,1: 47:[47, 26] Operation: 53-27=26 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 47:[47, 26], Operations: ['54-1=53', '53-27=26'] Exploring Operation: 47-26=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 47+26=73, Resulting Numbers: [73] 73,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 47:[53, 74], Operations: ['54-1=53', '47+27=74'] Exploring Operation: 53+74=127, Resulting Numbers: [127] 127,47 unequal: No Solution Exploring Operation: 74-53=21, Resulting Numbers: [21] 21,47 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 54, 36, 60, 39 ]
54
[ "54*39=2106", "36*60=2160", "2160-2106=54" ]
Current State: 54:[54, 36, 60, 39], Operations: [] Exploring Operation: 54*39=2106, Resulting Numbers: [36, 60, 2106] Generated Node #2: [36, 60, 2106] from Operation: 54*39=2106 Current State: 54:[36, 60, 2106], Operations: ['54*39=2106'] Exploring Operation: 36*60=2160, Resulting Numbers: [2106, 2160] Generated Node #3: [2106, 2160] from Operation: 36*60=2160 Current State: 54:[2106, 2160], Operations: ['54*39=2106', '36*60=2160'] Exploring Operation: 2160-2106=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[54, 36, 60, 39], Operations: [] Exploring Operation: 54-36=18, Resulting Numbers: [60, 39, 18] Generated Node #0,0: 54:[60, 39, 18] Operation: 54-36=18 Exploring Operation: 60-36=24, Resulting Numbers: [54, 39, 24] Generated Node #0,1: 54:[54, 39, 24] Operation: 60-36=24 Exploring Operation: 39-36=3, Resulting Numbers: [54, 60, 3] Generated Node #0,2: 54:[54, 60, 3] Operation: 39-36=3 Exploring Operation: 60-39=21, Resulting Numbers: [54, 36, 21] Generated Node #0,3: 54:[54, 36, 21] Operation: 60-39=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[54, 60, 3], Operations: ['39-36=3'] Exploring Operation: 54/3=18, Resulting Numbers: [60, 18] Generated Node #0,2,0: 54:[60, 18] Operation: 54/3=18 Exploring Operation: 60-3=57, Resulting Numbers: [54, 57] Generated Node #0,2,1: 54:[54, 57] Operation: 60-3=57 Exploring Operation: 60-54=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 54:[3, 6] Operation: 60-54=6 Exploring Operation: 60/3=20, Resulting Numbers: [54, 20] Generated Node #0,2,3: 54:[54, 20] Operation: 60/3=20 Moving to Node #0,2,2 Current State: 54:[3, 6], Operations: ['39-36=3', '60-54=6'] Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 6/3=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Moving to Node #0,2,3 Current State: 54:[54, 20], Operations: ['39-36=3', '60/3=20'] Exploring Operation: 54+20=74, Resulting Numbers: [74] 74,54 unequal: No Solution Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,54 unequal: No Solution Exploring Operation: 54*20=1080, Resulting Numbers: [1080] 1080,54 unequal: No Solution Moving to Node #0,2,1 Current State: 54:[54, 57], Operations: ['39-36=3', '60-3=57'] Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 54*57=3078, Resulting Numbers: [3078] 3078,54 unequal: No Solution Exploring Operation: 54+57=111, Resulting Numbers: [111] 111,54 unequal: No Solution Moving to Node #0,2,0 Current State: 54:[60, 18], Operations: ['39-36=3', '54/3=18'] Exploring Operation: 60-18=42, Resulting Numbers: [42] 42,54 unequal: No Solution Exploring Operation: 60+18=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 60*18=1080, Resulting Numbers: [1080] 1080,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[54, 36, 21], Operations: ['60-39=21'] Exploring Operation: 36-21=15, Resulting Numbers: [54, 15] Generated Node #0,3,0: 54:[54, 15] Operation: 36-21=15 Exploring Operation: 36+21=57, Resulting Numbers: [54, 57] Generated Node #0,3,1: 54:[54, 57] Operation: 36+21=57 Exploring Operation: 54-36=18, Resulting Numbers: [21, 18] Generated Node #0,3,2: 54:[21, 18] Operation: 54-36=18 Exploring Operation: 54-21=33, Resulting Numbers: [36, 33] Generated Node #0,3,3: 54:[36, 33] Operation: 54-21=33 Moving to Node #0,3,0 Current State: 54:[54, 15], Operations: ['60-39=21', '36-21=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[21, 18], Operations: ['60-39=21', '54-36=18'] Exploring Operation: 21*18=378, Resulting Numbers: [378] 378,54 unequal: No Solution Exploring Operation: 21+18=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[54, 57], Operations: ['60-39=21', '36+21=57'] Exploring Operation: 57-54=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 54+57=111, Resulting Numbers: [111] 111,54 unequal: No Solution Exploring Operation: 54*57=3078, Resulting Numbers: [3078] 3078,54 unequal: No Solution Moving to Node #0,3,3 Current State: 54:[36, 33], Operations: ['60-39=21', '54-21=33'] Exploring Operation: 36+33=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 36*33=1188, Resulting Numbers: [1188] 1188,54 unequal: No Solution Exploring Operation: 36-33=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[54, 39, 24], Operations: ['60-36=24'] Exploring Operation: 54-39=15, Resulting Numbers: [24, 15] Generated Node #0,1,0: 54:[24, 15] Operation: 54-39=15 Exploring Operation: 54-24=30, Resulting Numbers: [39, 30] Generated Node #0,1,1: 54:[39, 30] Operation: 54-24=30 Exploring Operation: 39+24=63, Resulting Numbers: [54, 63] Generated Node #0,1,2: 54:[54, 63] Operation: 39+24=63 Exploring Operation: 39-24=15, Resulting Numbers: [54, 15] Generated Node #0,1,3: 54:[54, 15] Operation: 39-24=15 Moving to Node #0,1,3 Current State: 54:[54, 15], Operations: ['60-36=24', '39-24=15'] Exploring Operation: 54-15=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 54+15=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 54*15=810, Resulting Numbers: [810] 810,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[24, 15], Operations: ['60-36=24', '54-39=15'] Exploring Operation: 24-15=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 24+15=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 24*15=360, Resulting Numbers: [360] 360,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[54, 63], Operations: ['60-36=24', '39+24=63'] Exploring Operation: 54+63=117, Resulting Numbers: [117] 117,54 unequal: No Solution Exploring Operation: 63-54=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 54*63=3402, Resulting Numbers: [3402] 3402,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[39, 30], Operations: ['60-36=24', '54-24=30'] Exploring Operation: 39*30=1170, Resulting Numbers: [1170] 1170,54 unequal: No Solution Exploring Operation: 39+30=69, Resulting Numbers: [69] 69,54 unequal: No Solution Exploring Operation: 39-30=9, Resulting Numbers: [9] 9,54 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 Current State: 54:[60, 39, 18], Operations: ['54-36=18'] Exploring Operation: 39-18=21, Resulting Numbers: [60, 21] Generated Node #0,0,0: 54:[60, 21] Operation: 39-18=21 Exploring Operation: 60-18=42, Resulting Numbers: [39, 42] Generated Node #0,0,1: 54:[39, 42] Operation: 60-18=42 Exploring Operation: 39+18=57, Resulting Numbers: [60, 57] Generated Node #0,0,2: 54:[60, 57] Operation: 39+18=57 Exploring Operation: 60-39=21, Resulting Numbers: [18, 21] Generated Node #0,0,3: 54:[18, 21] Operation: 60-39=21 Moving to Node #0,0,3 Current State: 54:[18, 21], Operations: ['54-36=18', '60-39=21'] Exploring Operation: 18*21=378, Resulting Numbers: [378] 378,54 unequal: No Solution Exploring Operation: 18+21=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 21-18=3, Resulting Numbers: [3] 3,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[60, 57], Operations: ['54-36=18', '39+18=57'] Exploring Operation: 60-57=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 60*57=3420, Resulting Numbers: [3420] 3420,54 unequal: No Solution Exploring Operation: 60+57=117, Resulting Numbers: [117] 117,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[60, 21], Operations: ['54-36=18', '39-18=21'] Exploring Operation: 60*21=1260, Resulting Numbers: [1260] 1260,54 unequal: No Solution Exploring Operation: 60-21=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 60+21=81, Resulting Numbers: [81] 81,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[39, 42], Operations: ['54-36=18', '60-18=42'] Exploring Operation: 42-39=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 39+42=81, Resulting Numbers: [81] 81,54 unequal: No Solution Exploring Operation: 39*42=1638, Resulting Numbers: [1638] 1638,54 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
[ 81, 7, 28, 4 ]
81
[ "81+7=88", "28/4=7", "88-7=81" ]
Current State: 81:[81, 7, 28, 4], Operations: [] Exploring Operation: 81+7=88, Resulting Numbers: [28, 4, 88] Generated Node #2: [28, 4, 88] from Operation: 81+7=88 Current State: 81:[28, 4, 88], Operations: ['81+7=88'] Exploring Operation: 28/4=7, Resulting Numbers: [88, 7] Generated Node #3: [88, 7] from Operation: 28/4=7 Current State: 81:[88, 7], Operations: ['81+7=88', '28/4=7'] Exploring Operation: 88-7=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[81, 7, 28, 4], Operations: [] Exploring Operation: 7+4=11, Resulting Numbers: [81, 28, 11] Generated Node #0,0: 81:[81, 28, 11] Operation: 7+4=11 Exploring Operation: 7*4=28, Resulting Numbers: [81, 28, 28] Generated Node #0,1: 81:[81, 28, 28] Operation: 7*4=28 Exploring Operation: 28/7=4, Resulting Numbers: [81, 4, 4] Generated Node #0,2: 81:[81, 4, 4] Operation: 28/7=4 Exploring Operation: 7-4=3, Resulting Numbers: [81, 28, 3] Generated Node #0,3: 81:[81, 28, 3] Operation: 7-4=3 Moving to Node #0,3 Current State: 81:[81, 28, 3], Operations: ['7-4=3'] Exploring Operation: 28-3=25, Resulting Numbers: [81, 25] Generated Node #0,3,0: 81:[81, 25] Operation: 28-3=25 Exploring Operation: 81+3=84, Resulting Numbers: [28, 84] Generated Node #0,3,1: 81:[28, 84] Operation: 81+3=84 Exploring Operation: 81/3=27, Resulting Numbers: [28, 27] Generated Node #0,3,2: 81:[28, 27] Operation: 81/3=27 Exploring Operation: 28*3=84, Resulting Numbers: [81, 84] Generated Node #0,3,3: 81:[81, 84] Operation: 28*3=84 Moving to Node #0,2 Current State: 81:[81, 4, 4], Operations: ['28/7=4'] Exploring Operation: 4+4=8, Resulting Numbers: [81, 8] Generated Node #0,2,0: 81:[81, 8] Operation: 4+4=8 Exploring Operation: 81+4=85, Resulting Numbers: [4, 85] Generated Node #0,2,1: 81:[4, 85] Operation: 81+4=85 Exploring Operation: 4-4=0, Resulting Numbers: [81, 0] Generated Node #0,2,2: 81:[81, 0] Operation: 4-4=0 Exploring Operation: 4/4=1, Resulting Numbers: [81, 1] Generated Node #0,2,3: 81:[81, 1] Operation: 4/4=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[81, 8], Operations: ['28/7=4', '4+4=8'] Exploring Operation: 81+8=89, Resulting Numbers: [89] 89,81 unequal: No Solution Exploring Operation: 81-8=73, Resulting Numbers: [73] 73,81 unequal: No Solution Exploring Operation: 81*8=648, Resulting Numbers: [648] 648,81 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 #0,2,3 Current State: 81:[81, 1], Operations: ['28/7=4', '4/4=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[81, 7, 28, 4], Operations: [] Exploring Operation: 28/7=4, Resulting Numbers: [81, 4, 4] Generated Node #0,2: 81:[81, 4, 4] Operation: 28/7=4 Moving to Node #0,2 Current State: 81:[81, 4, 4], Operations: ['28/7=4'] Exploring Operation: 4/4=1, Resulting Numbers: [81, 1] Generated Node #0,2,3: 81:[81, 1] Operation: 4/4=1 Moving to Node #0,2,3 Current State: 81:[81, 1], Operations: ['28/7=4', '4/4=1'] Exploring Operation: 81*1=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 75, 49, 51, 70 ]
45
[ "75-49=26", "70-51=19", "26+19=45" ]
Current State: 45:[75, 49, 51, 70], Operations: [] Exploring Operation: 75-49=26, Resulting Numbers: [51, 70, 26] Generated Node #2: [51, 70, 26] from Operation: 75-49=26 Current State: 45:[51, 70, 26], Operations: ['75-49=26'] Exploring Operation: 70-51=19, Resulting Numbers: [26, 19] Generated Node #3: [26, 19] from Operation: 70-51=19 Current State: 45:[26, 19], Operations: ['75-49=26', '70-51=19'] Exploring Operation: 26+19=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[75, 49, 51, 70], Operations: [] Exploring Operation: 75-51=24, Resulting Numbers: [49, 70, 24] Generated Node #0,0: 45:[49, 70, 24] Operation: 75-51=24 Exploring Operation: 70-51=19, Resulting Numbers: [75, 49, 19] Generated Node #0,1: 45:[75, 49, 19] Operation: 70-51=19 Exploring Operation: 75-49=26, Resulting Numbers: [51, 70, 26] Generated Node #0,2: 45:[51, 70, 26] Operation: 75-49=26 Exploring Operation: 75-70=5, Resulting Numbers: [49, 51, 5] Generated Node #0,3: 45:[49, 51, 5] Operation: 75-70=5 Moving to Node #0,3 Current State: 45:[49, 51, 5], Operations: ['75-70=5'] Exploring Operation: 49+5=54, Resulting Numbers: [51, 54] Generated Node #0,3,0: 45:[51, 54] Operation: 49+5=54 Exploring Operation: 49-5=44, Resulting Numbers: [51, 44] Generated Node #0,3,1: 45:[51, 44] Operation: 49-5=44 Exploring Operation: 51-5=46, Resulting Numbers: [49, 46] Generated Node #0,3,2: 45:[49, 46] Operation: 51-5=46 Exploring Operation: 51-49=2, Resulting Numbers: [5, 2] Generated Node #0,3,3: 45:[5, 2] Operation: 51-49=2 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 45:[5, 2], Operations: ['75-70=5', '51-49=2'] Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,45 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,45 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 #0,3,2 Current State: 45:[49, 46], Operations: ['75-70=5', '51-5=46'] Exploring Operation: 49-46=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 49*46=2254, Resulting Numbers: [2254] 2254,45 unequal: No Solution Exploring Operation: 49+46=95, Resulting Numbers: [95] 95,45 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 #0,3,1 Current State: 45:[51, 44], Operations: ['75-70=5', '49-5=44'] Exploring Operation: 51+44=95, Resulting Numbers: [95] 95,45 unequal: No Solution Exploring Operation: 51*44=2244, Resulting Numbers: [2244] 2244,45 unequal: No Solution Exploring Operation: 51-44=7, Resulting Numbers: [7] 7,45 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 #0,3,0 Current State: 45:[51, 54], Operations: ['75-70=5', '49+5=54'] Exploring Operation: 51*54=2754, Resulting Numbers: [2754] 2754,45 unequal: No Solution Exploring Operation: 54-51=3, Resulting Numbers: [3] 3,45 unequal: No Solution Exploring Operation: 51+54=105, Resulting Numbers: [105] 105,45 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:[75, 49, 19], Operations: ['70-51=19'] Exploring Operation: 75+19=94, Resulting Numbers: [49, 94] Generated Node #0,1,0: 45:[49, 94] Operation: 75+19=94 Exploring Operation: 49-19=30, Resulting Numbers: [75, 30] Generated Node #0,1,1: 45:[75, 30] Operation: 49-19=30 Exploring Operation: 75-49=26, Resulting Numbers: [19, 26] Generated Node #0,1,2: 45:[19, 26] Operation: 75-49=26 Exploring Operation: 75-19=56, Resulting Numbers: [49, 56] Generated Node #0,1,3: 45:[49, 56] Operation: 75-19=56 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 45:[19, 26], Operations: ['70-51=19', '75-49=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[75, 49, 51, 70], Operations: [] Exploring Operation: 70-51=19, Resulting Numbers: [75, 49, 19] Generated Node #0,1: 45:[75, 49, 19] Operation: 70-51=19 Moving to Node #0,1 Current State: 45:[75, 49, 19], Operations: ['70-51=19'] Exploring Operation: 75-49=26, Resulting Numbers: [19, 26] Generated Node #0,1,2: 45:[19, 26] Operation: 75-49=26 Moving to Node #0,1,2 Current State: 45:[19, 26], Operations: ['70-51=19', '75-49=26'] Exploring Operation: 19+26=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_4
mult_heuristic
[ 77, 6, 19, 21 ]
41
[ "77*6=462", "462/21=22", "19+22=41" ]
Current State: 41:[77, 6, 19, 21], Operations: [] Exploring Operation: 77*6=462, Resulting Numbers: [19, 21, 462] Generated Node #2: [19, 21, 462] from Operation: 77*6=462 Current State: 41:[19, 21, 462], Operations: ['77*6=462'] Exploring Operation: 462/21=22, Resulting Numbers: [19, 22] Generated Node #3: [19, 22] from Operation: 462/21=22 Current State: 41:[19, 22], Operations: ['77*6=462', '462/21=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[77, 6, 19, 21], Operations: [] Exploring Operation: 77-19=58, Resulting Numbers: [6, 21, 58] Generated Node #0,0: 41:[6, 21, 58] Operation: 77-19=58 Exploring Operation: 6+21=27, Resulting Numbers: [77, 19, 27] Generated Node #0,1: 41:[77, 19, 27] Operation: 6+21=27 Exploring Operation: 6+19=25, Resulting Numbers: [77, 21, 25] Generated Node #0,2: 41:[77, 21, 25] Operation: 6+19=25 Exploring Operation: 77-21=56, Resulting Numbers: [6, 19, 56] Generated Node #0,3: 41:[6, 19, 56] Operation: 77-21=56 Exploring Operation: 77-6=71, Resulting Numbers: [19, 21, 71] Generated Node #0,4: 41:[19, 21, 71] Operation: 77-6=71 Moving to Node #0,0 Current State: 41:[6, 21, 58], Operations: ['77-19=58'] Exploring Operation: 6+21=27, Resulting Numbers: [58, 27] Generated Node #0,0,0: 41:[58, 27] Operation: 6+21=27 Exploring Operation: 58-6=52, Resulting Numbers: [21, 52] Generated Node #0,0,1: 41:[21, 52] Operation: 58-6=52 Exploring Operation: 58-21=37, Resulting Numbers: [6, 37] Generated Node #0,0,2: 41:[6, 37] Operation: 58-21=37 Exploring Operation: 6+58=64, Resulting Numbers: [21, 64] Generated Node #0,0,3: 41:[21, 64] Operation: 6+58=64 Exploring Operation: 21-6=15, Resulting Numbers: [58, 15] Generated Node #0,0,4: 41:[58, 15] Operation: 21-6=15 Moving to Node #0,2 Current State: 41:[77, 21, 25], Operations: ['6+19=25'] Exploring Operation: 77-25=52, Resulting Numbers: [21, 52] Generated Node #0,2,0: 41:[21, 52] Operation: 77-25=52 Exploring Operation: 77+21=98, Resulting Numbers: [25, 98] Generated Node #0,2,1: 41:[25, 98] Operation: 77+21=98 Exploring Operation: 77-21=56, Resulting Numbers: [25, 56] Generated Node #0,2,2: 41:[25, 56] Operation: 77-21=56 Exploring Operation: 25-21=4, Resulting Numbers: [77, 4] Generated Node #0,2,3: 41:[77, 4] Operation: 25-21=4 Exploring Operation: 21+25=46, Resulting Numbers: [77, 46] Generated Node #0,2,4: 41:[77, 46] Operation: 21+25=46 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 41:[21, 52], Operations: ['6+19=25', '77-25=52'] Exploring Operation: 21+52=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 21*52=1092, Resulting Numbers: [1092] 1092,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[25, 56], Operations: ['6+19=25', '77-21=56'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 25*56=1400, Resulting Numbers: [1400] 1400,41 unequal: No Solution Exploring Operation: 25+56=81, Resulting Numbers: [81] 81,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 41:[77, 46], Operations: ['6+19=25', '21+25=46'] Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,41 unequal: No Solution Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 41:[25, 98], Operations: ['6+19=25', '77+21=98'] Exploring Operation: 98-25=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 25+98=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 25*98=2450, Resulting Numbers: [2450] 2450,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 41:[77, 4], Operations: ['6+19=25', '25-21=4'] Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 77*4=308, Resulting Numbers: [308] 308,41 unequal: No Solution Exploring Operation: 77+4=81, Resulting Numbers: [81] 81,41 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: 41:[19, 21, 71], Operations: ['77-6=71'] Exploring Operation: 19+21=40, Resulting Numbers: [71, 40] Generated Node #0,4,0: 41:[71, 40] Operation: 19+21=40 Exploring Operation: 21-19=2, Resulting Numbers: [71, 2] Generated Node #0,4,1: 41:[71, 2] Operation: 21-19=2 Exploring Operation: 71-21=50, Resulting Numbers: [19, 50] Generated Node #0,4,2: 41:[19, 50] Operation: 71-21=50 Exploring Operation: 71-19=52, Resulting Numbers: [21, 52] Generated Node #0,4,3: 41:[21, 52] Operation: 71-19=52 Exploring Operation: 19+71=90, Resulting Numbers: [21, 90] Generated Node #0,4,4: 41:[21, 90] Operation: 19+71=90 Moving to Node #0,1 Current State: 41:[77, 19, 27], Operations: ['6+21=27'] Exploring Operation: 77+19=96, Resulting Numbers: [27, 96] Generated Node #0,1,0: 41:[27, 96] Operation: 77+19=96 Exploring Operation: 77-19=58, Resulting Numbers: [27, 58] Generated Node #0,1,1: 41:[27, 58] Operation: 77-19=58 Exploring Operation: 27-19=8, Resulting Numbers: [77, 8] Generated Node #0,1,2: 41:[77, 8] Operation: 27-19=8 Exploring Operation: 77-27=50, Resulting Numbers: [19, 50] Generated Node #0,1,3: 41:[19, 50] Operation: 77-27=50 Exploring Operation: 19+27=46, Resulting Numbers: [77, 46] Generated Node #0,1,4: 41:[77, 46] Operation: 19+27=46 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 41:[27, 58], Operations: ['6+21=27', '77-19=58'] Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 27*58=1566, Resulting Numbers: [1566] 1566,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 41:[19, 50], Operations: ['6+21=27', '77-27=50'] Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,41 unequal: No Solution Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 41:[77, 46], Operations: ['6+21=27', '19+27=46'] Exploring Operation: 77+46=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 77-46=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 77*46=3542, Resulting Numbers: [3542] 3542,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[27, 96], Operations: ['6+21=27', '77+19=96'] Exploring Operation: 27*96=2592, Resulting Numbers: [2592] 2592,41 unequal: No Solution Exploring Operation: 96-27=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 27+96=123, Resulting Numbers: [123] 123,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 41:[77, 8], Operations: ['6+21=27', '27-19=8'] Exploring Operation: 77*8=616, Resulting Numbers: [616] 616,41 unequal: No Solution Exploring Operation: 77-8=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 77+8=85, Resulting Numbers: [85] 85,41 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: 41:[6, 19, 56], Operations: ['77-21=56'] Exploring Operation: 56-6=50, Resulting Numbers: [19, 50] Generated Node #0,3,0: 41:[19, 50] Operation: 56-6=50 Exploring Operation: 6+56=62, Resulting Numbers: [19, 62] Generated Node #0,3,1: 41:[19, 62] Operation: 6+56=62 Exploring Operation: 56-19=37, Resulting Numbers: [6, 37] Generated Node #0,3,2: 41:[6, 37] Operation: 56-19=37 Exploring Operation: 6+19=25, Resulting Numbers: [56, 25] Generated Node #0,3,3: 41:[56, 25] Operation: 6+19=25 Exploring Operation: 19-6=13, Resulting Numbers: [56, 13] Generated Node #0,3,4: 41:[56, 13] Operation: 19-6=13 Moving to Node #0,0,0 Current State: 41:[58, 27], Operations: ['77-19=58', '6+21=27'] Exploring Operation: 58-27=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 58*27=1566, Resulting Numbers: [1566] 1566,41 unequal: No Solution Exploring Operation: 58+27=85, Resulting Numbers: [85] 85,41 unequal: No Solution Moving to Node #0,4,0 Current State: 41:[71, 40], Operations: ['77-6=71', '19+21=40'] Exploring Operation: 71-40=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 71+40=111, Resulting Numbers: [111] 111,41 unequal: No Solution Exploring Operation: 71*40=2840, Resulting Numbers: [2840] 2840,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[19, 50], Operations: ['77-6=71', '71-21=50'] Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,41 unequal: No Solution Moving to Node #0,3,3 Current State: 41:[56, 25], Operations: ['77-21=56', '6+19=25'] Exploring Operation: 56-25=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 56*25=1400, Resulting Numbers: [1400] 1400,41 unequal: No Solution Exploring Operation: 56+25=81, Resulting Numbers: [81] 81,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[21, 52], Operations: ['77-19=58', '58-6=52'] Exploring Operation: 21*52=1092, Resulting Numbers: [1092] 1092,41 unequal: No Solution Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 21+52=73, Resulting Numbers: [73] 73,41 unequal: No Solution Moving to Node #0,3,0 Current State: 41:[19, 50], Operations: ['77-21=56', '56-6=50'] Exploring Operation: 19*50=950, Resulting Numbers: [950] 950,41 unequal: No Solution Exploring Operation: 19+50=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 50-19=31, Resulting Numbers: [31] 31,41 unequal: No Solution Moving to Node #0,4,3 Current State: 41:[21, 52], Operations: ['77-6=71', '71-19=52'] Exploring Operation: 52-21=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 21*52=1092, Resulting Numbers: [1092] 1092,41 unequal: No Solution Exploring Operation: 21+52=73, Resulting Numbers: [73] 73,41 unequal: No Solution Moving to Node #0,3,2 Current State: 41:[6, 37], Operations: ['77-21=56', '56-19=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,41 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[6, 37], Operations: ['77-19=58', '58-21=37'] Exploring Operation: 37-6=31, Resulting Numbers: [31] 31,41 unequal: No Solution Exploring Operation: 6*37=222, Resulting Numbers: [222] 222,41 unequal: No Solution Exploring Operation: 6+37=43, Resulting Numbers: [43] 43,41 unequal: No Solution Moving to Node #0,3,1 Current State: 41:[19, 62], Operations: ['77-21=56', '6+56=62'] Exploring Operation: 19+62=81, Resulting Numbers: [81] 81,41 unequal: No Solution Exploring Operation: 19*62=1178, Resulting Numbers: [1178] 1178,41 unequal: No Solution Exploring Operation: 62-19=43, Resulting Numbers: [43] 43,41 unequal: No Solution Moving to Node #0,3,4 Current State: 41:[56, 13], Operations: ['77-21=56', '19-6=13'] Exploring Operation: 56*13=728, Resulting Numbers: [728] 728,41 unequal: No Solution Exploring Operation: 56+13=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 56-13=43, Resulting Numbers: [43] 43,41 unequal: No Solution Moving to Node #0,0,4 Current State: 41:[58, 15], Operations: ['77-19=58', '21-6=15'] Exploring Operation: 58+15=73, Resulting Numbers: [73] 73,41 unequal: No Solution Exploring Operation: 58*15=870, Resulting Numbers: [870] 870,41 unequal: No Solution Exploring Operation: 58-15=43, Resulting Numbers: [43] 43,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[21, 64], Operations: ['77-19=58', '6+58=64'] Exploring Operation: 21*64=1344, Resulting Numbers: [1344] 1344,41 unequal: No Solution Exploring Operation: 64-21=43, Resulting Numbers: [43] 43,41 unequal: No Solution Exploring Operation: 21+64=85, Resulting Numbers: [85] 85,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[21, 90], Operations: ['77-6=71', '19+71=90'] Exploring Operation: 21+90=111, Resulting Numbers: [111] 111,41 unequal: No Solution Exploring Operation: 21*90=1890, Resulting Numbers: [1890] 1890,41 unequal: No Solution Exploring Operation: 90-21=69, Resulting Numbers: [69] 69,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[71, 2], Operations: ['77-6=71', '21-19=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,41 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,41 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,41 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 19, 47, 8, 14 ]
11
[ "19+47=66", "14-8=6", "66/6=11" ]
Current State: 11:[19, 47, 8, 14], Operations: [] Exploring Operation: 19+47=66, Resulting Numbers: [8, 14, 66] Generated Node #2: [8, 14, 66] from Operation: 19+47=66 Current State: 11:[8, 14, 66], Operations: ['19+47=66'] Exploring Operation: 14-8=6, Resulting Numbers: [66, 6] Generated Node #3: [66, 6] from Operation: 14-8=6 Current State: 11:[66, 6], Operations: ['19+47=66', '14-8=6'] Exploring Operation: 66/6=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[19, 47, 8, 14], Operations: [] Exploring Operation: 47-19=28, Resulting Numbers: [8, 14, 28] Generated Node #0,0: 11:[8, 14, 28] Operation: 47-19=28 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[8, 14, 28], Operations: ['47-19=28'] Exploring Operation: 28-14=14, Resulting Numbers: [8, 14] Generated Node #0,0,0: 11:[8, 14] Operation: 28-14=14 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[8, 14], Operations: ['47-19=28', '28-14=14'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 11, 7, 13, 41 ]
32
[ "11-7=4", "41-13=28", "4+28=32" ]
Current State: 32:[11, 7, 13, 41], Operations: [] Exploring Operation: 11-7=4, Resulting Numbers: [13, 41, 4] Generated Node #2: [13, 41, 4] from Operation: 11-7=4 Current State: 32:[13, 41, 4], Operations: ['11-7=4'] Exploring Operation: 41-13=28, Resulting Numbers: [4, 28] Generated Node #3: [4, 28] from Operation: 41-13=28 Current State: 32:[4, 28], Operations: ['11-7=4', '41-13=28'] Exploring Operation: 4+28=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[11, 7, 13, 41], Operations: [] Exploring Operation: 41-13=28, Resulting Numbers: [11, 7, 28] Generated Node #0,0: 32:[11, 7, 28] Operation: 41-13=28 Exploring Operation: 41-7=34, Resulting Numbers: [11, 13, 34] Generated Node #0,1: 32:[11, 13, 34] Operation: 41-7=34 Exploring Operation: 41-11=30, Resulting Numbers: [7, 13, 30] Generated Node #0,2: 32:[7, 13, 30] Operation: 41-11=30 Moving to Node #0,2 Current State: 32:[7, 13, 30], Operations: ['41-11=30'] Exploring Operation: 30-13=17, Resulting Numbers: [7, 17] Generated Node #0,2,0: 32:[7, 17] Operation: 30-13=17 Exploring Operation: 7+13=20, Resulting Numbers: [30, 20] Generated Node #0,2,1: 32:[30, 20] Operation: 7+13=20 Exploring Operation: 13-7=6, Resulting Numbers: [30, 6] Generated Node #0,2,2: 32:[30, 6] Operation: 13-7=6 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 32:[7, 17], Operations: ['41-11=30', '30-13=17'] Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 32:[30, 6], Operations: ['41-11=30', '13-7=6'] Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,32 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,32 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 32:[30, 20], Operations: ['41-11=30', '7+13=20'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,32 unequal: No Solution Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,32 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: 32:[11, 7, 28], Operations: ['41-13=28'] Exploring Operation: 11-7=4, Resulting Numbers: [28, 4] Generated Node #0,0,0: 32:[28, 4] Operation: 11-7=4 Exploring Operation: 28/7=4, Resulting Numbers: [11, 4] Generated Node #0,0,1: 32:[11, 4] Operation: 28/7=4 Exploring Operation: 28-11=17, Resulting Numbers: [7, 17] Generated Node #0,0,2: 32:[7, 17] Operation: 28-11=17 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 32:[7, 17], Operations: ['41-13=28', '28-11=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,32 unequal: No Solution Exploring Operation: 7*17=119, Resulting Numbers: [119] 119,32 unequal: No Solution Exploring Operation: 7+17=24, Resulting Numbers: [24] 24,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 32:[11, 4], Operations: ['41-13=28', '28/7=4'] Exploring Operation: 11-4=7, Resulting Numbers: [7] 7,32 unequal: No Solution Exploring Operation: 11+4=15, Resulting Numbers: [15] 15,32 unequal: No Solution Exploring Operation: 11*4=44, Resulting Numbers: [44] 44,32 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 32:[28, 4], Operations: ['41-13=28', '11-7=4'] Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,32 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,32 unequal: No Solution Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[11, 7, 13, 41], Operations: [] Exploring Operation: 41-13=28, Resulting Numbers: [11, 7, 28] Generated Node #0,0: 32:[11, 7, 28] Operation: 41-13=28 Moving to Node #0,0 Current State: 32:[11, 7, 28], Operations: ['41-13=28'] Exploring Operation: 11-7=4, Resulting Numbers: [28, 4] Generated Node #0,0,0: 32:[28, 4] Operation: 11-7=4 Moving to Node #0,0,0 Current State: 32:[28, 4], Operations: ['41-13=28', '11-7=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic