Datasets:
Parallel-Reasoning
/
sosp_sft_data

Dataset card Data Studio Files
xet
Community
nums
listlengths
4
4
target
int64
10
100
solution
listlengths
3
3
optimal_path
stringlengths
282
529
start_size
int64
4
4
search_path
stringlengths
505
16.8k
rating
float64
0
0.99
search_type
stringclasses
5 values
heuristic
stringclasses
2 values
[ 52, 59, 4, 9 ]
19
[ "59-52=7", "4*7=28", "28-9=19" ]
Current State: 19:[52, 59, 4, 9], Operations: [] Exploring Operation: 59-52=7, Resulting Numbers: [4, 9, 7] Generated Node #2: [4, 9, 7] from Operation: 59-52=7 Current State: 19:[4, 9, 7], Operations: ['59-52=7'] Exploring Operation: 4*7=28, Resulting Numbers: [9, 28] Generated Node #3: [9, 28] from Operation: 4*7=28 Current State: 19:[9, 28], Operations: ['59-52=7', '4*7=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[52, 59, 4, 9], Operations: [] Exploring Operation: 52/4=13, Resulting Numbers: [59, 9, 13] Generated Node #0,0: 19:[59, 9, 13] Operation: 52/4=13 Exploring Operation: 59-52=7, Resulting Numbers: [4, 9, 7] Generated Node #0,1: 19:[4, 9, 7] Operation: 59-52=7 Exploring Operation: 52-4=48, Resulting Numbers: [59, 9, 48] Generated Node #0,2: 19:[59, 9, 48] Operation: 52-4=48 Exploring Operation: 52-9=43, Resulting Numbers: [59, 4, 43] Generated Node #0,3: 19:[59, 4, 43] Operation: 52-9=43 Moving to Node #0,1 Current State: 19:[4, 9, 7], Operations: ['59-52=7'] Exploring Operation: 9+7=16, Resulting Numbers: [4, 16] Generated Node #0,1,0: 19:[4, 16] Operation: 9+7=16 Exploring Operation: 4*7=28, Resulting Numbers: [9, 28] Generated Node #0,1,1: 19:[9, 28] Operation: 4*7=28 Exploring Operation: 4+9=13, Resulting Numbers: [7, 13] Generated Node #0,1,2: 19:[7, 13] Operation: 4+9=13 Exploring Operation: 4+7=11, Resulting Numbers: [9, 11] Generated Node #0,1,3: 19:[9, 11] Operation: 4+7=11 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[4, 16], Operations: ['59-52=7', '9+7=16'] Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,19 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,19 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,19 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[7, 13], Operations: ['59-52=7', '4+9=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,19 unequal: No Solution Exploring Operation: 7*13=91, Resulting Numbers: [91] 91,19 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 19:[9, 11], Operations: ['59-52=7', '4+7=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,19 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,19 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[9, 28], Operations: ['59-52=7', '4*7=28'] Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,19 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[52, 59, 4, 9], Operations: [] Exploring Operation: 59-52=7, Resulting Numbers: [4, 9, 7] Generated Node #0,1: 19:[4, 9, 7] Operation: 59-52=7 Moving to Node #0,1 Current State: 19:[4, 9, 7], Operations: ['59-52=7'] Exploring Operation: 4*7=28, Resulting Numbers: [9, 28] Generated Node #0,1,1: 19:[9, 28] Operation: 4*7=28 Moving to Node #0,1,1 Current State: 19:[9, 28], Operations: ['59-52=7', '4*7=28'] Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_4
sum_heuristic
[ 47, 59, 92, 94 ]
13
[ "47*92=4324", "4324/94=46", "59-46=13" ]
Current State: 13:[47, 59, 92, 94], Operations: [] Exploring Operation: 47*92=4324, Resulting Numbers: [59, 94, 4324] Generated Node #2: [59, 94, 4324] from Operation: 47*92=4324 Current State: 13:[59, 94, 4324], Operations: ['47*92=4324'] Exploring Operation: 4324/94=46, Resulting Numbers: [59, 46] Generated Node #3: [59, 46] from Operation: 4324/94=46 Current State: 13:[59, 46], Operations: ['47*92=4324', '4324/94=46'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[47, 59, 92, 94], Operations: [] Exploring Operation: 94-92=2, Resulting Numbers: [47, 59, 2] Generated Node #0,0: 13:[47, 59, 2] Operation: 94-92=2 Exploring Operation: 94-59=35, Resulting Numbers: [47, 92, 35] Generated Node #0,1: 13:[47, 92, 35] Operation: 94-59=35 Exploring Operation: 92-59=33, Resulting Numbers: [47, 94, 33] Generated Node #0,2: 13:[47, 94, 33] Operation: 92-59=33 Moving to Node #0,0 Current State: 13:[47, 59, 2], Operations: ['94-92=2'] Exploring Operation: 59-47=12, Resulting Numbers: [2, 12] Generated Node #0,0,0: 13:[2, 12] Operation: 59-47=12 Exploring Operation: 59-2=57, Resulting Numbers: [47, 57] Generated Node #0,0,1: 13:[47, 57] Operation: 59-2=57 Exploring Operation: 47-2=45, Resulting Numbers: [59, 45] Generated Node #0,0,2: 13:[59, 45] Operation: 47-2=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 13:[2, 12], Operations: ['94-92=2', '59-47=12'] Exploring Operation: 2+12=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,13 unequal: No Solution No 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: 13:[47, 57], Operations: ['94-92=2', '59-2=57'] Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,13 unequal: No Solution Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,13 unequal: No Solution No 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: 13:[59, 45], Operations: ['94-92=2', '47-2=45'] Exploring Operation: 59*45=2655, Resulting Numbers: [2655] 2655,13 unequal: No Solution Exploring Operation: 59+45=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 59-45=14, Resulting Numbers: [14] 14,13 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: 13:[47, 92, 35], Operations: ['94-59=35'] Exploring Operation: 92-35=57, Resulting Numbers: [47, 57] Generated Node #0,1,0: 13:[47, 57] Operation: 92-35=57 Exploring Operation: 47-35=12, Resulting Numbers: [92, 12] Generated Node #0,1,1: 13:[92, 12] Operation: 47-35=12 Exploring Operation: 92-47=45, Resulting Numbers: [35, 45] Generated Node #0,1,2: 13:[35, 45] Operation: 92-47=45 Moving to Node #0,2 Current State: 13:[47, 94, 33], Operations: ['92-59=33'] Exploring Operation: 94-47=47, Resulting Numbers: [33, 47] Generated Node #0,2,0: 13:[33, 47] Operation: 94-47=47 Exploring Operation: 47-33=14, Resulting Numbers: [94, 14] Generated Node #0,2,1: 13:[94, 14] Operation: 47-33=14 Exploring Operation: 94/47=2, Resulting Numbers: [33, 2] Generated Node #0,2,2: 13:[33, 2] Operation: 94/47=2 Moving to Node #0,2,2 Current State: 13:[33, 2], Operations: ['92-59=33', '94/47=2'] Exploring Operation: 33+2=35, Resulting Numbers: [35] 35,13 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,13 unequal: No Solution Exploring Operation: 33*2=66, Resulting Numbers: [66] 66,13 unequal: No Solution Moving to Node #0,1,2 Current State: 13:[35, 45], Operations: ['94-59=35', '92-47=45'] Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 35+45=80, Resulting Numbers: [80] 80,13 unequal: No Solution Exploring Operation: 35*45=1575, Resulting Numbers: [1575] 1575,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[33, 47], Operations: ['92-59=33', '94-47=47'] Exploring Operation: 47-33=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 33+47=80, Resulting Numbers: [80] 80,13 unequal: No Solution Exploring Operation: 33*47=1551, Resulting Numbers: [1551] 1551,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[47, 57], Operations: ['94-59=35', '92-35=57'] Exploring Operation: 57-47=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 47+57=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 47*57=2679, Resulting Numbers: [2679] 2679,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[92, 12], Operations: ['94-59=35', '47-35=12'] Exploring Operation: 92*12=1104, Resulting Numbers: [1104] 1104,13 unequal: No Solution Exploring Operation: 92-12=80, Resulting Numbers: [80] 80,13 unequal: No Solution Exploring Operation: 92+12=104, Resulting Numbers: [104] 104,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[94, 14], Operations: ['92-59=33', '47-33=14'] Exploring Operation: 94+14=108, Resulting Numbers: [108] 108,13 unequal: No Solution Exploring Operation: 94-14=80, Resulting Numbers: [80] 80,13 unequal: No Solution Exploring Operation: 94*14=1316, Resulting Numbers: [1316] 1316,13 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 54, 78, 87, 47 ]
64
[ "78-54=24", "87-47=40", "24+40=64" ]
Current State: 64:[54, 78, 87, 47], Operations: [] Exploring Operation: 78-54=24, Resulting Numbers: [87, 47, 24] Generated Node #2: [87, 47, 24] from Operation: 78-54=24 Current State: 64:[87, 47, 24], Operations: ['78-54=24'] Exploring Operation: 87-47=40, Resulting Numbers: [24, 40] Generated Node #3: [24, 40] from Operation: 87-47=40 Current State: 64:[24, 40], Operations: ['78-54=24', '87-47=40'] Exploring Operation: 24+40=64, Resulting Numbers: [64] 64,64 equal: Goal Reached
4
Current State: 64:[54, 78, 87, 47], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [78, 87, 7] Generated Node #0,0: 64:[78, 87, 7] Operation: 54-47=7 Exploring Operation: 78-47=31, Resulting Numbers: [54, 87, 31] Generated Node #0,1: 64:[54, 87, 31] Operation: 78-47=31 Exploring Operation: 87-54=33, Resulting Numbers: [78, 47, 33] Generated Node #0,2: 64:[78, 47, 33] Operation: 87-54=33 Exploring Operation: 87-47=40, Resulting Numbers: [54, 78, 40] Generated Node #0,3: 64:[54, 78, 40] Operation: 87-47=40 Exploring Operation: 87-78=9, Resulting Numbers: [54, 47, 9] Generated Node #0,4: 64:[54, 47, 9] Operation: 87-78=9 Start Sub Search at level 1: Moving to Node #0,4 Current State: 64:[54, 47, 9], Operations: ['87-78=9'] Exploring Operation: 54+9=63, Resulting Numbers: [47, 63] Generated Node #0,4,0: 64:[47, 63] Operation: 54+9=63 Exploring Operation: 47+9=56, Resulting Numbers: [54, 56] Generated Node #0,4,1: 64:[54, 56] Operation: 47+9=56 Exploring Operation: 54/9=6, Resulting Numbers: [47, 6] Generated Node #0,4,2: 64:[47, 6] Operation: 54/9=6 Exploring Operation: 54-47=7, Resulting Numbers: [9, 7] Generated Node #0,4,3: 64:[9, 7] Operation: 54-47=7 Exploring Operation: 47-9=38, Resulting Numbers: [54, 38] Generated Node #0,4,4: 64:[54, 38] Operation: 47-9=38 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 64:[9, 7], Operations: ['87-78=9', '54-47=7'] Exploring Operation: 9-7=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 9+7=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 9*7=63, Resulting Numbers: [63] 63,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 64:[47, 63], Operations: ['87-78=9', '54+9=63'] Exploring Operation: 63-47=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 47+63=110, Resulting Numbers: [110] 110,64 unequal: No Solution Exploring Operation: 47*63=2961, Resulting Numbers: [2961] 2961,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 64:[54, 38], Operations: ['87-78=9', '47-9=38'] Exploring Operation: 54*38=2052, Resulting Numbers: [2052] 2052,64 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,64 unequal: No Solution Exploring Operation: 54+38=92, Resulting Numbers: [92] 92,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 64:[47, 6], Operations: ['87-78=9', '54/9=6'] Exploring Operation: 47*6=282, Resulting Numbers: [282] 282,64 unequal: No Solution Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,64 unequal: No Solution Exploring Operation: 47-6=41, Resulting Numbers: [41] 41,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 64:[54, 56], Operations: ['87-78=9', '47+9=56'] Exploring Operation: 54+56=110, Resulting Numbers: [110] 110,64 unequal: No Solution Exploring Operation: 56-54=2, Resulting Numbers: [2] 2,64 unequal: No Solution Exploring Operation: 54*56=3024, Resulting Numbers: [3024] 3024,64 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 64:[78, 47, 33], Operations: ['87-54=33'] Exploring Operation: 78-47=31, Resulting Numbers: [33, 31] Generated Node #0,2,0: 64:[33, 31] Operation: 78-47=31 Exploring Operation: 47-33=14, Resulting Numbers: [78, 14] Generated Node #0,2,1: 64:[78, 14] Operation: 47-33=14 Exploring Operation: 47+33=80, Resulting Numbers: [78, 80] Generated Node #0,2,2: 64:[78, 80] Operation: 47+33=80 Exploring Operation: 78+47=125, Resulting Numbers: [33, 125] Generated Node #0,2,3: 64:[33, 125] Operation: 78+47=125 Exploring Operation: 78-33=45, Resulting Numbers: [47, 45] Generated Node #0,2,4: 64:[47, 45] Operation: 78-33=45 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 64:[33, 31], Operations: ['87-54=33', '78-47=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Moving to Node #0 Current State: 64:[54, 78, 87, 47], Operations: [] Exploring Operation: 87-54=33, Resulting Numbers: [78, 47, 33] Generated Node #0,2: 64:[78, 47, 33] Operation: 87-54=33 Moving to Node #0,2 Current State: 64:[78, 47, 33], Operations: ['87-54=33'] Exploring Operation: 78-47=31, Resulting Numbers: [33, 31] Generated Node #0,2,0: 64:[33, 31] Operation: 78-47=31 Moving to Node #0,2,0 Current State: 64:[33, 31], Operations: ['87-54=33', '78-47=31'] Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,64 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 48, 87, 82, 7 ]
60
[ "48+87=135", "82-7=75", "135-75=60" ]
Current State: 60:[48, 87, 82, 7], Operations: [] Exploring Operation: 48+87=135, Resulting Numbers: [82, 7, 135] Generated Node #2: [82, 7, 135] from Operation: 48+87=135 Current State: 60:[82, 7, 135], Operations: ['48+87=135'] Exploring Operation: 82-7=75, Resulting Numbers: [135, 75] Generated Node #3: [135, 75] from Operation: 82-7=75 Current State: 60:[135, 75], Operations: ['48+87=135', '82-7=75'] Exploring Operation: 135-75=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[48, 87, 82, 7], Operations: [] Exploring Operation: 87-82=5, Resulting Numbers: [48, 7, 5] Generated Node #0,0: 60:[48, 7, 5] Operation: 87-82=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[48, 7, 5], Operations: ['87-82=5'] Exploring Operation: 48+7=55, Resulting Numbers: [5, 55] Generated Node #0,0,0: 60:[5, 55] Operation: 48+7=55 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[5, 55], Operations: ['87-82=5', '48+7=55'] Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[48, 87, 82, 7], Operations: [] Exploring Operation: 87-82=5, Resulting Numbers: [48, 7, 5] Generated Node #0,0: 60:[48, 7, 5] Operation: 87-82=5 Moving to Node #0,0 Current State: 60:[48, 7, 5], Operations: ['87-82=5'] Exploring Operation: 48+7=55, Resulting Numbers: [5, 55] Generated Node #0,0,0: 60:[5, 55] Operation: 48+7=55 Moving to Node #0,0,0 Current State: 60:[5, 55], Operations: ['87-82=5', '48+7=55'] Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 55, 40, 58, 49 ]
92
[ "55-40=15", "58+49=107", "107-15=92" ]
Current State: 92:[55, 40, 58, 49], Operations: [] Exploring Operation: 55-40=15, Resulting Numbers: [58, 49, 15] Generated Node #2: [58, 49, 15] from Operation: 55-40=15 Current State: 92:[58, 49, 15], Operations: ['55-40=15'] Exploring Operation: 58+49=107, Resulting Numbers: [15, 107] Generated Node #3: [15, 107] from Operation: 58+49=107 Current State: 92:[15, 107], Operations: ['55-40=15', '58+49=107'] Exploring Operation: 107-15=92, Resulting Numbers: [92] 92,92 equal: Goal Reached
4
Current State: 92:[55, 40, 58, 49], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [40, 49, 3] Generated Node #0,0: 92:[40, 49, 3] Operation: 58-55=3 Exploring Operation: 55+40=95, Resulting Numbers: [58, 49, 95] Generated Node #0,1: 92:[58, 49, 95] Operation: 55+40=95 Exploring Operation: 58-40=18, Resulting Numbers: [55, 49, 18] Generated Node #0,2: 92:[55, 49, 18] Operation: 58-40=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 92:[40, 49, 3], Operations: ['58-55=3'] Exploring Operation: 49-40=9, Resulting Numbers: [3, 9] Generated Node #0,0,0: 92:[3, 9] Operation: 49-40=9 Exploring Operation: 40+49=89, Resulting Numbers: [3, 89] Generated Node #0,0,1: 92:[3, 89] Operation: 40+49=89 Exploring Operation: 40+3=43, Resulting Numbers: [49, 43] Generated Node #0,0,2: 92:[49, 43] Operation: 40+3=43 Moving to Node #0,0,1 Current State: 92:[3, 89], Operations: ['58-55=3', '40+49=89'] Exploring Operation: 3*89=267, Resulting Numbers: [267] 267,92 unequal: No Solution Exploring Operation: 89-3=86, Resulting Numbers: [86] 86,92 unequal: No Solution Exploring Operation: 3+89=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Moving to Node #0 Current State: 92:[55, 40, 58, 49], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [40, 49, 3] Generated Node #0,0: 92:[40, 49, 3] Operation: 58-55=3 Moving to Node #0,0 Current State: 92:[40, 49, 3], Operations: ['58-55=3'] Exploring Operation: 40+49=89, Resulting Numbers: [3, 89] Generated Node #0,0,1: 92:[3, 89] Operation: 40+49=89 Moving to Node #0,0,1 Current State: 92:[3, 89], Operations: ['58-55=3', '40+49=89'] Exploring Operation: 3+89=92, Resulting Numbers: [92] 92,92 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 80, 28, 5, 62 ]
90
[ "62-28=34", "5*34=170", "170-80=90" ]
Current State: 90:[80, 28, 5, 62], Operations: [] Exploring Operation: 62-28=34, Resulting Numbers: [80, 5, 34] Generated Node #2: [80, 5, 34] from Operation: 62-28=34 Current State: 90:[80, 5, 34], Operations: ['62-28=34'] Exploring Operation: 5*34=170, Resulting Numbers: [80, 170] Generated Node #3: [80, 170] from Operation: 5*34=170 Current State: 90:[80, 170], Operations: ['62-28=34', '5*34=170'] Exploring Operation: 170-80=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[80, 28, 5, 62], Operations: [] Exploring Operation: 28+62=90, Resulting Numbers: [80, 5, 90] Generated Node #0,0: 90:[80, 5, 90] Operation: 28+62=90 Exploring Operation: 62-28=34, Resulting Numbers: [80, 5, 34] Generated Node #0,1: 90:[80, 5, 34] Operation: 62-28=34 Exploring Operation: 80/5=16, Resulting Numbers: [28, 62, 16] Generated Node #0,2: 90:[28, 62, 16] Operation: 80/5=16 Exploring Operation: 80-62=18, Resulting Numbers: [28, 5, 18] Generated Node #0,3: 90:[28, 5, 18] Operation: 80-62=18 Exploring Operation: 80-28=52, Resulting Numbers: [5, 62, 52] Generated Node #0,4: 90:[5, 62, 52] Operation: 80-28=52 Moving to Node #0,3 Current State: 90:[28, 5, 18], Operations: ['80-62=18'] Exploring Operation: 18-5=13, Resulting Numbers: [28, 13] Generated Node #0,3,0: 90:[28, 13] Operation: 18-5=13 Exploring Operation: 28-18=10, Resulting Numbers: [5, 10] Generated Node #0,3,1: 90:[5, 10] Operation: 28-18=10 Exploring Operation: 28+18=46, Resulting Numbers: [5, 46] Generated Node #0,3,2: 90:[5, 46] Operation: 28+18=46 Exploring Operation: 5*18=90, Resulting Numbers: [28, 90] Generated Node #0,3,3: 90:[28, 90] Operation: 5*18=90 Exploring Operation: 28+5=33, Resulting Numbers: [18, 33] Generated Node #0,3,4: 90:[18, 33] Operation: 28+5=33 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 90:[5, 10], Operations: ['80-62=18', '28-18=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 90:[5, 46], Operations: ['80-62=18', '28+18=46'] Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,90 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 90:[28, 90], Operations: ['80-62=18', '5*18=90'] Exploring Operation: 90-28=62, Resulting Numbers: [62] 62,90 unequal: No Solution Exploring Operation: 28*90=2520, Resulting Numbers: [2520] 2520,90 unequal: No Solution Exploring Operation: 28+90=118, Resulting Numbers: [118] 118,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 90:[18, 33], Operations: ['80-62=18', '28+5=33'] Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 18*33=594, Resulting Numbers: [594] 594,90 unequal: No Solution Exploring Operation: 18+33=51, Resulting Numbers: [51] 51,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 90:[28, 13], Operations: ['80-62=18', '18-5=13'] Exploring Operation: 28*13=364, Resulting Numbers: [364] 364,90 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 28+13=41, Resulting Numbers: [41] 41,90 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: 90:[80, 5, 90], Operations: ['28+62=90'] Exploring Operation: 80/5=16, Resulting Numbers: [90, 16] Generated Node #0,0,0: 90:[90, 16] Operation: 80/5=16 Exploring Operation: 80-5=75, Resulting Numbers: [90, 75] Generated Node #0,0,1: 90:[90, 75] Operation: 80-5=75 Exploring Operation: 90/5=18, Resulting Numbers: [80, 18] Generated Node #0,0,2: 90:[80, 18] Operation: 90/5=18 Exploring Operation: 90-80=10, Resulting Numbers: [5, 10] Generated Node #0,0,3: 90:[5, 10] Operation: 90-80=10 Exploring Operation: 80+5=85, Resulting Numbers: [90, 85] Generated Node #0,0,4: 90:[90, 85] Operation: 80+5=85 Moving to Node #0,1 Current State: 90:[80, 5, 34], Operations: ['62-28=34'] Exploring Operation: 5+34=39, Resulting Numbers: [80, 39] Generated Node #0,1,0: 90:[80, 39] Operation: 5+34=39 Exploring Operation: 34-5=29, Resulting Numbers: [80, 29] Generated Node #0,1,1: 90:[80, 29] Operation: 34-5=29 Exploring Operation: 80+5=85, Resulting Numbers: [34, 85] Generated Node #0,1,2: 90:[34, 85] Operation: 80+5=85 Exploring Operation: 80/5=16, Resulting Numbers: [34, 16] Generated Node #0,1,3: 90:[34, 16] Operation: 80/5=16 Exploring Operation: 80-34=46, Resulting Numbers: [5, 46] Generated Node #0,1,4: 90:[5, 46] Operation: 80-34=46 Moving to Node #0,2 Current State: 90:[28, 62, 16], Operations: ['80/5=16'] Exploring Operation: 62-28=34, Resulting Numbers: [16, 34] Generated Node #0,2,0: 90:[16, 34] Operation: 62-28=34 Exploring Operation: 28+16=44, Resulting Numbers: [62, 44] Generated Node #0,2,1: 90:[62, 44] Operation: 28+16=44 Exploring Operation: 62+16=78, Resulting Numbers: [28, 78] Generated Node #0,2,2: 90:[28, 78] Operation: 62+16=78 Exploring Operation: 28+62=90, Resulting Numbers: [16, 90] Generated Node #0,2,3: 90:[16, 90] Operation: 28+62=90 Exploring Operation: 62-16=46, Resulting Numbers: [28, 46] Generated Node #0,2,4: 90:[28, 46] Operation: 62-16=46 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 90:[16, 90], Operations: ['80/5=16', '28+62=90'] Exploring Operation: 16+90=106, Resulting Numbers: [106] 106,90 unequal: No Solution Exploring Operation: 16*90=1440, Resulting Numbers: [1440] 1440,90 unequal: No Solution Exploring Operation: 90-16=74, Resulting Numbers: [74] 74,90 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:[28, 46], Operations: ['80/5=16', '62-16=46'] Exploring Operation: 46-28=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 28*46=1288, Resulting Numbers: [1288] 1288,90 unequal: No Solution Exploring Operation: 28+46=74, Resulting Numbers: [74] 74,90 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:[16, 34], Operations: ['80/5=16', '62-28=34'] Exploring Operation: 16+34=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 16*34=544, Resulting Numbers: [544] 544,90 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,90 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 #0,2,2 Current State: 90:[28, 78], Operations: ['80/5=16', '62+16=78'] Exploring Operation: 78-28=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 28*78=2184, Resulting Numbers: [2184] 2184,90 unequal: No Solution Exploring Operation: 28+78=106, Resulting Numbers: [106] 106,90 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:[62, 44], Operations: ['80/5=16', '28+16=44'] Exploring Operation: 62+44=106, Resulting Numbers: [106] 106,90 unequal: No Solution Exploring Operation: 62*44=2728, Resulting Numbers: [2728] 2728,90 unequal: No Solution Exploring Operation: 62-44=18, Resulting Numbers: [18] 18,90 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:[5, 62, 52], Operations: ['80-28=52'] Exploring Operation: 5+62=67, Resulting Numbers: [52, 67] Generated Node #0,4,0: 90:[52, 67] Operation: 5+62=67 Exploring Operation: 62+52=114, Resulting Numbers: [5, 114] Generated Node #0,4,1: 90:[5, 114] Operation: 62+52=114 Exploring Operation: 52-5=47, Resulting Numbers: [62, 47] Generated Node #0,4,2: 90:[62, 47] Operation: 52-5=47 Exploring Operation: 62-52=10, Resulting Numbers: [5, 10] Generated Node #0,4,3: 90:[5, 10] Operation: 62-52=10 Exploring Operation: 62-5=57, Resulting Numbers: [52, 57] Generated Node #0,4,4: 90:[52, 57] Operation: 62-5=57 Moving to Node #0,0,3 Current State: 90:[5, 10], Operations: ['28+62=90', '90-80=10'] Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,90 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,90 unequal: No Solution Moving to Node #0,4,3 Current State: 90:[5, 10], Operations: ['80-28=52', '62-52=10'] Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,90 unequal: No Solution Moving to Node #0,1,4 Current State: 90:[5, 46], Operations: ['62-28=34', '80-34=46'] Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,90 unequal: No Solution Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,90 unequal: No Solution Moving to Node #0,0,0 Current State: 90:[90, 16], Operations: ['28+62=90', '80/5=16'] Exploring Operation: 90-16=74, Resulting Numbers: [74] 74,90 unequal: No Solution Exploring Operation: 90+16=106, Resulting Numbers: [106] 106,90 unequal: No Solution Exploring Operation: 90*16=1440, Resulting Numbers: [1440] 1440,90 unequal: No Solution Moving to Node #0,1,3 Current State: 90:[34, 16], Operations: ['62-28=34', '80/5=16'] Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,90 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,90 unequal: No Solution Moving to Node #0,0,4 Current State: 90:[90, 85], Operations: ['28+62=90', '80+5=85'] Exploring Operation: 90+85=175, Resulting Numbers: [175] 175,90 unequal: No Solution Exploring Operation: 90*85=7650, Resulting Numbers: [7650] 7650,90 unequal: No Solution Exploring Operation: 90-85=5, Resulting Numbers: [5] 5,90 unequal: No Solution Moving to Node #0,1,2 Current State: 90:[34, 85], Operations: ['62-28=34', '80+5=85'] Exploring Operation: 85-34=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 34*85=2890, Resulting Numbers: [2890] 2890,90 unequal: No Solution Exploring Operation: 34+85=119, Resulting Numbers: [119] 119,90 unequal: No Solution Moving to Node #0,0,2 Current State: 90:[80, 18], Operations: ['28+62=90', '90/5=18'] Exploring Operation: 80*18=1440, Resulting Numbers: [1440] 1440,90 unequal: No Solution Exploring Operation: 80+18=98, Resulting Numbers: [98] 98,90 unequal: No Solution Exploring Operation: 80-18=62, Resulting Numbers: [62] 62,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[80, 29], Operations: ['62-28=34', '34-5=29'] Exploring Operation: 80*29=2320, Resulting Numbers: [2320] 2320,90 unequal: No Solution Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,90 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[90, 75], Operations: ['28+62=90', '80-5=75'] Exploring Operation: 90*75=6750, Resulting Numbers: [6750] 6750,90 unequal: No Solution Exploring Operation: 90+75=165, Resulting Numbers: [165] 165,90 unequal: No Solution Exploring Operation: 90-75=15, Resulting Numbers: [15] 15,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[80, 39], Operations: ['62-28=34', '5+34=39'] Exploring Operation: 80*39=3120, Resulting Numbers: [3120] 3120,90 unequal: No Solution Exploring Operation: 80-39=41, Resulting Numbers: [41] 41,90 unequal: No Solution Exploring Operation: 80+39=119, Resulting Numbers: [119] 119,90 unequal: No Solution Moving to Node #0,4,2 Current State: 90:[62, 47], Operations: ['80-28=52', '52-5=47'] Exploring Operation: 62-47=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 62*47=2914, Resulting Numbers: [2914] 2914,90 unequal: No Solution Exploring Operation: 62+47=109, Resulting Numbers: [109] 109,90 unequal: No Solution Moving to Node #0,4,4 Current State: 90:[52, 57], Operations: ['80-28=52', '62-5=57'] Exploring Operation: 52*57=2964, Resulting Numbers: [2964] 2964,90 unequal: No Solution Exploring Operation: 57-52=5, Resulting Numbers: [5] 5,90 unequal: No Solution Exploring Operation: 52+57=109, Resulting Numbers: [109] 109,90 unequal: No Solution Moving to Node #0,4,1 Current State: 90:[5, 114], Operations: ['80-28=52', '62+52=114'] Exploring Operation: 114-5=109, Resulting Numbers: [109] 109,90 unequal: No Solution Exploring Operation: 5+114=119, Resulting Numbers: [119] 119,90 unequal: No Solution Exploring Operation: 5*114=570, Resulting Numbers: [570] 570,90 unequal: No Solution Moving to Node #0,4,0 Current State: 90:[52, 67], Operations: ['80-28=52', '5+62=67'] Exploring Operation: 67-52=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 52*67=3484, Resulting Numbers: [3484] 3484,90 unequal: No Solution Exploring Operation: 52+67=119, Resulting Numbers: [119] 119,90 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 64, 58, 2, 5 ]
85
[ "64/2=32", "58-5=53", "32+53=85" ]
Current State: 85:[64, 58, 2, 5], Operations: [] Exploring Operation: 64/2=32, Resulting Numbers: [58, 5, 32] Generated Node #2: [58, 5, 32] from Operation: 64/2=32 Current State: 85:[58, 5, 32], Operations: ['64/2=32'] Exploring Operation: 58-5=53, Resulting Numbers: [32, 53] Generated Node #3: [32, 53] from Operation: 58-5=53 Current State: 85:[32, 53], Operations: ['64/2=32', '58-5=53'] Exploring Operation: 32+53=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[64, 58, 2, 5], Operations: [] Exploring Operation: 64-58=6, Resulting Numbers: [2, 5, 6] Generated Node #0,0: 85:[2, 5, 6] Operation: 64-58=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[2, 5, 6], Operations: ['64-58=6'] Exploring Operation: 6-2=4, Resulting Numbers: [5, 4] Generated Node #0,0,0: 85:[5, 4] Operation: 6-2=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 85:[5, 4], Operations: ['64-58=6', '6-2=4'] Exploring Operation: 5*4=20, Resulting Numbers: [20] 20,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 71, 49, 70, 2 ]
90
[ "71-49=22", "70-2=68", "22+68=90" ]
Current State: 90:[71, 49, 70, 2], Operations: [] Exploring Operation: 71-49=22, Resulting Numbers: [70, 2, 22] Generated Node #2: [70, 2, 22] from Operation: 71-49=22 Current State: 90:[70, 2, 22], Operations: ['71-49=22'] Exploring Operation: 70-2=68, Resulting Numbers: [22, 68] Generated Node #3: [22, 68] from Operation: 70-2=68 Current State: 90:[22, 68], Operations: ['71-49=22', '70-2=68'] Exploring Operation: 22+68=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[71, 49, 70, 2], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [71, 49, 35] Generated Node #0,0: 90:[71, 49, 35] Operation: 70/2=35 Exploring Operation: 71-49=22, Resulting Numbers: [70, 2, 22] Generated Node #0,1: 90:[70, 2, 22] Operation: 71-49=22 Exploring Operation: 71-70=1, Resulting Numbers: [49, 2, 1] Generated Node #0,2: 90:[49, 2, 1] Operation: 71-70=1 Exploring Operation: 70-49=21, Resulting Numbers: [71, 2, 21] Generated Node #0,3: 90:[71, 2, 21] Operation: 70-49=21 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[49, 2, 1], Operations: ['71-70=1'] Exploring Operation: 49-2=47, Resulting Numbers: [1, 47] Generated Node #0,2,0: 90:[1, 47] Operation: 49-2=47 Exploring Operation: 49*1=49, Resulting Numbers: [2, 49] Generated Node #0,2,1: 90:[2, 49] Operation: 49*1=49 Exploring Operation: 49/1=49, Resulting Numbers: [2, 49] Generated Node #0,2,2: 90:[2, 49] Operation: 49/1=49 Exploring Operation: 49-1=48, Resulting Numbers: [2, 48] Generated Node #0,2,3: 90:[2, 48] Operation: 49-1=48 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 90:[1, 47], Operations: ['71-70=1', '49-2=47'] Exploring Operation: 47/1=47, Resulting Numbers: [47] 47,90 unequal: No Solution Exploring Operation: 1+47=48, Resulting Numbers: [48] 48,90 unequal: No Solution Exploring Operation: 47-1=46, Resulting Numbers: [46] 46,90 unequal: No Solution Exploring Operation: 1*47=47, Resulting Numbers: [47] 47,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 90:[2, 48], Operations: ['71-70=1', '49-1=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,90 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,90 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,90 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 90:[2, 49], Operations: ['71-70=1', '49*1=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,90 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 90:[2, 49], Operations: ['71-70=1', '49/1=49'] Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,90 unequal: No Solution Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,90 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[71, 2, 21], Operations: ['70-49=21'] Exploring Operation: 71+21=92, Resulting Numbers: [2, 92] Generated Node #0,3,0: 90:[2, 92] Operation: 71+21=92 Exploring Operation: 71+2=73, Resulting Numbers: [21, 73] Generated Node #0,3,1: 90:[21, 73] Operation: 71+2=73 Exploring Operation: 71-21=50, Resulting Numbers: [2, 50] Generated Node #0,3,2: 90:[2, 50] Operation: 71-21=50 Exploring Operation: 21-2=19, Resulting Numbers: [71, 19] Generated Node #0,3,3: 90:[71, 19] Operation: 21-2=19 Moving to Node #0,3,0 Current State: 90:[2, 92], Operations: ['70-49=21', '71+21=92'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Moving to Node #0 Current State: 90:[71, 49, 70, 2], Operations: [] Exploring Operation: 70-49=21, Resulting Numbers: [71, 2, 21] Generated Node #0,3: 90:[71, 2, 21] Operation: 70-49=21 Moving to Node #0,3 Current State: 90:[71, 2, 21], Operations: ['70-49=21'] Exploring Operation: 71+21=92, Resulting Numbers: [2, 92] Generated Node #0,3,0: 90:[2, 92] Operation: 71+21=92 Moving to Node #0,3,0 Current State: 90:[2, 92], Operations: ['70-49=21', '71+21=92'] Exploring Operation: 92-2=90, Resulting Numbers: [90] 90,90 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 14, 75, 34, 3 ]
83
[ "14*3=42", "75-34=41", "42+41=83" ]
Current State: 83:[14, 75, 34, 3], Operations: [] Exploring Operation: 14*3=42, Resulting Numbers: [75, 34, 42] Generated Node #2: [75, 34, 42] from Operation: 14*3=42 Current State: 83:[75, 34, 42], Operations: ['14*3=42'] Exploring Operation: 75-34=41, Resulting Numbers: [42, 41] Generated Node #3: [42, 41] from Operation: 75-34=41 Current State: 83:[42, 41], Operations: ['14*3=42', '75-34=41'] Exploring Operation: 42+41=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[14, 75, 34, 3], Operations: [] Exploring Operation: 14+34=48, Resulting Numbers: [75, 3, 48] Generated Node #0,0: 83:[75, 3, 48] Operation: 14+34=48 Exploring Operation: 14*3=42, Resulting Numbers: [75, 34, 42] Generated Node #0,1: 83:[75, 34, 42] Operation: 14*3=42 Exploring Operation: 34*3=102, Resulting Numbers: [14, 75, 102] Generated Node #0,2: 83:[14, 75, 102] Operation: 34*3=102 Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[14, 75, 102], Operations: ['34*3=102'] Exploring Operation: 14+75=89, Resulting Numbers: [102, 89] Generated Node #0,2,0: 83:[102, 89] Operation: 14+75=89 Exploring Operation: 102-14=88, Resulting Numbers: [75, 88] Generated Node #0,2,1: 83:[75, 88] Operation: 102-14=88 Exploring Operation: 75-14=61, Resulting Numbers: [102, 61] Generated Node #0,2,2: 83:[102, 61] Operation: 75-14=61 Moving to Node #0,2,1 Current State: 83:[75, 88], Operations: ['34*3=102', '102-14=88'] Exploring Operation: 75+88=163, Resulting Numbers: [163] 163,83 unequal: No Solution Exploring Operation: 75*88=6600, Resulting Numbers: [6600] 6600,83 unequal: No Solution Exploring Operation: 88-75=13, Resulting Numbers: [13] 13,83 unequal: No Solution Moving to Node #0,2,0 Current State: 83:[102, 89], Operations: ['34*3=102', '14+75=89'] Exploring Operation: 102*89=9078, Resulting Numbers: [9078] 9078,83 unequal: No Solution Exploring Operation: 102+89=191, Resulting Numbers: [191] 191,83 unequal: No Solution Exploring Operation: 102-89=13, Resulting Numbers: [13] 13,83 unequal: No Solution Moving to Node #0,2,2 Current State: 83:[102, 61], Operations: ['34*3=102', '75-14=61'] Exploring Operation: 102-61=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 102+61=163, Resulting Numbers: [163] 163,83 unequal: No Solution Exploring Operation: 102*61=6222, Resulting Numbers: [6222] 6222,83 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[75, 34, 42], Operations: ['14*3=42'] Exploring Operation: 75+34=109, Resulting Numbers: [42, 109] Generated Node #0,1,0: 83:[42, 109] Operation: 75+34=109 Exploring Operation: 34+42=76, Resulting Numbers: [75, 76] Generated Node #0,1,1: 83:[75, 76] Operation: 34+42=76 Exploring Operation: 75-34=41, Resulting Numbers: [42, 41] Generated Node #0,1,2: 83:[42, 41] Operation: 75-34=41 Moving to Node #0,1,1 Current State: 83:[75, 76], Operations: ['14*3=42', '34+42=76'] Exploring Operation: 75+76=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 76-75=1, Resulting Numbers: [1] 1,83 unequal: No Solution Exploring Operation: 75*76=5700, Resulting Numbers: [5700] 5700,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[42, 109], Operations: ['14*3=42', '75+34=109'] Exploring Operation: 42*109=4578, Resulting Numbers: [4578] 4578,83 unequal: No Solution Exploring Operation: 42+109=151, Resulting Numbers: [151] 151,83 unequal: No Solution Exploring Operation: 109-42=67, Resulting Numbers: [67] 67,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[42, 41], Operations: ['14*3=42', '75-34=41'] Exploring Operation: 42*41=1722, Resulting Numbers: [1722] 1722,83 unequal: No Solution Exploring Operation: 42-41=1, Resulting Numbers: [1] 1,83 unequal: No Solution Exploring Operation: 42+41=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[14, 75, 34, 3], Operations: [] Exploring Operation: 14*3=42, Resulting Numbers: [75, 34, 42] Generated Node #0,1: 83:[75, 34, 42] Operation: 14*3=42 Moving to Node #0,1 Current State: 83:[75, 34, 42], Operations: ['14*3=42'] Exploring Operation: 75-34=41, Resulting Numbers: [42, 41] Generated Node #0,1,2: 83:[42, 41] Operation: 75-34=41 Moving to Node #0,1,2 Current State: 83:[42, 41], Operations: ['14*3=42', '75-34=41'] Exploring Operation: 42+41=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.97309
hs_3
sum_heuristic
[ 3, 6, 23, 4 ]
47
[ "23-6=17", "3*17=51", "51-4=47" ]
Current State: 47:[3, 6, 23, 4], Operations: [] Exploring Operation: 23-6=17, Resulting Numbers: [3, 4, 17] Generated Node #2: [3, 4, 17] from Operation: 23-6=17 Current State: 47:[3, 4, 17], Operations: ['23-6=17'] Exploring Operation: 3*17=51, Resulting Numbers: [4, 51] Generated Node #3: [4, 51] from Operation: 3*17=51 Current State: 47:[4, 51], Operations: ['23-6=17', '3*17=51'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[3, 6, 23, 4], Operations: [] Exploring Operation: 3*4=12, Resulting Numbers: [6, 23, 12] Generated Node #0,0: 47:[6, 23, 12] Operation: 3*4=12 Exploring Operation: 3+23=26, Resulting Numbers: [6, 4, 26] Generated Node #0,1: 47:[6, 4, 26] Operation: 3+23=26 Exploring Operation: 3*6=18, Resulting Numbers: [23, 4, 18] Generated Node #0,2: 47:[23, 4, 18] Operation: 3*6=18 Exploring Operation: 6*4=24, Resulting Numbers: [3, 23, 24] Generated Node #0,3: 47:[3, 23, 24] Operation: 6*4=24 Exploring Operation: 3+6=9, Resulting Numbers: [23, 4, 9] Generated Node #0,4: 47:[23, 4, 9] Operation: 3+6=9 Start Sub Search at level 1: Moving to Node #0,3 Current State: 47:[3, 23, 24], Operations: ['6*4=24'] Exploring Operation: 3*23=69, Resulting Numbers: [24, 69] Generated Node #0,3,0: 47:[24, 69] Operation: 3*23=69 Exploring Operation: 3+24=27, Resulting Numbers: [23, 27] Generated Node #0,3,1: 47:[23, 27] Operation: 3+24=27 Exploring Operation: 3*24=72, Resulting Numbers: [23, 72] Generated Node #0,3,2: 47:[23, 72] Operation: 3*24=72 Exploring Operation: 3+23=26, Resulting Numbers: [24, 26] Generated Node #0,3,3: 47:[24, 26] Operation: 3+23=26 Exploring Operation: 23+24=47, Resulting Numbers: [3, 47] Generated Node #0,3,4: 47:[3, 47] Operation: 23+24=47 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 47:[23, 27], Operations: ['6*4=24', '3+24=27'] Exploring Operation: 23+27=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 23*27=621, Resulting Numbers: [621] 621,47 unequal: No Solution Exploring Operation: 27-23=4, Resulting Numbers: [4] 4,47 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 #0,3,3 Current State: 47:[24, 26], Operations: ['6*4=24', '3+23=26'] Exploring Operation: 24*26=624, Resulting Numbers: [624] 624,47 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 24+26=50, Resulting Numbers: [50] 50,47 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 #0,3,4 Current State: 47:[3, 47], Operations: ['6*4=24', '23+24=47'] Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,47 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,47 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 #0,3,0 Current State: 47:[24, 69], Operations: ['6*4=24', '3*23=69'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,47 unequal: No Solution Exploring Operation: 24+69=93, Resulting Numbers: [93] 93,47 unequal: No Solution Exploring Operation: 24*69=1656, Resulting Numbers: [1656] 1656,47 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 #0,3,2 Current State: 47:[23, 72], Operations: ['6*4=24', '3*24=72'] Exploring Operation: 23+72=95, Resulting Numbers: [95] 95,47 unequal: No Solution Exploring Operation: 23*72=1656, Resulting Numbers: [1656] 1656,47 unequal: No Solution Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,47 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 #0,2 Current State: 47:[23, 4, 18], Operations: ['3*6=18'] Exploring Operation: 23+4=27, Resulting Numbers: [18, 27] Generated Node #0,2,0: 47:[18, 27] Operation: 23+4=27 Exploring Operation: 4+18=22, Resulting Numbers: [23, 22] Generated Node #0,2,1: 47:[23, 22] Operation: 4+18=22 Exploring Operation: 4*18=72, Resulting Numbers: [23, 72] Generated Node #0,2,2: 47:[23, 72] Operation: 4*18=72 Exploring Operation: 23-4=19, Resulting Numbers: [18, 19] Generated Node #0,2,3: 47:[18, 19] Operation: 23-4=19 Exploring Operation: 23+18=41, Resulting Numbers: [4, 41] Generated Node #0,2,4: 47:[4, 41] Operation: 23+18=41 Moving to Node #0,2,0 Current State: 47:[18, 27], Operations: ['3*6=18', '23+4=27'] Exploring Operation: 18+27=45, Resulting Numbers: [45] 45,47 unequal: No Solution Exploring Operation: 27-18=9, Resulting Numbers: [9] 9,47 unequal: No Solution Exploring Operation: 18*27=486, Resulting Numbers: [486] 486,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[23, 72], Operations: ['3*6=18', '4*18=72'] Exploring Operation: 23*72=1656, Resulting Numbers: [1656] 1656,47 unequal: No Solution Exploring Operation: 23+72=95, Resulting Numbers: [95] 95,47 unequal: No Solution Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[23, 22], Operations: ['3*6=18', '4+18=22'] Exploring Operation: 23*22=506, Resulting Numbers: [506] 506,47 unequal: No Solution Exploring Operation: 23-22=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 23+22=45, Resulting Numbers: [45] 45,47 unequal: No Solution Moving to Node #0,2,4 Current State: 47:[4, 41], Operations: ['3*6=18', '23+18=41'] Exploring Operation: 4+41=45, Resulting Numbers: [45] 45,47 unequal: No Solution Exploring Operation: 41-4=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 4*41=164, Resulting Numbers: [164] 164,47 unequal: No Solution Moving to Node #0,2,3 Current State: 47:[18, 19], Operations: ['3*6=18', '23-4=19'] Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,47 unequal: No Solution Exploring Operation: 18*19=342, Resulting Numbers: [342] 342,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 47:[6, 23, 12], Operations: ['3*4=12'] Exploring Operation: 23-6=17, Resulting Numbers: [12, 17] Generated Node #0,0,0: 47:[12, 17] Operation: 23-6=17 Exploring Operation: 23+12=35, Resulting Numbers: [6, 35] Generated Node #0,0,1: 47:[6, 35] Operation: 23+12=35 Exploring Operation: 6+12=18, Resulting Numbers: [23, 18] Generated Node #0,0,2: 47:[23, 18] Operation: 6+12=18 Exploring Operation: 6+23=29, Resulting Numbers: [12, 29] Generated Node #0,0,3: 47:[12, 29] Operation: 6+23=29 Exploring Operation: 6*12=72, Resulting Numbers: [23, 72] Generated Node #0,0,4: 47:[23, 72] Operation: 6*12=72 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 47:[23, 72], Operations: ['3*4=12', '6*12=72'] Exploring Operation: 72-23=49, Resulting Numbers: [49] 49,47 unequal: No Solution Exploring Operation: 23*72=1656, Resulting Numbers: [1656] 1656,47 unequal: No Solution Exploring Operation: 23+72=95, Resulting Numbers: [95] 95,47 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 #0,0,1 Current State: 47:[6, 35], Operations: ['3*4=12', '23+12=35'] Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,47 unequal: No Solution Exploring Operation: 6*35=210, Resulting Numbers: [210] 210,47 unequal: No Solution Exploring Operation: 6+35=41, Resulting Numbers: [41] 41,47 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 #0,0,2 Current State: 47:[23, 18], Operations: ['3*4=12', '6+12=18'] Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 23+18=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 23*18=414, Resulting Numbers: [414] 414,47 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 #0,0,3 Current State: 47:[12, 29], Operations: ['3*4=12', '6+23=29'] Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,47 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,47 unequal: No Solution Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,47 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:[12, 17], Operations: ['3*4=12', '23-6=17'] Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,47 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,47 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:[6, 4, 26], Operations: ['3+23=26'] Exploring Operation: 6-4=2, Resulting Numbers: [26, 2] Generated Node #0,1,0: 47:[26, 2] Operation: 6-4=2 Exploring Operation: 6+4=10, Resulting Numbers: [26, 10] Generated Node #0,1,1: 47:[26, 10] Operation: 6+4=10 Exploring Operation: 4+26=30, Resulting Numbers: [6, 30] Generated Node #0,1,2: 47:[6, 30] Operation: 4+26=30 Exploring Operation: 6*4=24, Resulting Numbers: [26, 24] Generated Node #0,1,3: 47:[26, 24] Operation: 6*4=24 Exploring Operation: 6+26=32, Resulting Numbers: [4, 32] Generated Node #0,1,4: 47:[4, 32] Operation: 6+26=32 Moving to Node #0,1,3 Current State: 47:[26, 24], Operations: ['3+23=26', '6*4=24'] Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,47 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,47 unequal: No Solution Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[6, 30], Operations: ['3+23=26', '4+26=30'] Exploring Operation: 6+30=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,47 unequal: No Solution Exploring Operation: 6*30=180, Resulting Numbers: [180] 180,47 unequal: No Solution Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[26, 10], Operations: ['3+23=26', '6+4=10'] Exploring Operation: 26*10=260, Resulting Numbers: [260] 260,47 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,47 unequal: No Solution Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,47 unequal: No Solution Moving to Node #0,1,4 Current State: 47:[4, 32], Operations: ['3+23=26', '6+26=32'] Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,47 unequal: No Solution Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,47 unequal: No Solution Moving to Node #0,1,0 Current State: 47:[26, 2], Operations: ['3+23=26', '6-4=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,47 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,47 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 47:[23, 4, 9], Operations: ['3+6=9'] Exploring Operation: 4*9=36, Resulting Numbers: [23, 36] Generated Node #0,4,0: 47:[23, 36] Operation: 4*9=36 Exploring Operation: 23-4=19, Resulting Numbers: [9, 19] Generated Node #0,4,1: 47:[9, 19] Operation: 23-4=19 Exploring Operation: 23+9=32, Resulting Numbers: [4, 32] Generated Node #0,4,2: 47:[4, 32] Operation: 23+9=32 Exploring Operation: 23+4=27, Resulting Numbers: [9, 27] Generated Node #0,4,3: 47:[9, 27] Operation: 23+4=27 Exploring Operation: 4+9=13, Resulting Numbers: [23, 13] Generated Node #0,4,4: 47:[23, 13] Operation: 4+9=13 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 47:[23, 36], Operations: ['3+6=9', '4*9=36'] Exploring Operation: 23*36=828, Resulting Numbers: [828] 828,47 unequal: No Solution Exploring Operation: 23+36=59, Resulting Numbers: [59] 59,47 unequal: No Solution Exploring Operation: 36-23=13, Resulting Numbers: [13] 13,47 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 #0,4,2 Current State: 47:[4, 32], Operations: ['3+6=9', '23+9=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 32/4=8, Resulting Numbers: [8] 8,47 unequal: No Solution Exploring Operation: 4*32=128, Resulting Numbers: [128] 128,47 unequal: No Solution Exploring Operation: 32-4=28, Resulting Numbers: [28] 28,47 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 #0,4,3 Current State: 47:[9, 27], Operations: ['3+6=9', '23+4=27'] Exploring Operation: 27/9=3, Resulting Numbers: [3] 3,47 unequal: No Solution Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,47 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,47 unequal: No Solution Exploring Operation: 9*27=243, Resulting Numbers: [243] 243,47 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 #0,4,4 Current State: 47:[23, 13], Operations: ['3+6=9', '4+9=13'] Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,47 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,47 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,47 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 #0,4,1 Current State: 47:[9, 19], Operations: ['3+6=9', '23-4=19'] Exploring Operation: 19-9=10, Resulting Numbers: [10] 10,47 unequal: No Solution Exploring Operation: 9+19=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 9*19=171, Resulting Numbers: [171] 171,47 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_5
mult_heuristic
[ 61, 34, 62, 4 ]
85
[ "61-34=27", "62-4=58", "27+58=85" ]
Current State: 85:[61, 34, 62, 4], Operations: [] Exploring Operation: 61-34=27, Resulting Numbers: [62, 4, 27] Generated Node #2: [62, 4, 27] from Operation: 61-34=27 Current State: 85:[62, 4, 27], Operations: ['61-34=27'] Exploring Operation: 62-4=58, Resulting Numbers: [27, 58] Generated Node #3: [27, 58] from Operation: 62-4=58 Current State: 85:[27, 58], Operations: ['61-34=27', '62-4=58'] Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[61, 34, 62, 4], Operations: [] Exploring Operation: 61+34=95, Resulting Numbers: [62, 4, 95] Generated Node #0,0: 85:[62, 4, 95] Operation: 61+34=95 Exploring Operation: 62-61=1, Resulting Numbers: [34, 4, 1] Generated Node #0,1: 85:[34, 4, 1] Operation: 62-61=1 Start Sub Search at level 1: Moving to Node #0,1 Current State: 85:[34, 4, 1], Operations: ['62-61=1'] Exploring Operation: 34-4=30, Resulting Numbers: [1, 30] Generated Node #0,1,0: 85:[1, 30] Operation: 34-4=30 Exploring Operation: 34-1=33, Resulting Numbers: [4, 33] Generated Node #0,1,1: 85:[4, 33] Operation: 34-1=33 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 85:[1, 30], Operations: ['62-61=1', '34-4=30'] Exploring Operation: 30-1=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 1*30=30, Resulting Numbers: [30] 30,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 85:[4, 33], Operations: ['62-61=1', '34-1=33'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,85 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[62, 4, 95], Operations: ['61+34=95'] Exploring Operation: 62+4=66, Resulting Numbers: [95, 66] Generated Node #0,0,0: 85:[95, 66] Operation: 62+4=66 Exploring Operation: 95-62=33, Resulting Numbers: [4, 33] Generated Node #0,0,1: 85:[4, 33] Operation: 95-62=33 Moving to Node #0,0,1 Current State: 85:[4, 33], Operations: ['61+34=95', '95-62=33'] Exploring Operation: 4+33=37, Resulting Numbers: [37] 37,85 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,85 unequal: No Solution Moving to Node #0,0,0 Current State: 85:[95, 66], Operations: ['61+34=95', '62+4=66'] Exploring Operation: 95+66=161, Resulting Numbers: [161] 161,85 unequal: No Solution Exploring Operation: 95-66=29, Resulting Numbers: [29] 29,85 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
[ 77, 54, 7, 97 ]
41
[ "77+54=131", "97-7=90", "131-90=41" ]
Current State: 41:[77, 54, 7, 97], Operations: [] Exploring Operation: 77+54=131, Resulting Numbers: [7, 97, 131] Generated Node #2: [7, 97, 131] from Operation: 77+54=131 Current State: 41:[7, 97, 131], Operations: ['77+54=131'] Exploring Operation: 97-7=90, Resulting Numbers: [131, 90] Generated Node #3: [131, 90] from Operation: 97-7=90 Current State: 41:[131, 90], Operations: ['77+54=131', '97-7=90'] Exploring Operation: 131-90=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[77, 54, 7, 97], Operations: [] Exploring Operation: 97-54=43, Resulting Numbers: [77, 7, 43] Generated Node #0,0: 41:[77, 7, 43] Operation: 97-54=43 Exploring Operation: 97-77=20, Resulting Numbers: [54, 7, 20] Generated Node #0,1: 41:[54, 7, 20] Operation: 97-77=20 Moving to Node #0,1 Current State: 41:[54, 7, 20], Operations: ['97-77=20'] Exploring Operation: 7+20=27, Resulting Numbers: [54, 27] Generated Node #0,1,0: 41:[54, 27] Operation: 7+20=27 Exploring Operation: 54-7=47, Resulting Numbers: [20, 47] Generated Node #0,1,1: 41:[20, 47] Operation: 54-7=47 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 41:[54, 27], Operations: ['97-77=20', '7+20=27'] Exploring Operation: 54/27=2, Resulting Numbers: [2] 2,41 unequal: No Solution Exploring Operation: 54-27=27, Resulting Numbers: [27] 27,41 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:[20, 47], Operations: ['97-77=20', '54-7=47'] Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,41 unequal: No Solution Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,41 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: 41:[77, 7, 43], Operations: ['97-54=43'] Exploring Operation: 77/7=11, Resulting Numbers: [43, 11] Generated Node #0,0,0: 41:[43, 11] Operation: 77/7=11 Exploring Operation: 77-7=70, Resulting Numbers: [43, 70] Generated Node #0,0,1: 41:[43, 70] Operation: 77-7=70 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 41:[43, 70], Operations: ['97-54=43', '77-7=70'] Exploring Operation: 43+70=113, Resulting Numbers: [113] 113,41 unequal: No Solution Exploring Operation: 70-43=27, Resulting Numbers: [27] 27,41 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 #0,0,0 Current State: 41:[43, 11], Operations: ['97-54=43', '77/7=11'] Exploring Operation: 43-11=32, Resulting Numbers: [32] 32,41 unequal: No Solution Exploring Operation: 43+11=54, Resulting Numbers: [54] 54,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 52, 48, 53, 94 ]
59
[ "52+48=100", "94-53=41", "100-41=59" ]
Current State: 59:[52, 48, 53, 94], Operations: [] Exploring Operation: 52+48=100, Resulting Numbers: [53, 94, 100] Generated Node #2: [53, 94, 100] from Operation: 52+48=100 Current State: 59:[53, 94, 100], Operations: ['52+48=100'] Exploring Operation: 94-53=41, Resulting Numbers: [100, 41] Generated Node #3: [100, 41] from Operation: 94-53=41 Current State: 59:[100, 41], Operations: ['52+48=100', '94-53=41'] Exploring Operation: 100-41=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[52, 48, 53, 94], Operations: [] Exploring Operation: 94-48=46, Resulting Numbers: [52, 53, 46] Generated Node #0,0: 59:[52, 53, 46] Operation: 94-48=46 Moving to Node #0,0 Current State: 59:[52, 53, 46], Operations: ['94-48=46'] Exploring Operation: 52+46=98, Resulting Numbers: [53, 98] Generated Node #0,0,0: 59:[53, 98] Operation: 52+46=98 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[53, 98], Operations: ['94-48=46', '52+46=98'] Exploring Operation: 98-53=45, Resulting Numbers: [45] 45,59 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
[ 90, 34, 48, 9 ]
24
[ "90/9=10", "48-34=14", "10+14=24" ]
Current State: 24:[90, 34, 48, 9], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [34, 48, 10] Generated Node #2: [34, 48, 10] from Operation: 90/9=10 Current State: 24:[34, 48, 10], Operations: ['90/9=10'] Exploring Operation: 48-34=14, Resulting Numbers: [10, 14] Generated Node #3: [10, 14] from Operation: 48-34=14 Current State: 24:[10, 14], Operations: ['90/9=10', '48-34=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[90, 34, 48, 9], Operations: [] Exploring Operation: 48-34=14, Resulting Numbers: [90, 9, 14] Generated Node #0,0: 24:[90, 9, 14] Operation: 48-34=14 Exploring Operation: 90/9=10, Resulting Numbers: [34, 48, 10] Generated Node #0,1: 24:[34, 48, 10] Operation: 90/9=10 Exploring Operation: 90-9=81, Resulting Numbers: [34, 48, 81] Generated Node #0,2: 24:[34, 48, 81] Operation: 90-9=81 Exploring Operation: 90-48=42, Resulting Numbers: [34, 9, 42] Generated Node #0,3: 24:[34, 9, 42] Operation: 90-48=42 Exploring Operation: 90-34=56, Resulting Numbers: [48, 9, 56] Generated Node #0,4: 24:[48, 9, 56] Operation: 90-34=56 Moving to Node #0,3 Current State: 24:[34, 9, 42], Operations: ['90-48=42'] Exploring Operation: 9+42=51, Resulting Numbers: [34, 51] Generated Node #0,3,0: 24:[34, 51] Operation: 9+42=51 Exploring Operation: 42-9=33, Resulting Numbers: [34, 33] Generated Node #0,3,1: 24:[34, 33] Operation: 42-9=33 Exploring Operation: 34-9=25, Resulting Numbers: [42, 25] Generated Node #0,3,2: 24:[42, 25] Operation: 34-9=25 Exploring Operation: 42-34=8, Resulting Numbers: [9, 8] Generated Node #0,3,3: 24:[9, 8] Operation: 42-34=8 Exploring Operation: 34+9=43, Resulting Numbers: [42, 43] Generated Node #0,3,4: 24:[42, 43] Operation: 34+9=43 Moving to Node #0,1 Current State: 24:[34, 48, 10], Operations: ['90/9=10'] Exploring Operation: 48-10=38, Resulting Numbers: [34, 38] Generated Node #0,1,0: 24:[34, 38] Operation: 48-10=38 Exploring Operation: 34+10=44, Resulting Numbers: [48, 44] Generated Node #0,1,1: 24:[48, 44] Operation: 34+10=44 Exploring Operation: 48-34=14, Resulting Numbers: [10, 14] Generated Node #0,1,2: 24:[10, 14] Operation: 48-34=14 Exploring Operation: 48+10=58, Resulting Numbers: [34, 58] Generated Node #0,1,3: 24:[34, 58] Operation: 48+10=58 Exploring Operation: 34-10=24, Resulting Numbers: [48, 24] Generated Node #0,1,4: 24:[48, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 24:[10, 14], Operations: ['90/9=10', '48-34=14'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,24 unequal: No Solution Exploring Operation: 10*14=140, Resulting Numbers: [140] 140,24 unequal: No Solution Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[90, 34, 48, 9], Operations: [] Exploring Operation: 90/9=10, Resulting Numbers: [34, 48, 10] Generated Node #0,1: 24:[34, 48, 10] Operation: 90/9=10 Moving to Node #0,1 Current State: 24:[34, 48, 10], Operations: ['90/9=10'] Exploring Operation: 48-34=14, Resulting Numbers: [10, 14] Generated Node #0,1,2: 24:[10, 14] Operation: 48-34=14 Moving to Node #0,1,2 Current State: 24:[10, 14], Operations: ['90/9=10', '48-34=14'] Exploring Operation: 10+14=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 18, 32, 40, 2 ]
76
[ "40-18=22", "2*22=44", "32+44=76" ]
Current State: 76:[18, 32, 40, 2], Operations: [] Exploring Operation: 40-18=22, Resulting Numbers: [32, 2, 22] Generated Node #2: [32, 2, 22] from Operation: 40-18=22 Current State: 76:[32, 2, 22], Operations: ['40-18=22'] Exploring Operation: 2*22=44, Resulting Numbers: [32, 44] Generated Node #3: [32, 44] from Operation: 2*22=44 Current State: 76:[32, 44], Operations: ['40-18=22', '2*22=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[18, 32, 40, 2], Operations: [] Exploring Operation: 32+40=72, Resulting Numbers: [18, 2, 72] Generated Node #0,0: 76:[18, 2, 72] Operation: 32+40=72 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[18, 2, 72], Operations: ['32+40=72'] Exploring Operation: 72/18=4, Resulting Numbers: [2, 4] Generated Node #0,0,0: 76:[2, 4] Operation: 72/18=4 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[2, 4], Operations: ['32+40=72', '72/18=4'] Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,76 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 46, 61, 62, 9 ]
68
[ "61-46=15", "62-9=53", "15+53=68" ]
Current State: 68:[46, 61, 62, 9], Operations: [] Exploring Operation: 61-46=15, Resulting Numbers: [62, 9, 15] Generated Node #2: [62, 9, 15] from Operation: 61-46=15 Current State: 68:[62, 9, 15], Operations: ['61-46=15'] Exploring Operation: 62-9=53, Resulting Numbers: [15, 53] Generated Node #3: [15, 53] from Operation: 62-9=53 Current State: 68:[15, 53], Operations: ['61-46=15', '62-9=53'] Exploring Operation: 15+53=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[46, 61, 62, 9], Operations: [] Exploring Operation: 62-61=1, Resulting Numbers: [46, 9, 1] Generated Node #0,0: 68:[46, 9, 1] Operation: 62-61=1 Exploring Operation: 61-46=15, Resulting Numbers: [62, 9, 15] Generated Node #0,1: 68:[62, 9, 15] Operation: 61-46=15 Exploring Operation: 46-9=37, Resulting Numbers: [61, 62, 37] Generated Node #0,2: 68:[61, 62, 37] Operation: 46-9=37 Exploring Operation: 62-46=16, Resulting Numbers: [61, 9, 16] Generated Node #0,3: 68:[61, 9, 16] Operation: 62-46=16 Moving to Node #0,1 Current State: 68:[62, 9, 15], Operations: ['61-46=15'] Exploring Operation: 15-9=6, Resulting Numbers: [62, 6] Generated Node #0,1,0: 68:[62, 6] Operation: 15-9=6 Exploring Operation: 62+15=77, Resulting Numbers: [9, 77] Generated Node #0,1,1: 68:[9, 77] Operation: 62+15=77 Exploring Operation: 62+9=71, Resulting Numbers: [15, 71] Generated Node #0,1,2: 68:[15, 71] Operation: 62+9=71 Exploring Operation: 9+15=24, Resulting Numbers: [62, 24] Generated Node #0,1,3: 68:[62, 24] Operation: 9+15=24 Moving to Node #0,3 Current State: 68:[61, 9, 16], Operations: ['62-46=16'] Exploring Operation: 61+9=70, Resulting Numbers: [16, 70] Generated Node #0,3,0: 68:[16, 70] Operation: 61+9=70 Exploring Operation: 61+16=77, Resulting Numbers: [9, 77] Generated Node #0,3,1: 68:[9, 77] Operation: 61+16=77 Exploring Operation: 16-9=7, Resulting Numbers: [61, 7] Generated Node #0,3,2: 68:[61, 7] Operation: 16-9=7 Exploring Operation: 9+16=25, Resulting Numbers: [61, 25] Generated Node #0,3,3: 68:[61, 25] Operation: 9+16=25 Moving to Node #0,2 Current State: 68:[61, 62, 37], Operations: ['46-9=37'] Exploring Operation: 61+37=98, Resulting Numbers: [62, 98] Generated Node #0,2,0: 68:[62, 98] Operation: 61+37=98 Exploring Operation: 62-61=1, Resulting Numbers: [37, 1] Generated Node #0,2,1: 68:[37, 1] Operation: 62-61=1 Exploring Operation: 61-37=24, Resulting Numbers: [62, 24] Generated Node #0,2,2: 68:[62, 24] Operation: 61-37=24 Exploring Operation: 62-37=25, Resulting Numbers: [61, 25] Generated Node #0,2,3: 68:[61, 25] Operation: 62-37=25 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 68:[37, 1], Operations: ['46-9=37', '62-61=1'] Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 37+1=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 37*1=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 68:[62, 24], Operations: ['46-9=37', '61-37=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,68 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 68:[61, 25], Operations: ['46-9=37', '62-37=25'] Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,68 unequal: No Solution Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,68 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[62, 98], Operations: ['46-9=37', '61+37=98'] Exploring Operation: 62+98=160, Resulting Numbers: [160] 160,68 unequal: No Solution Exploring Operation: 98-62=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 62*98=6076, Resulting Numbers: [6076] 6076,68 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: 68:[46, 9, 1], Operations: ['62-61=1'] Exploring Operation: 46-1=45, Resulting Numbers: [9, 45] Generated Node #0,0,0: 68:[9, 45] Operation: 46-1=45 Exploring Operation: 46-9=37, Resulting Numbers: [1, 37] Generated Node #0,0,1: 68:[1, 37] Operation: 46-9=37 Exploring Operation: 9-1=8, Resulting Numbers: [46, 8] Generated Node #0,0,2: 68:[46, 8] Operation: 9-1=8 Exploring Operation: 46+9=55, Resulting Numbers: [1, 55] Generated Node #0,0,3: 68:[1, 55] Operation: 46+9=55 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 68:[1, 37], Operations: ['62-61=1', '46-9=37'] Exploring Operation: 37/1=37, Resulting Numbers: [37] 37,68 unequal: No Solution Exploring Operation: 37-1=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 1+37=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 1*37=37, Resulting Numbers: [37] 37,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 68:[1, 55], Operations: ['62-61=1', '46+9=55'] Exploring Operation: 1+55=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 1*55=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,68 unequal: No Solution Exploring Operation: 55-1=54, Resulting Numbers: [54] 54,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 68:[9, 45], Operations: ['62-61=1', '46-1=45'] Exploring Operation: 9*45=405, Resulting Numbers: [405] 405,68 unequal: No Solution Exploring Operation: 45/9=5, Resulting Numbers: [5] 5,68 unequal: No Solution Exploring Operation: 45-9=36, Resulting Numbers: [36] 36,68 unequal: No Solution Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 68:[46, 8], Operations: ['62-61=1', '9-1=8'] Exploring Operation: 46+8=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 46*8=368, Resulting Numbers: [368] 368,68 unequal: No Solution Exploring Operation: 46-8=38, Resulting Numbers: [38] 38,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 68:[16, 70], Operations: ['62-46=16', '61+9=70'] Exploring Operation: 70-16=54, Resulting Numbers: [54] 54,68 unequal: No Solution Exploring Operation: 16+70=86, Resulting Numbers: [86] 86,68 unequal: No Solution Exploring Operation: 16*70=1120, Resulting Numbers: [1120] 1120,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[15, 71], Operations: ['61-46=15', '62+9=71'] Exploring Operation: 71-15=56, Resulting Numbers: [56] 56,68 unequal: No Solution Exploring Operation: 15*71=1065, Resulting Numbers: [1065] 1065,68 unequal: No Solution Exploring Operation: 15+71=86, Resulting Numbers: [86] 86,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[62, 6], Operations: ['61-46=15', '15-9=6'] Exploring Operation: 62*6=372, Resulting Numbers: [372] 372,68 unequal: No Solution Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[46, 61, 62, 9], Operations: [] Exploring Operation: 61-46=15, Resulting Numbers: [62, 9, 15] Generated Node #0,1: 68:[62, 9, 15] Operation: 61-46=15 Moving to Node #0,1 Current State: 68:[62, 9, 15], Operations: ['61-46=15'] Exploring Operation: 15-9=6, Resulting Numbers: [62, 6] Generated Node #0,1,0: 68:[62, 6] Operation: 15-9=6 Moving to Node #0,1,0 Current State: 68:[62, 6], Operations: ['61-46=15', '15-9=6'] Exploring Operation: 62+6=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
0.947917
hs_4
mult_heuristic
[ 26, 40, 64, 88 ]
44
[ "26+40=66", "66-64=2", "88/2=44" ]
Current State: 44:[26, 40, 64, 88], Operations: [] Exploring Operation: 26+40=66, Resulting Numbers: [64, 88, 66] Generated Node #2: [64, 88, 66] from Operation: 26+40=66 Current State: 44:[64, 88, 66], Operations: ['26+40=66'] Exploring Operation: 66-64=2, Resulting Numbers: [88, 2] Generated Node #3: [88, 2] from Operation: 66-64=2 Current State: 44:[88, 2], Operations: ['26+40=66', '66-64=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[26, 40, 64, 88], Operations: [] Exploring Operation: 88-26=62, Resulting Numbers: [40, 64, 62] Generated Node #0,0: 44:[40, 64, 62] Operation: 88-26=62 Exploring Operation: 88-64=24, Resulting Numbers: [26, 40, 24] Generated Node #0,1: 44:[26, 40, 24] Operation: 88-64=24 Exploring Operation: 88-40=48, Resulting Numbers: [26, 64, 48] Generated Node #0,2: 44:[26, 64, 48] Operation: 88-40=48 Exploring Operation: 64-40=24, Resulting Numbers: [26, 88, 24] Generated Node #0,3: 44:[26, 88, 24] Operation: 64-40=24 Exploring Operation: 64-26=38, Resulting Numbers: [40, 88, 38] Generated Node #0,4: 44:[40, 88, 38] Operation: 64-26=38 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[26, 40, 24], Operations: ['88-64=24'] Exploring Operation: 26+40=66, Resulting Numbers: [24, 66] Generated Node #0,1,0: 44:[24, 66] Operation: 26+40=66 Exploring Operation: 26+24=50, Resulting Numbers: [40, 50] Generated Node #0,1,1: 44:[40, 50] Operation: 26+24=50 Exploring Operation: 40-24=16, Resulting Numbers: [26, 16] Generated Node #0,1,2: 44:[26, 16] Operation: 40-24=16 Exploring Operation: 26-24=2, Resulting Numbers: [40, 2] Generated Node #0,1,3: 44:[40, 2] Operation: 26-24=2 Exploring Operation: 40-26=14, Resulting Numbers: [24, 14] Generated Node #0,1,4: 44:[24, 14] Operation: 40-26=14 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 44:[40, 2], Operations: ['88-64=24', '26-24=2'] Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,44 unequal: No Solution No 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: 44:[24, 14], Operations: ['88-64=24', '40-26=14'] Exploring Operation: 24+14=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 24-14=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 24*14=336, Resulting Numbers: [336] 336,44 unequal: No Solution No 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: 44:[26, 16], Operations: ['88-64=24', '40-24=16'] Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,44 unequal: No Solution Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,44 unequal: No Solution No 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: 44:[40, 50], Operations: ['88-64=24', '26+24=50'] Exploring Operation: 40+50=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 50-40=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 40*50=2000, Resulting Numbers: [2000] 2000,44 unequal: No Solution No 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: 44:[24, 66], Operations: ['88-64=24', '26+40=66'] Exploring Operation: 24+66=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 66-24=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 24*66=1584, Resulting Numbers: [1584] 1584,44 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: 44:[26, 64, 48], Operations: ['88-40=48'] Exploring Operation: 26+48=74, Resulting Numbers: [64, 74] Generated Node #0,2,0: 44:[64, 74] Operation: 26+48=74 Exploring Operation: 64-48=16, Resulting Numbers: [26, 16] Generated Node #0,2,1: 44:[26, 16] Operation: 64-48=16 Exploring Operation: 64-26=38, Resulting Numbers: [48, 38] Generated Node #0,2,2: 44:[48, 38] Operation: 64-26=38 Exploring Operation: 48-26=22, Resulting Numbers: [64, 22] Generated Node #0,2,3: 44:[64, 22] Operation: 48-26=22 Exploring Operation: 26+64=90, Resulting Numbers: [48, 90] Generated Node #0,2,4: 44:[48, 90] Operation: 26+64=90 Moving to Node #0,2,1 Current State: 44:[26, 16], Operations: ['88-40=48', '64-48=16'] Exploring Operation: 26-16=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 26*16=416, Resulting Numbers: [416] 416,44 unequal: No Solution Exploring Operation: 26+16=42, Resulting Numbers: [42] 42,44 unequal: No Solution Moving to Node #0,2,2 Current State: 44:[48, 38], Operations: ['88-40=48', '64-26=38'] Exploring Operation: 48*38=1824, Resulting Numbers: [1824] 1824,44 unequal: No Solution Exploring Operation: 48-38=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 48+38=86, Resulting Numbers: [86] 86,44 unequal: No Solution Moving to Node #0,2,3 Current State: 44:[64, 22], Operations: ['88-40=48', '48-26=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,44 unequal: No Solution Moving to Node #0,2,0 Current State: 44:[64, 74], Operations: ['88-40=48', '26+48=74'] Exploring Operation: 64*74=4736, Resulting Numbers: [4736] 4736,44 unequal: No Solution Exploring Operation: 74-64=10, Resulting Numbers: [10] 10,44 unequal: No Solution Exploring Operation: 64+74=138, Resulting Numbers: [138] 138,44 unequal: No Solution Moving to Node #0,2,4 Current State: 44:[48, 90], Operations: ['88-40=48', '26+64=90'] Exploring Operation: 90-48=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 48+90=138, Resulting Numbers: [138] 138,44 unequal: No Solution Exploring Operation: 48*90=4320, Resulting Numbers: [4320] 4320,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[40, 64, 62], Operations: ['88-26=62'] Exploring Operation: 64-62=2, Resulting Numbers: [40, 2] Generated Node #0,0,0: 44:[40, 2] Operation: 64-62=2 Exploring Operation: 62-40=22, Resulting Numbers: [64, 22] Generated Node #0,0,1: 44:[64, 22] Operation: 62-40=22 Exploring Operation: 40+62=102, Resulting Numbers: [64, 102] Generated Node #0,0,2: 44:[64, 102] Operation: 40+62=102 Exploring Operation: 64-40=24, Resulting Numbers: [62, 24] Generated Node #0,0,3: 44:[62, 24] Operation: 64-40=24 Exploring Operation: 40+64=104, Resulting Numbers: [62, 104] Generated Node #0,0,4: 44:[62, 104] Operation: 40+64=104 Moving to Node #0,0,0 Current State: 44:[40, 2], Operations: ['88-26=62', '64-62=2'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,44 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,44 unequal: No Solution Moving to Node #0,0,3 Current State: 44:[62, 24], Operations: ['88-26=62', '64-40=24'] Exploring Operation: 62*24=1488, Resulting Numbers: [1488] 1488,44 unequal: No Solution Exploring Operation: 62+24=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,44 unequal: No Solution Moving to Node #0,0,1 Current State: 44:[64, 22], Operations: ['88-26=62', '62-40=22'] Exploring Operation: 64-22=42, Resulting Numbers: [42] 42,44 unequal: No Solution Exploring Operation: 64*22=1408, Resulting Numbers: [1408] 1408,44 unequal: No Solution Exploring Operation: 64+22=86, Resulting Numbers: [86] 86,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[64, 102], Operations: ['88-26=62', '40+62=102'] Exploring Operation: 64+102=166, Resulting Numbers: [166] 166,44 unequal: No Solution Exploring Operation: 102-64=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 64*102=6528, Resulting Numbers: [6528] 6528,44 unequal: No Solution Moving to Node #0,0,4 Current State: 44:[62, 104], Operations: ['88-26=62', '40+64=104'] Exploring Operation: 62+104=166, Resulting Numbers: [166] 166,44 unequal: No Solution Exploring Operation: 62*104=6448, Resulting Numbers: [6448] 6448,44 unequal: No Solution Exploring Operation: 104-62=42, Resulting Numbers: [42] 42,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 44:[26, 88, 24], Operations: ['64-40=24'] Exploring Operation: 26-24=2, Resulting Numbers: [88, 2] Generated Node #0,3,0: 44:[88, 2] Operation: 26-24=2 Exploring Operation: 26+88=114, Resulting Numbers: [24, 114] Generated Node #0,3,1: 44:[24, 114] Operation: 26+88=114 Exploring Operation: 26+24=50, Resulting Numbers: [88, 50] Generated Node #0,3,2: 44:[88, 50] Operation: 26+24=50 Exploring Operation: 88-24=64, Resulting Numbers: [26, 64] Generated Node #0,3,3: 44:[26, 64] Operation: 88-24=64 Exploring Operation: 88-26=62, Resulting Numbers: [24, 62] Generated Node #0,3,4: 44:[24, 62] Operation: 88-26=62 Moving to Node #0,3,4 Current State: 44:[24, 62], Operations: ['64-40=24', '88-26=62'] Exploring Operation: 24+62=86, Resulting Numbers: [86] 86,44 unequal: No Solution Exploring Operation: 62-24=38, Resulting Numbers: [38] 38,44 unequal: No Solution Exploring Operation: 24*62=1488, Resulting Numbers: [1488] 1488,44 unequal: No Solution Moving to Node #0,3,3 Current State: 44:[26, 64], Operations: ['64-40=24', '88-24=64'] Exploring Operation: 26*64=1664, Resulting Numbers: [1664] 1664,44 unequal: No Solution Exploring Operation: 26+64=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 64-26=38, Resulting Numbers: [38] 38,44 unequal: No Solution Moving to Node #0,3,0 Current State: 44:[88, 2], Operations: ['64-40=24', '26-24=2'] Exploring Operation: 88+2=90, Resulting Numbers: [90] 90,44 unequal: No Solution Exploring Operation: 88*2=176, Resulting Numbers: [176] 176,44 unequal: No Solution Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[26, 40, 64, 88], Operations: [] Exploring Operation: 64-40=24, Resulting Numbers: [26, 88, 24] Generated Node #0,3: 44:[26, 88, 24] Operation: 64-40=24 Moving to Node #0,3 Current State: 44:[26, 88, 24], Operations: ['64-40=24'] Exploring Operation: 26-24=2, Resulting Numbers: [88, 2] Generated Node #0,3,0: 44:[88, 2] Operation: 26-24=2 Moving to Node #0,3,0 Current State: 44:[88, 2], Operations: ['64-40=24', '26-24=2'] Exploring Operation: 88/2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 1
0.926215
hs_5
sum_heuristic
[ 24, 61, 2, 13 ]
86
[ "24/2=12", "61+13=74", "12+74=86" ]
Current State: 86:[24, 61, 2, 13], Operations: [] Exploring Operation: 24/2=12, Resulting Numbers: [61, 13, 12] Generated Node #2: [61, 13, 12] from Operation: 24/2=12 Current State: 86:[61, 13, 12], Operations: ['24/2=12'] Exploring Operation: 61+13=74, Resulting Numbers: [12, 74] Generated Node #3: [12, 74] from Operation: 61+13=74 Current State: 86:[12, 74], Operations: ['24/2=12', '61+13=74'] Exploring Operation: 12+74=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[24, 61, 2, 13], Operations: [] Exploring Operation: 24+61=85, Resulting Numbers: [2, 13, 85] Generated Node #0,0: 86:[2, 13, 85] Operation: 24+61=85 Moving to Node #0,0 Current State: 86:[2, 13, 85], Operations: ['24+61=85'] Exploring Operation: 13-2=11, Resulting Numbers: [85, 11] Generated Node #0,0,0: 86:[85, 11] Operation: 13-2=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[85, 11], Operations: ['24+61=85', '13-2=11'] Exploring Operation: 85+11=96, Resulting Numbers: [96] 96,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 72, 66, 85, 29 ]
82
[ "72+66=138", "85-29=56", "138-56=82" ]
Current State: 82:[72, 66, 85, 29], Operations: [] Exploring Operation: 72+66=138, Resulting Numbers: [85, 29, 138] Generated Node #2: [85, 29, 138] from Operation: 72+66=138 Current State: 82:[85, 29, 138], Operations: ['72+66=138'] Exploring Operation: 85-29=56, Resulting Numbers: [138, 56] Generated Node #3: [138, 56] from Operation: 85-29=56 Current State: 82:[138, 56], Operations: ['72+66=138', '85-29=56'] Exploring Operation: 138-56=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[72, 66, 85, 29], Operations: [] Exploring Operation: 72-66=6, Resulting Numbers: [85, 29, 6] Generated Node #0,0: 82:[85, 29, 6] Operation: 72-66=6 Exploring Operation: 66-29=37, Resulting Numbers: [72, 85, 37] Generated Node #0,1: 82:[72, 85, 37] Operation: 66-29=37 Moving to Node #0,1 Current State: 82:[72, 85, 37], Operations: ['66-29=37'] Exploring Operation: 72-37=35, Resulting Numbers: [85, 35] Generated Node #0,1,0: 82:[85, 35] Operation: 72-37=35 Exploring Operation: 85-72=13, Resulting Numbers: [37, 13] Generated Node #0,1,1: 82:[37, 13] Operation: 85-72=13 Moving to Node #0,0 Current State: 82:[85, 29, 6], Operations: ['72-66=6'] Exploring Operation: 85-6=79, Resulting Numbers: [29, 79] Generated Node #0,0,0: 82:[29, 79] Operation: 85-6=79 Exploring Operation: 29+6=35, Resulting Numbers: [85, 35] Generated Node #0,0,1: 82:[85, 35] Operation: 29+6=35 Moving to Node #0,1,0 Current State: 82:[85, 35], Operations: ['66-29=37', '72-37=35'] Exploring Operation: 85-35=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 85+35=120, Resulting Numbers: [120] 120,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[85, 35], Operations: ['72-66=6', '29+6=35'] Exploring Operation: 85-35=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 85+35=120, Resulting Numbers: [120] 120,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[37, 13], Operations: ['66-29=37', '85-72=13'] Exploring Operation: 37-13=24, Resulting Numbers: [24] 24,82 unequal: No Solution Exploring Operation: 37+13=50, Resulting Numbers: [50] 50,82 unequal: No Solution Moving to Node #0,0,0 Current State: 82:[29, 79], Operations: ['72-66=6', '85-6=79'] Exploring Operation: 29+79=108, Resulting Numbers: [108] 108,82 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,82 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 61, 67, 17, 6 ]
47
[ "67+17=84", "84/6=14", "61-14=47" ]
Current State: 47:[61, 67, 17, 6], Operations: [] Exploring Operation: 67+17=84, Resulting Numbers: [61, 6, 84] Generated Node #2: [61, 6, 84] from Operation: 67+17=84 Current State: 47:[61, 6, 84], Operations: ['67+17=84'] Exploring Operation: 84/6=14, Resulting Numbers: [61, 14] Generated Node #3: [61, 14] from Operation: 84/6=14 Current State: 47:[61, 14], Operations: ['67+17=84', '84/6=14'] Exploring Operation: 61-14=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[61, 67, 17, 6], Operations: [] Exploring Operation: 67-17=50, Resulting Numbers: [61, 6, 50] Generated Node #0,0: 47:[61, 6, 50] Operation: 67-17=50 Exploring Operation: 61-6=55, Resulting Numbers: [67, 17, 55] Generated Node #0,1: 47:[67, 17, 55] Operation: 61-6=55 Moving to Node #0,0 Current State: 47:[61, 6, 50], Operations: ['67-17=50'] Exploring Operation: 61-6=55, Resulting Numbers: [50, 55] Generated Node #0,0,0: 47:[50, 55] Operation: 61-6=55 Exploring Operation: 50-6=44, Resulting Numbers: [61, 44] Generated Node #0,0,1: 47:[61, 44] Operation: 50-6=44 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[50, 55], Operations: ['67-17=50', '61-6=55'] Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,47 unequal: No Solution Exploring Operation: 50+55=105, Resulting Numbers: [105] 105,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[61, 44], Operations: ['67-17=50', '50-6=44'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 47:[67, 17, 55], Operations: ['61-6=55'] Exploring Operation: 67-17=50, Resulting Numbers: [55, 50] Generated Node #0,1,0: 47:[55, 50] Operation: 67-17=50 Exploring Operation: 55-17=38, Resulting Numbers: [67, 38] Generated Node #0,1,1: 47:[67, 38] Operation: 55-17=38 Moving to Node #0,1,0 Current State: 47:[55, 50], Operations: ['61-6=55', '67-17=50'] Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,47 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,47 unequal: No Solution Moving to Node #0,1,1 Current State: 47:[67, 38], Operations: ['61-6=55', '55-17=38'] Exploring Operation: 67+38=105, Resulting Numbers: [105] 105,47 unequal: No Solution Exploring Operation: 67-38=29, Resulting Numbers: [29] 29,47 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 10, 30, 84, 21 ]
60
[ "30/10=3", "84-21=63", "63-3=60" ]
Current State: 60:[10, 30, 84, 21], Operations: [] Exploring Operation: 30/10=3, Resulting Numbers: [84, 21, 3] Generated Node #2: [84, 21, 3] from Operation: 30/10=3 Current State: 60:[84, 21, 3], Operations: ['30/10=3'] Exploring Operation: 84-21=63, Resulting Numbers: [3, 63] Generated Node #3: [3, 63] from Operation: 84-21=63 Current State: 60:[3, 63], Operations: ['30/10=3', '84-21=63'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[10, 30, 84, 21], Operations: [] Exploring Operation: 84-30=54, Resulting Numbers: [10, 21, 54] Generated Node #0,0: 60:[10, 21, 54] Operation: 84-30=54 Exploring Operation: 84-10=74, Resulting Numbers: [30, 21, 74] Generated Node #0,1: 60:[30, 21, 74] Operation: 84-10=74 Exploring Operation: 84-21=63, Resulting Numbers: [10, 30, 63] Generated Node #0,2: 60:[10, 30, 63] Operation: 84-21=63 Exploring Operation: 84/21=4, Resulting Numbers: [10, 30, 4] Generated Node #0,3: 60:[10, 30, 4] Operation: 84/21=4 Moving to Node #0,3 Current State: 60:[10, 30, 4], Operations: ['84/21=4'] Exploring Operation: 30/10=3, Resulting Numbers: [4, 3] Generated Node #0,3,0: 60:[4, 3] Operation: 30/10=3 Exploring Operation: 30-10=20, Resulting Numbers: [4, 20] Generated Node #0,3,1: 60:[4, 20] Operation: 30-10=20 Exploring Operation: 10-4=6, Resulting Numbers: [30, 6] Generated Node #0,3,2: 60:[30, 6] Operation: 10-4=6 Exploring Operation: 10+4=14, Resulting Numbers: [30, 14] Generated Node #0,3,3: 60:[30, 14] Operation: 10+4=14 Moving to Node #0,2 Current State: 60:[10, 30, 63], Operations: ['84-21=63'] Exploring Operation: 30/10=3, Resulting Numbers: [63, 3] Generated Node #0,2,0: 60:[63, 3] Operation: 30/10=3 Exploring Operation: 30-10=20, Resulting Numbers: [63, 20] Generated Node #0,2,1: 60:[63, 20] Operation: 30-10=20 Exploring Operation: 63-10=53, Resulting Numbers: [30, 53] Generated Node #0,2,2: 60:[30, 53] Operation: 63-10=53 Exploring Operation: 63-30=33, Resulting Numbers: [10, 33] Generated Node #0,2,3: 60:[10, 33] Operation: 63-30=33 Moving to Node #0,0 Current State: 60:[10, 21, 54], Operations: ['84-30=54'] Exploring Operation: 10+21=31, Resulting Numbers: [54, 31] Generated Node #0,0,0: 60:[54, 31] Operation: 10+21=31 Exploring Operation: 10+54=64, Resulting Numbers: [21, 64] Generated Node #0,0,1: 60:[21, 64] Operation: 10+54=64 Exploring Operation: 21-10=11, Resulting Numbers: [54, 11] Generated Node #0,0,2: 60:[54, 11] Operation: 21-10=11 Exploring Operation: 54-21=33, Resulting Numbers: [10, 33] Generated Node #0,0,3: 60:[10, 33] Operation: 54-21=33 Moving to Node #0,1 Current State: 60:[30, 21, 74], Operations: ['84-10=74'] Exploring Operation: 74-30=44, Resulting Numbers: [21, 44] Generated Node #0,1,0: 60:[21, 44] Operation: 74-30=44 Exploring Operation: 30-21=9, Resulting Numbers: [74, 9] Generated Node #0,1,1: 60:[74, 9] Operation: 30-21=9 Exploring Operation: 30+21=51, Resulting Numbers: [74, 51] Generated Node #0,1,2: 60:[74, 51] Operation: 30+21=51 Exploring Operation: 74-21=53, Resulting Numbers: [30, 53] Generated Node #0,1,3: 60:[30, 53] Operation: 74-21=53 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 60:[30, 53], Operations: ['84-10=74', '74-21=53'] Exploring Operation: 53-30=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 30*53=1590, Resulting Numbers: [1590] 1590,60 unequal: No Solution Exploring Operation: 30+53=83, Resulting Numbers: [83] 83,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 60:[21, 44], Operations: ['84-10=74', '74-30=44'] Exploring Operation: 21*44=924, Resulting Numbers: [924] 924,60 unequal: No Solution Exploring Operation: 44-21=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 21+44=65, Resulting Numbers: [65] 65,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 60:[74, 9], Operations: ['84-10=74', '30-21=9'] Exploring Operation: 74+9=83, Resulting Numbers: [83] 83,60 unequal: No Solution Exploring Operation: 74-9=65, Resulting Numbers: [65] 65,60 unequal: No Solution Exploring Operation: 74*9=666, Resulting Numbers: [666] 666,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 60:[74, 51], Operations: ['84-10=74', '30+21=51'] Exploring Operation: 74+51=125, Resulting Numbers: [125] 125,60 unequal: No Solution Exploring Operation: 74-51=23, Resulting Numbers: [23] 23,60 unequal: No Solution Exploring Operation: 74*51=3774, Resulting Numbers: [3774] 3774,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 60:[4, 3], Operations: ['84/21=4', '30/10=3'] Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,60 unequal: No Solution Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,60 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,60 unequal: No Solution Moving to Node #0,3,2 Current State: 60:[30, 6], Operations: ['84/21=4', '10-4=6'] Exploring Operation: 30/6=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 30*6=180, Resulting Numbers: [180] 180,60 unequal: No Solution Exploring Operation: 30+6=36, Resulting Numbers: [36] 36,60 unequal: No Solution Exploring Operation: 30-6=24, Resulting Numbers: [24] 24,60 unequal: No Solution Moving to Node #0,3,1 Current State: 60:[4, 20], Operations: ['84/21=4', '30-10=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 4*20=80, Resulting Numbers: [80] 80,60 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,60 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,60 unequal: No Solution Moving to Node #0,3,3 Current State: 60:[30, 14], Operations: ['84/21=4', '10+4=14'] Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,60 unequal: No Solution Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,60 unequal: No Solution Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,60 unequal: No Solution Moving to Node #0,2,3 Current State: 60:[10, 33], Operations: ['84-21=63', '63-30=33'] Exploring Operation: 10+33=43, Resulting Numbers: [43] 43,60 unequal: No Solution Exploring Operation: 10*33=330, Resulting Numbers: [330] 330,60 unequal: No Solution Exploring Operation: 33-10=23, Resulting Numbers: [23] 23,60 unequal: No Solution Moving to Node #0,2,1 Current State: 60:[63, 20], Operations: ['84-21=63', '30-10=20'] Exploring Operation: 63+20=83, Resulting Numbers: [83] 83,60 unequal: No Solution Exploring Operation: 63*20=1260, Resulting Numbers: [1260] 1260,60 unequal: No Solution Exploring Operation: 63-20=43, Resulting Numbers: [43] 43,60 unequal: No Solution Moving to Node #0,2,0 Current State: 60:[63, 3], Operations: ['84-21=63', '30/10=3'] Exploring Operation: 63/3=21, Resulting Numbers: [21] 21,60 unequal: No Solution Exploring Operation: 63*3=189, Resulting Numbers: [189] 189,60 unequal: No Solution Exploring Operation: 63+3=66, Resulting Numbers: [66] 66,60 unequal: No Solution Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[10, 30, 84, 21], Operations: [] Exploring Operation: 84-21=63, Resulting Numbers: [10, 30, 63] Generated Node #0,2: 60:[10, 30, 63] Operation: 84-21=63 Moving to Node #0,2 Current State: 60:[10, 30, 63], Operations: ['84-21=63'] Exploring Operation: 30/10=3, Resulting Numbers: [63, 3] Generated Node #0,2,0: 60:[63, 3] Operation: 30/10=3 Moving to Node #0,2,0 Current State: 60:[63, 3], Operations: ['84-21=63', '30/10=3'] Exploring Operation: 63-3=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
0.947917
hs_4
sum_heuristic
[ 31, 1, 34, 9 ]
55
[ "31-1=30", "34-9=25", "30+25=55" ]
Current State: 55:[31, 1, 34, 9], Operations: [] Exploring Operation: 31-1=30, Resulting Numbers: [34, 9, 30] Generated Node #2: [34, 9, 30] from Operation: 31-1=30 Current State: 55:[34, 9, 30], Operations: ['31-1=30'] Exploring Operation: 34-9=25, Resulting Numbers: [30, 25] Generated Node #3: [30, 25] from Operation: 34-9=25 Current State: 55:[30, 25], Operations: ['31-1=30', '34-9=25'] Exploring Operation: 30+25=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[31, 1, 34, 9], Operations: [] Exploring Operation: 31-9=22, Resulting Numbers: [1, 34, 22] Generated Node #0,0: 55:[1, 34, 22] Operation: 31-9=22 Exploring Operation: 34-31=3, Resulting Numbers: [1, 9, 3] Generated Node #0,1: 55:[1, 9, 3] Operation: 34-31=3 Exploring Operation: 31+34=65, Resulting Numbers: [1, 9, 65] Generated Node #0,2: 55:[1, 9, 65] Operation: 31+34=65 Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[1, 9, 3], Operations: ['34-31=3'] Exploring Operation: 1+9=10, Resulting Numbers: [3, 10] Generated Node #0,1,0: 55:[3, 10] Operation: 1+9=10 Exploring Operation: 1+3=4, Resulting Numbers: [9, 4] Generated Node #0,1,1: 55:[9, 4] Operation: 1+3=4 Exploring Operation: 1*9=9, Resulting Numbers: [3, 9] Generated Node #0,1,2: 55:[3, 9] Operation: 1*9=9 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[3, 10], Operations: ['34-31=3', '1+9=10'] Exploring Operation: 10-3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 3+10=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 3*10=30, Resulting Numbers: [30] 30,55 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 #0,1,1 Current State: 55:[9, 4], Operations: ['34-31=3', '1+3=4'] Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,55 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,55 unequal: No Solution Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,55 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:[3, 9], Operations: ['34-31=3', '1*9=9'] Exploring Operation: 3+9=12, Resulting Numbers: [12] 12,55 unequal: No Solution Exploring Operation: 9/3=3, Resulting Numbers: [3] 3,55 unequal: No Solution Exploring Operation: 9-3=6, Resulting Numbers: [6] 6,55 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 #0,2 Current State: 55:[1, 9, 65], Operations: ['31+34=65'] Exploring Operation: 1+9=10, Resulting Numbers: [65, 10] Generated Node #0,2,0: 55:[65, 10] Operation: 1+9=10 Exploring Operation: 65-9=56, Resulting Numbers: [1, 56] Generated Node #0,2,1: 55:[1, 56] Operation: 65-9=56 Exploring Operation: 65-1=64, Resulting Numbers: [9, 64] Generated Node #0,2,2: 55:[9, 64] Operation: 65-1=64 Moving to Node #0,2,1 Current State: 55:[1, 56], Operations: ['31+34=65', '65-9=56'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[31, 1, 34, 9], Operations: [] Exploring Operation: 31+34=65, Resulting Numbers: [1, 9, 65] Generated Node #0,2: 55:[1, 9, 65] Operation: 31+34=65 Moving to Node #0,2 Current State: 55:[1, 9, 65], Operations: ['31+34=65'] Exploring Operation: 65-9=56, Resulting Numbers: [1, 56] Generated Node #0,2,1: 55:[1, 56] Operation: 65-9=56 Moving to Node #0,2,1 Current State: 55:[1, 56], Operations: ['31+34=65', '65-9=56'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 4, 2, 79, 4 ]
40
[ "4/4=1", "79+1=80", "80/2=40" ]
Current State: 40:[4, 2, 79, 4], Operations: [] Exploring Operation: 4/4=1, Resulting Numbers: [2, 79, 1] Generated Node #2: [2, 79, 1] from Operation: 4/4=1 Current State: 40:[2, 79, 1], Operations: ['4/4=1'] Exploring Operation: 79+1=80, Resulting Numbers: [2, 80] Generated Node #3: [2, 80] from Operation: 79+1=80 Current State: 40:[2, 80], Operations: ['4/4=1', '79+1=80'] Exploring Operation: 80/2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[4, 2, 79, 4], Operations: [] Exploring Operation: 79-4=75, Resulting Numbers: [2, 4, 75] Generated Node #0,0: 40:[2, 4, 75] Operation: 79-4=75 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[2, 4, 75], Operations: ['79-4=75'] Exploring Operation: 75-4=71, Resulting Numbers: [2, 71] Generated Node #0,0,0: 40:[2, 71] Operation: 75-4=71 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[2, 71], Operations: ['79-4=75', '75-4=71'] Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,40 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 No solution found.
0
hs_1
mult_heuristic
[ 71, 3, 11, 1 ]
49
[ "3-1=2", "11*2=22", "71-22=49" ]
Current State: 49:[71, 3, 11, 1], Operations: [] Exploring Operation: 3-1=2, Resulting Numbers: [71, 11, 2] Generated Node #2: [71, 11, 2] from Operation: 3-1=2 Current State: 49:[71, 11, 2], Operations: ['3-1=2'] Exploring Operation: 11*2=22, Resulting Numbers: [71, 22] Generated Node #3: [71, 22] from Operation: 11*2=22 Current State: 49:[71, 22], Operations: ['3-1=2', '11*2=22'] Exploring Operation: 71-22=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[71, 3, 11, 1], Operations: [] Exploring Operation: 71-3=68, Resulting Numbers: [11, 1, 68] Generated Node #0,0: 49:[11, 1, 68] Operation: 71-3=68 Exploring Operation: 71-11=60, Resulting Numbers: [3, 1, 60] Generated Node #0,1: 49:[3, 1, 60] Operation: 71-11=60 Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[3, 1, 60], Operations: ['71-11=60'] Exploring Operation: 60-3=57, Resulting Numbers: [1, 57] Generated Node #0,1,0: 49:[1, 57] Operation: 60-3=57 Exploring Operation: 3+1=4, Resulting Numbers: [60, 4] Generated Node #0,1,1: 49:[60, 4] Operation: 3+1=4 Moving to Node #0,1,0 Current State: 49:[1, 57], Operations: ['71-11=60', '60-3=57'] Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,49 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,49 unequal: No Solution Moving to Node #0,1,1 Current State: 49:[60, 4], Operations: ['71-11=60', '3+1=4'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[11, 1, 68], Operations: ['71-3=68'] Exploring Operation: 68-11=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 49:[1, 57] Operation: 68-11=57 Exploring Operation: 11-1=10, Resulting Numbers: [68, 10] Generated Node #0,0,1: 49:[68, 10] Operation: 11-1=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[1, 57], Operations: ['71-3=68', '68-11=57'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,49 unequal: No Solution Exploring Operation: 1*57=57, Resulting Numbers: [57] 57,49 unequal: No Solution No 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: 49:[68, 10], Operations: ['71-3=68', '11-1=10'] Exploring Operation: 68+10=78, Resulting Numbers: [78] 78,49 unequal: No Solution Exploring Operation: 68-10=58, Resulting Numbers: [58] 58,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 21, 81, 45, 87 ]
72
[ "81-21=60", "45+87=132", "132-60=72" ]
Current State: 72:[21, 81, 45, 87], Operations: [] Exploring Operation: 81-21=60, Resulting Numbers: [45, 87, 60] Generated Node #2: [45, 87, 60] from Operation: 81-21=60 Current State: 72:[45, 87, 60], Operations: ['81-21=60'] Exploring Operation: 45+87=132, Resulting Numbers: [60, 132] Generated Node #3: [60, 132] from Operation: 45+87=132 Current State: 72:[60, 132], Operations: ['81-21=60', '45+87=132'] Exploring Operation: 132-60=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[21, 81, 45, 87], Operations: [] Exploring Operation: 87-81=6, Resulting Numbers: [21, 45, 6] Generated Node #0,0: 72:[21, 45, 6] Operation: 87-81=6 Exploring Operation: 81-45=36, Resulting Numbers: [21, 87, 36] Generated Node #0,1: 72:[21, 87, 36] Operation: 81-45=36 Exploring Operation: 45-21=24, Resulting Numbers: [81, 87, 24] Generated Node #0,2: 72:[81, 87, 24] Operation: 45-21=24 Exploring Operation: 87-45=42, Resulting Numbers: [21, 81, 42] Generated Node #0,3: 72:[21, 81, 42] Operation: 87-45=42 Moving to Node #0,0 Current State: 72:[21, 45, 6], Operations: ['87-81=6'] Exploring Operation: 21+45=66, Resulting Numbers: [6, 66] Generated Node #0,0,0: 72:[6, 66] Operation: 21+45=66 Exploring Operation: 45-6=39, Resulting Numbers: [21, 39] Generated Node #0,0,1: 72:[21, 39] Operation: 45-6=39 Exploring Operation: 45-21=24, Resulting Numbers: [6, 24] Generated Node #0,0,2: 72:[6, 24] Operation: 45-21=24 Exploring Operation: 21+6=27, Resulting Numbers: [45, 27] Generated Node #0,0,3: 72:[45, 27] Operation: 21+6=27 Moving to Node #0,3 Current State: 72:[21, 81, 42], Operations: ['87-45=42'] Exploring Operation: 81-42=39, Resulting Numbers: [21, 39] Generated Node #0,3,0: 72:[21, 39] Operation: 81-42=39 Exploring Operation: 42/21=2, Resulting Numbers: [81, 2] Generated Node #0,3,1: 72:[81, 2] Operation: 42/21=2 Exploring Operation: 81-21=60, Resulting Numbers: [42, 60] Generated Node #0,3,2: 72:[42, 60] Operation: 81-21=60 Exploring Operation: 42-21=21, Resulting Numbers: [81, 21] Generated Node #0,3,3: 72:[81, 21] Operation: 42-21=21 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 72:[21, 39], Operations: ['87-45=42', '81-42=39'] Exploring Operation: 21*39=819, Resulting Numbers: [819] 819,72 unequal: No Solution Exploring Operation: 39-21=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 21+39=60, Resulting Numbers: [60] 60,72 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 #0,3,1 Current State: 72:[81, 2], Operations: ['87-45=42', '42/21=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 81*2=162, Resulting Numbers: [162] 162,72 unequal: No Solution Exploring Operation: 81+2=83, Resulting Numbers: [83] 83,72 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 #0,3,3 Current State: 72:[81, 21], Operations: ['87-45=42', '42-21=21'] Exploring Operation: 81*21=1701, Resulting Numbers: [1701] 1701,72 unequal: No Solution Exploring Operation: 81+21=102, Resulting Numbers: [102] 102,72 unequal: No Solution Exploring Operation: 81-21=60, Resulting Numbers: [60] 60,72 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 #0,3,2 Current State: 72:[42, 60], Operations: ['87-45=42', '81-21=60'] Exploring Operation: 42+60=102, Resulting Numbers: [102] 102,72 unequal: No Solution Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,72 unequal: No Solution Exploring Operation: 42*60=2520, Resulting Numbers: [2520] 2520,72 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: 72:[21, 87, 36], Operations: ['81-45=36'] Exploring Operation: 87-21=66, Resulting Numbers: [36, 66] Generated Node #0,1,0: 72:[36, 66] Operation: 87-21=66 Exploring Operation: 21+36=57, Resulting Numbers: [87, 57] Generated Node #0,1,1: 72:[87, 57] Operation: 21+36=57 Exploring Operation: 87-36=51, Resulting Numbers: [21, 51] Generated Node #0,1,2: 72:[21, 51] Operation: 87-36=51 Exploring Operation: 36-21=15, Resulting Numbers: [87, 15] Generated Node #0,1,3: 72:[87, 15] Operation: 36-21=15 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 72:[36, 66], Operations: ['81-45=36', '87-21=66'] Exploring Operation: 36*66=2376, Resulting Numbers: [2376] 2376,72 unequal: No Solution Exploring Operation: 36+66=102, Resulting Numbers: [102] 102,72 unequal: No Solution Exploring Operation: 66-36=30, Resulting Numbers: [30] 30,72 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 #0,1,2 Current State: 72:[21, 51], Operations: ['81-45=36', '87-36=51'] Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[21, 81, 45, 87], Operations: [] Exploring Operation: 81-45=36, Resulting Numbers: [21, 87, 36] Generated Node #0,1: 72:[21, 87, 36] Operation: 81-45=36 Moving to Node #0,1 Current State: 72:[21, 87, 36], Operations: ['81-45=36'] Exploring Operation: 87-36=51, Resulting Numbers: [21, 51] Generated Node #0,1,2: 72:[21, 51] Operation: 87-36=51 Moving to Node #0,1,2 Current State: 72:[21, 51], Operations: ['81-45=36', '87-36=51'] Exploring Operation: 21+51=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.96875
hs_4
mult_heuristic
[ 75, 57, 69, 80 ]
12
[ "75+57=132", "80-69=11", "132/11=12" ]
Current State: 12:[75, 57, 69, 80], Operations: [] Exploring Operation: 75+57=132, Resulting Numbers: [69, 80, 132] Generated Node #2: [69, 80, 132] from Operation: 75+57=132 Current State: 12:[69, 80, 132], Operations: ['75+57=132'] Exploring Operation: 80-69=11, Resulting Numbers: [132, 11] Generated Node #3: [132, 11] from Operation: 80-69=11 Current State: 12:[132, 11], Operations: ['75+57=132', '80-69=11'] Exploring Operation: 132/11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[75, 57, 69, 80], Operations: [] Exploring Operation: 80-75=5, Resulting Numbers: [57, 69, 5] Generated Node #0,0: 12:[57, 69, 5] Operation: 80-75=5 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[57, 69, 5], Operations: ['80-75=5'] Exploring Operation: 69-57=12, Resulting Numbers: [5, 12] Generated Node #0,0,0: 12:[5, 12] Operation: 69-57=12 Moving to Node #0,0,0 Current State: 12:[5, 12], Operations: ['80-75=5', '69-57=12'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,12 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
[ 27, 71, 30, 70 ]
58
[ "27+71=98", "70-30=40", "98-40=58" ]
Current State: 58:[27, 71, 30, 70], Operations: [] Exploring Operation: 27+71=98, Resulting Numbers: [30, 70, 98] Generated Node #2: [30, 70, 98] from Operation: 27+71=98 Current State: 58:[30, 70, 98], Operations: ['27+71=98'] Exploring Operation: 70-30=40, Resulting Numbers: [98, 40] Generated Node #3: [98, 40] from Operation: 70-30=40 Current State: 58:[98, 40], Operations: ['27+71=98', '70-30=40'] Exploring Operation: 98-40=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[27, 71, 30, 70], Operations: [] Exploring Operation: 71-70=1, Resulting Numbers: [27, 30, 1] Generated Node #0,0: 58:[27, 30, 1] Operation: 71-70=1 Exploring Operation: 71-30=41, Resulting Numbers: [27, 70, 41] Generated Node #0,1: 58:[27, 70, 41] Operation: 71-30=41 Exploring Operation: 27+30=57, Resulting Numbers: [71, 70, 57] Generated Node #0,2: 58:[71, 70, 57] Operation: 27+30=57 Exploring Operation: 30-27=3, Resulting Numbers: [71, 70, 3] Generated Node #0,3: 58:[71, 70, 3] Operation: 30-27=3 Moving to Node #0,0 Current State: 58:[27, 30, 1], Operations: ['71-70=1'] Exploring Operation: 27+30=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 58:[1, 57] Operation: 27+30=57 Exploring Operation: 30-1=29, Resulting Numbers: [27, 29] Generated Node #0,0,1: 58:[27, 29] Operation: 30-1=29 Exploring Operation: 27+1=28, Resulting Numbers: [30, 28] Generated Node #0,0,2: 58:[30, 28] Operation: 27+1=28 Exploring Operation: 30-27=3, Resulting Numbers: [1, 3] Generated Node #0,0,3: 58:[1, 3] Operation: 30-27=3 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[1, 57], Operations: ['71-70=1', '27+30=57'] Exploring Operation: 57/1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,58 unequal: No Solution Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[27, 71, 30, 70], Operations: [] Exploring Operation: 71-70=1, Resulting Numbers: [27, 30, 1] Generated Node #0,0: 58:[27, 30, 1] Operation: 71-70=1 Moving to Node #0,0 Current State: 58:[27, 30, 1], Operations: ['71-70=1'] Exploring Operation: 27+30=57, Resulting Numbers: [1, 57] Generated Node #0,0,0: 58:[1, 57] Operation: 27+30=57 Moving to Node #0,0,0 Current State: 58:[1, 57], Operations: ['71-70=1', '27+30=57'] Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 4, 96, 48, 85 ]
79
[ "85-4=81", "96/48=2", "81-2=79" ]
Current State: 79:[4, 96, 48, 85], Operations: [] Exploring Operation: 85-4=81, Resulting Numbers: [96, 48, 81] Generated Node #2: [96, 48, 81] from Operation: 85-4=81 Current State: 79:[96, 48, 81], Operations: ['85-4=81'] Exploring Operation: 96/48=2, Resulting Numbers: [81, 2] Generated Node #3: [81, 2] from Operation: 96/48=2 Current State: 79:[81, 2], Operations: ['85-4=81', '96/48=2'] Exploring Operation: 81-2=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[4, 96, 48, 85], Operations: [] Exploring Operation: 4+48=52, Resulting Numbers: [96, 85, 52] Generated Node #0,0: 79:[96, 85, 52] Operation: 4+48=52 Exploring Operation: 96-4=92, Resulting Numbers: [48, 85, 92] Generated Node #0,1: 79:[48, 85, 92] Operation: 96-4=92 Moving to Node #0,0 Current State: 79:[96, 85, 52], Operations: ['4+48=52'] Exploring Operation: 85-52=33, Resulting Numbers: [96, 33] Generated Node #0,0,0: 79:[96, 33] Operation: 85-52=33 Exploring Operation: 96-52=44, Resulting Numbers: [85, 44] Generated Node #0,0,1: 79:[85, 44] Operation: 96-52=44 Moving to Node #0,1 Current State: 79:[48, 85, 92], Operations: ['96-4=92'] Exploring Operation: 85-48=37, Resulting Numbers: [92, 37] Generated Node #0,1,0: 79:[92, 37] Operation: 85-48=37 Exploring Operation: 92-48=44, Resulting Numbers: [85, 44] Generated Node #0,1,1: 79:[85, 44] Operation: 92-48=44 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[85, 44], Operations: ['96-4=92', '92-48=44'] Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 85+44=129, Resulting Numbers: [129] 129,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[92, 37], Operations: ['96-4=92', '85-48=37'] Exploring Operation: 92+37=129, Resulting Numbers: [129] 129,79 unequal: No Solution Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 79:[85, 44], Operations: ['4+48=52', '96-52=44'] Exploring Operation: 85-44=41, Resulting Numbers: [41] 41,79 unequal: No Solution Exploring Operation: 85+44=129, Resulting Numbers: [129] 129,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[96, 33], Operations: ['4+48=52', '85-52=33'] Exploring Operation: 96-33=63, Resulting Numbers: [63] 63,79 unequal: No Solution Exploring Operation: 96+33=129, Resulting Numbers: [129] 129,79 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 10, 49, 10, 22 ]
72
[ "10/10=1", "49+22=71", "1+71=72" ]
Current State: 72:[10, 49, 10, 22], Operations: [] Exploring Operation: 10/10=1, Resulting Numbers: [49, 22, 1] Generated Node #2: [49, 22, 1] from Operation: 10/10=1 Current State: 72:[49, 22, 1], Operations: ['10/10=1'] Exploring Operation: 49+22=71, Resulting Numbers: [1, 71] Generated Node #3: [1, 71] from Operation: 49+22=71 Current State: 72:[1, 71], Operations: ['10/10=1', '49+22=71'] Exploring Operation: 1+71=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[10, 49, 10, 22], Operations: [] Exploring Operation: 49-22=27, Resulting Numbers: [10, 10, 27] Generated Node #0,0: 72:[10, 10, 27] Operation: 49-22=27 Exploring Operation: 49+22=71, Resulting Numbers: [10, 10, 71] Generated Node #0,1: 72:[10, 10, 71] Operation: 49+22=71 Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[10, 10, 71], Operations: ['49+22=71'] Exploring Operation: 10/10=1, Resulting Numbers: [71, 1] Generated Node #0,1,0: 72:[71, 1] Operation: 10/10=1 Exploring Operation: 10+10=20, Resulting Numbers: [71, 20] Generated Node #0,1,1: 72:[71, 20] Operation: 10+10=20 Moving to Node #0,1,0 Current State: 72:[71, 1], Operations: ['49+22=71', '10/10=1'] Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[10, 49, 10, 22], Operations: [] Exploring Operation: 49+22=71, Resulting Numbers: [10, 10, 71] Generated Node #0,1: 72:[10, 10, 71] Operation: 49+22=71 Moving to Node #0,1 Current State: 72:[10, 10, 71], Operations: ['49+22=71'] Exploring Operation: 10/10=1, Resulting Numbers: [71, 1] Generated Node #0,1,0: 72:[71, 1] Operation: 10/10=1 Moving to Node #0,1,0 Current State: 72:[71, 1], Operations: ['49+22=71', '10/10=1'] Exploring Operation: 71+1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 76, 80, 18, 97 ]
83
[ "80-76=4", "97-18=79", "4+79=83" ]
Current State: 83:[76, 80, 18, 97], Operations: [] Exploring Operation: 80-76=4, Resulting Numbers: [18, 97, 4] Generated Node #2: [18, 97, 4] from Operation: 80-76=4 Current State: 83:[18, 97, 4], Operations: ['80-76=4'] Exploring Operation: 97-18=79, Resulting Numbers: [4, 79] Generated Node #3: [4, 79] from Operation: 97-18=79 Current State: 83:[4, 79], Operations: ['80-76=4', '97-18=79'] Exploring Operation: 4+79=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[76, 80, 18, 97], Operations: [] Exploring Operation: 76-18=58, Resulting Numbers: [80, 97, 58] Generated Node #0,0: 83:[80, 97, 58] Operation: 76-18=58 Exploring Operation: 80+18=98, Resulting Numbers: [76, 97, 98] Generated Node #0,1: 83:[76, 97, 98] Operation: 80+18=98 Exploring Operation: 97-18=79, Resulting Numbers: [76, 80, 79] Generated Node #0,2: 83:[76, 80, 79] Operation: 97-18=79 Exploring Operation: 76+18=94, Resulting Numbers: [80, 97, 94] Generated Node #0,3: 83:[80, 97, 94] Operation: 76+18=94 Moving to Node #0,2 Current State: 83:[76, 80, 79], Operations: ['97-18=79'] Exploring Operation: 79-76=3, Resulting Numbers: [80, 3] Generated Node #0,2,0: 83:[80, 3] Operation: 79-76=3 Exploring Operation: 76+80=156, Resulting Numbers: [79, 156] Generated Node #0,2,1: 83:[79, 156] Operation: 76+80=156 Exploring Operation: 80-76=4, Resulting Numbers: [79, 4] Generated Node #0,2,2: 83:[79, 4] Operation: 80-76=4 Exploring Operation: 76+79=155, Resulting Numbers: [80, 155] Generated Node #0,2,3: 83:[80, 155] Operation: 76+79=155 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 83:[80, 155], Operations: ['97-18=79', '76+79=155'] Exploring Operation: 80+155=235, Resulting Numbers: [235] 235,83 unequal: No Solution Exploring Operation: 80*155=12400, Resulting Numbers: [12400] 12400,83 unequal: No Solution Exploring Operation: 155-80=75, Resulting Numbers: [75] 75,83 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:[79, 156], Operations: ['97-18=79', '76+80=156'] Exploring Operation: 156-79=77, Resulting Numbers: [77] 77,83 unequal: No Solution Exploring Operation: 79*156=12324, Resulting Numbers: [12324] 12324,83 unequal: No Solution Exploring Operation: 79+156=235, Resulting Numbers: [235] 235,83 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:[80, 3], Operations: ['97-18=79', '79-76=3'] Exploring Operation: 80-3=77, Resulting Numbers: [77] 77,83 unequal: No Solution Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[76, 80, 18, 97], Operations: [] Exploring Operation: 97-18=79, Resulting Numbers: [76, 80, 79] Generated Node #0,2: 83:[76, 80, 79] Operation: 97-18=79 Moving to Node #0,2 Current State: 83:[76, 80, 79], Operations: ['97-18=79'] Exploring Operation: 79-76=3, Resulting Numbers: [80, 3] Generated Node #0,2,0: 83:[80, 3] Operation: 79-76=3 Moving to Node #0,2,0 Current State: 83:[80, 3], Operations: ['97-18=79', '79-76=3'] Exploring Operation: 80+3=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
mult_heuristic
[ 98, 11, 32, 38 ]
81
[ "98-11=87", "38-32=6", "87-6=81" ]
Current State: 81:[98, 11, 32, 38], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [32, 38, 87] Generated Node #2: [32, 38, 87] from Operation: 98-11=87 Current State: 81:[32, 38, 87], Operations: ['98-11=87'] Exploring Operation: 38-32=6, Resulting Numbers: [87, 6] Generated Node #3: [87, 6] from Operation: 38-32=6 Current State: 81:[87, 6], Operations: ['98-11=87', '38-32=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[98, 11, 32, 38], Operations: [] Exploring Operation: 38-11=27, Resulting Numbers: [98, 32, 27] Generated Node #0,0: 81:[98, 32, 27] Operation: 38-11=27 Exploring Operation: 98-11=87, Resulting Numbers: [32, 38, 87] Generated Node #0,1: 81:[32, 38, 87] Operation: 98-11=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 81:[98, 32, 27], Operations: ['38-11=27'] Exploring Operation: 98-32=66, Resulting Numbers: [27, 66] Generated Node #0,0,0: 81:[27, 66] Operation: 98-32=66 Exploring Operation: 98-27=71, Resulting Numbers: [32, 71] Generated Node #0,0,1: 81:[32, 71] Operation: 98-27=71 Moving to Node #0,0,0 Current State: 81:[27, 66], Operations: ['38-11=27', '98-32=66'] Exploring Operation: 27+66=93, Resulting Numbers: [93] 93,81 unequal: No Solution Exploring Operation: 66-27=39, Resulting Numbers: [39] 39,81 unequal: No Solution Moving to Node #0,0,1 Current State: 81:[32, 71], Operations: ['38-11=27', '98-27=71'] Exploring Operation: 32+71=103, Resulting Numbers: [103] 103,81 unequal: No Solution Exploring Operation: 71-32=39, Resulting Numbers: [39] 39,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[32, 38, 87], Operations: ['98-11=87'] Exploring Operation: 38-32=6, Resulting Numbers: [87, 6] Generated Node #0,1,0: 81:[87, 6] Operation: 38-32=6 Exploring Operation: 32+38=70, Resulting Numbers: [87, 70] Generated Node #0,1,1: 81:[87, 70] Operation: 32+38=70 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 81:[87, 6], Operations: ['98-11=87', '38-32=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[98, 11, 32, 38], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [32, 38, 87] Generated Node #0,1: 81:[32, 38, 87] Operation: 98-11=87 Moving to Node #0,1 Current State: 81:[32, 38, 87], Operations: ['98-11=87'] Exploring Operation: 38-32=6, Resulting Numbers: [87, 6] Generated Node #0,1,0: 81:[87, 6] Operation: 38-32=6 Moving to Node #0,1,0 Current State: 81:[87, 6], Operations: ['98-11=87', '38-32=6'] Exploring Operation: 87-6=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
sum_heuristic
[ 31, 80, 46, 14 ]
18
[ "31*46=1426", "14+1426=1440", "1440/80=18" ]
Current State: 18:[31, 80, 46, 14], Operations: [] Exploring Operation: 31*46=1426, Resulting Numbers: [80, 14, 1426] Generated Node #2: [80, 14, 1426] from Operation: 31*46=1426 Current State: 18:[80, 14, 1426], Operations: ['31*46=1426'] Exploring Operation: 14+1426=1440, Resulting Numbers: [80, 1440] Generated Node #3: [80, 1440] from Operation: 14+1426=1440 Current State: 18:[80, 1440], Operations: ['31*46=1426', '14+1426=1440'] Exploring Operation: 1440/80=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[31, 80, 46, 14], Operations: [] Exploring Operation: 80-14=66, Resulting Numbers: [31, 46, 66] Generated Node #0,0: 18:[31, 46, 66] Operation: 80-14=66 Exploring Operation: 80-31=49, Resulting Numbers: [46, 14, 49] Generated Node #0,1: 18:[46, 14, 49] Operation: 80-31=49 Exploring Operation: 46-31=15, Resulting Numbers: [80, 14, 15] Generated Node #0,2: 18:[80, 14, 15] Operation: 46-31=15 Exploring Operation: 80-46=34, Resulting Numbers: [31, 14, 34] Generated Node #0,3: 18:[31, 14, 34] Operation: 80-46=34 Start Sub Search at level 1: Moving to Node #0,3 Current State: 18:[31, 14, 34], Operations: ['80-46=34'] Exploring Operation: 34-14=20, Resulting Numbers: [31, 20] Generated Node #0,3,0: 18:[31, 20] Operation: 34-14=20 Exploring Operation: 31-14=17, Resulting Numbers: [34, 17] Generated Node #0,3,1: 18:[34, 17] Operation: 31-14=17 Exploring Operation: 34-31=3, Resulting Numbers: [14, 3] Generated Node #0,3,2: 18:[14, 3] Operation: 34-31=3 Exploring Operation: 31+14=45, Resulting Numbers: [34, 45] Generated Node #0,3,3: 18:[34, 45] Operation: 31+14=45 Moving to Node #0,3,2 Current State: 18:[14, 3], Operations: ['80-46=34', '34-31=3'] Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,18 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[31, 20], Operations: ['80-46=34', '34-14=20'] Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,18 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[34, 17], Operations: ['80-46=34', '31-14=17'] Exploring Operation: 34*17=578, Resulting Numbers: [578] 578,18 unequal: No Solution Exploring Operation: 34+17=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 34-17=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 34/17=2, Resulting Numbers: [2] 2,18 unequal: No Solution Moving to Node #0,3,3 Current State: 18:[34, 45], Operations: ['80-46=34', '31+14=45'] Exploring Operation: 34*45=1530, Resulting Numbers: [1530] 1530,18 unequal: No Solution Exploring Operation: 45-34=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 34+45=79, Resulting Numbers: [79] 79,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[46, 14, 49], Operations: ['80-31=49'] Exploring Operation: 46+14=60, Resulting Numbers: [49, 60] Generated Node #0,1,0: 18:[49, 60] Operation: 46+14=60 Exploring Operation: 49-14=35, Resulting Numbers: [46, 35] Generated Node #0,1,1: 18:[46, 35] Operation: 49-14=35 Exploring Operation: 46-14=32, Resulting Numbers: [49, 32] Generated Node #0,1,2: 18:[49, 32] Operation: 46-14=32 Exploring Operation: 49-46=3, Resulting Numbers: [14, 3] Generated Node #0,1,3: 18:[14, 3] Operation: 49-46=3 Moving to Node #0,1,3 Current State: 18:[14, 3], Operations: ['80-31=49', '49-46=3'] Exploring Operation: 14*3=42, Resulting Numbers: [42] 42,18 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 14+3=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[49, 32], Operations: ['80-31=49', '46-14=32'] Exploring Operation: 49*32=1568, Resulting Numbers: [1568] 1568,18 unequal: No Solution Exploring Operation: 49+32=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[46, 35], Operations: ['80-31=49', '49-14=35'] Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[49, 60], Operations: ['80-31=49', '46+14=60'] Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,18 unequal: No Solution Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,18 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[80, 14, 15], Operations: ['46-31=15'] Exploring Operation: 80-15=65, Resulting Numbers: [14, 65] Generated Node #0,2,0: 18:[14, 65] Operation: 80-15=65 Exploring Operation: 80-14=66, Resulting Numbers: [15, 66] Generated Node #0,2,1: 18:[15, 66] Operation: 80-14=66 Exploring Operation: 15-14=1, Resulting Numbers: [80, 1] Generated Node #0,2,2: 18:[80, 1] Operation: 15-14=1 Exploring Operation: 14+15=29, Resulting Numbers: [80, 29] Generated Node #0,2,3: 18:[80, 29] Operation: 14+15=29 Moving to Node #0,2,0 Current State: 18:[14, 65], Operations: ['46-31=15', '80-15=65'] Exploring Operation: 14*65=910, Resulting Numbers: [910] 910,18 unequal: No Solution Exploring Operation: 14+65=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 65-14=51, Resulting Numbers: [51] 51,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[15, 66], Operations: ['46-31=15', '80-14=66'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 15*66=990, Resulting Numbers: [990] 990,18 unequal: No Solution Exploring Operation: 15+66=81, Resulting Numbers: [81] 81,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[80, 1], Operations: ['46-31=15', '15-14=1'] Exploring Operation: 80+1=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 80-1=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 80*1=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 80/1=80, Resulting Numbers: [80] 80,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[80, 29], Operations: ['46-31=15', '14+15=29'] Exploring Operation: 80*29=2320, Resulting Numbers: [2320] 2320,18 unequal: No Solution Exploring Operation: 80-29=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 80+29=109, Resulting Numbers: [109] 109,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[31, 46, 66], Operations: ['80-14=66'] Exploring Operation: 66-31=35, Resulting Numbers: [46, 35] Generated Node #0,0,0: 18:[46, 35] Operation: 66-31=35 Exploring Operation: 66-46=20, Resulting Numbers: [31, 20] Generated Node #0,0,1: 18:[31, 20] Operation: 66-46=20 Exploring Operation: 46-31=15, Resulting Numbers: [66, 15] Generated Node #0,0,2: 18:[66, 15] Operation: 46-31=15 Exploring Operation: 31+46=77, Resulting Numbers: [66, 77] Generated Node #0,0,3: 18:[66, 77] Operation: 31+46=77 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 18:[31, 20], Operations: ['80-14=66', '66-46=20'] Exploring Operation: 31-20=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 31*20=620, Resulting Numbers: [620] 620,18 unequal: No Solution Exploring Operation: 31+20=51, Resulting Numbers: [51] 51,18 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 #0,0,0 Current State: 18:[46, 35], Operations: ['80-14=66', '66-31=35'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,18 unequal: No Solution Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,18 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 #0,0,2 Current State: 18:[66, 15], Operations: ['80-14=66', '46-31=15'] Exploring Operation: 66-15=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 66*15=990, Resulting Numbers: [990] 990,18 unequal: No Solution Exploring Operation: 66+15=81, Resulting Numbers: [81] 81,18 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 #0,0,3 Current State: 18:[66, 77], Operations: ['80-14=66', '31+46=77'] Exploring Operation: 66*77=5082, Resulting Numbers: [5082] 5082,18 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,18 unequal: No Solution Exploring Operation: 66+77=143, Resulting Numbers: [143] 143,18 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 No solution found.
0
hs_4
sum_heuristic
[ 39, 44, 14, 7 ]
34
[ "39*14=546", "546/7=78", "78-44=34" ]
Current State: 34:[39, 44, 14, 7], Operations: [] Exploring Operation: 39*14=546, Resulting Numbers: [44, 7, 546] Generated Node #2: [44, 7, 546] from Operation: 39*14=546 Current State: 34:[44, 7, 546], Operations: ['39*14=546'] Exploring Operation: 546/7=78, Resulting Numbers: [44, 78] Generated Node #3: [44, 78] from Operation: 546/7=78 Current State: 34:[44, 78], Operations: ['39*14=546', '546/7=78'] Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[39, 44, 14, 7], Operations: [] Exploring Operation: 44-39=5, Resulting Numbers: [14, 7, 5] Generated Node #0,0: 34:[14, 7, 5] Operation: 44-39=5 Exploring Operation: 44-14=30, Resulting Numbers: [39, 7, 30] Generated Node #0,1: 34:[39, 7, 30] Operation: 44-14=30 Exploring Operation: 44-7=37, Resulting Numbers: [39, 14, 37] Generated Node #0,2: 34:[39, 14, 37] Operation: 44-7=37 Start Sub Search at level 1: Moving to Node #0,0 Current State: 34:[14, 7, 5], Operations: ['44-39=5'] Exploring Operation: 7-5=2, Resulting Numbers: [14, 2] Generated Node #0,0,0: 34:[14, 2] Operation: 7-5=2 Exploring Operation: 7*5=35, Resulting Numbers: [14, 35] Generated Node #0,0,1: 34:[14, 35] Operation: 7*5=35 Exploring Operation: 14/7=2, Resulting Numbers: [5, 2] Generated Node #0,0,2: 34:[5, 2] Operation: 14/7=2 Moving to Node #0,0,0 Current State: 34:[14, 2], Operations: ['44-39=5', '7-5=2'] Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Moving to Node #0,0,2 Current State: 34:[5, 2], Operations: ['44-39=5', '14/7=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,34 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,34 unequal: No Solution Exploring Operation: 5+2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Moving to Node #0,0,1 Current State: 34:[14, 35], Operations: ['44-39=5', '7*5=35'] Exploring Operation: 14*35=490, Resulting Numbers: [490] 490,34 unequal: No Solution Exploring Operation: 14+35=49, Resulting Numbers: [49] 49,34 unequal: No Solution Exploring Operation: 35-14=21, Resulting Numbers: [21] 21,34 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 #0,2 Current State: 34:[39, 14, 37], Operations: ['44-7=37'] Exploring Operation: 37-14=23, Resulting Numbers: [39, 23] Generated Node #0,2,0: 34:[39, 23] Operation: 37-14=23 Exploring Operation: 39-14=25, Resulting Numbers: [37, 25] Generated Node #0,2,1: 34:[37, 25] Operation: 39-14=25 Exploring Operation: 39-37=2, Resulting Numbers: [14, 2] Generated Node #0,2,2: 34:[14, 2] Operation: 39-37=2 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 34:[14, 2], Operations: ['44-7=37', '39-37=2'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,34 unequal: No Solution Exploring Operation: 14+2=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,34 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 #0,2,0 Current State: 34:[39, 23], Operations: ['44-7=37', '37-14=23'] Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,34 unequal: No Solution Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,34 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,34 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 #0,2,1 Current State: 34:[37, 25], Operations: ['44-7=37', '39-14=25'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,34 unequal: No Solution Exploring Operation: 37*25=925, Resulting Numbers: [925] 925,34 unequal: No Solution Exploring Operation: 37+25=62, Resulting Numbers: [62] 62,34 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 34:[39, 7, 30], Operations: ['44-14=30'] Exploring Operation: 39-7=32, Resulting Numbers: [30, 32] Generated Node #0,1,0: 34:[30, 32] Operation: 39-7=32 Exploring Operation: 30-7=23, Resulting Numbers: [39, 23] Generated Node #0,1,1: 34:[39, 23] Operation: 30-7=23 Exploring Operation: 7+30=37, Resulting Numbers: [39, 37] Generated Node #0,1,2: 34:[39, 37] Operation: 7+30=37 Moving to Node #0,1,0 Current State: 34:[30, 32], Operations: ['44-14=30', '39-7=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,34 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,34 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,34 unequal: No Solution Moving to Node #0,1,2 Current State: 34:[39, 37], Operations: ['44-14=30', '7+30=37'] Exploring Operation: 39*37=1443, Resulting Numbers: [1443] 1443,34 unequal: No Solution Exploring Operation: 39+37=76, Resulting Numbers: [76] 76,34 unequal: No Solution Exploring Operation: 39-37=2, Resulting Numbers: [2] 2,34 unequal: No Solution Moving to Node #0,1,1 Current State: 34:[39, 23], Operations: ['44-14=30', '30-7=23'] Exploring Operation: 39*23=897, Resulting Numbers: [897] 897,34 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,34 unequal: No Solution Exploring Operation: 39+23=62, Resulting Numbers: [62] 62,34 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
[ 98, 96, 71, 70 ]
53
[ "98+96=194", "71+70=141", "194-141=53" ]
Current State: 53:[98, 96, 71, 70], Operations: [] Exploring Operation: 98+96=194, Resulting Numbers: [71, 70, 194] Generated Node #2: [71, 70, 194] from Operation: 98+96=194 Current State: 53:[71, 70, 194], Operations: ['98+96=194'] Exploring Operation: 71+70=141, Resulting Numbers: [194, 141] Generated Node #3: [194, 141] from Operation: 71+70=141 Current State: 53:[194, 141], Operations: ['98+96=194', '71+70=141'] Exploring Operation: 194-141=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[98, 96, 71, 70], Operations: [] Exploring Operation: 98-96=2, Resulting Numbers: [71, 70, 2] Generated Node #0,0: 53:[71, 70, 2] Operation: 98-96=2 Exploring Operation: 96-71=25, Resulting Numbers: [98, 70, 25] Generated Node #0,1: 53:[98, 70, 25] Operation: 96-71=25 Exploring Operation: 96-70=26, Resulting Numbers: [98, 71, 26] Generated Node #0,2: 53:[98, 71, 26] Operation: 96-70=26 Exploring Operation: 98-71=27, Resulting Numbers: [96, 70, 27] Generated Node #0,3: 53:[96, 70, 27] Operation: 98-71=27 Exploring Operation: 98-70=28, Resulting Numbers: [96, 71, 28] Generated Node #0,4: 53:[96, 71, 28] Operation: 98-70=28 Moving to Node #0,0 Current State: 53:[71, 70, 2], Operations: ['98-96=2'] Exploring Operation: 71-2=69, Resulting Numbers: [70, 69] Generated Node #0,0,0: 53:[70, 69] Operation: 71-2=69 Exploring Operation: 71+2=73, Resulting Numbers: [70, 73] Generated Node #0,0,1: 53:[70, 73] Operation: 71+2=73 Exploring Operation: 70+2=72, Resulting Numbers: [71, 72] Generated Node #0,0,2: 53:[71, 72] Operation: 70+2=72 Exploring Operation: 70/2=35, Resulting Numbers: [71, 35] Generated Node #0,0,3: 53:[71, 35] Operation: 70/2=35 Exploring Operation: 70-2=68, Resulting Numbers: [71, 68] Generated Node #0,0,4: 53:[71, 68] Operation: 70-2=68 Moving to Node #0,4 Current State: 53:[96, 71, 28], Operations: ['98-70=28'] Exploring Operation: 96+28=124, Resulting Numbers: [71, 124] Generated Node #0,4,0: 53:[71, 124] Operation: 96+28=124 Exploring Operation: 96-28=68, Resulting Numbers: [71, 68] Generated Node #0,4,1: 53:[71, 68] Operation: 96-28=68 Exploring Operation: 71+28=99, Resulting Numbers: [96, 99] Generated Node #0,4,2: 53:[96, 99] Operation: 71+28=99 Exploring Operation: 71-28=43, Resulting Numbers: [96, 43] Generated Node #0,4,3: 53:[96, 43] Operation: 71-28=43 Exploring Operation: 96-71=25, Resulting Numbers: [28, 25] Generated Node #0,4,4: 53:[28, 25] Operation: 96-71=25 Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 53:[71, 68], Operations: ['98-70=28', '96-28=68'] Exploring Operation: 71+68=139, Resulting Numbers: [139] 139,53 unequal: No Solution Exploring Operation: 71*68=4828, Resulting Numbers: [4828] 4828,53 unequal: No Solution Exploring Operation: 71-68=3, Resulting Numbers: [3] 3,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 53:[96, 43], Operations: ['98-70=28', '71-28=43'] Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[98, 96, 71, 70], Operations: [] Exploring Operation: 98-70=28, Resulting Numbers: [96, 71, 28] Generated Node #0,4: 53:[96, 71, 28] Operation: 98-70=28 Moving to Node #0,4 Current State: 53:[96, 71, 28], Operations: ['98-70=28'] Exploring Operation: 71-28=43, Resulting Numbers: [96, 43] Generated Node #0,4,3: 53:[96, 43] Operation: 71-28=43 Moving to Node #0,4,3 Current State: 53:[96, 43], Operations: ['98-70=28', '71-28=43'] Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 23, 1, 84, 17 ]
15
[ "23-17=6", "84/6=14", "1+14=15" ]
Current State: 15:[23, 1, 84, 17], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [1, 84, 6] Generated Node #2: [1, 84, 6] from Operation: 23-17=6 Current State: 15:[1, 84, 6], Operations: ['23-17=6'] Exploring Operation: 84/6=14, Resulting Numbers: [1, 14] Generated Node #3: [1, 14] from Operation: 84/6=14 Current State: 15:[1, 14], Operations: ['23-17=6', '84/6=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[23, 1, 84, 17], Operations: [] Exploring Operation: 84-23=61, Resulting Numbers: [1, 17, 61] Generated Node #0,0: 15:[1, 17, 61] Operation: 84-23=61 Exploring Operation: 84-17=67, Resulting Numbers: [23, 1, 67] Generated Node #0,1: 15:[23, 1, 67] Operation: 84-17=67 Exploring Operation: 23-17=6, Resulting Numbers: [1, 84, 6] Generated Node #0,2: 15:[1, 84, 6] Operation: 23-17=6 Exploring Operation: 23-1=22, Resulting Numbers: [84, 17, 22] Generated Node #0,3: 15:[84, 17, 22] Operation: 23-1=22 Moving to Node #0,0 Current State: 15:[1, 17, 61], Operations: ['84-23=61'] Exploring Operation: 1*17=17, Resulting Numbers: [61, 17] Generated Node #0,0,0: 15:[61, 17] Operation: 1*17=17 Exploring Operation: 17-1=16, Resulting Numbers: [61, 16] Generated Node #0,0,1: 15:[61, 16] Operation: 17-1=16 Exploring Operation: 61-1=60, Resulting Numbers: [17, 60] Generated Node #0,0,2: 15:[17, 60] Operation: 61-1=60 Exploring Operation: 61-17=44, Resulting Numbers: [1, 44] Generated Node #0,0,3: 15:[1, 44] Operation: 61-17=44 Moving to Node #0,1 Current State: 15:[23, 1, 67], Operations: ['84-17=67'] Exploring Operation: 67-23=44, Resulting Numbers: [1, 44] Generated Node #0,1,0: 15:[1, 44] Operation: 67-23=44 Exploring Operation: 67-1=66, Resulting Numbers: [23, 66] Generated Node #0,1,1: 15:[23, 66] Operation: 67-1=66 Exploring Operation: 23-1=22, Resulting Numbers: [67, 22] Generated Node #0,1,2: 15:[67, 22] Operation: 23-1=22 Exploring Operation: 23*1=23, Resulting Numbers: [67, 23] Generated Node #0,1,3: 15:[67, 23] Operation: 23*1=23 Moving to Node #0,2 Current State: 15:[1, 84, 6], Operations: ['23-17=6'] Exploring Operation: 84-6=78, Resulting Numbers: [1, 78] Generated Node #0,2,0: 15:[1, 78] Operation: 84-6=78 Exploring Operation: 84/6=14, Resulting Numbers: [1, 14] Generated Node #0,2,1: 15:[1, 14] Operation: 84/6=14 Exploring Operation: 84-1=83, Resulting Numbers: [6, 83] Generated Node #0,2,2: 15:[6, 83] Operation: 84-1=83 Exploring Operation: 6-1=5, Resulting Numbers: [84, 5] Generated Node #0,2,3: 15:[84, 5] Operation: 6-1=5 Moving to Node #0,3 Current State: 15:[84, 17, 22], Operations: ['23-1=22'] Exploring Operation: 84-17=67, Resulting Numbers: [22, 67] Generated Node #0,3,0: 15:[22, 67] Operation: 84-17=67 Exploring Operation: 84-22=62, Resulting Numbers: [17, 62] Generated Node #0,3,1: 15:[17, 62] Operation: 84-22=62 Exploring Operation: 84+17=101, Resulting Numbers: [22, 101] Generated Node #0,3,2: 15:[22, 101] Operation: 84+17=101 Exploring Operation: 22-17=5, Resulting Numbers: [84, 5] Generated Node #0,3,3: 15:[84, 5] Operation: 22-17=5 Moving to Node #0,2,1 Current State: 15:[1, 14], Operations: ['23-17=6', '84/6=14'] Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,15 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[23, 1, 84, 17], Operations: [] Exploring Operation: 23-17=6, Resulting Numbers: [1, 84, 6] Generated Node #0,2: 15:[1, 84, 6] Operation: 23-17=6 Moving to Node #0,2 Current State: 15:[1, 84, 6], Operations: ['23-17=6'] Exploring Operation: 84/6=14, Resulting Numbers: [1, 14] Generated Node #0,2,1: 15:[1, 14] Operation: 84/6=14 Moving to Node #0,2,1 Current State: 15:[1, 14], Operations: ['23-17=6', '84/6=14'] Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
0.977431
hs_4
sum_heuristic
[ 26, 57, 82, 88 ]
80
[ "26+88=114", "114/57=2", "82-2=80" ]
Current State: 80:[26, 57, 82, 88], Operations: [] Exploring Operation: 26+88=114, Resulting Numbers: [57, 82, 114] Generated Node #2: [57, 82, 114] from Operation: 26+88=114 Current State: 80:[57, 82, 114], Operations: ['26+88=114'] Exploring Operation: 114/57=2, Resulting Numbers: [82, 2] Generated Node #3: [82, 2] from Operation: 114/57=2 Current State: 80:[82, 2], Operations: ['26+88=114', '114/57=2'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[26, 57, 82, 88], Operations: [] Exploring Operation: 88-82=6, Resulting Numbers: [26, 57, 6] Generated Node #0,0: 80:[26, 57, 6] Operation: 88-82=6 Exploring Operation: 82-57=25, Resulting Numbers: [26, 88, 25] Generated Node #0,1: 80:[26, 88, 25] Operation: 82-57=25 Exploring Operation: 57-26=31, Resulting Numbers: [82, 88, 31] Generated Node #0,2: 80:[82, 88, 31] Operation: 57-26=31 Exploring Operation: 26+57=83, Resulting Numbers: [82, 88, 83] Generated Node #0,3: 80:[82, 88, 83] Operation: 26+57=83 Exploring Operation: 88-57=31, Resulting Numbers: [26, 82, 31] Generated Node #0,4: 80:[26, 82, 31] Operation: 88-57=31 Moving to Node #0,3 Current State: 80:[82, 88, 83], Operations: ['26+57=83'] Exploring Operation: 82+88=170, Resulting Numbers: [83, 170] Generated Node #0,3,0: 80:[83, 170] Operation: 82+88=170 Exploring Operation: 88-82=6, Resulting Numbers: [83, 6] Generated Node #0,3,1: 80:[83, 6] Operation: 88-82=6 Exploring Operation: 88-83=5, Resulting Numbers: [82, 5] Generated Node #0,3,2: 80:[82, 5] Operation: 88-83=5 Exploring Operation: 82+83=165, Resulting Numbers: [88, 165] Generated Node #0,3,3: 80:[88, 165] Operation: 82+83=165 Exploring Operation: 83-82=1, Resulting Numbers: [88, 1] Generated Node #0,3,4: 80:[88, 1] Operation: 83-82=1 Moving to Node #0,4 Current State: 80:[26, 82, 31], Operations: ['88-57=31'] Exploring Operation: 26+82=108, Resulting Numbers: [31, 108] Generated Node #0,4,0: 80:[31, 108] Operation: 26+82=108 Exploring Operation: 31-26=5, Resulting Numbers: [82, 5] Generated Node #0,4,1: 80:[82, 5] Operation: 31-26=5 Exploring Operation: 26+31=57, Resulting Numbers: [82, 57] Generated Node #0,4,2: 80:[82, 57] Operation: 26+31=57 Exploring Operation: 82-26=56, Resulting Numbers: [31, 56] Generated Node #0,4,3: 80:[31, 56] Operation: 82-26=56 Exploring Operation: 82-31=51, Resulting Numbers: [26, 51] Generated Node #0,4,4: 80:[26, 51] Operation: 82-31=51 Moving to Node #0,1 Current State: 80:[26, 88, 25], Operations: ['82-57=25'] Exploring Operation: 88-26=62, Resulting Numbers: [25, 62] Generated Node #0,1,0: 80:[25, 62] Operation: 88-26=62 Exploring Operation: 26+88=114, Resulting Numbers: [25, 114] Generated Node #0,1,1: 80:[25, 114] Operation: 26+88=114 Exploring Operation: 26-25=1, Resulting Numbers: [88, 1] Generated Node #0,1,2: 80:[88, 1] Operation: 26-25=1 Exploring Operation: 26+25=51, Resulting Numbers: [88, 51] Generated Node #0,1,3: 80:[88, 51] Operation: 26+25=51 Exploring Operation: 88-25=63, Resulting Numbers: [26, 63] Generated Node #0,1,4: 80:[26, 63] Operation: 88-25=63 Moving to Node #0,2 Current State: 80:[82, 88, 31], Operations: ['57-26=31'] Exploring Operation: 82-31=51, Resulting Numbers: [88, 51] Generated Node #0,2,0: 80:[88, 51] Operation: 82-31=51 Exploring Operation: 82+31=113, Resulting Numbers: [88, 113] Generated Node #0,2,1: 80:[88, 113] Operation: 82+31=113 Exploring Operation: 88+31=119, Resulting Numbers: [82, 119] Generated Node #0,2,2: 80:[82, 119] Operation: 88+31=119 Exploring Operation: 88-82=6, Resulting Numbers: [31, 6] Generated Node #0,2,3: 80:[31, 6] Operation: 88-82=6 Exploring Operation: 88-31=57, Resulting Numbers: [82, 57] Generated Node #0,2,4: 80:[82, 57] Operation: 88-31=57 Moving to Node #0,0 Current State: 80:[26, 57, 6], Operations: ['88-82=6'] Exploring Operation: 57-26=31, Resulting Numbers: [6, 31] Generated Node #0,0,0: 80:[6, 31] Operation: 57-26=31 Exploring Operation: 57-6=51, Resulting Numbers: [26, 51] Generated Node #0,0,1: 80:[26, 51] Operation: 57-6=51 Exploring Operation: 26-6=20, Resulting Numbers: [57, 20] Generated Node #0,0,2: 80:[57, 20] Operation: 26-6=20 Exploring Operation: 57+6=63, Resulting Numbers: [26, 63] Generated Node #0,0,3: 80:[26, 63] Operation: 57+6=63 Exploring Operation: 26+57=83, Resulting Numbers: [6, 83] Generated Node #0,0,4: 80:[6, 83] Operation: 26+57=83 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 80:[6, 83], Operations: ['88-82=6', '26+57=83'] Exploring Operation: 6+83=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 6*83=498, Resulting Numbers: [498] 498,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[6, 31], Operations: ['88-82=6', '57-26=31'] Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,80 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[26, 51], Operations: ['88-82=6', '57-6=51'] Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 26+51=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 26*51=1326, Resulting Numbers: [1326] 1326,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[57, 20], Operations: ['88-82=6', '26-6=20'] Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 57*20=1140, Resulting Numbers: [1140] 1140,80 unequal: No Solution Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 80:[26, 63], Operations: ['88-82=6', '57+6=63'] Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 26*63=1638, Resulting Numbers: [1638] 1638,80 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,80 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: 80:[82, 5], Operations: ['26+57=83', '88-83=5'] Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,80 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,4,1 Current State: 80:[82, 5], Operations: ['88-57=31', '31-26=5'] Exploring Operation: 82*5=410, Resulting Numbers: [410] 410,80 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 82+5=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[83, 6], Operations: ['26+57=83', '88-82=6'] Exploring Operation: 83*6=498, Resulting Numbers: [498] 498,80 unequal: No Solution Exploring Operation: 83+6=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 83-6=77, Resulting Numbers: [77] 77,80 unequal: No Solution Moving to Node #0,3,4 Current State: 80:[88, 1], Operations: ['26+57=83', '83-82=1'] Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[88, 1], Operations: ['82-57=25', '26-25=1'] Exploring Operation: 88*1=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 88/1=88, Resulting Numbers: [88] 88,80 unequal: No Solution Exploring Operation: 88+1=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 88-1=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,2,3 Current State: 80:[31, 6], Operations: ['57-26=31', '88-82=6'] Exploring Operation: 31*6=186, Resulting Numbers: [186] 186,80 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 31+6=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,4,4 Current State: 80:[26, 51], Operations: ['88-57=31', '82-31=51'] Exploring Operation: 26+51=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 26*51=1326, Resulting Numbers: [1326] 1326,80 unequal: No Solution Exploring Operation: 51-26=25, Resulting Numbers: [25] 25,80 unequal: No Solution Moving to Node #0,1,3 Current State: 80:[88, 51], Operations: ['82-57=25', '26+25=51'] Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,80 unequal: No Solution Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,80 unequal: No Solution Moving to Node #0,2,4 Current State: 80:[82, 57], Operations: ['57-26=31', '88-31=57'] Exploring Operation: 82+57=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 82*57=4674, Resulting Numbers: [4674] 4674,80 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[88, 51], Operations: ['57-26=31', '82-31=51'] Exploring Operation: 88+51=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 88-51=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 88*51=4488, Resulting Numbers: [4488] 4488,80 unequal: No Solution Moving to Node #0,4,2 Current State: 80:[82, 57], Operations: ['88-57=31', '26+31=57'] Exploring Operation: 82+57=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 82-57=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 82*57=4674, Resulting Numbers: [4674] 4674,80 unequal: No Solution Moving to Node #0,1,4 Current State: 80:[26, 63], Operations: ['82-57=25', '88-25=63'] Exploring Operation: 26+63=89, Resulting Numbers: [89] 89,80 unequal: No Solution Exploring Operation: 26*63=1638, Resulting Numbers: [1638] 1638,80 unequal: No Solution Exploring Operation: 63-26=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[25, 62], Operations: ['82-57=25', '88-26=62'] Exploring Operation: 25*62=1550, Resulting Numbers: [1550] 1550,80 unequal: No Solution Exploring Operation: 25+62=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,4,3 Current State: 80:[31, 56], Operations: ['88-57=31', '82-26=56'] Exploring Operation: 56-31=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 31+56=87, Resulting Numbers: [87] 87,80 unequal: No Solution Exploring Operation: 31*56=1736, Resulting Numbers: [1736] 1736,80 unequal: No Solution Moving to Node #0,4,0 Current State: 80:[31, 108], Operations: ['88-57=31', '26+82=108'] Exploring Operation: 108-31=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 31*108=3348, Resulting Numbers: [3348] 3348,80 unequal: No Solution Exploring Operation: 31+108=139, Resulting Numbers: [139] 139,80 unequal: No Solution Moving to Node #0,1,1 Current State: 80:[25, 114], Operations: ['82-57=25', '26+88=114'] Exploring Operation: 25+114=139, Resulting Numbers: [139] 139,80 unequal: No Solution Exploring Operation: 25*114=2850, Resulting Numbers: [2850] 2850,80 unequal: No Solution Exploring Operation: 114-25=89, Resulting Numbers: [89] 89,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[88, 113], Operations: ['57-26=31', '82+31=113'] Exploring Operation: 88*113=9944, Resulting Numbers: [9944] 9944,80 unequal: No Solution Exploring Operation: 113-88=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 88+113=201, Resulting Numbers: [201] 201,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[82, 119], Operations: ['57-26=31', '88+31=119'] Exploring Operation: 119-82=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 82+119=201, Resulting Numbers: [201] 201,80 unequal: No Solution Exploring Operation: 82*119=9758, Resulting Numbers: [9758] 9758,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[83, 170], Operations: ['26+57=83', '82+88=170'] Exploring Operation: 83*170=14110, Resulting Numbers: [14110] 14110,80 unequal: No Solution Exploring Operation: 83+170=253, Resulting Numbers: [253] 253,80 unequal: No Solution Exploring Operation: 170-83=87, Resulting Numbers: [87] 87,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[88, 165], Operations: ['26+57=83', '82+83=165'] Exploring Operation: 165-88=77, Resulting Numbers: [77] 77,80 unequal: No Solution Exploring Operation: 88*165=14520, Resulting Numbers: [14520] 14520,80 unequal: No Solution Exploring Operation: 88+165=253, Resulting Numbers: [253] 253,80 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 84, 10, 58, 69 ]
63
[ "84-10=74", "69-58=11", "74-11=63" ]
Current State: 63:[84, 10, 58, 69], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [58, 69, 74] Generated Node #2: [58, 69, 74] from Operation: 84-10=74 Current State: 63:[58, 69, 74], Operations: ['84-10=74'] Exploring Operation: 69-58=11, Resulting Numbers: [74, 11] Generated Node #3: [74, 11] from Operation: 69-58=11 Current State: 63:[74, 11], Operations: ['84-10=74', '69-58=11'] Exploring Operation: 74-11=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[84, 10, 58, 69], Operations: [] Exploring Operation: 84-10=74, Resulting Numbers: [58, 69, 74] Generated Node #0,0: 63:[58, 69, 74] Operation: 84-10=74 Exploring Operation: 84-69=15, Resulting Numbers: [10, 58, 15] Generated Node #0,1: 63:[10, 58, 15] Operation: 84-69=15 Exploring Operation: 84-58=26, Resulting Numbers: [10, 69, 26] Generated Node #0,2: 63:[10, 69, 26] Operation: 84-58=26 Start Sub Search at level 1: Moving to Node #0,1 Current State: 63:[10, 58, 15], Operations: ['84-69=15'] Exploring Operation: 15-10=5, Resulting Numbers: [58, 5] Generated Node #0,1,0: 63:[58, 5] Operation: 15-10=5 Exploring Operation: 10+58=68, Resulting Numbers: [15, 68] Generated Node #0,1,1: 63:[15, 68] Operation: 10+58=68 Exploring Operation: 10+15=25, Resulting Numbers: [58, 25] Generated Node #0,1,2: 63:[58, 25] Operation: 10+15=25 Moving to Node #0,1,0 Current State: 63:[58, 5], Operations: ['84-69=15', '15-10=5'] Exploring Operation: 58*5=290, Resulting Numbers: [290] 290,63 unequal: No Solution Exploring Operation: 58-5=53, Resulting Numbers: [53] 53,63 unequal: No Solution Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[84, 10, 58, 69], Operations: [] Exploring Operation: 84-69=15, Resulting Numbers: [10, 58, 15] Generated Node #0,1: 63:[10, 58, 15] Operation: 84-69=15 Moving to Node #0,1 Current State: 63:[10, 58, 15], Operations: ['84-69=15'] Exploring Operation: 15-10=5, Resulting Numbers: [58, 5] Generated Node #0,1,0: 63:[58, 5] Operation: 15-10=5 Moving to Node #0,1,0 Current State: 63:[58, 5], Operations: ['84-69=15', '15-10=5'] Exploring Operation: 58+5=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 98, 1, 23, 5 ]
15
[ "98*1=98", "98-23=75", "75/5=15" ]
Current State: 15:[98, 1, 23, 5], Operations: [] Exploring Operation: 98*1=98, Resulting Numbers: [23, 5, 98] Generated Node #2: [23, 5, 98] from Operation: 98*1=98 Current State: 15:[23, 5, 98], Operations: ['98*1=98'] Exploring Operation: 98-23=75, Resulting Numbers: [5, 75] Generated Node #3: [5, 75] from Operation: 98-23=75 Current State: 15:[5, 75], Operations: ['98*1=98', '98-23=75'] Exploring Operation: 75/5=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[98, 1, 23, 5], Operations: [] Exploring Operation: 98-23=75, Resulting Numbers: [1, 5, 75] Generated Node #0,0: 15:[1, 5, 75] Operation: 98-23=75 Exploring Operation: 98-5=93, Resulting Numbers: [1, 23, 93] Generated Node #0,1: 15:[1, 23, 93] Operation: 98-5=93 Moving to Node #0,0 Current State: 15:[1, 5, 75], Operations: ['98-23=75'] Exploring Operation: 75-5=70, Resulting Numbers: [1, 70] Generated Node #0,0,0: 15:[1, 70] Operation: 75-5=70 Exploring Operation: 75/5=15, Resulting Numbers: [1, 15] Generated Node #0,0,1: 15:[1, 15] Operation: 75/5=15 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[1, 15], Operations: ['98-23=75', '75/5=15'] Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Moving to Node #0 Current State: 15:[98, 1, 23, 5], Operations: [] Exploring Operation: 98-23=75, Resulting Numbers: [1, 5, 75] Generated Node #0,0: 15:[1, 5, 75] Operation: 98-23=75 Moving to Node #0,0 Current State: 15:[1, 5, 75], Operations: ['98-23=75'] Exploring Operation: 75/5=15, Resulting Numbers: [1, 15] Generated Node #0,0,1: 15:[1, 15] Operation: 75/5=15 Moving to Node #0,0,1 Current State: 15:[1, 15], Operations: ['98-23=75', '75/5=15'] Exploring Operation: 1*15=15, Resulting Numbers: [15] 15,15 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 44, 73, 6, 85 ]
88
[ "85-73=12", "44*12=528", "528/6=88" ]
Current State: 88:[44, 73, 6, 85], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [44, 6, 12] Generated Node #2: [44, 6, 12] from Operation: 85-73=12 Current State: 88:[44, 6, 12], Operations: ['85-73=12'] Exploring Operation: 44*12=528, Resulting Numbers: [6, 528] Generated Node #3: [6, 528] from Operation: 44*12=528 Current State: 88:[6, 528], Operations: ['85-73=12', '44*12=528'] Exploring Operation: 528/6=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[44, 73, 6, 85], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [44, 6, 12] Generated Node #0,0: 88:[44, 6, 12] Operation: 85-73=12 Exploring Operation: 73+6=79, Resulting Numbers: [44, 85, 79] Generated Node #0,1: 88:[44, 85, 79] Operation: 73+6=79 Exploring Operation: 73-44=29, Resulting Numbers: [6, 85, 29] Generated Node #0,2: 88:[6, 85, 29] Operation: 73-44=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[44, 6, 12], Operations: ['85-73=12'] Exploring Operation: 6+12=18, Resulting Numbers: [44, 18] Generated Node #0,0,0: 88:[44, 18] Operation: 6+12=18 Exploring Operation: 12-6=6, Resulting Numbers: [44, 6] Generated Node #0,0,1: 88:[44, 6] Operation: 12-6=6 Exploring Operation: 12/6=2, Resulting Numbers: [44, 2] Generated Node #0,0,2: 88:[44, 2] Operation: 12/6=2 Moving to Node #0,0,2 Current State: 88:[44, 2], Operations: ['85-73=12', '12/6=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[44, 73, 6, 85], Operations: [] Exploring Operation: 85-73=12, Resulting Numbers: [44, 6, 12] Generated Node #0,0: 88:[44, 6, 12] Operation: 85-73=12 Moving to Node #0,0 Current State: 88:[44, 6, 12], Operations: ['85-73=12'] Exploring Operation: 12/6=2, Resulting Numbers: [44, 2] Generated Node #0,0,2: 88:[44, 2] Operation: 12/6=2 Moving to Node #0,0,2 Current State: 88:[44, 2], Operations: ['85-73=12', '12/6=2'] Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 18, 90, 3, 5 ]
72
[ "18*3=54", "90/5=18", "54+18=72" ]
Current State: 72:[18, 90, 3, 5], Operations: [] Exploring Operation: 18*3=54, Resulting Numbers: [90, 5, 54] Generated Node #2: [90, 5, 54] from Operation: 18*3=54 Current State: 72:[90, 5, 54], Operations: ['18*3=54'] Exploring Operation: 90/5=18, Resulting Numbers: [54, 18] Generated Node #3: [54, 18] from Operation: 90/5=18 Current State: 72:[54, 18], Operations: ['18*3=54', '90/5=18'] Exploring Operation: 54+18=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[18, 90, 3, 5], Operations: [] Exploring Operation: 90/5=18, Resulting Numbers: [18, 3, 18] Generated Node #0,0: 72:[18, 3, 18] Operation: 90/5=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[18, 3, 18], Operations: ['90/5=18'] Exploring Operation: 18/3=6, Resulting Numbers: [18, 6] Generated Node #0,0,0: 72:[18, 6] Operation: 18/3=6 Moving to Node #0,0,0 Current State: 72:[18, 6], Operations: ['90/5=18', '18/3=6'] Exploring Operation: 18+6=24, Resulting Numbers: [24] 24,72 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, 37, 8, 20 ]
85
[ "37-20=17", "8*17=136", "136-51=85" ]
Current State: 85:[51, 37, 8, 20], Operations: [] Exploring Operation: 37-20=17, Resulting Numbers: [51, 8, 17] Generated Node #2: [51, 8, 17] from Operation: 37-20=17 Current State: 85:[51, 8, 17], Operations: ['37-20=17'] Exploring Operation: 8*17=136, Resulting Numbers: [51, 136] Generated Node #3: [51, 136] from Operation: 8*17=136 Current State: 85:[51, 136], Operations: ['37-20=17', '8*17=136'] Exploring Operation: 136-51=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[51, 37, 8, 20], Operations: [] Exploring Operation: 51+37=88, Resulting Numbers: [8, 20, 88] Generated Node #0,0: 85:[8, 20, 88] Operation: 51+37=88 Exploring Operation: 51-20=31, Resulting Numbers: [37, 8, 31] Generated Node #0,1: 85:[37, 8, 31] Operation: 51-20=31 Exploring Operation: 37-20=17, Resulting Numbers: [51, 8, 17] Generated Node #0,2: 85:[51, 8, 17] Operation: 37-20=17 Exploring Operation: 51+20=71, Resulting Numbers: [37, 8, 71] Generated Node #0,3: 85:[37, 8, 71] Operation: 51+20=71 Exploring Operation: 51-37=14, Resulting Numbers: [8, 20, 14] Generated Node #0,4: 85:[8, 20, 14] Operation: 51-37=14 Moving to Node #0,0 Current State: 85:[8, 20, 88], Operations: ['51+37=88'] Exploring Operation: 88-8=80, Resulting Numbers: [20, 80] Generated Node #0,0,0: 85:[20, 80] Operation: 88-8=80 Exploring Operation: 8+88=96, Resulting Numbers: [20, 96] Generated Node #0,0,1: 85:[20, 96] Operation: 8+88=96 Exploring Operation: 8+20=28, Resulting Numbers: [88, 28] Generated Node #0,0,2: 85:[88, 28] Operation: 8+20=28 Exploring Operation: 20-8=12, Resulting Numbers: [88, 12] Generated Node #0,0,3: 85:[88, 12] Operation: 20-8=12 Exploring Operation: 88/8=11, Resulting Numbers: [20, 11] Generated Node #0,0,4: 85:[20, 11] Operation: 88/8=11 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[20, 80], Operations: ['51+37=88', '88-8=80'] Exploring Operation: 20+80=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 20*80=1600, Resulting Numbers: [1600] 1600,85 unequal: No Solution Exploring Operation: 80-20=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 80/20=4, Resulting Numbers: [4] 4,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 85:[88, 12], Operations: ['51+37=88', '20-8=12'] Exploring Operation: 88+12=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 88*12=1056, Resulting Numbers: [1056] 1056,85 unequal: No Solution Exploring Operation: 88-12=76, Resulting Numbers: [76] 76,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 85:[20, 11], Operations: ['51+37=88', '88/8=11'] Exploring Operation: 20+11=31, Resulting Numbers: [31] 31,85 unequal: No Solution Exploring Operation: 20*11=220, Resulting Numbers: [220] 220,85 unequal: No Solution Exploring Operation: 20-11=9, Resulting Numbers: [9] 9,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[20, 96], Operations: ['51+37=88', '8+88=96'] Exploring Operation: 20*96=1920, Resulting Numbers: [1920] 1920,85 unequal: No Solution Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 20+96=116, Resulting Numbers: [116] 116,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 85:[88, 28], Operations: ['51+37=88', '8+20=28'] Exploring Operation: 88+28=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 88-28=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 88*28=2464, Resulting Numbers: [2464] 2464,85 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: 85:[8, 20, 14], Operations: ['51-37=14'] Exploring Operation: 14-8=6, Resulting Numbers: [20, 6] Generated Node #0,4,0: 85:[20, 6] Operation: 14-8=6 Exploring Operation: 8+14=22, Resulting Numbers: [20, 22] Generated Node #0,4,1: 85:[20, 22] Operation: 8+14=22 Exploring Operation: 20-8=12, Resulting Numbers: [14, 12] Generated Node #0,4,2: 85:[14, 12] Operation: 20-8=12 Exploring Operation: 20-14=6, Resulting Numbers: [8, 6] Generated Node #0,4,3: 85:[8, 6] Operation: 20-14=6 Exploring Operation: 8+20=28, Resulting Numbers: [14, 28] Generated Node #0,4,4: 85:[14, 28] Operation: 8+20=28 Moving to Node #0,1 Current State: 85:[37, 8, 31], Operations: ['51-20=31'] Exploring Operation: 37-8=29, Resulting Numbers: [31, 29] Generated Node #0,1,0: 85:[31, 29] Operation: 37-8=29 Exploring Operation: 37+31=68, Resulting Numbers: [8, 68] Generated Node #0,1,1: 85:[8, 68] Operation: 37+31=68 Exploring Operation: 31-8=23, Resulting Numbers: [37, 23] Generated Node #0,1,2: 85:[37, 23] Operation: 31-8=23 Exploring Operation: 37+8=45, Resulting Numbers: [31, 45] Generated Node #0,1,3: 85:[31, 45] Operation: 37+8=45 Exploring Operation: 37-31=6, Resulting Numbers: [8, 6] Generated Node #0,1,4: 85:[8, 6] Operation: 37-31=6 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 85:[8, 6], Operations: ['51-20=31', '37-31=6'] Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,85 unequal: No Solution Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[8, 68], Operations: ['51-20=31', '37+31=68'] Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 8*68=544, Resulting Numbers: [544] 544,85 unequal: No Solution Exploring Operation: 8+68=76, Resulting Numbers: [76] 76,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[31, 29], Operations: ['51-20=31', '37-8=29'] Exploring Operation: 31+29=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 31*29=899, Resulting Numbers: [899] 899,85 unequal: No Solution Exploring Operation: 31-29=2, Resulting Numbers: [2] 2,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 85:[37, 23], Operations: ['51-20=31', '31-8=23'] Exploring Operation: 37+23=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 37-23=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 37*23=851, Resulting Numbers: [851] 851,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 85:[31, 45], Operations: ['51-20=31', '37+8=45'] Exploring Operation: 31*45=1395, Resulting Numbers: [1395] 1395,85 unequal: No Solution Exploring Operation: 45-31=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 31+45=76, Resulting Numbers: [76] 76,85 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: 85:[51, 8, 17], Operations: ['37-20=17'] Exploring Operation: 51/17=3, Resulting Numbers: [8, 3] Generated Node #0,2,0: 85:[8, 3] Operation: 51/17=3 Exploring Operation: 51-17=34, Resulting Numbers: [8, 34] Generated Node #0,2,1: 85:[8, 34] Operation: 51-17=34 Exploring Operation: 51-8=43, Resulting Numbers: [17, 43] Generated Node #0,2,2: 85:[17, 43] Operation: 51-8=43 Exploring Operation: 51+17=68, Resulting Numbers: [8, 68] Generated Node #0,2,3: 85:[8, 68] Operation: 51+17=68 Exploring Operation: 51+8=59, Resulting Numbers: [17, 59] Generated Node #0,2,4: 85:[17, 59] Operation: 51+8=59 Moving to Node #0,3 Current State: 85:[37, 8, 71], Operations: ['51+20=71'] Exploring Operation: 71-37=34, Resulting Numbers: [8, 34] Generated Node #0,3,0: 85:[8, 34] Operation: 71-37=34 Exploring Operation: 37+71=108, Resulting Numbers: [8, 108] Generated Node #0,3,1: 85:[8, 108] Operation: 37+71=108 Exploring Operation: 37-8=29, Resulting Numbers: [71, 29] Generated Node #0,3,2: 85:[71, 29] Operation: 37-8=29 Exploring Operation: 37+8=45, Resulting Numbers: [71, 45] Generated Node #0,3,3: 85:[71, 45] Operation: 37+8=45 Exploring Operation: 8+71=79, Resulting Numbers: [37, 79] Generated Node #0,3,4: 85:[37, 79] Operation: 8+71=79 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 85:[8, 34], Operations: ['51+20=71', '71-37=34'] Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 85:[8, 108], Operations: ['51+20=71', '37+71=108'] Exploring Operation: 8*108=864, Resulting Numbers: [864] 864,85 unequal: No Solution Exploring Operation: 108-8=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 8+108=116, Resulting Numbers: [116] 116,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 85:[71, 29], Operations: ['51+20=71', '37-8=29'] Exploring Operation: 71*29=2059, Resulting Numbers: [2059] 2059,85 unequal: No Solution Exploring Operation: 71+29=100, Resulting Numbers: [100] 100,85 unequal: No Solution Exploring Operation: 71-29=42, Resulting Numbers: [42] 42,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 85:[37, 79], Operations: ['51+20=71', '8+71=79'] Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 37+79=116, Resulting Numbers: [116] 116,85 unequal: No Solution Exploring Operation: 37*79=2923, Resulting Numbers: [2923] 2923,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 85:[71, 45], Operations: ['51+20=71', '37+8=45'] Exploring Operation: 71-45=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 71*45=3195, Resulting Numbers: [3195] 3195,85 unequal: No Solution Exploring Operation: 71+45=116, Resulting Numbers: [116] 116,85 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: 85:[20, 6], Operations: ['51-37=14', '14-8=6'] Exploring Operation: 20+6=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 20*6=120, Resulting Numbers: [120] 120,85 unequal: No Solution Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,85 unequal: No Solution Moving to Node #0,4,3 Current State: 85:[8, 6], Operations: ['51-37=14', '20-14=6'] Exploring Operation: 8+6=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 8*6=48, Resulting Numbers: [48] 48,85 unequal: No Solution Moving to Node #0,2,0 Current State: 85:[8, 3], Operations: ['37-20=17', '51/17=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,85 unequal: No Solution Exploring Operation: 8+3=11, Resulting Numbers: [11] 11,85 unequal: No Solution Exploring Operation: 8-3=5, Resulting Numbers: [5] 5,85 unequal: No Solution Moving to Node #0,4,1 Current State: 85:[20, 22], Operations: ['51-37=14', '8+14=22'] Exploring Operation: 22-20=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 20+22=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 20*22=440, Resulting Numbers: [440] 440,85 unequal: No Solution Moving to Node #0,4,2 Current State: 85:[14, 12], Operations: ['51-37=14', '20-8=12'] Exploring Operation: 14*12=168, Resulting Numbers: [168] 168,85 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 14+12=26, Resulting Numbers: [26] 26,85 unequal: No Solution Moving to Node #0,4,4 Current State: 85:[14, 28], Operations: ['51-37=14', '8+20=28'] Exploring Operation: 28/14=2, Resulting Numbers: [2] 2,85 unequal: No Solution Exploring Operation: 14*28=392, Resulting Numbers: [392] 392,85 unequal: No Solution Exploring Operation: 28-14=14, Resulting Numbers: [14] 14,85 unequal: No Solution Exploring Operation: 14+28=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,2,1 Current State: 85:[8, 34], Operations: ['37-20=17', '51-17=34'] Exploring Operation: 8*34=272, Resulting Numbers: [272] 272,85 unequal: No Solution Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 8+34=42, Resulting Numbers: [42] 42,85 unequal: No Solution Moving to Node #0,2,3 Current State: 85:[8, 68], Operations: ['37-20=17', '51+17=68'] Exploring Operation: 68-8=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 8*68=544, Resulting Numbers: [544] 544,85 unequal: No Solution Exploring Operation: 8+68=76, Resulting Numbers: [76] 76,85 unequal: No Solution Moving to Node #0,2,2 Current State: 85:[17, 43], Operations: ['37-20=17', '51-8=43'] Exploring Operation: 17+43=60, Resulting Numbers: [60] 60,85 unequal: No Solution Exploring Operation: 43-17=26, Resulting Numbers: [26] 26,85 unequal: No Solution Exploring Operation: 17*43=731, Resulting Numbers: [731] 731,85 unequal: No Solution Moving to Node #0,2,4 Current State: 85:[17, 59], Operations: ['37-20=17', '51+8=59'] Exploring Operation: 17+59=76, Resulting Numbers: [76] 76,85 unequal: No Solution Exploring Operation: 59-17=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 17*59=1003, Resulting Numbers: [1003] 1003,85 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 14, 23, 17, 48 ]
68
[ "14+23=37", "48-17=31", "37+31=68" ]
Current State: 68:[14, 23, 17, 48], Operations: [] Exploring Operation: 14+23=37, Resulting Numbers: [17, 48, 37] Generated Node #2: [17, 48, 37] from Operation: 14+23=37 Current State: 68:[17, 48, 37], Operations: ['14+23=37'] Exploring Operation: 48-17=31, Resulting Numbers: [37, 31] Generated Node #3: [37, 31] from Operation: 48-17=31 Current State: 68:[37, 31], Operations: ['14+23=37', '48-17=31'] Exploring Operation: 37+31=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[14, 23, 17, 48], Operations: [] Exploring Operation: 48-14=34, Resulting Numbers: [23, 17, 34] Generated Node #0,0: 68:[23, 17, 34] Operation: 48-14=34 Exploring Operation: 23+48=71, Resulting Numbers: [14, 17, 71] Generated Node #0,1: 68:[14, 17, 71] Operation: 23+48=71 Exploring Operation: 14+48=62, Resulting Numbers: [23, 17, 62] Generated Node #0,2: 68:[23, 17, 62] Operation: 14+48=62 Exploring Operation: 48-23=25, Resulting Numbers: [14, 17, 25] Generated Node #0,3: 68:[14, 17, 25] Operation: 48-23=25 Exploring Operation: 17+48=65, Resulting Numbers: [14, 23, 65] Generated Node #0,4: 68:[14, 23, 65] Operation: 17+48=65 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[23, 17, 34], Operations: ['48-14=34'] Exploring Operation: 34-17=17, Resulting Numbers: [23, 17] Generated Node #0,0,0: 68:[23, 17] Operation: 34-17=17 Exploring Operation: 23+17=40, Resulting Numbers: [34, 40] Generated Node #0,0,1: 68:[34, 40] Operation: 23+17=40 Exploring Operation: 23-17=6, Resulting Numbers: [34, 6] Generated Node #0,0,2: 68:[34, 6] Operation: 23-17=6 Exploring Operation: 34/17=2, Resulting Numbers: [23, 2] Generated Node #0,0,3: 68:[23, 2] Operation: 34/17=2 Exploring Operation: 34-23=11, Resulting Numbers: [17, 11] Generated Node #0,0,4: 68:[17, 11] Operation: 34-23=11 Moving to Node #0,0,2 Current State: 68:[34, 6], Operations: ['48-14=34', '23-17=6'] Exploring Operation: 34*6=204, Resulting Numbers: [204] 204,68 unequal: No Solution Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[34, 40], Operations: ['48-14=34', '23+17=40'] Exploring Operation: 34*40=1360, Resulting Numbers: [1360] 1360,68 unequal: No Solution Exploring Operation: 34+40=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 40-34=6, Resulting Numbers: [6] 6,68 unequal: No Solution Moving to Node #0,0,4 Current State: 68:[17, 11], Operations: ['48-14=34', '34-23=11'] Exploring Operation: 17+11=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,68 unequal: No Solution Exploring Operation: 17*11=187, Resulting Numbers: [187] 187,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[23, 17], Operations: ['48-14=34', '34-17=17'] Exploring Operation: 23*17=391, Resulting Numbers: [391] 391,68 unequal: No Solution Exploring Operation: 23+17=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 23-17=6, Resulting Numbers: [6] 6,68 unequal: No Solution Moving to Node #0,0,3 Current State: 68:[23, 2], Operations: ['48-14=34', '34/17=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,68 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,68 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[14, 17, 71], Operations: ['23+48=71'] Exploring Operation: 71-17=54, Resulting Numbers: [14, 54] Generated Node #0,1,0: 68:[14, 54] Operation: 71-17=54 Exploring Operation: 14+71=85, Resulting Numbers: [17, 85] Generated Node #0,1,1: 68:[17, 85] Operation: 14+71=85 Exploring Operation: 14+17=31, Resulting Numbers: [71, 31] Generated Node #0,1,2: 68:[71, 31] Operation: 14+17=31 Exploring Operation: 71-14=57, Resulting Numbers: [17, 57] Generated Node #0,1,3: 68:[17, 57] Operation: 71-14=57 Exploring Operation: 17-14=3, Resulting Numbers: [71, 3] Generated Node #0,1,4: 68:[71, 3] Operation: 17-14=3 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 68:[71, 3], Operations: ['23+48=71', '17-14=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[14, 23, 17, 48], Operations: [] Exploring Operation: 23+48=71, Resulting Numbers: [14, 17, 71] Generated Node #0,1: 68:[14, 17, 71] Operation: 23+48=71 Moving to Node #0,1 Current State: 68:[14, 17, 71], Operations: ['23+48=71'] Exploring Operation: 17-14=3, Resulting Numbers: [71, 3] Generated Node #0,1,4: 68:[71, 3] Operation: 17-14=3 Moving to Node #0,1,4 Current State: 68:[71, 3], Operations: ['23+48=71', '17-14=3'] Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_5
mult_heuristic
[ 42, 28, 24, 70 ]
18
[ "24*70=1680", "1680/28=60", "60-42=18" ]
Current State: 18:[42, 28, 24, 70], Operations: [] Exploring Operation: 24*70=1680, Resulting Numbers: [42, 28, 1680] Generated Node #2: [42, 28, 1680] from Operation: 24*70=1680 Current State: 18:[42, 28, 1680], Operations: ['24*70=1680'] Exploring Operation: 1680/28=60, Resulting Numbers: [42, 60] Generated Node #3: [42, 60] from Operation: 1680/28=60 Current State: 18:[42, 60], Operations: ['24*70=1680', '1680/28=60'] Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[42, 28, 24, 70], Operations: [] Exploring Operation: 42-28=14, Resulting Numbers: [24, 70, 14] Generated Node #0,0: 18:[24, 70, 14] Operation: 42-28=14 Exploring Operation: 42-24=18, Resulting Numbers: [28, 70, 18] Generated Node #0,1: 18:[28, 70, 18] Operation: 42-24=18 Exploring Operation: 70-28=42, Resulting Numbers: [42, 24, 42] Generated Node #0,2: 18:[42, 24, 42] Operation: 70-28=42 Exploring Operation: 70-42=28, Resulting Numbers: [28, 24, 28] Generated Node #0,3: 18:[28, 24, 28] Operation: 70-42=28 Moving to Node #0,3 Current State: 18:[28, 24, 28], Operations: ['70-42=28'] Exploring Operation: 28-28=0, Resulting Numbers: [24, 0] Generated Node #0,3,0: 18:[24, 0] Operation: 28-28=0 Exploring Operation: 28-24=4, Resulting Numbers: [28, 4] Generated Node #0,3,1: 18:[28, 4] Operation: 28-24=4 Exploring Operation: 28-24=4, Resulting Numbers: [28, 4] Generated Node #0,3,2: 18:[28, 4] Operation: 28-24=4 Exploring Operation: 28/28=1, Resulting Numbers: [24, 1] Generated Node #0,3,3: 18:[24, 1] Operation: 28/28=1 Moving to Node #0,2 Current State: 18:[42, 24, 42], Operations: ['70-28=42'] Exploring Operation: 42/42=1, Resulting Numbers: [24, 1] Generated Node #0,2,0: 18:[24, 1] Operation: 42/42=1 Exploring Operation: 42-24=18, Resulting Numbers: [42, 18] Generated Node #0,2,1: 18:[42, 18] Operation: 42-24=18 Exploring Operation: 42-24=18, Resulting Numbers: [42, 18] Generated Node #0,2,2: 18:[42, 18] Operation: 42-24=18 Exploring Operation: 42-42=0, Resulting Numbers: [24, 0] Generated Node #0,2,3: 18:[24, 0] Operation: 42-42=0 Moving to Node #0,1 Current State: 18:[28, 70, 18], Operations: ['42-24=18'] Exploring Operation: 28-18=10, Resulting Numbers: [70, 10] Generated Node #0,1,0: 18:[70, 10] Operation: 28-18=10 Exploring Operation: 28+70=98, Resulting Numbers: [18, 98] Generated Node #0,1,1: 18:[18, 98] Operation: 28+70=98 Exploring Operation: 70-28=42, Resulting Numbers: [18, 42] Generated Node #0,1,2: 18:[18, 42] Operation: 70-28=42 Exploring Operation: 70-18=52, Resulting Numbers: [28, 52] Generated Node #0,1,3: 18:[28, 52] Operation: 70-18=52 Moving to Node #0,0 Current State: 18:[24, 70, 14], Operations: ['42-28=14'] Exploring Operation: 24-14=10, Resulting Numbers: [70, 10] Generated Node #0,0,0: 18:[70, 10] Operation: 24-14=10 Exploring Operation: 70/14=5, Resulting Numbers: [24, 5] Generated Node #0,0,1: 18:[24, 5] Operation: 70/14=5 Exploring Operation: 70-24=46, Resulting Numbers: [14, 46] Generated Node #0,0,2: 18:[14, 46] Operation: 70-24=46 Exploring Operation: 70-14=56, Resulting Numbers: [24, 56] Generated Node #0,0,3: 18:[24, 56] Operation: 70-14=56 Moving to Node #0,3,3 Current State: 18:[24, 1], Operations: ['70-42=28', '28/28=1'] Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[24, 5], Operations: ['42-28=14', '70/14=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,18 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,18 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,18 unequal: No Solution Moving to Node #0,2,0 Current State: 18:[24, 1], Operations: ['70-28=42', '42/42=1'] Exploring Operation: 24-1=23, Resulting Numbers: [23] 23,18 unequal: No Solution Exploring Operation: 24*1=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24/1=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24+1=25, Resulting Numbers: [25] 25,18 unequal: No Solution Moving to Node #0,2,3 Current State: 18:[24, 0], Operations: ['70-28=42', '42-42=0'] Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,18 unequal: No Solution Moving to Node #0,3,0 Current State: 18:[24, 0], Operations: ['70-42=28', '28-28=0'] Exploring Operation: 24-0=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24+0=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 24*0=0, Resulting Numbers: [0] 0,18 unequal: No Solution Moving to Node #0,3,1 Current State: 18:[28, 4], Operations: ['70-42=28', '28-24=4'] Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,18 unequal: No Solution Moving to Node #0,3,2 Current State: 18:[28, 4], Operations: ['70-42=28', '28-24=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 28/4=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 28-4=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,18 unequal: No Solution Moving to Node #0,2,1 Current State: 18:[42, 18], Operations: ['70-28=42', '42-24=18'] Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,18 unequal: No Solution Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[18, 42], Operations: ['42-24=18', '70-28=42'] Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 18+42=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 18*42=756, Resulting Numbers: [756] 756,18 unequal: No Solution Moving to Node #0,2,2 Current State: 18:[42, 18], Operations: ['70-28=42', '42-24=18'] Exploring Operation: 42+18=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 42*18=756, Resulting Numbers: [756] 756,18 unequal: No Solution Exploring Operation: 42-18=24, Resulting Numbers: [24] 24,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[14, 46], Operations: ['42-28=14', '70-24=46'] Exploring Operation: 14*46=644, Resulting Numbers: [644] 644,18 unequal: No Solution Exploring Operation: 14+46=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 46-14=32, Resulting Numbers: [32] 32,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[24, 56], Operations: ['42-28=14', '70-14=56'] Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,18 unequal: No Solution Exploring Operation: 24*56=1344, Resulting Numbers: [1344] 1344,18 unequal: No Solution Moving to Node #0,1,3 Current State: 18:[28, 52], Operations: ['42-24=18', '70-18=52'] Exploring Operation: 28*52=1456, Resulting Numbers: [1456] 1456,18 unequal: No Solution Exploring Operation: 52-28=24, Resulting Numbers: [24] 24,18 unequal: No Solution Exploring Operation: 28+52=80, Resulting Numbers: [80] 80,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[70, 10], Operations: ['42-24=18', '28-18=10'] Exploring Operation: 70+10=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 70-10=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 70/10=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 70*10=700, Resulting Numbers: [700] 700,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[70, 10], Operations: ['42-28=14', '24-14=10'] Exploring Operation: 70-10=60, Resulting Numbers: [60] 60,18 unequal: No Solution Exploring Operation: 70+10=80, Resulting Numbers: [80] 80,18 unequal: No Solution Exploring Operation: 70*10=700, Resulting Numbers: [700] 700,18 unequal: No Solution Exploring Operation: 70/10=7, Resulting Numbers: [7] 7,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[18, 98], Operations: ['42-24=18', '28+70=98'] Exploring Operation: 18+98=116, Resulting Numbers: [116] 116,18 unequal: No Solution Exploring Operation: 18*98=1764, Resulting Numbers: [1764] 1764,18 unequal: No Solution Exploring Operation: 98-18=80, Resulting Numbers: [80] 80,18 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 54, 41, 78, 73 ]
100
[ "54+41=95", "78-73=5", "95+5=100" ]
Current State: 100:[54, 41, 78, 73], Operations: [] Exploring Operation: 54+41=95, Resulting Numbers: [78, 73, 95] Generated Node #2: [78, 73, 95] from Operation: 54+41=95 Current State: 100:[78, 73, 95], Operations: ['54+41=95'] Exploring Operation: 78-73=5, Resulting Numbers: [95, 5] Generated Node #3: [95, 5] from Operation: 78-73=5 Current State: 100:[95, 5], Operations: ['54+41=95', '78-73=5'] Exploring Operation: 95+5=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[54, 41, 78, 73], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [54, 41, 5] Generated Node #0,0: 100:[54, 41, 5] Operation: 78-73=5 Exploring Operation: 78-54=24, Resulting Numbers: [41, 73, 24] Generated Node #0,1: 100:[41, 73, 24] Operation: 78-54=24 Exploring Operation: 73-54=19, Resulting Numbers: [41, 78, 19] Generated Node #0,2: 100:[41, 78, 19] Operation: 73-54=19 Moving to Node #0,0 Current State: 100:[54, 41, 5], Operations: ['78-73=5'] Exploring Operation: 54+41=95, Resulting Numbers: [5, 95] Generated Node #0,0,0: 100:[5, 95] Operation: 54+41=95 Exploring Operation: 41+5=46, Resulting Numbers: [54, 46] Generated Node #0,0,1: 100:[54, 46] Operation: 41+5=46 Exploring Operation: 54-41=13, Resulting Numbers: [5, 13] Generated Node #0,0,2: 100:[5, 13] Operation: 54-41=13 Moving to Node #0,2 Current State: 100:[41, 78, 19], Operations: ['73-54=19'] Exploring Operation: 78-41=37, Resulting Numbers: [19, 37] Generated Node #0,2,0: 100:[19, 37] Operation: 78-41=37 Exploring Operation: 78+19=97, Resulting Numbers: [41, 97] Generated Node #0,2,1: 100:[41, 97] Operation: 78+19=97 Exploring Operation: 78-19=59, Resulting Numbers: [41, 59] Generated Node #0,2,2: 100:[41, 59] Operation: 78-19=59 Moving to Node #0,1 Current State: 100:[41, 73, 24], Operations: ['78-54=24'] Exploring Operation: 73-41=32, Resulting Numbers: [24, 32] Generated Node #0,1,0: 100:[24, 32] Operation: 73-41=32 Exploring Operation: 73+24=97, Resulting Numbers: [41, 97] Generated Node #0,1,1: 100:[41, 97] Operation: 73+24=97 Exploring Operation: 73-24=49, Resulting Numbers: [41, 49] Generated Node #0,1,2: 100:[41, 49] Operation: 73-24=49 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[24, 32], Operations: ['78-54=24', '73-41=32'] Exploring Operation: 32-24=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 24*32=768, Resulting Numbers: [768] 768,100 unequal: No Solution Exploring Operation: 24+32=56, Resulting Numbers: [56] 56,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[41, 49], Operations: ['78-54=24', '73-24=49'] Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,100 unequal: No Solution Exploring Operation: 41+49=90, Resulting Numbers: [90] 90,100 unequal: No Solution Exploring Operation: 41*49=2009, Resulting Numbers: [2009] 2009,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[41, 97], Operations: ['78-54=24', '73+24=97'] Exploring Operation: 41*97=3977, Resulting Numbers: [3977] 3977,100 unequal: No Solution Exploring Operation: 97-41=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 41+97=138, Resulting Numbers: [138] 138,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 100:[5, 13], Operations: ['78-73=5', '54-41=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,100 unequal: No Solution Exploring Operation: 5+13=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[5, 95], Operations: ['78-73=5', '54+41=95'] Exploring Operation: 95/5=19, Resulting Numbers: [19] 19,100 unequal: No Solution Exploring Operation: 95-5=90, Resulting Numbers: [90] 90,100 unequal: No Solution Exploring Operation: 5+95=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[54, 41, 78, 73], Operations: [] Exploring Operation: 78-73=5, Resulting Numbers: [54, 41, 5] Generated Node #0,0: 100:[54, 41, 5] Operation: 78-73=5 Moving to Node #0,0 Current State: 100:[54, 41, 5], Operations: ['78-73=5'] Exploring Operation: 54+41=95, Resulting Numbers: [5, 95] Generated Node #0,0,0: 100:[5, 95] Operation: 54+41=95 Moving to Node #0,0,0 Current State: 100:[5, 95], Operations: ['78-73=5', '54+41=95'] Exploring Operation: 5+95=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.97309
hs_3
sum_heuristic
[ 6, 99, 26, 93 ]
14
[ "6+99=105", "26+93=119", "119-105=14" ]
Current State: 14:[6, 99, 26, 93], Operations: [] Exploring Operation: 6+99=105, Resulting Numbers: [26, 93, 105] Generated Node #2: [26, 93, 105] from Operation: 6+99=105 Current State: 14:[26, 93, 105], Operations: ['6+99=105'] Exploring Operation: 26+93=119, Resulting Numbers: [105, 119] Generated Node #3: [105, 119] from Operation: 26+93=119 Current State: 14:[105, 119], Operations: ['6+99=105', '26+93=119'] Exploring Operation: 119-105=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[6, 99, 26, 93], Operations: [] Exploring Operation: 99-93=6, Resulting Numbers: [6, 26, 6] Generated Node #0,0: 14:[6, 26, 6] Operation: 99-93=6 Exploring Operation: 99-26=73, Resulting Numbers: [6, 93, 73] Generated Node #0,1: 14:[6, 93, 73] Operation: 99-26=73 Exploring Operation: 93-26=67, Resulting Numbers: [6, 99, 67] Generated Node #0,2: 14:[6, 99, 67] Operation: 93-26=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[6, 26, 6], Operations: ['99-93=6'] Exploring Operation: 6/6=1, Resulting Numbers: [26, 1] Generated Node #0,0,0: 14:[26, 1] Operation: 6/6=1 Exploring Operation: 26-6=20, Resulting Numbers: [6, 20] Generated Node #0,0,1: 14:[6, 20] Operation: 26-6=20 Exploring Operation: 26-6=20, Resulting Numbers: [6, 20] Generated Node #0,0,2: 14:[6, 20] Operation: 26-6=20 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 14:[6, 20], Operations: ['99-93=6', '26-6=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[6, 99, 26, 93], Operations: [] Exploring Operation: 99-93=6, Resulting Numbers: [6, 26, 6] Generated Node #0,0: 14:[6, 26, 6] Operation: 99-93=6 Moving to Node #0,0 Current State: 14:[6, 26, 6], Operations: ['99-93=6'] Exploring Operation: 26-6=20, Resulting Numbers: [6, 20] Generated Node #0,0,1: 14:[6, 20] Operation: 26-6=20 Moving to Node #0,0,1 Current State: 14:[6, 20], Operations: ['99-93=6', '26-6=20'] Exploring Operation: 20-6=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 70, 11, 18, 3 ]
38
[ "70-11=59", "18+3=21", "59-21=38" ]
Current State: 38:[70, 11, 18, 3], Operations: [] Exploring Operation: 70-11=59, Resulting Numbers: [18, 3, 59] Generated Node #2: [18, 3, 59] from Operation: 70-11=59 Current State: 38:[18, 3, 59], Operations: ['70-11=59'] Exploring Operation: 18+3=21, Resulting Numbers: [59, 21] Generated Node #3: [59, 21] from Operation: 18+3=21 Current State: 38:[59, 21], Operations: ['70-11=59', '18+3=21'] Exploring Operation: 59-21=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[70, 11, 18, 3], Operations: [] Exploring Operation: 18-11=7, Resulting Numbers: [70, 3, 7] Generated Node #0,0: 38:[70, 3, 7] Operation: 18-11=7 Exploring Operation: 70-18=52, Resulting Numbers: [11, 3, 52] Generated Node #0,1: 38:[11, 3, 52] Operation: 70-18=52 Exploring Operation: 11+3=14, Resulting Numbers: [70, 18, 14] Generated Node #0,2: 38:[70, 18, 14] Operation: 11+3=14 Exploring Operation: 70-3=67, Resulting Numbers: [11, 18, 67] Generated Node #0,3: 38:[11, 18, 67] Operation: 70-3=67 Exploring Operation: 70-11=59, Resulting Numbers: [18, 3, 59] Generated Node #0,4: 38:[18, 3, 59] Operation: 70-11=59 Moving to Node #0,1 Current State: 38:[11, 3, 52], Operations: ['70-18=52'] Exploring Operation: 11-3=8, Resulting Numbers: [52, 8] Generated Node #0,1,0: 38:[52, 8] Operation: 11-3=8 Exploring Operation: 11*3=33, Resulting Numbers: [52, 33] Generated Node #0,1,1: 38:[52, 33] Operation: 11*3=33 Exploring Operation: 11+3=14, Resulting Numbers: [52, 14] Generated Node #0,1,2: 38:[52, 14] Operation: 11+3=14 Exploring Operation: 52-11=41, Resulting Numbers: [3, 41] Generated Node #0,1,3: 38:[3, 41] Operation: 52-11=41 Exploring Operation: 52-3=49, Resulting Numbers: [11, 49] Generated Node #0,1,4: 38:[11, 49] Operation: 52-3=49 Moving to Node #0,4 Current State: 38:[18, 3, 59], Operations: ['70-11=59'] Exploring Operation: 18-3=15, Resulting Numbers: [59, 15] Generated Node #0,4,0: 38:[59, 15] Operation: 18-3=15 Exploring Operation: 18+3=21, Resulting Numbers: [59, 21] Generated Node #0,4,1: 38:[59, 21] Operation: 18+3=21 Exploring Operation: 59-3=56, Resulting Numbers: [18, 56] Generated Node #0,4,2: 38:[18, 56] Operation: 59-3=56 Exploring Operation: 59-18=41, Resulting Numbers: [3, 41] Generated Node #0,4,3: 38:[3, 41] Operation: 59-18=41 Exploring Operation: 18/3=6, Resulting Numbers: [59, 6] Generated Node #0,4,4: 38:[59, 6] Operation: 18/3=6 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 38:[3, 41], Operations: ['70-11=59', '59-18=41'] Exploring Operation: 3*41=123, Resulting Numbers: [123] 123,38 unequal: No Solution Exploring Operation: 3+41=44, Resulting Numbers: [44] 44,38 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[70, 11, 18, 3], Operations: [] Exploring Operation: 70-11=59, Resulting Numbers: [18, 3, 59] Generated Node #0,4: 38:[18, 3, 59] Operation: 70-11=59 Moving to Node #0,4 Current State: 38:[18, 3, 59], Operations: ['70-11=59'] Exploring Operation: 59-18=41, Resulting Numbers: [3, 41] Generated Node #0,4,3: 38:[3, 41] Operation: 59-18=41 Moving to Node #0,4,3 Current State: 38:[3, 41], Operations: ['70-11=59', '59-18=41'] Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_5
sum_heuristic
[ 5, 47, 62, 48 ]
68
[ "47-5=42", "62+48=110", "110-42=68" ]
Current State: 68:[5, 47, 62, 48], Operations: [] Exploring Operation: 47-5=42, Resulting Numbers: [62, 48, 42] Generated Node #2: [62, 48, 42] from Operation: 47-5=42 Current State: 68:[62, 48, 42], Operations: ['47-5=42'] Exploring Operation: 62+48=110, Resulting Numbers: [42, 110] Generated Node #3: [42, 110] from Operation: 62+48=110 Current State: 68:[42, 110], Operations: ['47-5=42', '62+48=110'] Exploring Operation: 110-42=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[5, 47, 62, 48], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [5, 62, 1] Generated Node #0,0: 68:[5, 62, 1] Operation: 48-47=1 Exploring Operation: 62-48=14, Resulting Numbers: [5, 47, 14] Generated Node #0,1: 68:[5, 47, 14] Operation: 62-48=14 Exploring Operation: 62-47=15, Resulting Numbers: [5, 48, 15] Generated Node #0,2: 68:[5, 48, 15] Operation: 62-47=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 68:[5, 62, 1], Operations: ['48-47=1'] Exploring Operation: 5+62=67, Resulting Numbers: [1, 67] Generated Node #0,0,0: 68:[1, 67] Operation: 5+62=67 Exploring Operation: 5-1=4, Resulting Numbers: [62, 4] Generated Node #0,0,1: 68:[62, 4] Operation: 5-1=4 Exploring Operation: 62+1=63, Resulting Numbers: [5, 63] Generated Node #0,0,2: 68:[5, 63] Operation: 62+1=63 Moving to Node #0,0,0 Current State: 68:[1, 67], Operations: ['48-47=1', '5+62=67'] Exploring Operation: 1*67=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 1+67=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[5, 47, 62, 48], Operations: [] Exploring Operation: 48-47=1, Resulting Numbers: [5, 62, 1] Generated Node #0,0: 68:[5, 62, 1] Operation: 48-47=1 Moving to Node #0,0 Current State: 68:[5, 62, 1], Operations: ['48-47=1'] Exploring Operation: 5+62=67, Resulting Numbers: [1, 67] Generated Node #0,0,0: 68:[1, 67] Operation: 5+62=67 Moving to Node #0,0,0 Current State: 68:[1, 67], Operations: ['48-47=1', '5+62=67'] Exploring Operation: 1+67=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 91, 34, 38, 18 ]
19
[ "38-34=4", "18*4=72", "91-72=19" ]
Current State: 19:[91, 34, 38, 18], Operations: [] Exploring Operation: 38-34=4, Resulting Numbers: [91, 18, 4] Generated Node #2: [91, 18, 4] from Operation: 38-34=4 Current State: 19:[91, 18, 4], Operations: ['38-34=4'] Exploring Operation: 18*4=72, Resulting Numbers: [91, 72] Generated Node #3: [91, 72] from Operation: 18*4=72 Current State: 19:[91, 72], Operations: ['38-34=4', '18*4=72'] Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[91, 34, 38, 18], Operations: [] Exploring Operation: 91-34=57, Resulting Numbers: [38, 18, 57] Generated Node #0,0: 19:[38, 18, 57] Operation: 91-34=57 Exploring Operation: 91-38=53, Resulting Numbers: [34, 18, 53] Generated Node #0,1: 19:[34, 18, 53] Operation: 91-38=53 Moving to Node #0,1 Current State: 19:[34, 18, 53], Operations: ['91-38=53'] Exploring Operation: 53-34=19, Resulting Numbers: [18, 19] Generated Node #0,1,0: 19:[18, 19] Operation: 53-34=19 Exploring Operation: 53-18=35, Resulting Numbers: [34, 35] Generated Node #0,1,1: 19:[34, 35] Operation: 53-18=35 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[18, 19], Operations: ['91-38=53', '53-34=19'] Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[34, 35], Operations: ['91-38=53', '53-18=35'] Exploring Operation: 34+35=69, Resulting Numbers: [69] 69,19 unequal: No Solution Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,19 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: 19:[38, 18, 57], Operations: ['91-34=57'] Exploring Operation: 38-18=20, Resulting Numbers: [57, 20] Generated Node #0,0,0: 19:[57, 20] Operation: 38-18=20 Exploring Operation: 57-38=19, Resulting Numbers: [18, 19] Generated Node #0,0,1: 19:[18, 19] Operation: 57-38=19 Moving to Node #0,0,1 Current State: 19:[18, 19], Operations: ['91-34=57', '57-38=19'] Exploring Operation: 18+19=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 19-18=1, Resulting Numbers: [1] 1,19 unequal: No Solution Moving to Node #0,0,0 Current State: 19:[57, 20], Operations: ['91-34=57', '38-18=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,19 unequal: No Solution Exploring Operation: 57+20=77, Resulting Numbers: [77] 77,19 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 3, 63, 70, 72 ]
18
[ "3+63=66", "70-66=4", "72/4=18" ]
Current State: 18:[3, 63, 70, 72], Operations: [] Exploring Operation: 3+63=66, Resulting Numbers: [70, 72, 66] Generated Node #2: [70, 72, 66] from Operation: 3+63=66 Current State: 18:[70, 72, 66], Operations: ['3+63=66'] Exploring Operation: 70-66=4, Resulting Numbers: [72, 4] Generated Node #3: [72, 4] from Operation: 70-66=4 Current State: 18:[72, 4], Operations: ['3+63=66', '70-66=4'] Exploring Operation: 72/4=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[3, 63, 70, 72], Operations: [] Exploring Operation: 72-63=9, Resulting Numbers: [3, 70, 9] Generated Node #0,0: 18:[3, 70, 9] Operation: 72-63=9 Exploring Operation: 72-70=2, Resulting Numbers: [3, 63, 2] Generated Node #0,1: 18:[3, 63, 2] Operation: 72-70=2 Moving to Node #0,1 Current State: 18:[3, 63, 2], Operations: ['72-70=2'] Exploring Operation: 63/3=21, Resulting Numbers: [2, 21] Generated Node #0,1,0: 18:[2, 21] Operation: 63/3=21 Exploring Operation: 63-3=60, Resulting Numbers: [2, 60] Generated Node #0,1,1: 18:[2, 60] Operation: 63-3=60 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[2, 21], Operations: ['72-70=2', '63/3=21'] Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[2, 60], Operations: ['72-70=2', '63-3=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 60/2=30, Resulting Numbers: [30] 30,18 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: 18:[3, 70, 9], Operations: ['72-63=9'] Exploring Operation: 70-9=61, Resulting Numbers: [3, 61] Generated Node #0,0,0: 18:[3, 61] Operation: 70-9=61 Exploring Operation: 70-3=67, Resulting Numbers: [9, 67] Generated Node #0,0,1: 18:[9, 67] Operation: 70-3=67 Moving to Node #0,0,0 Current State: 18:[3, 61], Operations: ['72-63=9', '70-9=61'] Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,18 unequal: No Solution Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[9, 67], Operations: ['72-63=9', '70-3=67'] Exploring Operation: 9+67=76, Resulting Numbers: [76] 76,18 unequal: No Solution Exploring Operation: 67-9=58, Resulting Numbers: [58] 58,18 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 58, 61, 56, 11 ]
23
[ "61-58=3", "11*3=33", "56-33=23" ]
Current State: 23:[58, 61, 56, 11], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [56, 11, 3] Generated Node #2: [56, 11, 3] from Operation: 61-58=3 Current State: 23:[56, 11, 3], Operations: ['61-58=3'] Exploring Operation: 11*3=33, Resulting Numbers: [56, 33] Generated Node #3: [56, 33] from Operation: 11*3=33 Current State: 23:[56, 33], Operations: ['61-58=3', '11*3=33'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[58, 61, 56, 11], Operations: [] Exploring Operation: 61-56=5, Resulting Numbers: [58, 11, 5] Generated Node #0,0: 23:[58, 11, 5] Operation: 61-56=5 Exploring Operation: 61-11=50, Resulting Numbers: [58, 56, 50] Generated Node #0,1: 23:[58, 56, 50] Operation: 61-11=50 Exploring Operation: 58-11=47, Resulting Numbers: [61, 56, 47] Generated Node #0,2: 23:[61, 56, 47] Operation: 58-11=47 Exploring Operation: 58-56=2, Resulting Numbers: [61, 11, 2] Generated Node #0,3: 23:[61, 11, 2] Operation: 58-56=2 Exploring Operation: 61-58=3, Resulting Numbers: [56, 11, 3] Generated Node #0,4: 23:[56, 11, 3] Operation: 61-58=3 Moving to Node #0,0 Current State: 23:[58, 11, 5], Operations: ['61-56=5'] Exploring Operation: 11-5=6, Resulting Numbers: [58, 6] Generated Node #0,0,0: 23:[58, 6] Operation: 11-5=6 Exploring Operation: 11+5=16, Resulting Numbers: [58, 16] Generated Node #0,0,1: 23:[58, 16] Operation: 11+5=16 Exploring Operation: 58-11=47, Resulting Numbers: [5, 47] Generated Node #0,0,2: 23:[5, 47] Operation: 58-11=47 Exploring Operation: 58+5=63, Resulting Numbers: [11, 63] Generated Node #0,0,3: 23:[11, 63] Operation: 58+5=63 Exploring Operation: 58-5=53, Resulting Numbers: [11, 53] Generated Node #0,0,4: 23:[11, 53] Operation: 58-5=53 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 23:[58, 16], Operations: ['61-56=5', '11+5=16'] Exploring Operation: 58+16=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 58*16=928, Resulting Numbers: [928] 928,23 unequal: No Solution Exploring Operation: 58-16=42, Resulting Numbers: [42] 42,23 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 #0,0,2 Current State: 23:[5, 47], Operations: ['61-56=5', '58-11=47'] Exploring Operation: 5*47=235, Resulting Numbers: [235] 235,23 unequal: No Solution Exploring Operation: 5+47=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,23 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 #0,0,4 Current State: 23:[11, 53], Operations: ['61-56=5', '58-5=53'] Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,23 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,23 unequal: No Solution Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,23 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 #0,0,0 Current State: 23:[58, 6], Operations: ['61-56=5', '11-5=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 58*6=348, Resulting Numbers: [348] 348,23 unequal: No Solution Exploring Operation: 58+6=64, Resulting Numbers: [64] 64,23 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 #0,0,3 Current State: 23:[11, 63], Operations: ['61-56=5', '58+5=63'] Exploring Operation: 11+63=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 11*63=693, Resulting Numbers: [693] 693,23 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: 23:[56, 11, 3], Operations: ['61-58=3'] Exploring Operation: 56-11=45, Resulting Numbers: [3, 45] Generated Node #0,4,0: 23:[3, 45] Operation: 56-11=45 Exploring Operation: 11+3=14, Resulting Numbers: [56, 14] Generated Node #0,4,1: 23:[56, 14] Operation: 11+3=14 Exploring Operation: 56+3=59, Resulting Numbers: [11, 59] Generated Node #0,4,2: 23:[11, 59] Operation: 56+3=59 Exploring Operation: 56-3=53, Resulting Numbers: [11, 53] Generated Node #0,4,3: 23:[11, 53] Operation: 56-3=53 Exploring Operation: 11*3=33, Resulting Numbers: [56, 33] Generated Node #0,4,4: 23:[56, 33] Operation: 11*3=33 Moving to Node #0,3 Current State: 23:[61, 11, 2], Operations: ['58-56=2'] Exploring Operation: 61-11=50, Resulting Numbers: [2, 50] Generated Node #0,3,0: 23:[2, 50] Operation: 61-11=50 Exploring Operation: 11*2=22, Resulting Numbers: [61, 22] Generated Node #0,3,1: 23:[61, 22] Operation: 11*2=22 Exploring Operation: 11+2=13, Resulting Numbers: [61, 13] Generated Node #0,3,2: 23:[61, 13] Operation: 11+2=13 Exploring Operation: 61-2=59, Resulting Numbers: [11, 59] Generated Node #0,3,3: 23:[11, 59] Operation: 61-2=59 Exploring Operation: 61+2=63, Resulting Numbers: [11, 63] Generated Node #0,3,4: 23:[11, 63] Operation: 61+2=63 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 23:[61, 22], Operations: ['58-56=2', '11*2=22'] Exploring Operation: 61*22=1342, Resulting Numbers: [1342] 1342,23 unequal: No Solution Exploring Operation: 61+22=83, Resulting Numbers: [83] 83,23 unequal: No Solution Exploring Operation: 61-22=39, Resulting Numbers: [39] 39,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 23:[2, 50], Operations: ['58-56=2', '61-11=50'] Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,23 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 23:[61, 13], Operations: ['58-56=2', '11+2=13'] Exploring Operation: 61+13=74, Resulting Numbers: [74] 74,23 unequal: No Solution Exploring Operation: 61*13=793, Resulting Numbers: [793] 793,23 unequal: No Solution Exploring Operation: 61-13=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 #0,3,3 Current State: 23:[11, 59], Operations: ['58-56=2', '61-2=59'] Exploring Operation: 11*59=649, Resulting Numbers: [649] 649,23 unequal: No Solution Exploring Operation: 59-11=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 11+59=70, Resulting Numbers: [70] 70,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 23:[11, 63], Operations: ['58-56=2', '61+2=63'] Exploring Operation: 63-11=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 11*63=693, Resulting Numbers: [693] 693,23 unequal: No Solution Exploring Operation: 11+63=74, Resulting Numbers: [74] 74,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 23:[58, 56, 50], Operations: ['61-11=50'] Exploring Operation: 56-50=6, Resulting Numbers: [58, 6] Generated Node #0,1,0: 23:[58, 6] Operation: 56-50=6 Exploring Operation: 58-56=2, Resulting Numbers: [50, 2] Generated Node #0,1,1: 23:[50, 2] Operation: 58-56=2 Exploring Operation: 58+50=108, Resulting Numbers: [56, 108] Generated Node #0,1,2: 23:[56, 108] Operation: 58+50=108 Exploring Operation: 58-50=8, Resulting Numbers: [56, 8] Generated Node #0,1,3: 23:[56, 8] Operation: 58-50=8 Exploring Operation: 58+56=114, Resulting Numbers: [50, 114] Generated Node #0,1,4: 23:[50, 114] Operation: 58+56=114 Moving to Node #0,2 Current State: 23:[61, 56, 47], Operations: ['58-11=47'] Exploring Operation: 61-47=14, Resulting Numbers: [56, 14] Generated Node #0,2,0: 23:[56, 14] Operation: 61-47=14 Exploring Operation: 61+56=117, Resulting Numbers: [47, 117] Generated Node #0,2,1: 23:[47, 117] Operation: 61+56=117 Exploring Operation: 61-56=5, Resulting Numbers: [47, 5] Generated Node #0,2,2: 23:[47, 5] Operation: 61-56=5 Exploring Operation: 56-47=9, Resulting Numbers: [61, 9] Generated Node #0,2,3: 23:[61, 9] Operation: 56-47=9 Exploring Operation: 61+47=108, Resulting Numbers: [56, 108] Generated Node #0,2,4: 23:[56, 108] Operation: 61+47=108 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 23:[56, 14], Operations: ['58-11=47', '61-47=14'] Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,23 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 23:[47, 5], Operations: ['58-11=47', '61-56=5'] Exploring Operation: 47+5=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 47*5=235, Resulting Numbers: [235] 235,23 unequal: No Solution Exploring Operation: 47-5=42, Resulting Numbers: [42] 42,23 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 #0,2,3 Current State: 23:[61, 9], Operations: ['58-11=47', '56-47=9'] Exploring Operation: 61*9=549, Resulting Numbers: [549] 549,23 unequal: No Solution Exploring Operation: 61-9=52, Resulting Numbers: [52] 52,23 unequal: No Solution Exploring Operation: 61+9=70, Resulting Numbers: [70] 70,23 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 #0,2,1 Current State: 23:[47, 117], Operations: ['58-11=47', '61+56=117'] Exploring Operation: 47+117=164, Resulting Numbers: [164] 164,23 unequal: No Solution Exploring Operation: 117-47=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 47*117=5499, Resulting Numbers: [5499] 5499,23 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 #0,2,4 Current State: 23:[56, 108], Operations: ['58-11=47', '61+47=108'] Exploring Operation: 56*108=6048, Resulting Numbers: [6048] 6048,23 unequal: No Solution Exploring Operation: 56+108=164, Resulting Numbers: [164] 164,23 unequal: No Solution Exploring Operation: 108-56=52, Resulting Numbers: [52] 52,23 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: 23:[3, 45], Operations: ['61-58=3', '56-11=45'] Exploring Operation: 45/3=15, Resulting Numbers: [15] 15,23 unequal: No Solution Exploring Operation: 45-3=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 3+45=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 3*45=135, Resulting Numbers: [135] 135,23 unequal: No Solution Moving to Node #0,4,3 Current State: 23:[11, 53], Operations: ['61-58=3', '56-3=53'] Exploring Operation: 11*53=583, Resulting Numbers: [583] 583,23 unequal: No Solution Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 11+53=64, Resulting Numbers: [64] 64,23 unequal: No Solution Moving to Node #0,4,1 Current State: 23:[56, 14], Operations: ['61-58=3', '11+3=14'] Exploring Operation: 56-14=42, Resulting Numbers: [42] 42,23 unequal: No Solution Exploring Operation: 56+14=70, Resulting Numbers: [70] 70,23 unequal: No Solution Exploring Operation: 56/14=4, Resulting Numbers: [4] 4,23 unequal: No Solution Exploring Operation: 56*14=784, Resulting Numbers: [784] 784,23 unequal: No Solution Moving to Node #0,4,4 Current State: 23:[56, 33], Operations: ['61-58=3', '11*3=33'] Exploring Operation: 56*33=1848, Resulting Numbers: [1848] 1848,23 unequal: No Solution Exploring Operation: 56+33=89, Resulting Numbers: [89] 89,23 unequal: No Solution Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[58, 61, 56, 11], Operations: [] Exploring Operation: 61-58=3, Resulting Numbers: [56, 11, 3] Generated Node #0,4: 23:[56, 11, 3] Operation: 61-58=3 Moving to Node #0,4 Current State: 23:[56, 11, 3], Operations: ['61-58=3'] Exploring Operation: 11*3=33, Resulting Numbers: [56, 33] Generated Node #0,4,4: 23:[56, 33] Operation: 11*3=33 Moving to Node #0,4,4 Current State: 23:[56, 33], Operations: ['61-58=3', '11*3=33'] Exploring Operation: 56-33=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
0.917535
hs_5
mult_heuristic
[ 31, 20, 61, 18 ]
27
[ "61-31=30", "18*30=540", "540/20=27" ]
Current State: 27:[31, 20, 61, 18], Operations: [] Exploring Operation: 61-31=30, Resulting Numbers: [20, 18, 30] Generated Node #2: [20, 18, 30] from Operation: 61-31=30 Current State: 27:[20, 18, 30], Operations: ['61-31=30'] Exploring Operation: 18*30=540, Resulting Numbers: [20, 540] Generated Node #3: [20, 540] from Operation: 18*30=540 Current State: 27:[20, 540], Operations: ['61-31=30', '18*30=540'] Exploring Operation: 540/20=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[31, 20, 61, 18], Operations: [] Exploring Operation: 61-31=30, Resulting Numbers: [20, 18, 30] Generated Node #0,0: 27:[20, 18, 30] Operation: 61-31=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[20, 18, 30], Operations: ['61-31=30'] Exploring Operation: 20-18=2, Resulting Numbers: [30, 2] Generated Node #0,0,0: 27:[30, 2] Operation: 20-18=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[30, 2], Operations: ['61-31=30', '20-18=2'] Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 12, 2, 28, 49 ]
41
[ "28-12=16", "16/2=8", "49-8=41" ]
Current State: 41:[12, 2, 28, 49], Operations: [] Exploring Operation: 28-12=16, Resulting Numbers: [2, 49, 16] Generated Node #2: [2, 49, 16] from Operation: 28-12=16 Current State: 41:[2, 49, 16], Operations: ['28-12=16'] Exploring Operation: 16/2=8, Resulting Numbers: [49, 8] Generated Node #3: [49, 8] from Operation: 16/2=8 Current State: 41:[49, 8], Operations: ['28-12=16', '16/2=8'] Exploring Operation: 49-8=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[12, 2, 28, 49], Operations: [] Exploring Operation: 12+2=14, Resulting Numbers: [28, 49, 14] Generated Node #0,0: 41:[28, 49, 14] Operation: 12+2=14 Exploring Operation: 12*2=24, Resulting Numbers: [28, 49, 24] Generated Node #0,1: 41:[28, 49, 24] Operation: 12*2=24 Exploring Operation: 12+28=40, Resulting Numbers: [2, 49, 40] Generated Node #0,2: 41:[2, 49, 40] Operation: 12+28=40 Moving to Node #0,1 Current State: 41:[28, 49, 24], Operations: ['12*2=24'] Exploring Operation: 49-28=21, Resulting Numbers: [24, 21] Generated Node #0,1,0: 41:[24, 21] Operation: 49-28=21 Exploring Operation: 49-24=25, Resulting Numbers: [28, 25] Generated Node #0,1,1: 41:[28, 25] Operation: 49-24=25 Exploring Operation: 28+24=52, Resulting Numbers: [49, 52] Generated Node #0,1,2: 41:[49, 52] Operation: 28+24=52 Moving to Node #0,0 Current State: 41:[28, 49, 14], Operations: ['12+2=14'] Exploring Operation: 49-14=35, Resulting Numbers: [28, 35] Generated Node #0,0,0: 41:[28, 35] Operation: 49-14=35 Exploring Operation: 28-14=14, Resulting Numbers: [49, 14] Generated Node #0,0,1: 41:[49, 14] Operation: 28-14=14 Exploring Operation: 28+14=42, Resulting Numbers: [49, 42] Generated Node #0,0,2: 41:[49, 42] Operation: 28+14=42 Moving to Node #0,2 Current State: 41:[2, 49, 40], Operations: ['12+28=40'] Exploring Operation: 2+49=51, Resulting Numbers: [40, 51] Generated Node #0,2,0: 41:[40, 51] Operation: 2+49=51 Exploring Operation: 2+40=42, Resulting Numbers: [49, 42] Generated Node #0,2,1: 41:[49, 42] Operation: 2+40=42 Exploring Operation: 49-2=47, Resulting Numbers: [40, 47] Generated Node #0,2,2: 41:[40, 47] Operation: 49-2=47 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 41:[40, 47], Operations: ['12+28=40', '49-2=47'] Exploring Operation: 40+47=87, Resulting Numbers: [87] 87,41 unequal: No Solution Exploring Operation: 40*47=1880, Resulting Numbers: [1880] 1880,41 unequal: No Solution Exploring Operation: 47-40=7, Resulting Numbers: [7] 7,41 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:[49, 42], Operations: ['12+28=40', '2+40=42'] Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,41 unequal: No Solution Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,41 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 #0,2,0 Current State: 41:[40, 51], Operations: ['12+28=40', '2+49=51'] Exploring Operation: 51-40=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 40+51=91, Resulting Numbers: [91] 91,41 unequal: No Solution Exploring Operation: 40*51=2040, Resulting Numbers: [2040] 2040,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 41:[49, 42], Operations: ['12+2=14', '28+14=42'] Exploring Operation: 49*42=2058, Resulting Numbers: [2058] 2058,41 unequal: No Solution Exploring Operation: 49-42=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 49+42=91, Resulting Numbers: [91] 91,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[49, 52], Operations: ['12*2=24', '28+24=52'] Exploring Operation: 49*52=2548, Resulting Numbers: [2548] 2548,41 unequal: No Solution Exploring Operation: 52-49=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 49+52=101, Resulting Numbers: [101] 101,41 unequal: No Solution Moving to Node #0,0,0 Current State: 41:[28, 35], Operations: ['12+2=14', '49-14=35'] Exploring Operation: 28+35=63, Resulting Numbers: [63] 63,41 unequal: No Solution Exploring Operation: 35-28=7, Resulting Numbers: [7] 7,41 unequal: No Solution Exploring Operation: 28*35=980, Resulting Numbers: [980] 980,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[28, 25], Operations: ['12*2=24', '49-24=25'] Exploring Operation: 28+25=53, Resulting Numbers: [53] 53,41 unequal: No Solution Exploring Operation: 28-25=3, Resulting Numbers: [3] 3,41 unequal: No Solution Exploring Operation: 28*25=700, Resulting Numbers: [700] 700,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[49, 14], Operations: ['12+2=14', '28-14=14'] Exploring Operation: 49-14=35, Resulting Numbers: [35] 35,41 unequal: No Solution Exploring Operation: 49*14=686, Resulting Numbers: [686] 686,41 unequal: No Solution Exploring Operation: 49+14=63, Resulting Numbers: [63] 63,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[24, 21], Operations: ['12*2=24', '49-28=21'] Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,41 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,41 unequal: No Solution Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,41 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 92, 79, 26, 38 ]
40
[ "92-79=13", "26/13=2", "38+2=40" ]
Current State: 40:[92, 79, 26, 38], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [26, 38, 13] Generated Node #2: [26, 38, 13] from Operation: 92-79=13 Current State: 40:[26, 38, 13], Operations: ['92-79=13'] Exploring Operation: 26/13=2, Resulting Numbers: [38, 2] Generated Node #3: [38, 2] from Operation: 26/13=2 Current State: 40:[38, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[92, 79, 26, 38], Operations: [] Exploring Operation: 92-26=66, Resulting Numbers: [79, 38, 66] Generated Node #0,0: 40:[79, 38, 66] Operation: 92-26=66 Exploring Operation: 79-38=41, Resulting Numbers: [92, 26, 41] Generated Node #0,1: 40:[92, 26, 41] Operation: 79-38=41 Exploring Operation: 92-38=54, Resulting Numbers: [79, 26, 54] Generated Node #0,2: 40:[79, 26, 54] Operation: 92-38=54 Exploring Operation: 92-79=13, Resulting Numbers: [26, 38, 13] Generated Node #0,3: 40:[26, 38, 13] Operation: 92-79=13 Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[26, 38, 13], Operations: ['92-79=13'] Exploring Operation: 26/13=2, Resulting Numbers: [38, 2] Generated Node #0,3,0: 40:[38, 2] Operation: 26/13=2 Exploring Operation: 26-13=13, Resulting Numbers: [38, 13] Generated Node #0,3,1: 40:[38, 13] Operation: 26-13=13 Exploring Operation: 38-26=12, Resulting Numbers: [13, 12] Generated Node #0,3,2: 40:[13, 12] Operation: 38-26=12 Exploring Operation: 26+13=39, Resulting Numbers: [38, 39] Generated Node #0,3,3: 40:[38, 39] Operation: 26+13=39 Moving to Node #0,3,0 Current State: 40:[38, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[92, 79, 26, 38], Operations: [] Exploring Operation: 92-79=13, Resulting Numbers: [26, 38, 13] Generated Node #0,3: 40:[26, 38, 13] Operation: 92-79=13 Moving to Node #0,3 Current State: 40:[26, 38, 13], Operations: ['92-79=13'] Exploring Operation: 26/13=2, Resulting Numbers: [38, 2] Generated Node #0,3,0: 40:[38, 2] Operation: 26/13=2 Moving to Node #0,3,0 Current State: 40:[38, 2], Operations: ['92-79=13', '26/13=2'] Exploring Operation: 38+2=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 63, 21, 9, 6 ]
81
[ "63+21=84", "9-6=3", "84-3=81" ]
Current State: 81:[63, 21, 9, 6], Operations: [] Exploring Operation: 63+21=84, Resulting Numbers: [9, 6, 84] Generated Node #2: [9, 6, 84] from Operation: 63+21=84 Current State: 81:[9, 6, 84], Operations: ['63+21=84'] Exploring Operation: 9-6=3, Resulting Numbers: [84, 3] Generated Node #3: [84, 3] from Operation: 9-6=3 Current State: 81:[84, 3], Operations: ['63+21=84', '9-6=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[63, 21, 9, 6], Operations: [] Exploring Operation: 63+21=84, Resulting Numbers: [9, 6, 84] Generated Node #0,0: 81:[9, 6, 84] Operation: 63+21=84 Exploring Operation: 63/21=3, Resulting Numbers: [9, 6, 3] Generated Node #0,1: 81:[9, 6, 3] Operation: 63/21=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[9, 6, 3], Operations: ['63/21=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9, 9] Generated Node #0,1,0: 81:[9, 9] Operation: 6+3=9 Exploring Operation: 9-6=3, Resulting Numbers: [3, 3] Generated Node #0,1,1: 81:[3, 3] Operation: 9-6=3 Moving to Node #0,1,0 Current State: 81:[9, 9], Operations: ['63/21=3', '6+3=9'] Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[63, 21, 9, 6], Operations: [] Exploring Operation: 63/21=3, Resulting Numbers: [9, 6, 3] Generated Node #0,1: 81:[9, 6, 3] Operation: 63/21=3 Moving to Node #0,1 Current State: 81:[9, 6, 3], Operations: ['63/21=3'] Exploring Operation: 6+3=9, Resulting Numbers: [9, 9] Generated Node #0,1,0: 81:[9, 9] Operation: 6+3=9 Moving to Node #0,1,0 Current State: 81:[9, 9], Operations: ['63/21=3', '6+3=9'] Exploring Operation: 9*9=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 10, 33, 88, 3 ]
80
[ "10*88=880", "33/3=11", "880/11=80" ]
Current State: 80:[10, 33, 88, 3], Operations: [] Exploring Operation: 10*88=880, Resulting Numbers: [33, 3, 880] Generated Node #2: [33, 3, 880] from Operation: 10*88=880 Current State: 80:[33, 3, 880], Operations: ['10*88=880'] Exploring Operation: 33/3=11, Resulting Numbers: [880, 11] Generated Node #3: [880, 11] from Operation: 33/3=11 Current State: 80:[880, 11], Operations: ['10*88=880', '33/3=11'] Exploring Operation: 880/11=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[10, 33, 88, 3], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [10, 88, 11] Generated Node #0,0: 80:[10, 88, 11] Operation: 33/3=11 Exploring Operation: 88-10=78, Resulting Numbers: [33, 3, 78] Generated Node #0,1: 80:[33, 3, 78] Operation: 88-10=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[10, 88, 11], Operations: ['33/3=11'] Exploring Operation: 88/11=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 88/11=8 Exploring Operation: 88-10=78, Resulting Numbers: [11, 78] Generated Node #0,0,1: 80:[11, 78] Operation: 88-10=78 Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['33/3=11', '88/11=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[10, 33, 88, 3], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [10, 88, 11] Generated Node #0,0: 80:[10, 88, 11] Operation: 33/3=11 Moving to Node #0,0 Current State: 80:[10, 88, 11], Operations: ['33/3=11'] Exploring Operation: 88/11=8, Resulting Numbers: [10, 8] Generated Node #0,0,0: 80:[10, 8] Operation: 88/11=8 Moving to Node #0,0,0 Current State: 80:[10, 8], Operations: ['33/3=11', '88/11=8'] Exploring Operation: 10*8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 14, 7, 1, 65 ]
12
[ "14-1=13", "65/13=5", "7+5=12" ]
Current State: 12:[14, 7, 1, 65], Operations: [] Exploring Operation: 14-1=13, Resulting Numbers: [7, 65, 13] Generated Node #2: [7, 65, 13] from Operation: 14-1=13 Current State: 12:[7, 65, 13], Operations: ['14-1=13'] Exploring Operation: 65/13=5, Resulting Numbers: [7, 5] Generated Node #3: [7, 5] from Operation: 65/13=5 Current State: 12:[7, 5], Operations: ['14-1=13', '65/13=5'] Exploring Operation: 7+5=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[14, 7, 1, 65], Operations: [] Exploring Operation: 65-7=58, Resulting Numbers: [14, 1, 58] Generated Node #0,0: 12:[14, 1, 58] Operation: 65-7=58 Exploring Operation: 65-14=51, Resulting Numbers: [7, 1, 51] Generated Node #0,1: 12:[7, 1, 51] Operation: 65-14=51 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[7, 1, 51], Operations: ['65-14=51'] Exploring Operation: 51-7=44, Resulting Numbers: [1, 44] Generated Node #0,1,0: 12:[1, 44] Operation: 51-7=44 Exploring Operation: 7-1=6, Resulting Numbers: [51, 6] Generated Node #0,1,1: 12:[51, 6] Operation: 7-1=6 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 12:[1, 44], Operations: ['65-14=51', '51-7=44'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,12 unequal: No Solution Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,12 unequal: No Solution No 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: 12:[51, 6], Operations: ['65-14=51', '7-1=6'] Exploring Operation: 51-6=45, Resulting Numbers: [45] 45,12 unequal: No Solution Exploring Operation: 51+6=57, Resulting Numbers: [57] 57,12 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: 12:[14, 1, 58], Operations: ['65-7=58'] Exploring Operation: 58-14=44, Resulting Numbers: [1, 44] Generated Node #0,0,0: 12:[1, 44] Operation: 58-14=44 Exploring Operation: 14-1=13, Resulting Numbers: [58, 13] Generated Node #0,0,1: 12:[58, 13] Operation: 14-1=13 Moving to Node #0,0,0 Current State: 12:[1, 44], Operations: ['65-7=58', '58-14=44'] Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,12 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,12 unequal: No Solution Moving to Node #0,0,1 Current State: 12:[58, 13], Operations: ['65-7=58', '14-1=13'] Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,12 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,12 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
[ 3, 64, 40, 22 ]
94
[ "64-40=24", "3*24=72", "22+72=94" ]
Current State: 94:[3, 64, 40, 22], Operations: [] Exploring Operation: 64-40=24, Resulting Numbers: [3, 22, 24] Generated Node #2: [3, 22, 24] from Operation: 64-40=24 Current State: 94:[3, 22, 24], Operations: ['64-40=24'] Exploring Operation: 3*24=72, Resulting Numbers: [22, 72] Generated Node #3: [22, 72] from Operation: 3*24=72 Current State: 94:[22, 72], Operations: ['64-40=24', '3*24=72'] Exploring Operation: 22+72=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[3, 64, 40, 22], Operations: [] Exploring Operation: 64-22=42, Resulting Numbers: [3, 40, 42] Generated Node #0,0: 94:[3, 40, 42] Operation: 64-22=42 Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[3, 40, 42], Operations: ['64-22=42'] Exploring Operation: 42-40=2, Resulting Numbers: [3, 2] Generated Node #0,0,0: 94:[3, 2] Operation: 42-40=2 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 94:[3, 2], Operations: ['64-22=42', '42-40=2'] Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,94 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
[ 8, 44, 93, 79 ]
50
[ "44-8=36", "93-79=14", "36+14=50" ]
Current State: 50:[8, 44, 93, 79], Operations: [] Exploring Operation: 44-8=36, Resulting Numbers: [93, 79, 36] Generated Node #2: [93, 79, 36] from Operation: 44-8=36 Current State: 50:[93, 79, 36], Operations: ['44-8=36'] Exploring Operation: 93-79=14, Resulting Numbers: [36, 14] Generated Node #3: [36, 14] from Operation: 93-79=14 Current State: 50:[36, 14], Operations: ['44-8=36', '93-79=14'] Exploring Operation: 36+14=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[8, 44, 93, 79], Operations: [] Exploring Operation: 93-79=14, Resulting Numbers: [8, 44, 14] Generated Node #0,0: 50:[8, 44, 14] Operation: 93-79=14 Exploring Operation: 93-8=85, Resulting Numbers: [44, 79, 85] Generated Node #0,1: 50:[44, 79, 85] Operation: 93-8=85 Exploring Operation: 93-44=49, Resulting Numbers: [8, 79, 49] Generated Node #0,2: 50:[8, 79, 49] Operation: 93-44=49 Exploring Operation: 79-44=35, Resulting Numbers: [8, 93, 35] Generated Node #0,3: 50:[8, 93, 35] Operation: 79-44=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[8, 44, 14], Operations: ['93-79=14'] Exploring Operation: 8+14=22, Resulting Numbers: [44, 22] Generated Node #0,0,0: 50:[44, 22] Operation: 8+14=22 Exploring Operation: 14-8=6, Resulting Numbers: [44, 6] Generated Node #0,0,1: 50:[44, 6] Operation: 14-8=6 Exploring Operation: 8+44=52, Resulting Numbers: [14, 52] Generated Node #0,0,2: 50:[14, 52] Operation: 8+44=52 Exploring Operation: 44-14=30, Resulting Numbers: [8, 30] Generated Node #0,0,3: 50:[8, 30] Operation: 44-14=30 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 50:[14, 52], Operations: ['93-79=14', '8+44=52'] Exploring Operation: 14+52=66, Resulting Numbers: [66] 66,50 unequal: No Solution Exploring Operation: 14*52=728, Resulting Numbers: [728] 728,50 unequal: No Solution Exploring Operation: 52-14=38, Resulting Numbers: [38] 38,50 unequal: No Solution No 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: 50:[44, 6], Operations: ['93-79=14', '14-8=6'] Exploring Operation: 44-6=38, Resulting Numbers: [38] 38,50 unequal: No Solution Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[8, 44, 93, 79], Operations: [] Exploring Operation: 93-79=14, Resulting Numbers: [8, 44, 14] Generated Node #0,0: 50:[8, 44, 14] Operation: 93-79=14 Moving to Node #0,0 Current State: 50:[8, 44, 14], Operations: ['93-79=14'] Exploring Operation: 14-8=6, Resulting Numbers: [44, 6] Generated Node #0,0,1: 50:[44, 6] Operation: 14-8=6 Moving to Node #0,0,1 Current State: 50:[44, 6], Operations: ['93-79=14', '14-8=6'] Exploring Operation: 44+6=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 56, 98, 16, 4 ]
22
[ "98-56=42", "16+4=20", "42-20=22" ]
Current State: 22:[56, 98, 16, 4], Operations: [] Exploring Operation: 98-56=42, Resulting Numbers: [16, 4, 42] Generated Node #2: [16, 4, 42] from Operation: 98-56=42 Current State: 22:[16, 4, 42], Operations: ['98-56=42'] Exploring Operation: 16+4=20, Resulting Numbers: [42, 20] Generated Node #3: [42, 20] from Operation: 16+4=20 Current State: 22:[42, 20], Operations: ['98-56=42', '16+4=20'] Exploring Operation: 42-20=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[56, 98, 16, 4], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [98, 16, 14] Generated Node #0,0: 22:[98, 16, 14] Operation: 56/4=14 Exploring Operation: 56-16=40, Resulting Numbers: [98, 4, 40] Generated Node #0,1: 22:[98, 4, 40] Operation: 56-16=40 Exploring Operation: 98-56=42, Resulting Numbers: [16, 4, 42] Generated Node #0,2: 22:[16, 4, 42] Operation: 98-56=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 22:[16, 4, 42], Operations: ['98-56=42'] Exploring Operation: 16-4=12, Resulting Numbers: [42, 12] Generated Node #0,2,0: 22:[42, 12] Operation: 16-4=12 Exploring Operation: 42-4=38, Resulting Numbers: [16, 38] Generated Node #0,2,1: 22:[16, 38] Operation: 42-4=38 Exploring Operation: 42-16=26, Resulting Numbers: [4, 26] Generated Node #0,2,2: 22:[4, 26] Operation: 42-16=26 Moving to Node #0,2,2 Current State: 22:[4, 26], Operations: ['98-56=42', '42-16=26'] Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,22 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[56, 98, 16, 4], Operations: [] Exploring Operation: 98-56=42, Resulting Numbers: [16, 4, 42] Generated Node #0,2: 22:[16, 4, 42] Operation: 98-56=42 Moving to Node #0,2 Current State: 22:[16, 4, 42], Operations: ['98-56=42'] Exploring Operation: 42-16=26, Resulting Numbers: [4, 26] Generated Node #0,2,2: 22:[4, 26] Operation: 42-16=26 Moving to Node #0,2,2 Current State: 22:[4, 26], Operations: ['98-56=42', '42-16=26'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 85, 77, 91, 30 ]
72
[ "91-85=6", "30/6=5", "77-5=72" ]
Current State: 72:[85, 77, 91, 30], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [77, 30, 6] Generated Node #2: [77, 30, 6] from Operation: 91-85=6 Current State: 72:[77, 30, 6], Operations: ['91-85=6'] Exploring Operation: 30/6=5, Resulting Numbers: [77, 5] Generated Node #3: [77, 5] from Operation: 30/6=5 Current State: 72:[77, 5], Operations: ['91-85=6', '30/6=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[85, 77, 91, 30], Operations: [] Exploring Operation: 91-85=6, Resulting Numbers: [77, 30, 6] Generated Node #0,0: 72:[77, 30, 6] Operation: 91-85=6 Moving to Node #0,0 Current State: 72:[77, 30, 6], Operations: ['91-85=6'] Exploring Operation: 30+6=36, Resulting Numbers: [77, 36] Generated Node #0,0,0: 72:[77, 36] Operation: 30+6=36 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 72:[77, 36], Operations: ['91-85=6', '30+6=36'] Exploring Operation: 77-36=41, Resulting Numbers: [41] 41,72 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, 78, 54, 87 ]
60
[ "87-78=9", "54/9=6", "54+6=60" ]
Current State: 60:[54, 78, 54, 87], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [54, 54, 9] Generated Node #2: [54, 54, 9] from Operation: 87-78=9 Current State: 60:[54, 54, 9], Operations: ['87-78=9'] Exploring Operation: 54/9=6, Resulting Numbers: [6] 6,60 equal: Goal Reached Exploring Operation: 54+6=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[54, 78, 54, 87], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [54, 54, 9] Generated Node #0,0: 60:[54, 54, 9] Operation: 87-78=9 Moving to Node #0,0 Current State: 60:[54, 54, 9], Operations: ['87-78=9'] Exploring Operation: 54/54=1, Resulting Numbers: [9, 1] Generated Node #0,0,0: 60:[9, 1] Operation: 54/54=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[9, 1], Operations: ['87-78=9', '54/54=1'] Exploring Operation: 9+1=10, Resulting Numbers: [10] 10,60 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
[ 20, 23, 76, 69 ]
21
[ "23-20=3", "76-69=7", "3*7=21" ]
Current State: 21:[20, 23, 76, 69], Operations: [] Exploring Operation: 23-20=3, Resulting Numbers: [76, 69, 3] Generated Node #2: [76, 69, 3] from Operation: 23-20=3 Current State: 21:[76, 69, 3], Operations: ['23-20=3'] Exploring Operation: 76-69=7, Resulting Numbers: [3, 7] Generated Node #3: [3, 7] from Operation: 76-69=7 Current State: 21:[3, 7], Operations: ['23-20=3', '76-69=7'] Exploring Operation: 3*7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 23, 76, 69], Operations: [] Exploring Operation: 69/23=3, Resulting Numbers: [20, 76, 3] Generated Node #0,0: 21:[20, 76, 3] Operation: 69/23=3 Exploring Operation: 76-69=7, Resulting Numbers: [20, 23, 7] Generated Node #0,1: 21:[20, 23, 7] Operation: 76-69=7 Exploring Operation: 76-23=53, Resulting Numbers: [20, 69, 53] Generated Node #0,2: 21:[20, 69, 53] Operation: 76-23=53 Exploring Operation: 69-23=46, Resulting Numbers: [20, 76, 46] Generated Node #0,3: 21:[20, 76, 46] Operation: 69-23=46 Moving to Node #0,1 Current State: 21:[20, 23, 7], Operations: ['76-69=7'] Exploring Operation: 20-7=13, Resulting Numbers: [23, 13] Generated Node #0,1,0: 21:[23, 13] Operation: 20-7=13 Exploring Operation: 23-20=3, Resulting Numbers: [7, 3] Generated Node #0,1,1: 21:[7, 3] Operation: 23-20=3 Exploring Operation: 23-7=16, Resulting Numbers: [20, 16] Generated Node #0,1,2: 21:[20, 16] Operation: 23-7=16 Exploring Operation: 20+7=27, Resulting Numbers: [23, 27] Generated Node #0,1,3: 21:[23, 27] Operation: 20+7=27 Moving to Node #0,0 Current State: 21:[20, 76, 3], Operations: ['69/23=3'] Exploring Operation: 20-3=17, Resulting Numbers: [76, 17] Generated Node #0,0,0: 21:[76, 17] Operation: 20-3=17 Exploring Operation: 20+3=23, Resulting Numbers: [76, 23] Generated Node #0,0,1: 21:[76, 23] Operation: 20+3=23 Exploring Operation: 76-3=73, Resulting Numbers: [20, 73] Generated Node #0,0,2: 21:[20, 73] Operation: 76-3=73 Exploring Operation: 76-20=56, Resulting Numbers: [3, 56] Generated Node #0,0,3: 21:[3, 56] Operation: 76-20=56 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 21:[3, 56], Operations: ['69/23=3', '76-20=56'] Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,21 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 21:[20, 73], Operations: ['69/23=3', '76-3=73'] Exploring Operation: 73-20=53, Resulting Numbers: [53] 53,21 unequal: No Solution Exploring Operation: 20*73=1460, Resulting Numbers: [1460] 1460,21 unequal: No Solution Exploring Operation: 20+73=93, Resulting Numbers: [93] 93,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 21:[76, 23], Operations: ['69/23=3', '20+3=23'] Exploring Operation: 76-23=53, Resulting Numbers: [53] 53,21 unequal: No Solution Exploring Operation: 76+23=99, Resulting Numbers: [99] 99,21 unequal: No Solution Exploring Operation: 76*23=1748, Resulting Numbers: [1748] 1748,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 21:[76, 17], Operations: ['69/23=3', '20-3=17'] Exploring Operation: 76-17=59, Resulting Numbers: [59] 59,21 unequal: No Solution Exploring Operation: 76+17=93, Resulting Numbers: [93] 93,21 unequal: No Solution Exploring Operation: 76*17=1292, Resulting Numbers: [1292] 1292,21 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: 21:[20, 76, 46], Operations: ['69-23=46'] Exploring Operation: 46-20=26, Resulting Numbers: [76, 26] Generated Node #0,3,0: 21:[76, 26] Operation: 46-20=26 Exploring Operation: 20+76=96, Resulting Numbers: [46, 96] Generated Node #0,3,1: 21:[46, 96] Operation: 20+76=96 Exploring Operation: 76-46=30, Resulting Numbers: [20, 30] Generated Node #0,3,2: 21:[20, 30] Operation: 76-46=30 Exploring Operation: 76-20=56, Resulting Numbers: [46, 56] Generated Node #0,3,3: 21:[46, 56] Operation: 76-20=56 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 21:[20, 30], Operations: ['69-23=46', '76-46=30'] Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,21 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,21 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 #0,3,0 Current State: 21:[76, 26], Operations: ['69-23=46', '46-20=26'] Exploring Operation: 76*26=1976, Resulting Numbers: [1976] 1976,21 unequal: No Solution Exploring Operation: 76+26=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,21 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 #0,3,3 Current State: 21:[46, 56], Operations: ['69-23=46', '76-20=56'] Exploring Operation: 56-46=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 46+56=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 46*56=2576, Resulting Numbers: [2576] 2576,21 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 #0,3,1 Current State: 21:[46, 96], Operations: ['69-23=46', '20+76=96'] Exploring Operation: 96-46=50, Resulting Numbers: [50] 50,21 unequal: No Solution Exploring Operation: 46+96=142, Resulting Numbers: [142] 142,21 unequal: No Solution Exploring Operation: 46*96=4416, Resulting Numbers: [4416] 4416,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 21:[20, 69, 53], Operations: ['76-23=53'] Exploring Operation: 20+69=89, Resulting Numbers: [53, 89] Generated Node #0,2,0: 21:[53, 89] Operation: 20+69=89 Exploring Operation: 69-20=49, Resulting Numbers: [53, 49] Generated Node #0,2,1: 21:[53, 49] Operation: 69-20=49 Exploring Operation: 53-20=33, Resulting Numbers: [69, 33] Generated Node #0,2,2: 21:[69, 33] Operation: 53-20=33 Exploring Operation: 69-53=16, Resulting Numbers: [20, 16] Generated Node #0,2,3: 21:[20, 16] Operation: 69-53=16 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[20, 16], Operations: ['76-23=53', '69-53=16'] Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,21 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[53, 49], Operations: ['76-23=53', '69-20=49'] Exploring Operation: 53*49=2597, Resulting Numbers: [2597] 2597,21 unequal: No Solution Exploring Operation: 53-49=4, Resulting Numbers: [4] 4,21 unequal: No Solution Exploring Operation: 53+49=102, Resulting Numbers: [102] 102,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[69, 33], Operations: ['76-23=53', '53-20=33'] Exploring Operation: 69-33=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 69+33=102, Resulting Numbers: [102] 102,21 unequal: No Solution Exploring Operation: 69*33=2277, Resulting Numbers: [2277] 2277,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[53, 89], Operations: ['76-23=53', '20+69=89'] Exploring Operation: 89-53=36, Resulting Numbers: [36] 36,21 unequal: No Solution Exploring Operation: 53+89=142, Resulting Numbers: [142] 142,21 unequal: No Solution Exploring Operation: 53*89=4717, Resulting Numbers: [4717] 4717,21 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: 21:[7, 3], Operations: ['76-69=7', '23-20=3'] Exploring Operation: 7+3=10, Resulting Numbers: [10] 10,21 unequal: No Solution Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[20, 23, 76, 69], Operations: [] Exploring Operation: 76-69=7, Resulting Numbers: [20, 23, 7] Generated Node #0,1: 21:[20, 23, 7] Operation: 76-69=7 Moving to Node #0,1 Current State: 21:[20, 23, 7], Operations: ['76-69=7'] Exploring Operation: 23-20=3, Resulting Numbers: [7, 3] Generated Node #0,1,1: 21:[7, 3] Operation: 23-20=3 Moving to Node #0,1,1 Current State: 21:[7, 3], Operations: ['76-69=7', '23-20=3'] Exploring Operation: 7*3=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.946181
hs_4
mult_heuristic
[ 11, 53, 26, 62 ]
100
[ "11+53=64", "62-26=36", "64+36=100" ]
Current State: 100:[11, 53, 26, 62], Operations: [] Exploring Operation: 11+53=64, Resulting Numbers: [26, 62, 64] Generated Node #2: [26, 62, 64] from Operation: 11+53=64 Current State: 100:[26, 62, 64], Operations: ['11+53=64'] Exploring Operation: 62-26=36, Resulting Numbers: [64, 36] Generated Node #3: [64, 36] from Operation: 62-26=36 Current State: 100:[64, 36], Operations: ['11+53=64', '62-26=36'] Exploring Operation: 64+36=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[11, 53, 26, 62], Operations: [] Exploring Operation: 53-26=27, Resulting Numbers: [11, 62, 27] Generated Node #0,0: 100:[11, 62, 27] Operation: 53-26=27 Exploring Operation: 62-53=9, Resulting Numbers: [11, 26, 9] Generated Node #0,1: 100:[11, 26, 9] Operation: 62-53=9 Exploring Operation: 62-11=51, Resulting Numbers: [53, 26, 51] Generated Node #0,2: 100:[53, 26, 51] Operation: 62-11=51 Exploring Operation: 62-26=36, Resulting Numbers: [11, 53, 36] Generated Node #0,3: 100:[11, 53, 36] Operation: 62-26=36 Moving to Node #0,1 Current State: 100:[11, 26, 9], Operations: ['62-53=9'] Exploring Operation: 11*9=99, Resulting Numbers: [26, 99] Generated Node #0,1,0: 100:[26, 99] Operation: 11*9=99 Exploring Operation: 26-9=17, Resulting Numbers: [11, 17] Generated Node #0,1,1: 100:[11, 17] Operation: 26-9=17 Exploring Operation: 11+9=20, Resulting Numbers: [26, 20] Generated Node #0,1,2: 100:[26, 20] Operation: 11+9=20 Exploring Operation: 11-9=2, Resulting Numbers: [26, 2] Generated Node #0,1,3: 100:[26, 2] Operation: 11-9=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 100:[26, 20], Operations: ['62-53=9', '11+9=20'] Exploring Operation: 26-20=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 26*20=520, Resulting Numbers: [520] 520,100 unequal: No Solution Exploring Operation: 26+20=46, Resulting Numbers: [46] 46,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 100:[26, 2], Operations: ['62-53=9', '11-9=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,100 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 100:[26, 99], Operations: ['62-53=9', '11*9=99'] Exploring Operation: 26+99=125, Resulting Numbers: [125] 125,100 unequal: No Solution Exploring Operation: 99-26=73, Resulting Numbers: [73] 73,100 unequal: No Solution Exploring Operation: 26*99=2574, Resulting Numbers: [2574] 2574,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 100:[11, 17], Operations: ['62-53=9', '26-9=17'] Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,100 unequal: No Solution Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,100 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: 100:[53, 26, 51], Operations: ['62-11=51'] Exploring Operation: 53-26=27, Resulting Numbers: [51, 27] Generated Node #0,2,0: 100:[51, 27] Operation: 53-26=27 Exploring Operation: 51-26=25, Resulting Numbers: [53, 25] Generated Node #0,2,1: 100:[53, 25] Operation: 51-26=25 Exploring Operation: 53-51=2, Resulting Numbers: [26, 2] Generated Node #0,2,2: 100:[26, 2] Operation: 53-51=2 Exploring Operation: 53+51=104, Resulting Numbers: [26, 104] Generated Node #0,2,3: 100:[26, 104] Operation: 53+51=104 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[26, 2], Operations: ['62-11=51', '53-51=2'] Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,100 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,100 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:[51, 27], Operations: ['62-11=51', '53-26=27'] Exploring Operation: 51+27=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 51*27=1377, Resulting Numbers: [1377] 1377,100 unequal: No Solution Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,100 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:[53, 25], Operations: ['62-11=51', '51-26=25'] Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 53*25=1325, Resulting Numbers: [1325] 1325,100 unequal: No Solution Exploring Operation: 53+25=78, Resulting Numbers: [78] 78,100 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 #0,2,3 Current State: 100:[26, 104], Operations: ['62-11=51', '53+51=104'] Exploring Operation: 104-26=78, Resulting Numbers: [78] 78,100 unequal: No Solution Exploring Operation: 104/26=4, Resulting Numbers: [4] 4,100 unequal: No Solution Exploring Operation: 26+104=130, Resulting Numbers: [130] 130,100 unequal: No Solution Exploring Operation: 26*104=2704, Resulting Numbers: [2704] 2704,100 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: 100:[11, 53, 36], Operations: ['62-26=36'] Exploring Operation: 11+36=47, Resulting Numbers: [53, 47] Generated Node #0,3,0: 100:[53, 47] Operation: 11+36=47 Exploring Operation: 53-36=17, Resulting Numbers: [11, 17] Generated Node #0,3,1: 100:[11, 17] Operation: 53-36=17 Exploring Operation: 53+36=89, Resulting Numbers: [11, 89] Generated Node #0,3,2: 100:[11, 89] Operation: 53+36=89 Exploring Operation: 36-11=25, Resulting Numbers: [53, 25] Generated Node #0,3,3: 100:[53, 25] Operation: 36-11=25 Moving to Node #0,0 Current State: 100:[11, 62, 27], Operations: ['53-26=27'] Exploring Operation: 62+27=89, Resulting Numbers: [11, 89] Generated Node #0,0,0: 100:[11, 89] Operation: 62+27=89 Exploring Operation: 62-27=35, Resulting Numbers: [11, 35] Generated Node #0,0,1: 100:[11, 35] Operation: 62-27=35 Exploring Operation: 27-11=16, Resulting Numbers: [62, 16] Generated Node #0,0,2: 100:[62, 16] Operation: 27-11=16 Exploring Operation: 62-11=51, Resulting Numbers: [27, 51] Generated Node #0,0,3: 100:[27, 51] Operation: 62-11=51 Moving to Node #0,3,3 Current State: 100:[53, 25], Operations: ['62-26=36', '36-11=25'] Exploring Operation: 53-25=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 53*25=1325, Resulting Numbers: [1325] 1325,100 unequal: No Solution Exploring Operation: 53+25=78, Resulting Numbers: [78] 78,100 unequal: No Solution Moving to Node #0,0,3 Current State: 100:[27, 51], Operations: ['53-26=27', '62-11=51'] Exploring Operation: 51-27=24, Resulting Numbers: [24] 24,100 unequal: No Solution Exploring Operation: 27*51=1377, Resulting Numbers: [1377] 1377,100 unequal: No Solution Exploring Operation: 27+51=78, Resulting Numbers: [78] 78,100 unequal: No Solution Moving to Node #0,3,1 Current State: 100:[11, 17], Operations: ['62-26=36', '53-36=17'] Exploring Operation: 11+17=28, Resulting Numbers: [28] 28,100 unequal: No Solution Exploring Operation: 17-11=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 11*17=187, Resulting Numbers: [187] 187,100 unequal: No Solution Moving to Node #0,3,0 Current State: 100:[53, 47], Operations: ['62-26=36', '11+36=47'] Exploring Operation: 53-47=6, Resulting Numbers: [6] 6,100 unequal: No Solution Exploring Operation: 53+47=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[11, 53, 26, 62], Operations: [] Exploring Operation: 62-26=36, Resulting Numbers: [11, 53, 36] Generated Node #0,3: 100:[11, 53, 36] Operation: 62-26=36 Moving to Node #0,3 Current State: 100:[11, 53, 36], Operations: ['62-26=36'] Exploring Operation: 11+36=47, Resulting Numbers: [53, 47] Generated Node #0,3,0: 100:[53, 47] Operation: 11+36=47 Moving to Node #0,3,0 Current State: 100:[53, 47], Operations: ['62-26=36', '11+36=47'] Exploring Operation: 53+47=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
0.946181
hs_4
mult_heuristic
[ 59, 55, 3, 57 ]
69
[ "59-55=4", "3*4=12", "57+12=69" ]
Current State: 69:[59, 55, 3, 57], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [3, 57, 4] Generated Node #2: [3, 57, 4] from Operation: 59-55=4 Current State: 69:[3, 57, 4], Operations: ['59-55=4'] Exploring Operation: 3*4=12, Resulting Numbers: [57, 12] Generated Node #3: [57, 12] from Operation: 3*4=12 Current State: 69:[57, 12], Operations: ['59-55=4', '3*4=12'] Exploring Operation: 57+12=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[59, 55, 3, 57], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [55, 3, 2] Generated Node #0,0: 69:[55, 3, 2] Operation: 59-57=2 Exploring Operation: 57-55=2, Resulting Numbers: [59, 3, 2] Generated Node #0,1: 69:[59, 3, 2] Operation: 57-55=2 Exploring Operation: 59-55=4, Resulting Numbers: [3, 57, 4] Generated Node #0,2: 69:[3, 57, 4] Operation: 59-55=4 Start Sub Search at level 1: Moving to Node #0,1 Current State: 69:[59, 3, 2], Operations: ['57-55=2'] Exploring Operation: 59+3=62, Resulting Numbers: [2, 62] Generated Node #0,1,0: 69:[2, 62] Operation: 59+3=62 Exploring Operation: 59-2=57, Resulting Numbers: [3, 57] Generated Node #0,1,1: 69:[3, 57] Operation: 59-2=57 Exploring Operation: 59+2=61, Resulting Numbers: [3, 61] Generated Node #0,1,2: 69:[3, 61] Operation: 59+2=61 Moving to Node #0,1,0 Current State: 69:[2, 62], Operations: ['57-55=2', '59+3=62'] Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,69 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,69 unequal: No Solution Moving to Node #0,1,2 Current State: 69:[3, 61], Operations: ['57-55=2', '59+2=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,69 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,69 unequal: No Solution Moving to Node #0,1,1 Current State: 69:[3, 57], Operations: ['57-55=2', '59-2=57'] Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 69:[3, 57, 4], Operations: ['59-55=4'] Exploring Operation: 57+4=61, Resulting Numbers: [3, 61] Generated Node #0,2,0: 69:[3, 61] Operation: 57+4=61 Exploring Operation: 57/3=19, Resulting Numbers: [4, 19] Generated Node #0,2,1: 69:[4, 19] Operation: 57/3=19 Exploring Operation: 3+57=60, Resulting Numbers: [4, 60] Generated Node #0,2,2: 69:[4, 60] Operation: 3+57=60 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 69:[4, 19], Operations: ['59-55=4', '57/3=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,69 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,69 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 #0,2,0 Current State: 69:[3, 61], Operations: ['59-55=4', '57+4=61'] Exploring Operation: 3+61=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 3*61=183, Resulting Numbers: [183] 183,69 unequal: No Solution Exploring Operation: 61-3=58, Resulting Numbers: [58] 58,69 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:[4, 60], Operations: ['59-55=4', '3+57=60'] Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,69 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,69 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:[55, 3, 2], Operations: ['59-57=2'] Exploring Operation: 55+3=58, Resulting Numbers: [2, 58] Generated Node #0,0,0: 69:[2, 58] Operation: 55+3=58 Exploring Operation: 55-2=53, Resulting Numbers: [3, 53] Generated Node #0,0,1: 69:[3, 53] Operation: 55-2=53 Exploring Operation: 55+2=57, Resulting Numbers: [3, 57] Generated Node #0,0,2: 69:[3, 57] Operation: 55+2=57 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 69:[2, 58], Operations: ['59-57=2', '55+3=58'] Exploring Operation: 2+58=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 58/2=29, Resulting Numbers: [29] 29,69 unequal: No Solution Exploring Operation: 58-2=56, Resulting Numbers: [56] 56,69 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:[3, 57], Operations: ['59-57=2', '55+2=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,69 unequal: No Solution Exploring Operation: 3+57=60, Resulting Numbers: [60] 60,69 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,69 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:[3, 53], Operations: ['59-57=2', '55-2=53'] Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,69 unequal: No Solution Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,69 unequal: No Solution Exploring Operation: 3*53=159, Resulting Numbers: [159] 159,69 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
sum_heuristic
[ 74, 85, 76, 18 ]
83
[ "74*85=6290", "18+6290=6308", "6308/76=83" ]
Current State: 83:[74, 85, 76, 18], Operations: [] Exploring Operation: 74*85=6290, Resulting Numbers: [76, 18, 6290] Generated Node #2: [76, 18, 6290] from Operation: 74*85=6290 Current State: 83:[76, 18, 6290], Operations: ['74*85=6290'] Exploring Operation: 18+6290=6308, Resulting Numbers: [76, 6308] Generated Node #3: [76, 6308] from Operation: 18+6290=6308 Current State: 83:[76, 6308], Operations: ['74*85=6290', '18+6290=6308'] Exploring Operation: 6308/76=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[74, 85, 76, 18], Operations: [] Exploring Operation: 74+18=92, Resulting Numbers: [85, 76, 92] Generated Node #0,0: 83:[85, 76, 92] Operation: 74+18=92 Exploring Operation: 85-18=67, Resulting Numbers: [74, 76, 67] Generated Node #0,1: 83:[74, 76, 67] Operation: 85-18=67 Exploring Operation: 74-18=56, Resulting Numbers: [85, 76, 56] Generated Node #0,2: 83:[85, 76, 56] Operation: 74-18=56 Exploring Operation: 76+18=94, Resulting Numbers: [74, 85, 94] Generated Node #0,3: 83:[74, 85, 94] Operation: 76+18=94 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[85, 76, 92], Operations: ['74+18=92'] Exploring Operation: 85+76=161, Resulting Numbers: [92, 161] Generated Node #0,0,0: 83:[92, 161] Operation: 85+76=161 Exploring Operation: 92-85=7, Resulting Numbers: [76, 7] Generated Node #0,0,1: 83:[76, 7] Operation: 92-85=7 Exploring Operation: 92-76=16, Resulting Numbers: [85, 16] Generated Node #0,0,2: 83:[85, 16] Operation: 92-76=16 Exploring Operation: 85-76=9, Resulting Numbers: [92, 9] Generated Node #0,0,3: 83:[92, 9] Operation: 85-76=9 Moving to Node #0,0,2 Current State: 83:[85, 16], Operations: ['74+18=92', '92-76=16'] Exploring Operation: 85*16=1360, Resulting Numbers: [1360] 1360,83 unequal: No Solution Exploring Operation: 85-16=69, Resulting Numbers: [69] 69,83 unequal: No Solution Exploring Operation: 85+16=101, Resulting Numbers: [101] 101,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[92, 9], Operations: ['74+18=92', '85-76=9'] Exploring Operation: 92+9=101, Resulting Numbers: [101] 101,83 unequal: No Solution Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[74, 85, 76, 18], Operations: [] Exploring Operation: 74+18=92, Resulting Numbers: [85, 76, 92] Generated Node #0,0: 83:[85, 76, 92] Operation: 74+18=92 Moving to Node #0,0 Current State: 83:[85, 76, 92], Operations: ['74+18=92'] Exploring Operation: 85-76=9, Resulting Numbers: [92, 9] Generated Node #0,0,3: 83:[92, 9] Operation: 85-76=9 Moving to Node #0,0,3 Current State: 83:[92, 9], Operations: ['74+18=92', '85-76=9'] Exploring Operation: 92-9=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_4
mult_heuristic
[ 64, 26, 83, 37 ]
82
[ "64-26=38", "83+37=120", "120-38=82" ]
Current State: 82:[64, 26, 83, 37], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [83, 37, 38] Generated Node #2: [83, 37, 38] from Operation: 64-26=38 Current State: 82:[83, 37, 38], Operations: ['64-26=38'] Exploring Operation: 83+37=120, Resulting Numbers: [38, 120] Generated Node #3: [38, 120] from Operation: 83+37=120 Current State: 82:[38, 120], Operations: ['64-26=38', '83+37=120'] Exploring Operation: 120-38=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[64, 26, 83, 37], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [83, 37, 38] Generated Node #0,0: 82:[83, 37, 38] Operation: 64-26=38 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[83, 37, 38], Operations: ['64-26=38'] Exploring Operation: 38-37=1, Resulting Numbers: [83, 1] Generated Node #0,0,0: 82:[83, 1] Operation: 38-37=1 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 82:[83, 1], Operations: ['64-26=38', '38-37=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[64, 26, 83, 37], Operations: [] Exploring Operation: 64-26=38, Resulting Numbers: [83, 37, 38] Generated Node #0,0: 82:[83, 37, 38] Operation: 64-26=38 Moving to Node #0,0 Current State: 82:[83, 37, 38], Operations: ['64-26=38'] Exploring Operation: 38-37=1, Resulting Numbers: [83, 1] Generated Node #0,0,0: 82:[83, 1] Operation: 38-37=1 Moving to Node #0,0,0 Current State: 82:[83, 1], Operations: ['64-26=38', '38-37=1'] Exploring Operation: 83-1=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 4, 43, 97, 72 ]
17
[ "43+97=140", "140-72=68", "68/4=17" ]
Current State: 17:[4, 43, 97, 72], Operations: [] Exploring Operation: 43+97=140, Resulting Numbers: [4, 72, 140] Generated Node #2: [4, 72, 140] from Operation: 43+97=140 Current State: 17:[4, 72, 140], Operations: ['43+97=140'] Exploring Operation: 140-72=68, Resulting Numbers: [4, 68] Generated Node #3: [4, 68] from Operation: 140-72=68 Current State: 17:[4, 68], Operations: ['43+97=140', '140-72=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[4, 43, 97, 72], Operations: [] Exploring Operation: 72/4=18, Resulting Numbers: [43, 97, 18] Generated Node #0,0: 17:[43, 97, 18] Operation: 72/4=18 Exploring Operation: 43-4=39, Resulting Numbers: [97, 72, 39] Generated Node #0,1: 17:[97, 72, 39] Operation: 43-4=39 Exploring Operation: 72-43=29, Resulting Numbers: [4, 97, 29] Generated Node #0,2: 17:[4, 97, 29] Operation: 72-43=29 Exploring Operation: 97-72=25, Resulting Numbers: [4, 43, 25] Generated Node #0,3: 17:[4, 43, 25] Operation: 97-72=25 Exploring Operation: 97-43=54, Resulting Numbers: [4, 72, 54] Generated Node #0,4: 17:[4, 72, 54] Operation: 97-43=54 Moving to Node #0,3 Current State: 17:[4, 43, 25], Operations: ['97-72=25'] Exploring Operation: 43-4=39, Resulting Numbers: [25, 39] Generated Node #0,3,0: 17:[25, 39] Operation: 43-4=39 Exploring Operation: 4+43=47, Resulting Numbers: [25, 47] Generated Node #0,3,1: 17:[25, 47] Operation: 4+43=47 Exploring Operation: 25-4=21, Resulting Numbers: [43, 21] Generated Node #0,3,2: 17:[43, 21] Operation: 25-4=21 Exploring Operation: 4+25=29, Resulting Numbers: [43, 29] Generated Node #0,3,3: 17:[43, 29] Operation: 4+25=29 Exploring Operation: 43-25=18, Resulting Numbers: [4, 18] Generated Node #0,3,4: 17:[4, 18] Operation: 43-25=18 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 17:[4, 18], Operations: ['97-72=25', '43-25=18'] Exploring Operation: 18-4=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 4*18=72, Resulting Numbers: [72] 72,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 17:[25, 39], Operations: ['97-72=25', '43-4=39'] Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,17 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,17 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 17:[43, 21], Operations: ['97-72=25', '25-4=21'] Exploring Operation: 43*21=903, Resulting Numbers: [903] 903,17 unequal: No Solution Exploring Operation: 43-21=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 43+21=64, Resulting Numbers: [64] 64,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 17:[25, 47], Operations: ['97-72=25', '4+43=47'] Exploring Operation: 25+47=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 25*47=1175, Resulting Numbers: [1175] 1175,17 unequal: No Solution Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 17:[43, 29], Operations: ['97-72=25', '4+25=29'] Exploring Operation: 43*29=1247, Resulting Numbers: [1247] 1247,17 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,17 unequal: No Solution Exploring Operation: 43+29=72, Resulting Numbers: [72] 72,17 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: 17:[4, 72, 54], Operations: ['97-43=54'] Exploring Operation: 72-54=18, Resulting Numbers: [4, 18] Generated Node #0,4,0: 17:[4, 18] Operation: 72-54=18 Exploring Operation: 72-4=68, Resulting Numbers: [54, 68] Generated Node #0,4,1: 17:[54, 68] Operation: 72-4=68 Exploring Operation: 54-4=50, Resulting Numbers: [72, 50] Generated Node #0,4,2: 17:[72, 50] Operation: 54-4=50 Exploring Operation: 72/4=18, Resulting Numbers: [54, 18] Generated Node #0,4,3: 17:[54, 18] Operation: 72/4=18 Exploring Operation: 4+72=76, Resulting Numbers: [54, 76] Generated Node #0,4,4: 17:[54, 76] Operation: 4+72=76 Moving to Node #0,2 Current State: 17:[4, 97, 29], Operations: ['72-43=29'] Exploring Operation: 29-4=25, Resulting Numbers: [97, 25] Generated Node #0,2,0: 17:[97, 25] Operation: 29-4=25 Exploring Operation: 97-4=93, Resulting Numbers: [29, 93] Generated Node #0,2,1: 17:[29, 93] Operation: 97-4=93 Exploring Operation: 4+97=101, Resulting Numbers: [29, 101] Generated Node #0,2,2: 17:[29, 101] Operation: 4+97=101 Exploring Operation: 4+29=33, Resulting Numbers: [97, 33] Generated Node #0,2,3: 17:[97, 33] Operation: 4+29=33 Exploring Operation: 97-29=68, Resulting Numbers: [4, 68] Generated Node #0,2,4: 17:[4, 68] Operation: 97-29=68 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 17:[4, 68], Operations: ['72-43=29', '97-29=68'] Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,17 unequal: No Solution Exploring Operation: 4*68=272, Resulting Numbers: [272] 272,17 unequal: No Solution Exploring Operation: 4+68=72, Resulting Numbers: [72] 72,17 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Moving to Node #0 Current State: 17:[4, 43, 97, 72], Operations: [] Exploring Operation: 72-43=29, Resulting Numbers: [4, 97, 29] Generated Node #0,2: 17:[4, 97, 29] Operation: 72-43=29 Moving to Node #0,2 Current State: 17:[4, 97, 29], Operations: ['72-43=29'] Exploring Operation: 97-29=68, Resulting Numbers: [4, 68] Generated Node #0,2,4: 17:[4, 68] Operation: 97-29=68 Moving to Node #0,2,4 Current State: 17:[4, 68], Operations: ['72-43=29', '97-29=68'] Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,17 equal: Goal Reached Exit Sub Search at level 1
0.962674
hs_5
mult_heuristic
[ 62, 43, 66, 7 ]
54
[ "62-43=19", "66+7=73", "73-19=54" ]
Current State: 54:[62, 43, 66, 7], Operations: [] Exploring Operation: 62-43=19, Resulting Numbers: [66, 7, 19] Generated Node #2: [66, 7, 19] from Operation: 62-43=19 Current State: 54:[66, 7, 19], Operations: ['62-43=19'] Exploring Operation: 66+7=73, Resulting Numbers: [19, 73] Generated Node #3: [19, 73] from Operation: 66+7=73 Current State: 54:[19, 73], Operations: ['62-43=19', '66+7=73'] Exploring Operation: 73-19=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[62, 43, 66, 7], Operations: [] Exploring Operation: 66-43=23, Resulting Numbers: [62, 7, 23] Generated Node #0,0: 54:[62, 7, 23] Operation: 66-43=23 Exploring Operation: 62-43=19, Resulting Numbers: [66, 7, 19] Generated Node #0,1: 54:[66, 7, 19] Operation: 62-43=19 Exploring Operation: 66-62=4, Resulting Numbers: [43, 7, 4] Generated Node #0,2: 54:[43, 7, 4] Operation: 66-62=4 Moving to Node #0,0 Current State: 54:[62, 7, 23], Operations: ['66-43=23'] Exploring Operation: 23-7=16, Resulting Numbers: [62, 16] Generated Node #0,0,0: 54:[62, 16] Operation: 23-7=16 Exploring Operation: 7+23=30, Resulting Numbers: [62, 30] Generated Node #0,0,1: 54:[62, 30] Operation: 7+23=30 Exploring Operation: 62-7=55, Resulting Numbers: [23, 55] Generated Node #0,0,2: 54:[23, 55] Operation: 62-7=55 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 54:[23, 55], Operations: ['66-43=23', '62-7=55'] Exploring Operation: 23*55=1265, Resulting Numbers: [1265] 1265,54 unequal: No Solution Exploring Operation: 55-23=32, Resulting Numbers: [32] 32,54 unequal: No Solution Exploring Operation: 23+55=78, Resulting Numbers: [78] 78,54 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 #0,0,0 Current State: 54:[62, 16], Operations: ['66-43=23', '23-7=16'] Exploring Operation: 62*16=992, Resulting Numbers: [992] 992,54 unequal: No Solution Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,54 unequal: No Solution Exploring Operation: 62+16=78, Resulting Numbers: [78] 78,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 54:[62, 30], Operations: ['66-43=23', '7+23=30'] Exploring Operation: 62+30=92, Resulting Numbers: [92] 92,54 unequal: No Solution Exploring Operation: 62*30=1860, Resulting Numbers: [1860] 1860,54 unequal: No Solution Exploring Operation: 62-30=32, Resulting Numbers: [32] 32,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 54:[43, 7, 4], Operations: ['66-62=4'] Exploring Operation: 43+4=47, Resulting Numbers: [7, 47] Generated Node #0,2,0: 54:[7, 47] Operation: 43+4=47 Exploring Operation: 43-7=36, Resulting Numbers: [4, 36] Generated Node #0,2,1: 54:[4, 36] Operation: 43-7=36 Exploring Operation: 43+7=50, Resulting Numbers: [4, 50] Generated Node #0,2,2: 54:[4, 50] Operation: 43+7=50 Moving to Node #0,1 Current State: 54:[66, 7, 19], Operations: ['62-43=19'] Exploring Operation: 66-7=59, Resulting Numbers: [19, 59] Generated Node #0,1,0: 54:[19, 59] Operation: 66-7=59 Exploring Operation: 66-19=47, Resulting Numbers: [7, 47] Generated Node #0,1,1: 54:[7, 47] Operation: 66-19=47 Exploring Operation: 7+19=26, Resulting Numbers: [66, 26] Generated Node #0,1,2: 54:[66, 26] Operation: 7+19=26 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[19, 59], Operations: ['62-43=19', '66-7=59'] Exploring Operation: 59-19=40, Resulting Numbers: [40] 40,54 unequal: No Solution Exploring Operation: 19+59=78, Resulting Numbers: [78] 78,54 unequal: No Solution Exploring Operation: 19*59=1121, Resulting Numbers: [1121] 1121,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 54:[7, 47], Operations: ['62-43=19', '66-19=47'] Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[62, 43, 66, 7], Operations: [] Exploring Operation: 62-43=19, Resulting Numbers: [66, 7, 19] Generated Node #0,1: 54:[66, 7, 19] Operation: 62-43=19 Moving to Node #0,1 Current State: 54:[66, 7, 19], Operations: ['62-43=19'] Exploring Operation: 66-19=47, Resulting Numbers: [7, 47] Generated Node #0,1,1: 54:[7, 47] Operation: 66-19=47 Moving to Node #0,1,1 Current State: 54:[7, 47], Operations: ['62-43=19', '66-19=47'] Exploring Operation: 7+47=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
sum_heuristic
[ 20, 41, 86, 2 ]
67
[ "41-20=21", "86+2=88", "88-21=67" ]
Current State: 67:[20, 41, 86, 2], Operations: [] Exploring Operation: 41-20=21, Resulting Numbers: [86, 2, 21] Generated Node #2: [86, 2, 21] from Operation: 41-20=21 Current State: 67:[86, 2, 21], Operations: ['41-20=21'] Exploring Operation: 86+2=88, Resulting Numbers: [21, 88] Generated Node #3: [21, 88] from Operation: 86+2=88 Current State: 67:[21, 88], Operations: ['41-20=21', '86+2=88'] Exploring Operation: 88-21=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[20, 41, 86, 2], Operations: [] Exploring Operation: 20+41=61, Resulting Numbers: [86, 2, 61] Generated Node #0,0: 67:[86, 2, 61] Operation: 20+41=61 Exploring Operation: 20+2=22, Resulting Numbers: [41, 86, 22] Generated Node #0,1: 67:[41, 86, 22] Operation: 20+2=22 Exploring Operation: 41+2=43, Resulting Numbers: [20, 86, 43] Generated Node #0,2: 67:[20, 86, 43] Operation: 41+2=43 Exploring Operation: 20*2=40, Resulting Numbers: [41, 86, 40] Generated Node #0,3: 67:[41, 86, 40] Operation: 20*2=40 Exploring Operation: 41*2=82, Resulting Numbers: [20, 86, 82] Generated Node #0,4: 67:[20, 86, 82] Operation: 41*2=82 Moving to Node #0,3 Current State: 67:[41, 86, 40], Operations: ['20*2=40'] Exploring Operation: 41-40=1, Resulting Numbers: [86, 1] Generated Node #0,3,0: 67:[86, 1] Operation: 41-40=1 Exploring Operation: 86+40=126, Resulting Numbers: [41, 126] Generated Node #0,3,1: 67:[41, 126] Operation: 86+40=126 Exploring Operation: 86-41=45, Resulting Numbers: [40, 45] Generated Node #0,3,2: 67:[40, 45] Operation: 86-41=45 Exploring Operation: 86-40=46, Resulting Numbers: [41, 46] Generated Node #0,3,3: 67:[41, 46] Operation: 86-40=46 Exploring Operation: 41+40=81, Resulting Numbers: [86, 81] Generated Node #0,3,4: 67:[86, 81] Operation: 41+40=81 Moving to Node #0,4 Current State: 67:[20, 86, 82], Operations: ['41*2=82'] Exploring Operation: 82-20=62, Resulting Numbers: [86, 62] Generated Node #0,4,0: 67:[86, 62] Operation: 82-20=62 Exploring Operation: 20+82=102, Resulting Numbers: [86, 102] Generated Node #0,4,1: 67:[86, 102] Operation: 20+82=102 Exploring Operation: 86-20=66, Resulting Numbers: [82, 66] Generated Node #0,4,2: 67:[82, 66] Operation: 86-20=66 Exploring Operation: 20+86=106, Resulting Numbers: [82, 106] Generated Node #0,4,3: 67:[82, 106] Operation: 20+86=106 Exploring Operation: 86-82=4, Resulting Numbers: [20, 4] Generated Node #0,4,4: 67:[20, 4] Operation: 86-82=4 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 67:[82, 66], Operations: ['41*2=82', '86-20=66'] Exploring Operation: 82+66=148, Resulting Numbers: [148] 148,67 unequal: No Solution Exploring Operation: 82-66=16, Resulting Numbers: [16] 16,67 unequal: No Solution Exploring Operation: 82*66=5412, Resulting Numbers: [5412] 5412,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 67:[86, 62], Operations: ['41*2=82', '82-20=62'] Exploring Operation: 86-62=24, Resulting Numbers: [24] 24,67 unequal: No Solution Exploring Operation: 86*62=5332, Resulting Numbers: [5332] 5332,67 unequal: No Solution Exploring Operation: 86+62=148, Resulting Numbers: [148] 148,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 67:[86, 102], Operations: ['41*2=82', '20+82=102'] Exploring Operation: 86*102=8772, Resulting Numbers: [8772] 8772,67 unequal: No Solution Exploring Operation: 86+102=188, Resulting Numbers: [188] 188,67 unequal: No Solution Exploring Operation: 102-86=16, Resulting Numbers: [16] 16,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 67:[82, 106], Operations: ['41*2=82', '20+86=106'] Exploring Operation: 82*106=8692, Resulting Numbers: [8692] 8692,67 unequal: No Solution Exploring Operation: 106-82=24, Resulting Numbers: [24] 24,67 unequal: No Solution Exploring Operation: 82+106=188, Resulting Numbers: [188] 188,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 67:[20, 4], Operations: ['41*2=82', '86-82=4'] Exploring Operation: 20+4=24, Resulting Numbers: [24] 24,67 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,67 unequal: No Solution Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,67 unequal: No Solution Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,67 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: 67:[86, 2, 61], Operations: ['20+41=61'] Exploring Operation: 86-2=84, Resulting Numbers: [61, 84] Generated Node #0,0,0: 67:[61, 84] Operation: 86-2=84 Exploring Operation: 2+61=63, Resulting Numbers: [86, 63] Generated Node #0,0,1: 67:[86, 63] Operation: 2+61=63 Exploring Operation: 61-2=59, Resulting Numbers: [86, 59] Generated Node #0,0,2: 67:[86, 59] Operation: 61-2=59 Exploring Operation: 86/2=43, Resulting Numbers: [61, 43] Generated Node #0,0,3: 67:[61, 43] Operation: 86/2=43 Exploring Operation: 86+2=88, Resulting Numbers: [61, 88] Generated Node #0,0,4: 67:[61, 88] Operation: 86+2=88 Moving to Node #0,1 Current State: 67:[41, 86, 22], Operations: ['20+2=22'] Exploring Operation: 86+22=108, Resulting Numbers: [41, 108] Generated Node #0,1,0: 67:[41, 108] Operation: 86+22=108 Exploring Operation: 86-22=64, Resulting Numbers: [41, 64] Generated Node #0,1,1: 67:[41, 64] Operation: 86-22=64 Exploring Operation: 86-41=45, Resulting Numbers: [22, 45] Generated Node #0,1,2: 67:[22, 45] Operation: 86-41=45 Exploring Operation: 41+22=63, Resulting Numbers: [86, 63] Generated Node #0,1,3: 67:[86, 63] Operation: 41+22=63 Exploring Operation: 41-22=19, Resulting Numbers: [86, 19] Generated Node #0,1,4: 67:[86, 19] Operation: 41-22=19 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 67:[86, 63], Operations: ['20+2=22', '41+22=63'] Exploring Operation: 86-63=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 86+63=149, Resulting Numbers: [149] 149,67 unequal: No Solution Exploring Operation: 86*63=5418, Resulting Numbers: [5418] 5418,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 67:[41, 64], Operations: ['20+2=22', '86-22=64'] Exploring Operation: 64-41=23, Resulting Numbers: [23] 23,67 unequal: No Solution Exploring Operation: 41*64=2624, Resulting Numbers: [2624] 2624,67 unequal: No Solution Exploring Operation: 41+64=105, Resulting Numbers: [105] 105,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 67:[41, 108], Operations: ['20+2=22', '86+22=108'] Exploring Operation: 41+108=149, Resulting Numbers: [149] 149,67 unequal: No Solution Exploring Operation: 41*108=4428, Resulting Numbers: [4428] 4428,67 unequal: No Solution Exploring Operation: 108-41=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[20, 41, 86, 2], Operations: [] Exploring Operation: 20+2=22, Resulting Numbers: [41, 86, 22] Generated Node #0,1: 67:[41, 86, 22] Operation: 20+2=22 Moving to Node #0,1 Current State: 67:[41, 86, 22], Operations: ['20+2=22'] Exploring Operation: 86+22=108, Resulting Numbers: [41, 108] Generated Node #0,1,0: 67:[41, 108] Operation: 86+22=108 Moving to Node #0,1,0 Current State: 67:[41, 108], Operations: ['20+2=22', '86+22=108'] Exploring Operation: 108-41=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.953125
hs_5
sum_heuristic
[ 23, 6, 2, 27 ]
85
[ "23+6=29", "2*29=58", "27+58=85" ]
Current State: 85:[23, 6, 2, 27], Operations: [] Exploring Operation: 23+6=29, Resulting Numbers: [2, 27, 29] Generated Node #2: [2, 27, 29] from Operation: 23+6=29 Current State: 85:[2, 27, 29], Operations: ['23+6=29'] Exploring Operation: 2*29=58, Resulting Numbers: [27, 58] Generated Node #3: [27, 58] from Operation: 2*29=58 Current State: 85:[27, 58], Operations: ['23+6=29', '2*29=58'] Exploring Operation: 27+58=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[23, 6, 2, 27], Operations: [] Exploring Operation: 27-23=4, Resulting Numbers: [6, 2, 4] Generated Node #0,0: 85:[6, 2, 4] Operation: 27-23=4 Exploring Operation: 23-6=17, Resulting Numbers: [2, 27, 17] Generated Node #0,1: 85:[2, 27, 17] Operation: 23-6=17 Moving to Node #0,0 Current State: 85:[6, 2, 4], Operations: ['27-23=4'] Exploring Operation: 6-2=4, Resulting Numbers: [4, 4] Generated Node #0,0,0: 85:[4, 4] Operation: 6-2=4 Exploring Operation: 2+4=6, Resulting Numbers: [6, 6] Generated Node #0,0,1: 85:[6, 6] Operation: 2+4=6 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[4, 4], Operations: ['27-23=4', '6-2=4'] Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,85 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[6, 6], Operations: ['27-23=4', '2+4=6'] Exploring Operation: 6+6=12, Resulting Numbers: [12] 12,85 unequal: No Solution Exploring Operation: 6/6=1, Resulting Numbers: [1] 1,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 85:[2, 27, 17], Operations: ['23-6=17'] Exploring Operation: 27-2=25, Resulting Numbers: [17, 25] Generated Node #0,1,0: 85:[17, 25] Operation: 27-2=25 Exploring Operation: 27-17=10, Resulting Numbers: [2, 10] Generated Node #0,1,1: 85:[2, 10] Operation: 27-17=10 Moving to Node #0,1,0 Current State: 85:[17, 25], Operations: ['23-6=17', '27-2=25'] Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,85 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,85 unequal: No Solution Moving to Node #0,1,1 Current State: 85:[2, 10], Operations: ['23-6=17', '27-17=10'] Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,85 unequal: No Solution Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,85 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 20, 56, 41, 24 ]
19
[ "56-20=36", "41-24=17", "36-17=19" ]
Current State: 19:[20, 56, 41, 24], Operations: [] Exploring Operation: 56-20=36, Resulting Numbers: [41, 24, 36] Generated Node #2: [41, 24, 36] from Operation: 56-20=36 Current State: 19:[41, 24, 36], Operations: ['56-20=36'] Exploring Operation: 41-24=17, Resulting Numbers: [36, 17] Generated Node #3: [36, 17] from Operation: 41-24=17 Current State: 19:[36, 17], Operations: ['56-20=36', '41-24=17'] Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[20, 56, 41, 24], Operations: [] Exploring Operation: 56-41=15, Resulting Numbers: [20, 24, 15] Generated Node #0,0: 19:[20, 24, 15] Operation: 56-41=15 Exploring Operation: 56-24=32, Resulting Numbers: [20, 41, 32] Generated Node #0,1: 19:[20, 41, 32] Operation: 56-24=32 Exploring Operation: 41-24=17, Resulting Numbers: [20, 56, 17] Generated Node #0,2: 19:[20, 56, 17] Operation: 41-24=17 Exploring Operation: 56-20=36, Resulting Numbers: [41, 24, 36] Generated Node #0,3: 19:[41, 24, 36] Operation: 56-20=36 Exploring Operation: 41-20=21, Resulting Numbers: [56, 24, 21] Generated Node #0,4: 19:[56, 24, 21] Operation: 41-20=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[20, 24, 15], Operations: ['56-41=15'] Exploring Operation: 24-20=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 19:[15, 4] Operation: 24-20=4 Exploring Operation: 24-15=9, Resulting Numbers: [20, 9] Generated Node #0,0,1: 19:[20, 9] Operation: 24-15=9 Exploring Operation: 24+15=39, Resulting Numbers: [20, 39] Generated Node #0,0,2: 19:[20, 39] Operation: 24+15=39 Exploring Operation: 20-15=5, Resulting Numbers: [24, 5] Generated Node #0,0,3: 19:[24, 5] Operation: 20-15=5 Exploring Operation: 20+15=35, Resulting Numbers: [24, 35] Generated Node #0,0,4: 19:[24, 35] Operation: 20+15=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 19:[20, 9], Operations: ['56-41=15', '24-15=9'] Exploring Operation: 20-9=11, Resulting Numbers: [11] 11,19 unequal: No Solution Exploring Operation: 20*9=180, Resulting Numbers: [180] 180,19 unequal: No Solution Exploring Operation: 20+9=29, Resulting Numbers: [29] 29,19 unequal: No Solution No 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: 19:[15, 4], Operations: ['56-41=15', '24-20=4'] Exploring Operation: 15*4=60, Resulting Numbers: [60] 60,19 unequal: No Solution Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,19 unequal: No Solution Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[20, 56, 41, 24], Operations: [] Exploring Operation: 56-41=15, Resulting Numbers: [20, 24, 15] Generated Node #0,0: 19:[20, 24, 15] Operation: 56-41=15 Moving to Node #0,0 Current State: 19:[20, 24, 15], Operations: ['56-41=15'] Exploring Operation: 24-20=4, Resulting Numbers: [15, 4] Generated Node #0,0,0: 19:[15, 4] Operation: 24-20=4 Moving to Node #0,0,0 Current State: 19:[15, 4], Operations: ['56-41=15', '24-20=4'] Exploring Operation: 15+4=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 25, 98, 3, 16 ]
13
[ "98+16=114", "114/3=38", "38-25=13" ]
Current State: 13:[25, 98, 3, 16], Operations: [] Exploring Operation: 98+16=114, Resulting Numbers: [25, 3, 114] Generated Node #2: [25, 3, 114] from Operation: 98+16=114 Current State: 13:[25, 3, 114], Operations: ['98+16=114'] Exploring Operation: 114/3=38, Resulting Numbers: [25, 38] Generated Node #3: [25, 38] from Operation: 114/3=38 Current State: 13:[25, 38], Operations: ['98+16=114', '114/3=38'] Exploring Operation: 38-25=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[25, 98, 3, 16], Operations: [] Exploring Operation: 98-16=82, Resulting Numbers: [25, 3, 82] Generated Node #0,0: 13:[25, 3, 82] Operation: 98-16=82 Exploring Operation: 98-25=73, Resulting Numbers: [3, 16, 73] Generated Node #0,1: 13:[3, 16, 73] Operation: 98-25=73 Moving to Node #0,1 Current State: 13:[3, 16, 73], Operations: ['98-25=73'] Exploring Operation: 73-16=57, Resulting Numbers: [3, 57] Generated Node #0,1,0: 13:[3, 57] Operation: 73-16=57 Exploring Operation: 16-3=13, Resulting Numbers: [73, 13] Generated Node #0,1,1: 13:[73, 13] Operation: 16-3=13 Moving to Node #0,0 Current State: 13:[25, 3, 82], Operations: ['98-16=82'] Exploring Operation: 25-3=22, Resulting Numbers: [82, 22] Generated Node #0,0,0: 13:[82, 22] Operation: 25-3=22 Exploring Operation: 82-25=57, Resulting Numbers: [3, 57] Generated Node #0,0,1: 13:[3, 57] Operation: 82-25=57 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 13:[3, 57], Operations: ['98-16=82', '82-25=57'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,13 unequal: No Solution Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,13 unequal: No Solution No 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: 13:[82, 22], Operations: ['98-16=82', '25-3=22'] Exploring Operation: 82+22=104, Resulting Numbers: [104] 104,13 unequal: No Solution Exploring Operation: 82-22=60, Resulting Numbers: [60] 60,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 13:[3, 57], Operations: ['98-25=73', '73-16=57'] Exploring Operation: 57-3=54, Resulting Numbers: [54] 54,13 unequal: No Solution Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[73, 13], Operations: ['98-25=73', '16-3=13'] Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,13 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 24, 36, 41, 72 ]
19
[ "36-24=12", "72-41=31", "31-12=19" ]
Current State: 19:[24, 36, 41, 72], Operations: [] Exploring Operation: 36-24=12, Resulting Numbers: [41, 72, 12] Generated Node #2: [41, 72, 12] from Operation: 36-24=12 Current State: 19:[41, 72, 12], Operations: ['36-24=12'] Exploring Operation: 72-41=31, Resulting Numbers: [12, 31] Generated Node #3: [12, 31] from Operation: 72-41=31 Current State: 19:[12, 31], Operations: ['36-24=12', '72-41=31'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[24, 36, 41, 72], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [24, 41, 2] Generated Node #0,0: 19:[24, 41, 2] Operation: 72/36=2 Exploring Operation: 72-41=31, Resulting Numbers: [24, 36, 31] Generated Node #0,1: 19:[24, 36, 31] Operation: 72-41=31 Exploring Operation: 72-24=48, Resulting Numbers: [36, 41, 48] Generated Node #0,2: 19:[36, 41, 48] Operation: 72-24=48 Exploring Operation: 72/24=3, Resulting Numbers: [36, 41, 3] Generated Node #0,3: 19:[36, 41, 3] Operation: 72/24=3 Exploring Operation: 72-36=36, Resulting Numbers: [24, 41, 36] Generated Node #0,4: 19:[24, 41, 36] Operation: 72-36=36 Start Sub Search at level 1: Moving to Node #0,1 Current State: 19:[24, 36, 31], Operations: ['72-41=31'] Exploring Operation: 24+36=60, Resulting Numbers: [31, 60] Generated Node #0,1,0: 19:[31, 60] Operation: 24+36=60 Exploring Operation: 36-24=12, Resulting Numbers: [31, 12] Generated Node #0,1,1: 19:[31, 12] Operation: 36-24=12 Exploring Operation: 31-24=7, Resulting Numbers: [36, 7] Generated Node #0,1,2: 19:[36, 7] Operation: 31-24=7 Exploring Operation: 24+31=55, Resulting Numbers: [36, 55] Generated Node #0,1,3: 19:[36, 55] Operation: 24+31=55 Exploring Operation: 36-31=5, Resulting Numbers: [24, 5] Generated Node #0,1,4: 19:[24, 5] Operation: 36-31=5 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 19:[31, 12], Operations: ['72-41=31', '36-24=12'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[24, 36, 41, 72], Operations: [] Exploring Operation: 72-41=31, Resulting Numbers: [24, 36, 31] Generated Node #0,1: 19:[24, 36, 31] Operation: 72-41=31 Moving to Node #0,1 Current State: 19:[24, 36, 31], Operations: ['72-41=31'] Exploring Operation: 36-24=12, Resulting Numbers: [31, 12] Generated Node #0,1,1: 19:[31, 12] Operation: 36-24=12 Moving to Node #0,1,1 Current State: 19:[31, 12], Operations: ['72-41=31', '36-24=12'] Exploring Operation: 31-12=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 40, 67, 23, 2 ]
73
[ "67-40=27", "23*2=46", "27+46=73" ]
Current State: 73:[40, 67, 23, 2], Operations: [] Exploring Operation: 67-40=27, Resulting Numbers: [23, 2, 27] Generated Node #2: [23, 2, 27] from Operation: 67-40=27 Current State: 73:[23, 2, 27], Operations: ['67-40=27'] Exploring Operation: 23*2=46, Resulting Numbers: [27, 46] Generated Node #3: [27, 46] from Operation: 23*2=46 Current State: 73:[27, 46], Operations: ['67-40=27', '23*2=46'] Exploring Operation: 27+46=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[40, 67, 23, 2], Operations: [] Exploring Operation: 40*2=80, Resulting Numbers: [67, 23, 80] Generated Node #0,0: 73:[67, 23, 80] Operation: 40*2=80 Exploring Operation: 23*2=46, Resulting Numbers: [40, 67, 46] Generated Node #0,1: 73:[40, 67, 46] Operation: 23*2=46 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[67, 23, 80], Operations: ['40*2=80'] Exploring Operation: 67+23=90, Resulting Numbers: [80, 90] Generated Node #0,0,0: 73:[80, 90] Operation: 67+23=90 Exploring Operation: 80-23=57, Resulting Numbers: [67, 57] Generated Node #0,0,1: 73:[67, 57] Operation: 80-23=57 Moving to Node #0,0,1 Current State: 73:[67, 57], Operations: ['40*2=80', '80-23=57'] Exploring Operation: 67+57=124, Resulting Numbers: [124] 124,73 unequal: No Solution Exploring Operation: 67-57=10, Resulting Numbers: [10] 10,73 unequal: No Solution Moving to Node #0,0,0 Current State: 73:[80, 90], Operations: ['40*2=80', '67+23=90'] Exploring Operation: 90-80=10, Resulting Numbers: [10] 10,73 unequal: No Solution Exploring Operation: 80+90=170, Resulting Numbers: [170] 170,73 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 73:[40, 67, 46], Operations: ['23*2=46'] Exploring Operation: 40+67=107, Resulting Numbers: [46, 107] Generated Node #0,1,0: 73:[46, 107] Operation: 40+67=107 Exploring Operation: 40+46=86, Resulting Numbers: [67, 86] Generated Node #0,1,1: 73:[67, 86] Operation: 40+46=86 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 73:[67, 86], Operations: ['23*2=46', '40+46=86'] Exploring Operation: 86-67=19, Resulting Numbers: [19] 19,73 unequal: No Solution Exploring Operation: 67+86=153, Resulting Numbers: [153] 153,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 73:[46, 107], Operations: ['23*2=46', '40+67=107'] Exploring Operation: 46+107=153, Resulting Numbers: [153] 153,73 unequal: No Solution Exploring Operation: 107-46=61, Resulting Numbers: [61] 61,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 67, 5, 44, 69 ]
83
[ "69-67=2", "44*2=88", "88-5=83" ]
Current State: 83:[67, 5, 44, 69], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [5, 44, 2] Generated Node #2: [5, 44, 2] from Operation: 69-67=2 Current State: 83:[5, 44, 2], Operations: ['69-67=2'] Exploring Operation: 44*2=88, Resulting Numbers: [5, 88] Generated Node #3: [5, 88] from Operation: 44*2=88 Current State: 83:[5, 88], Operations: ['69-67=2', '44*2=88'] Exploring Operation: 88-5=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[67, 5, 44, 69], Operations: [] Exploring Operation: 67-5=62, Resulting Numbers: [44, 69, 62] Generated Node #0,0: 83:[44, 69, 62] Operation: 67-5=62 Exploring Operation: 5+69=74, Resulting Numbers: [67, 44, 74] Generated Node #0,1: 83:[67, 44, 74] Operation: 5+69=74 Exploring Operation: 5+44=49, Resulting Numbers: [67, 69, 49] Generated Node #0,2: 83:[67, 69, 49] Operation: 5+44=49 Exploring Operation: 67+5=72, Resulting Numbers: [44, 69, 72] Generated Node #0,3: 83:[44, 69, 72] Operation: 67+5=72 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[67, 44, 74], Operations: ['5+69=74'] Exploring Operation: 44+74=118, Resulting Numbers: [67, 118] Generated Node #0,1,0: 83:[67, 118] Operation: 44+74=118 Exploring Operation: 74-44=30, Resulting Numbers: [67, 30] Generated Node #0,1,1: 83:[67, 30] Operation: 74-44=30 Exploring Operation: 67-44=23, Resulting Numbers: [74, 23] Generated Node #0,1,2: 83:[74, 23] Operation: 67-44=23 Exploring Operation: 67+44=111, Resulting Numbers: [74, 111] Generated Node #0,1,3: 83:[74, 111] Operation: 67+44=111 Moving to Node #0,1,3 Current State: 83:[74, 111], Operations: ['5+69=74', '67+44=111'] Exploring Operation: 111-74=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 74+111=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 74*111=8214, Resulting Numbers: [8214] 8214,83 unequal: No Solution Moving to Node #0,1,0 Current State: 83:[67, 118], Operations: ['5+69=74', '44+74=118'] Exploring Operation: 67+118=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 67*118=7906, Resulting Numbers: [7906] 7906,83 unequal: No Solution Exploring Operation: 118-67=51, Resulting Numbers: [51] 51,83 unequal: No Solution Moving to Node #0,1,2 Current State: 83:[74, 23], Operations: ['5+69=74', '67-44=23'] Exploring Operation: 74-23=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 74*23=1702, Resulting Numbers: [1702] 1702,83 unequal: No Solution Exploring Operation: 74+23=97, Resulting Numbers: [97] 97,83 unequal: No Solution Moving to Node #0,1,1 Current State: 83:[67, 30], Operations: ['5+69=74', '74-44=30'] Exploring Operation: 67*30=2010, Resulting Numbers: [2010] 2010,83 unequal: No Solution Exploring Operation: 67+30=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 67-30=37, Resulting Numbers: [37] 37,83 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 Current State: 83:[67, 69, 49], Operations: ['5+44=49'] Exploring Operation: 69+49=118, Resulting Numbers: [67, 118] Generated Node #0,2,0: 83:[67, 118] Operation: 69+49=118 Exploring Operation: 67+49=116, Resulting Numbers: [69, 116] Generated Node #0,2,1: 83:[69, 116] Operation: 67+49=116 Exploring Operation: 67-49=18, Resulting Numbers: [69, 18] Generated Node #0,2,2: 83:[69, 18] Operation: 67-49=18 Exploring Operation: 69-49=20, Resulting Numbers: [67, 20] Generated Node #0,2,3: 83:[67, 20] Operation: 69-49=20 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[69, 116], Operations: ['5+44=49', '67+49=116'] Exploring Operation: 69*116=8004, Resulting Numbers: [8004] 8004,83 unequal: No Solution Exploring Operation: 116-69=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 69+116=185, Resulting Numbers: [185] 185,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[67, 118], Operations: ['5+44=49', '69+49=118'] Exploring Operation: 67+118=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 118-67=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 67*118=7906, Resulting Numbers: [7906] 7906,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 83:[69, 18], Operations: ['5+44=49', '67-49=18'] Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,83 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[67, 20], Operations: ['5+44=49', '69-49=20'] Exploring Operation: 67*20=1340, Resulting Numbers: [1340] 1340,83 unequal: No Solution Exploring Operation: 67-20=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 67+20=87, Resulting Numbers: [87] 87,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 83:[44, 69, 72], Operations: ['67+5=72'] Exploring Operation: 44+72=116, Resulting Numbers: [69, 116] Generated Node #0,3,0: 83:[69, 116] Operation: 44+72=116 Exploring Operation: 72-44=28, Resulting Numbers: [69, 28] Generated Node #0,3,1: 83:[69, 28] Operation: 72-44=28 Exploring Operation: 44+69=113, Resulting Numbers: [72, 113] Generated Node #0,3,2: 83:[72, 113] Operation: 44+69=113 Exploring Operation: 69-44=25, Resulting Numbers: [72, 25] Generated Node #0,3,3: 83:[72, 25] Operation: 69-44=25 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 83:[72, 113], Operations: ['67+5=72', '44+69=113'] Exploring Operation: 72+113=185, Resulting Numbers: [185] 185,83 unequal: No Solution Exploring Operation: 113-72=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 72*113=8136, Resulting Numbers: [8136] 8136,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 83:[69, 116], Operations: ['67+5=72', '44+72=116'] Exploring Operation: 69*116=8004, Resulting Numbers: [8004] 8004,83 unequal: No Solution Exploring Operation: 116-69=47, Resulting Numbers: [47] 47,83 unequal: No Solution Exploring Operation: 69+116=185, Resulting Numbers: [185] 185,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 83:[69, 28], Operations: ['67+5=72', '72-44=28'] Exploring Operation: 69+28=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,83 unequal: No Solution Exploring Operation: 69*28=1932, Resulting Numbers: [1932] 1932,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 83:[72, 25], Operations: ['67+5=72', '69-44=25'] Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,83 unequal: No Solution Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[44, 69, 62], Operations: ['67-5=62'] Exploring Operation: 44+62=106, Resulting Numbers: [69, 106] Generated Node #0,0,0: 83:[69, 106] Operation: 44+62=106 Exploring Operation: 44+69=113, Resulting Numbers: [62, 113] Generated Node #0,0,1: 83:[62, 113] Operation: 44+69=113 Exploring Operation: 62-44=18, Resulting Numbers: [69, 18] Generated Node #0,0,2: 83:[69, 18] Operation: 62-44=18 Exploring Operation: 69-44=25, Resulting Numbers: [62, 25] Generated Node #0,0,3: 83:[62, 25] Operation: 69-44=25 Moving to Node #0,0,0 Current State: 83:[69, 106], Operations: ['67-5=62', '44+62=106'] Exploring Operation: 69+106=175, Resulting Numbers: [175] 175,83 unequal: No Solution Exploring Operation: 106-69=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 69*106=7314, Resulting Numbers: [7314] 7314,83 unequal: No Solution Moving to Node #0,0,1 Current State: 83:[62, 113], Operations: ['67-5=62', '44+69=113'] Exploring Operation: 62*113=7006, Resulting Numbers: [7006] 7006,83 unequal: No Solution Exploring Operation: 113-62=51, Resulting Numbers: [51] 51,83 unequal: No Solution Exploring Operation: 62+113=175, Resulting Numbers: [175] 175,83 unequal: No Solution Moving to Node #0,0,3 Current State: 83:[62, 25], Operations: ['67-5=62', '69-44=25'] Exploring Operation: 62-25=37, Resulting Numbers: [37] 37,83 unequal: No Solution Exploring Operation: 62*25=1550, Resulting Numbers: [1550] 1550,83 unequal: No Solution Exploring Operation: 62+25=87, Resulting Numbers: [87] 87,83 unequal: No Solution Moving to Node #0,0,2 Current State: 83:[69, 18], Operations: ['67-5=62', '62-44=18'] Exploring Operation: 69*18=1242, Resulting Numbers: [1242] 1242,83 unequal: No Solution Exploring Operation: 69+18=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 69-18=51, Resulting Numbers: [51] 51,83 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
[ 88, 27, 62, 55 ]
55
[ "88-27=61", "62-61=1", "55*1=55" ]
Current State: 55:[88, 27, 62, 55], Operations: [] Exploring Operation: 88-27=61, Resulting Numbers: [62, 55, 61] Generated Node #2: [62, 55, 61] from Operation: 88-27=61 Current State: 55:[62, 55, 61], Operations: ['88-27=61'] Exploring Operation: 62-61=1, Resulting Numbers: [55, 1] Generated Node #3: [55, 1] from Operation: 62-61=1 Current State: 55:[55, 1], Operations: ['88-27=61', '62-61=1'] Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[88, 27, 62, 55], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [27, 62, 33] Generated Node #0,0: 55:[27, 62, 33] Operation: 88-55=33 Exploring Operation: 88-62=26, Resulting Numbers: [27, 55, 26] Generated Node #0,1: 55:[27, 55, 26] Operation: 88-62=26 Exploring Operation: 88-27=61, Resulting Numbers: [62, 55, 61] Generated Node #0,2: 55:[62, 55, 61] Operation: 88-27=61 Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[62, 55, 61], Operations: ['88-27=61'] Exploring Operation: 61-55=6, Resulting Numbers: [62, 6] Generated Node #0,2,0: 55:[62, 6] Operation: 61-55=6 Exploring Operation: 62-61=1, Resulting Numbers: [55, 1] Generated Node #0,2,1: 55:[55, 1] Operation: 62-61=1 Exploring Operation: 62-55=7, Resulting Numbers: [61, 7] Generated Node #0,2,2: 55:[61, 7] Operation: 62-55=7 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[55, 1], Operations: ['88-27=61', '62-61=1'] Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,55 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Moving to Node #0 Current State: 55:[88, 27, 62, 55], Operations: [] Exploring Operation: 88-27=61, Resulting Numbers: [62, 55, 61] Generated Node #0,2: 55:[62, 55, 61] Operation: 88-27=61 Moving to Node #0,2 Current State: 55:[62, 55, 61], Operations: ['88-27=61'] Exploring Operation: 62-61=1, Resulting Numbers: [55, 1] Generated Node #0,2,1: 55:[55, 1] Operation: 62-61=1 Moving to Node #0,2,1 Current State: 55:[55, 1], Operations: ['88-27=61', '62-61=1'] Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,55 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 11, 59, 24, 25 ]
47
[ "59-11=48", "25-24=1", "48-1=47" ]
Current State: 47:[11, 59, 24, 25], Operations: [] Exploring Operation: 59-11=48, Resulting Numbers: [24, 25, 48] Generated Node #2: [24, 25, 48] from Operation: 59-11=48 Current State: 47:[24, 25, 48], Operations: ['59-11=48'] Exploring Operation: 25-24=1, Resulting Numbers: [48, 1] Generated Node #3: [48, 1] from Operation: 25-24=1 Current State: 47:[48, 1], Operations: ['59-11=48', '25-24=1'] Exploring Operation: 48-1=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[11, 59, 24, 25], Operations: [] Exploring Operation: 11+24=35, Resulting Numbers: [59, 25, 35] Generated Node #0,0: 47:[59, 25, 35] Operation: 11+24=35 Exploring Operation: 59-11=48, Resulting Numbers: [24, 25, 48] Generated Node #0,1: 47:[24, 25, 48] Operation: 59-11=48 Exploring Operation: 24+25=49, Resulting Numbers: [11, 59, 49] Generated Node #0,2: 47:[11, 59, 49] Operation: 24+25=49 Exploring Operation: 11+25=36, Resulting Numbers: [59, 24, 36] Generated Node #0,3: 47:[59, 24, 36] Operation: 11+25=36 Exploring Operation: 11+59=70, Resulting Numbers: [24, 25, 70] Generated Node #0,4: 47:[24, 25, 70] Operation: 11+59=70 Moving to Node #0,0 Current State: 47:[59, 25, 35], Operations: ['11+24=35'] Exploring Operation: 59-35=24, Resulting Numbers: [25, 24] Generated Node #0,0,0: 47:[25, 24] Operation: 59-35=24 Exploring Operation: 59+25=84, Resulting Numbers: [35, 84] Generated Node #0,0,1: 47:[35, 84] Operation: 59+25=84 Exploring Operation: 59-25=34, Resulting Numbers: [35, 34] Generated Node #0,0,2: 47:[35, 34] Operation: 59-25=34 Exploring Operation: 25+35=60, Resulting Numbers: [59, 60] Generated Node #0,0,3: 47:[59, 60] Operation: 25+35=60 Exploring Operation: 35-25=10, Resulting Numbers: [59, 10] Generated Node #0,0,4: 47:[59, 10] Operation: 35-25=10 Moving to Node #0,3 Current State: 47:[59, 24, 36], Operations: ['11+25=36'] Exploring Operation: 59-24=35, Resulting Numbers: [36, 35] Generated Node #0,3,0: 47:[36, 35] Operation: 59-24=35 Exploring Operation: 36-24=12, Resulting Numbers: [59, 12] Generated Node #0,3,1: 47:[59, 12] Operation: 36-24=12 Exploring Operation: 59-36=23, Resulting Numbers: [24, 23] Generated Node #0,3,2: 47:[24, 23] Operation: 59-36=23 Exploring Operation: 24+36=60, Resulting Numbers: [59, 60] Generated Node #0,3,3: 47:[59, 60] Operation: 24+36=60 Exploring Operation: 59+24=83, Resulting Numbers: [36, 83] Generated Node #0,3,4: 47:[36, 83] Operation: 59+24=83 Moving to Node #0,1 Current State: 47:[24, 25, 48], Operations: ['59-11=48'] Exploring Operation: 25-24=1, Resulting Numbers: [48, 1] Generated Node #0,1,0: 47:[48, 1] Operation: 25-24=1 Exploring Operation: 24+25=49, Resulting Numbers: [48, 49] Generated Node #0,1,1: 47:[48, 49] Operation: 24+25=49 Exploring Operation: 48-24=24, Resulting Numbers: [25, 24] Generated Node #0,1,2: 47:[25, 24] Operation: 48-24=24 Exploring Operation: 48-25=23, Resulting Numbers: [24, 23] Generated Node #0,1,3: 47:[24, 23] Operation: 48-25=23 Exploring Operation: 24+48=72, Resulting Numbers: [25, 72] Generated Node #0,1,4: 47:[25, 72] Operation: 24+48=72 Moving to Node #0,2 Current State: 47:[11, 59, 49], Operations: ['24+25=49'] Exploring Operation: 59-11=48, Resulting Numbers: [49, 48] Generated Node #0,2,0: 47:[49, 48] Operation: 59-11=48 Exploring Operation: 49-11=38, Resulting Numbers: [59, 38] Generated Node #0,2,1: 47:[59, 38] Operation: 49-11=38 Exploring Operation: 11+49=60, Resulting Numbers: [59, 60] Generated Node #0,2,2: 47:[59, 60] Operation: 11+49=60 Exploring Operation: 59-49=10, Resulting Numbers: [11, 10] Generated Node #0,2,3: 47:[11, 10] Operation: 59-49=10 Exploring Operation: 11+59=70, Resulting Numbers: [49, 70] Generated Node #0,2,4: 47:[49, 70] Operation: 11+59=70 Moving to Node #0,4 Current State: 47:[24, 25, 70], Operations: ['11+59=70'] Exploring Operation: 24+70=94, Resulting Numbers: [25, 94] Generated Node #0,4,0: 47:[25, 94] Operation: 24+70=94 Exploring Operation: 24+25=49, Resulting Numbers: [70, 49] Generated Node #0,4,1: 47:[70, 49] Operation: 24+25=49 Exploring Operation: 70-24=46, Resulting Numbers: [25, 46] Generated Node #0,4,2: 47:[25, 46] Operation: 70-24=46 Exploring Operation: 25-24=1, Resulting Numbers: [70, 1] Generated Node #0,4,3: 47:[70, 1] Operation: 25-24=1 Exploring Operation: 70-25=45, Resulting Numbers: [24, 45] Generated Node #0,4,4: 47:[24, 45] Operation: 70-25=45 Moving to Node #0,1,1 Current State: 47:[48, 49], Operations: ['59-11=48', '24+25=49'] Exploring Operation: 48*49=2352, Resulting Numbers: [2352] 2352,47 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 48+49=97, Resulting Numbers: [97] 97,47 unequal: No Solution Moving to Node #0,2,0 Current State: 47:[49, 48], Operations: ['24+25=49', '59-11=48'] Exploring Operation: 49+48=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 49-48=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 49*48=2352, Resulting Numbers: [2352] 2352,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[59, 38], Operations: ['24+25=49', '49-11=38'] Exploring Operation: 59+38=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 59-38=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 59*38=2242, Resulting Numbers: [2242] 2242,47 unequal: No Solution Moving to Node #0,4,2 Current State: 47:[25, 46], Operations: ['11+59=70', '70-24=46'] Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,47 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,47 unequal: No Solution Moving to Node #0,3,0 Current State: 47:[36, 35], Operations: ['11+25=36', '59-24=35'] Exploring Operation: 36+35=71, Resulting Numbers: [71] 71,47 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 36*35=1260, Resulting Numbers: [1260] 1260,47 unequal: No Solution Moving to Node #0,0,2 Current State: 47:[35, 34], Operations: ['11+24=35', '59-25=34'] Exploring Operation: 35-34=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 35*34=1190, Resulting Numbers: [1190] 1190,47 unequal: No Solution Exploring Operation: 35+34=69, Resulting Numbers: [69] 69,47 unequal: No Solution Moving to Node #0,3,3 Current State: 47:[59, 60], Operations: ['11+25=36', '24+36=60'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,47 unequal: No Solution Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,47 unequal: No Solution Moving to Node #0,4,1 Current State: 47:[70, 49], Operations: ['11+59=70', '24+25=49'] Exploring Operation: 70+49=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 70*49=3430, Resulting Numbers: [3430] 3430,47 unequal: No Solution Moving to Node #0,4,4 Current State: 47:[24, 45], Operations: ['11+59=70', '70-25=45'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,47 unequal: No Solution Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,47 unequal: No Solution Moving to Node #0,0,3 Current State: 47:[59, 60], Operations: ['11+24=35', '25+35=60'] Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[59, 60], Operations: ['24+25=49', '11+49=60'] Exploring Operation: 60-59=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 59*60=3540, Resulting Numbers: [3540] 3540,47 unequal: No Solution Exploring Operation: 59+60=119, Resulting Numbers: [119] 119,47 unequal: No Solution Moving to Node #0,2,4 Current State: 47:[49, 70], Operations: ['24+25=49', '11+59=70'] Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,47 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,47 unequal: No Solution Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,47 unequal: No Solution Moving to Node #0,0,0 Current State: 47:[25, 24], Operations: ['11+24=35', '59-35=24'] Exploring Operation: 25+24=49, Resulting Numbers: [49] 49,47 unequal: No Solution Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 25*24=600, Resulting Numbers: [600] 600,47 unequal: No Solution Moving to Node #0,1,2 Current State: 47:[25, 24], Operations: ['59-11=48', '48-24=24'] Exploring Operation: 25-24=1, Resulting Numbers: [1] 1,47 unequal: No Solution Exploring Operation: 25*24=600, Resulting Numbers: [600] 600,47 unequal: No Solution Exploring Operation: 25+24=49, Resulting Numbers: [49] 49,47 unequal: No Solution Moving to Node #0,1,4 Current State: 47:[25, 72], Operations: ['59-11=48', '24+48=72'] Exploring Operation: 25*72=1800, Resulting Numbers: [1800] 1800,47 unequal: No Solution Exploring Operation: 25+72=97, Resulting Numbers: [97] 97,47 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,47 equal: Goal Reached Moving to Node #0 Current State: 47:[11, 59, 24, 25], Operations: [] Exploring Operation: 59-11=48, Resulting Numbers: [24, 25, 48] Generated Node #0,1: 47:[24, 25, 48] Operation: 59-11=48 Moving to Node #0,1 Current State: 47:[24, 25, 48], Operations: ['59-11=48'] Exploring Operation: 24+48=72, Resulting Numbers: [25, 72] Generated Node #0,1,4: 47:[25, 72] Operation: 24+48=72 Moving to Node #0,1,4 Current State: 47:[25, 72], Operations: ['59-11=48', '24+48=72'] Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
0.931424
hs_5
mult_heuristic
[ 5, 3, 4, 33 ]
22
[ "5*3=15", "4+33=37", "37-15=22" ]
Current State: 22:[5, 3, 4, 33], Operations: [] Exploring Operation: 5*3=15, Resulting Numbers: [4, 33, 15] Generated Node #2: [4, 33, 15] from Operation: 5*3=15 Current State: 22:[4, 33, 15], Operations: ['5*3=15'] Exploring Operation: 4+33=37, Resulting Numbers: [15, 37] Generated Node #3: [15, 37] from Operation: 4+33=37 Current State: 22:[15, 37], Operations: ['5*3=15', '4+33=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[5, 3, 4, 33], Operations: [] Exploring Operation: 33/3=11, Resulting Numbers: [5, 4, 11] Generated Node #0,0: 22:[5, 4, 11] Operation: 33/3=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 22:[5, 4, 11], Operations: ['33/3=11'] Exploring Operation: 5-4=1, Resulting Numbers: [11, 1] Generated Node #0,0,0: 22:[11, 1] Operation: 5-4=1 Moving to Node #0,0,0 Current State: 22:[11, 1], Operations: ['33/3=11', '5-4=1'] Exploring Operation: 11*1=11, Resulting Numbers: [11] 11,22 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
[ 11, 93, 26, 98 ]
32
[ "11+93=104", "98-26=72", "104-72=32" ]
Current State: 32:[11, 93, 26, 98], Operations: [] Exploring Operation: 11+93=104, Resulting Numbers: [26, 98, 104] Generated Node #2: [26, 98, 104] from Operation: 11+93=104 Current State: 32:[26, 98, 104], Operations: ['11+93=104'] Exploring Operation: 98-26=72, Resulting Numbers: [104, 72] Generated Node #3: [104, 72] from Operation: 98-26=72 Current State: 32:[104, 72], Operations: ['11+93=104', '98-26=72'] Exploring Operation: 104-72=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[11, 93, 26, 98], Operations: [] Exploring Operation: 98-26=72, Resulting Numbers: [11, 93, 72] Generated Node #0,0: 32:[11, 93, 72] Operation: 98-26=72 Exploring Operation: 93-26=67, Resulting Numbers: [11, 98, 67] Generated Node #0,1: 32:[11, 98, 67] Operation: 93-26=67 Exploring Operation: 98-93=5, Resulting Numbers: [11, 26, 5] Generated Node #0,2: 32:[11, 26, 5] Operation: 98-93=5 Start Sub Search at level 1: Moving to Node #0,2 Current State: 32:[11, 26, 5], Operations: ['98-93=5'] Exploring Operation: 26-11=15, Resulting Numbers: [5, 15] Generated Node #0,2,0: 32:[5, 15] Operation: 26-11=15 Exploring Operation: 11+26=37, Resulting Numbers: [5, 37] Generated Node #0,2,1: 32:[5, 37] Operation: 11+26=37 Exploring Operation: 26+5=31, Resulting Numbers: [11, 31] Generated Node #0,2,2: 32:[11, 31] Operation: 26+5=31 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 32:[5, 15], Operations: ['98-93=5', '26-11=15'] Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,32 unequal: No Solution Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,32 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 32:[11, 31], Operations: ['98-93=5', '26+5=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,32 unequal: No Solution Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,32 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,32 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 32:[5, 37], Operations: ['98-93=5', '11+26=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[11, 93, 26, 98], Operations: [] Exploring Operation: 98-93=5, Resulting Numbers: [11, 26, 5] Generated Node #0,2: 32:[11, 26, 5] Operation: 98-93=5 Moving to Node #0,2 Current State: 32:[11, 26, 5], Operations: ['98-93=5'] Exploring Operation: 11+26=37, Resulting Numbers: [5, 37] Generated Node #0,2,1: 32:[5, 37] Operation: 11+26=37 Moving to Node #0,2,1 Current State: 32:[5, 37], Operations: ['98-93=5', '11+26=37'] Exploring Operation: 37-5=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 4, 30, 11, 57 ]
52
[ "4*30=120", "11+57=68", "120-68=52" ]
Current State: 52:[4, 30, 11, 57], Operations: [] Exploring Operation: 4*30=120, Resulting Numbers: [11, 57, 120] Generated Node #2: [11, 57, 120] from Operation: 4*30=120 Current State: 52:[11, 57, 120], Operations: ['4*30=120'] Exploring Operation: 11+57=68, Resulting Numbers: [120, 68] Generated Node #3: [120, 68] from Operation: 11+57=68 Current State: 52:[120, 68], Operations: ['4*30=120', '11+57=68'] Exploring Operation: 120-68=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[4, 30, 11, 57], Operations: [] Exploring Operation: 30-4=26, Resulting Numbers: [11, 57, 26] Generated Node #0,0: 52:[11, 57, 26] Operation: 30-4=26 Exploring Operation: 57-4=53, Resulting Numbers: [30, 11, 53] Generated Node #0,1: 52:[30, 11, 53] Operation: 57-4=53 Exploring Operation: 4+11=15, Resulting Numbers: [30, 57, 15] Generated Node #0,2: 52:[30, 57, 15] Operation: 4+11=15 Exploring Operation: 57-11=46, Resulting Numbers: [4, 30, 46] Generated Node #0,3: 52:[4, 30, 46] Operation: 57-11=46 Exploring Operation: 57-30=27, Resulting Numbers: [4, 11, 27] Generated Node #0,4: 52:[4, 11, 27] Operation: 57-30=27 Start Sub Search at level 1: Moving to Node #0,4 Current State: 52:[4, 11, 27], Operations: ['57-30=27'] Exploring Operation: 27-4=23, Resulting Numbers: [11, 23] Generated Node #0,4,0: 52:[11, 23] Operation: 27-4=23 Exploring Operation: 4+27=31, Resulting Numbers: [11, 31] Generated Node #0,4,1: 52:[11, 31] Operation: 4+27=31 Exploring Operation: 4+11=15, Resulting Numbers: [27, 15] Generated Node #0,4,2: 52:[27, 15] Operation: 4+11=15 Exploring Operation: 11-4=7, Resulting Numbers: [27, 7] Generated Node #0,4,3: 52:[27, 7] Operation: 11-4=7 Exploring Operation: 27-11=16, Resulting Numbers: [4, 16] Generated Node #0,4,4: 52:[4, 16] Operation: 27-11=16 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 52:[27, 15], Operations: ['57-30=27', '4+11=15'] Exploring Operation: 27+15=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 27*15=405, Resulting Numbers: [405] 405,52 unequal: No Solution No 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: 52:[4, 16], Operations: ['57-30=27', '27-11=16'] Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 52:[27, 7], Operations: ['57-30=27', '11-4=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 27*7=189, Resulting Numbers: [189] 189,52 unequal: No Solution Exploring Operation: 27+7=34, Resulting Numbers: [34] 34,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 52:[11, 23], Operations: ['57-30=27', '27-4=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 52:[11, 31], Operations: ['57-30=27', '4+27=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,52 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,52 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: 52:[11, 57, 26], Operations: ['30-4=26'] Exploring Operation: 57-26=31, Resulting Numbers: [11, 31] Generated Node #0,0,0: 52:[11, 31] Operation: 57-26=31 Exploring Operation: 57-11=46, Resulting Numbers: [26, 46] Generated Node #0,0,1: 52:[26, 46] Operation: 57-11=46 Exploring Operation: 11+26=37, Resulting Numbers: [57, 37] Generated Node #0,0,2: 52:[57, 37] Operation: 11+26=37 Exploring Operation: 11+57=68, Resulting Numbers: [26, 68] Generated Node #0,0,3: 52:[26, 68] Operation: 11+57=68 Exploring Operation: 26-11=15, Resulting Numbers: [57, 15] Generated Node #0,0,4: 52:[57, 15] Operation: 26-11=15 Moving to Node #0,0,1 Current State: 52:[26, 46], Operations: ['30-4=26', '57-11=46'] Exploring Operation: 26+46=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 26*46=1196, Resulting Numbers: [1196] 1196,52 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[57, 15], Operations: ['30-4=26', '26-11=15'] Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[11, 31], Operations: ['30-4=26', '57-26=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,52 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[57, 37], Operations: ['30-4=26', '11+26=37'] Exploring Operation: 57*37=2109, Resulting Numbers: [2109] 2109,52 unequal: No Solution Exploring Operation: 57-37=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 57+37=94, Resulting Numbers: [94] 94,52 unequal: No Solution Moving to Node #0,0,3 Current State: 52:[26, 68], Operations: ['30-4=26', '11+57=68'] Exploring Operation: 68-26=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 26+68=94, Resulting Numbers: [94] 94,52 unequal: No Solution Exploring Operation: 26*68=1768, Resulting Numbers: [1768] 1768,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 52:[30, 11, 53], Operations: ['57-4=53'] Exploring Operation: 53-11=42, Resulting Numbers: [30, 42] Generated Node #0,1,0: 52:[30, 42] Operation: 53-11=42 Exploring Operation: 30-11=19, Resulting Numbers: [53, 19] Generated Node #0,1,1: 52:[53, 19] Operation: 30-11=19 Exploring Operation: 30+11=41, Resulting Numbers: [53, 41] Generated Node #0,1,2: 52:[53, 41] Operation: 30+11=41 Exploring Operation: 11+53=64, Resulting Numbers: [30, 64] Generated Node #0,1,3: 52:[30, 64] Operation: 11+53=64 Exploring Operation: 53-30=23, Resulting Numbers: [11, 23] Generated Node #0,1,4: 52:[11, 23] Operation: 53-30=23 Moving to Node #0,1,4 Current State: 52:[11, 23], Operations: ['57-4=53', '53-30=23'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,52 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,52 unequal: No Solution Moving to Node #0,1,1 Current State: 52:[53, 19], Operations: ['57-4=53', '30-11=19'] Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 53*19=1007, Resulting Numbers: [1007] 1007,52 unequal: No Solution Moving to Node #0,1,2 Current State: 52:[53, 41], Operations: ['57-4=53', '30+11=41'] Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,52 unequal: No Solution Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,52 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,52 unequal: No Solution Moving to Node #0,1,0 Current State: 52:[30, 42], Operations: ['57-4=53', '53-11=42'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,52 unequal: No Solution Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,52 unequal: No Solution Moving to Node #0,1,3 Current State: 52:[30, 64], Operations: ['57-4=53', '11+53=64'] Exploring Operation: 30+64=94, Resulting Numbers: [94] 94,52 unequal: No Solution Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,52 unequal: No Solution Exploring Operation: 30*64=1920, Resulting Numbers: [1920] 1920,52 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 52:[4, 30, 46], Operations: ['57-11=46'] Exploring Operation: 4+30=34, Resulting Numbers: [46, 34] Generated Node #0,3,0: 52:[46, 34] Operation: 4+30=34 Exploring Operation: 46-4=42, Resulting Numbers: [30, 42] Generated Node #0,3,1: 52:[30, 42] Operation: 46-4=42 Exploring Operation: 46-30=16, Resulting Numbers: [4, 16] Generated Node #0,3,2: 52:[4, 16] Operation: 46-30=16 Exploring Operation: 30-4=26, Resulting Numbers: [46, 26] Generated Node #0,3,3: 52:[46, 26] Operation: 30-4=26 Exploring Operation: 4+46=50, Resulting Numbers: [30, 50] Generated Node #0,3,4: 52:[30, 50] Operation: 4+46=50 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 52:[4, 16], Operations: ['57-11=46', '46-30=16'] Exploring Operation: 4*16=64, Resulting Numbers: [64] 64,52 unequal: No Solution Exploring Operation: 16-4=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,52 unequal: No Solution No 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: 52:[46, 26], Operations: ['57-11=46', '30-4=26'] Exploring Operation: 46+26=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 46*26=1196, Resulting Numbers: [1196] 1196,52 unequal: No Solution Exploring Operation: 46-26=20, Resulting Numbers: [20] 20,52 unequal: No Solution No 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: 52:[30, 50], Operations: ['57-11=46', '4+46=50'] Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,52 unequal: No Solution Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,52 unequal: No Solution No 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: 52:[46, 34], Operations: ['57-11=46', '4+30=34'] Exploring Operation: 46+34=80, Resulting Numbers: [80] 80,52 unequal: No Solution Exploring Operation: 46-34=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 46*34=1564, Resulting Numbers: [1564] 1564,52 unequal: No Solution No 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: 52:[30, 42], Operations: ['57-11=46', '46-4=42'] Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,52 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: 52:[30, 57, 15], Operations: ['4+11=15'] Exploring Operation: 57-30=27, Resulting Numbers: [15, 27] Generated Node #0,2,0: 52:[15, 27] Operation: 57-30=27 Exploring Operation: 30+15=45, Resulting Numbers: [57, 45] Generated Node #0,2,1: 52:[57, 45] Operation: 30+15=45 Exploring Operation: 30-15=15, Resulting Numbers: [57, 15] Generated Node #0,2,2: 52:[57, 15] Operation: 30-15=15 Exploring Operation: 57-15=42, Resulting Numbers: [30, 42] Generated Node #0,2,3: 52:[30, 42] Operation: 57-15=42 Exploring Operation: 30/15=2, Resulting Numbers: [57, 2] Generated Node #0,2,4: 52:[57, 2] Operation: 30/15=2 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 52:[15, 27], Operations: ['4+11=15', '57-30=27'] Exploring Operation: 15+27=42, Resulting Numbers: [42] 42,52 unequal: No Solution Exploring Operation: 27-15=12, Resulting Numbers: [12] 12,52 unequal: No Solution Exploring Operation: 15*27=405, Resulting Numbers: [405] 405,52 unequal: No Solution No 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: 52:[57, 2], Operations: ['4+11=15', '30/15=2'] Exploring Operation: 57*2=114, Resulting Numbers: [114] 114,52 unequal: No Solution Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,52 unequal: No Solution No 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: 52:[57, 15], Operations: ['4+11=15', '30-15=15'] Exploring Operation: 57+15=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 57*15=855, Resulting Numbers: [855] 855,52 unequal: No Solution Exploring Operation: 57-15=42, Resulting Numbers: [42] 42,52 unequal: No Solution No 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: 52:[57, 45], Operations: ['4+11=15', '30+15=45'] Exploring Operation: 57+45=102, Resulting Numbers: [102] 102,52 unequal: No Solution Exploring Operation: 57*45=2565, Resulting Numbers: [2565] 2565,52 unequal: No Solution Exploring Operation: 57-45=12, Resulting Numbers: [12] 12,52 unequal: No Solution No 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: 52:[30, 42], Operations: ['4+11=15', '57-15=42'] Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,52 unequal: No Solution Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,52 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,52 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 37, 46, 33, 23 ]
46
[ "37-33=4", "23*4=92", "92-46=46" ]
Current State: 46:[37, 46, 33, 23], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [46, 23, 4] Generated Node #2: [46, 23, 4] from Operation: 37-33=4 Current State: 46:[46, 23, 4], Operations: ['37-33=4'] Exploring Operation: 23*4=92, Resulting Numbers: [46, 92] Generated Node #3: [46, 92] from Operation: 23*4=92 Current State: 46:[46, 92], Operations: ['37-33=4', '23*4=92'] Exploring Operation: 92-46=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[37, 46, 33, 23], Operations: [] Exploring Operation: 37-33=4, Resulting Numbers: [46, 23, 4] Generated Node #0,0: 46:[46, 23, 4] Operation: 37-33=4 Exploring Operation: 46-33=13, Resulting Numbers: [37, 23, 13] Generated Node #0,1: 46:[37, 23, 13] Operation: 46-33=13 Exploring Operation: 37-23=14, Resulting Numbers: [46, 33, 14] Generated Node #0,2: 46:[46, 33, 14] Operation: 37-23=14 Exploring Operation: 46-37=9, Resulting Numbers: [33, 23, 9] Generated Node #0,3: 46:[33, 23, 9] Operation: 46-37=9 Exploring Operation: 33-23=10, Resulting Numbers: [37, 46, 10] Generated Node #0,4: 46:[37, 46, 10] Operation: 33-23=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[46, 23, 4], Operations: ['37-33=4'] Exploring Operation: 46-23=23, Resulting Numbers: [4, 23] Generated Node #0,0,0: 46:[4, 23] Operation: 46-23=23 Exploring Operation: 46+4=50, Resulting Numbers: [23, 50] Generated Node #0,0,1: 46:[23, 50] Operation: 46+4=50 Exploring Operation: 46/23=2, Resulting Numbers: [4, 2] Generated Node #0,0,2: 46:[4, 2] Operation: 46/23=2 Exploring Operation: 46-4=42, Resulting Numbers: [23, 42] Generated Node #0,0,3: 46:[23, 42] Operation: 46-4=42 Exploring Operation: 23+4=27, Resulting Numbers: [46, 27] Generated Node #0,0,4: 46:[46, 27] Operation: 23+4=27 Moving to Node #0,0,0 Current State: 46:[4, 23], Operations: ['37-33=4', '46-23=23'] Exploring Operation: 4+23=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 4*23=92, Resulting Numbers: [92] 92,46 unequal: No Solution Exploring Operation: 23-4=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,0,2 Current State: 46:[4, 2], Operations: ['37-33=4', '46/23=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,46 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,46 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[23, 50], Operations: ['37-33=4', '46+4=50'] Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,46 unequal: No Solution Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,46 unequal: No Solution Moving to Node #0,0,3 Current State: 46:[23, 42], Operations: ['37-33=4', '46-4=42'] Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,46 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,0,4 Current State: 46:[46, 27], Operations: ['37-33=4', '23+4=27'] Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,46 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 46:[33, 23, 9], Operations: ['46-37=9'] Exploring Operation: 33+23=56, Resulting Numbers: [9, 56] Generated Node #0,3,0: 46:[9, 56] Operation: 33+23=56 Exploring Operation: 23+9=32, Resulting Numbers: [33, 32] Generated Node #0,3,1: 46:[33, 32] Operation: 23+9=32 Exploring Operation: 33+9=42, Resulting Numbers: [23, 42] Generated Node #0,3,2: 46:[23, 42] Operation: 33+9=42 Exploring Operation: 33-23=10, Resulting Numbers: [9, 10] Generated Node #0,3,3: 46:[9, 10] Operation: 33-23=10 Exploring Operation: 33-9=24, Resulting Numbers: [23, 24] Generated Node #0,3,4: 46:[23, 24] Operation: 33-9=24 Moving to Node #0,3,4 Current State: 46:[23, 24], Operations: ['46-37=9', '33-9=24'] Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,46 unequal: No Solution Moving to Node #0,3,2 Current State: 46:[23, 42], Operations: ['46-37=9', '33+9=42'] Exploring Operation: 23*42=966, Resulting Numbers: [966] 966,46 unequal: No Solution Exploring Operation: 23+42=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 42-23=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,3,3 Current State: 46:[9, 10], Operations: ['46-37=9', '33-23=10'] Exploring Operation: 9*10=90, Resulting Numbers: [90] 90,46 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 9+10=19, Resulting Numbers: [19] 19,46 unequal: No Solution Moving to Node #0,3,0 Current State: 46:[9, 56], Operations: ['46-37=9', '33+23=56'] Exploring Operation: 9*56=504, Resulting Numbers: [504] 504,46 unequal: No Solution Exploring Operation: 56-9=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 9+56=65, Resulting Numbers: [65] 65,46 unequal: No Solution Moving to Node #0,3,1 Current State: 46:[33, 32], Operations: ['46-37=9', '23+9=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 46:[37, 46, 10], Operations: ['33-23=10'] Exploring Operation: 37+10=47, Resulting Numbers: [46, 47] Generated Node #0,4,0: 46:[46, 47] Operation: 37+10=47 Exploring Operation: 46-37=9, Resulting Numbers: [10, 9] Generated Node #0,4,1: 46:[10, 9] Operation: 46-37=9 Exploring Operation: 46+10=56, Resulting Numbers: [37, 56] Generated Node #0,4,2: 46:[37, 56] Operation: 46+10=56 Exploring Operation: 46-10=36, Resulting Numbers: [37, 36] Generated Node #0,4,3: 46:[37, 36] Operation: 46-10=36 Exploring Operation: 37-10=27, Resulting Numbers: [46, 27] Generated Node #0,4,4: 46:[46, 27] Operation: 37-10=27 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 46:[46, 47], Operations: ['33-23=10', '37+10=47'] Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,46 unequal: No Solution Exploring Operation: 46*47=2162, Resulting Numbers: [2162] 2162,46 unequal: No Solution No 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: 46:[46, 27], Operations: ['33-23=10', '37-10=27'] Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 46:[10, 9], Operations: ['33-23=10', '46-37=9'] Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 10*9=90, Resulting Numbers: [90] 90,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 46:[37, 56], Operations: ['33-23=10', '46+10=56'] Exploring Operation: 37*56=2072, Resulting Numbers: [2072] 2072,46 unequal: No Solution Exploring Operation: 56-37=19, Resulting Numbers: [19] 19,46 unequal: No Solution Exploring Operation: 37+56=93, Resulting Numbers: [93] 93,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 46:[37, 36], Operations: ['33-23=10', '46-10=36'] Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,46 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 46:[37, 23, 13], Operations: ['46-33=13'] Exploring Operation: 23+13=36, Resulting Numbers: [37, 36] Generated Node #0,1,0: 46:[37, 36] Operation: 23+13=36 Exploring Operation: 23-13=10, Resulting Numbers: [37, 10] Generated Node #0,1,1: 46:[37, 10] Operation: 23-13=10 Exploring Operation: 37+13=50, Resulting Numbers: [23, 50] Generated Node #0,1,2: 46:[23, 50] Operation: 37+13=50 Exploring Operation: 37-23=14, Resulting Numbers: [13, 14] Generated Node #0,1,3: 46:[13, 14] Operation: 37-23=14 Exploring Operation: 37-13=24, Resulting Numbers: [23, 24] Generated Node #0,1,4: 46:[23, 24] Operation: 37-13=24 Moving to Node #0,1,4 Current State: 46:[23, 24], Operations: ['46-33=13', '37-13=24'] Exploring Operation: 24-23=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 23+24=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 23*24=552, Resulting Numbers: [552] 552,46 unequal: No Solution Moving to Node #0,1,2 Current State: 46:[23, 50], Operations: ['46-33=13', '37+13=50'] Exploring Operation: 50-23=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 23*50=1150, Resulting Numbers: [1150] 1150,46 unequal: No Solution Exploring Operation: 23+50=73, Resulting Numbers: [73] 73,46 unequal: No Solution Moving to Node #0,1,1 Current State: 46:[37, 10], Operations: ['46-33=13', '23-13=10'] Exploring Operation: 37-10=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 37+10=47, Resulting Numbers: [47] 47,46 unequal: No Solution Exploring Operation: 37*10=370, Resulting Numbers: [370] 370,46 unequal: No Solution Moving to Node #0,1,0 Current State: 46:[37, 36], Operations: ['46-33=13', '23+13=36'] Exploring Operation: 37*36=1332, Resulting Numbers: [1332] 1332,46 unequal: No Solution Exploring Operation: 37+36=73, Resulting Numbers: [73] 73,46 unequal: No Solution Exploring Operation: 37-36=1, Resulting Numbers: [1] 1,46 unequal: No Solution Moving to Node #0,1,3 Current State: 46:[13, 14], Operations: ['46-33=13', '37-23=14'] Exploring Operation: 13*14=182, Resulting Numbers: [182] 182,46 unequal: No Solution Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 46:[46, 33, 14], Operations: ['37-23=14'] Exploring Operation: 46+14=60, Resulting Numbers: [33, 60] Generated Node #0,2,0: 46:[33, 60] Operation: 46+14=60 Exploring Operation: 33+14=47, Resulting Numbers: [46, 47] Generated Node #0,2,1: 46:[46, 47] Operation: 33+14=47 Exploring Operation: 46-33=13, Resulting Numbers: [14, 13] Generated Node #0,2,2: 46:[14, 13] Operation: 46-33=13 Exploring Operation: 33-14=19, Resulting Numbers: [46, 19] Generated Node #0,2,3: 46:[46, 19] Operation: 33-14=19 Exploring Operation: 46-14=32, Resulting Numbers: [33, 32] Generated Node #0,2,4: 46:[33, 32] Operation: 46-14=32 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 46:[46, 47], Operations: ['37-23=14', '33+14=47'] Exploring Operation: 46+47=93, Resulting Numbers: [93] 93,46 unequal: No Solution Exploring Operation: 47-46=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 46*47=2162, Resulting Numbers: [2162] 2162,46 unequal: No Solution No 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: 46:[46, 19], Operations: ['37-23=14', '33-14=19'] Exploring Operation: 46+19=65, Resulting Numbers: [65] 65,46 unequal: No Solution Exploring Operation: 46*19=874, Resulting Numbers: [874] 874,46 unequal: No Solution Exploring Operation: 46-19=27, Resulting Numbers: [27] 27,46 unequal: No Solution No 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: 46:[14, 13], Operations: ['37-23=14', '46-33=13'] Exploring Operation: 14*13=182, Resulting Numbers: [182] 182,46 unequal: No Solution Exploring Operation: 14+13=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 14-13=1, Resulting Numbers: [1] 1,46 unequal: No Solution No 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: 46:[33, 32], Operations: ['37-23=14', '46-14=32'] Exploring Operation: 33-32=1, Resulting Numbers: [1] 1,46 unequal: No Solution Exploring Operation: 33*32=1056, Resulting Numbers: [1056] 1056,46 unequal: No Solution Exploring Operation: 33+32=65, Resulting Numbers: [65] 65,46 unequal: No Solution No 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: 46:[33, 60], Operations: ['37-23=14', '46+14=60'] Exploring Operation: 33*60=1980, Resulting Numbers: [1980] 1980,46 unequal: No Solution Exploring Operation: 60-33=27, Resulting Numbers: [27] 27,46 unequal: No Solution Exploring Operation: 33+60=93, Resulting Numbers: [93] 93,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 63, 28, 32, 39 ]
36
[ "63-28=35", "32+39=71", "71-35=36" ]
Current State: 36:[63, 28, 32, 39], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [32, 39, 35] Generated Node #2: [32, 39, 35] from Operation: 63-28=35 Current State: 36:[32, 39, 35], Operations: ['63-28=35'] Exploring Operation: 32+39=71, Resulting Numbers: [35, 71] Generated Node #3: [35, 71] from Operation: 32+39=71 Current State: 36:[35, 71], Operations: ['63-28=35', '32+39=71'] Exploring Operation: 71-35=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[63, 28, 32, 39], Operations: [] Exploring Operation: 32-28=4, Resulting Numbers: [63, 39, 4] Generated Node #0,0: 36:[63, 39, 4] Operation: 32-28=4 Exploring Operation: 63-39=24, Resulting Numbers: [28, 32, 24] Generated Node #0,1: 36:[28, 32, 24] Operation: 63-39=24 Exploring Operation: 63-28=35, Resulting Numbers: [32, 39, 35] Generated Node #0,2: 36:[32, 39, 35] Operation: 63-28=35 Exploring Operation: 63-32=31, Resulting Numbers: [28, 39, 31] Generated Node #0,3: 36:[28, 39, 31] Operation: 63-32=31 Start Sub Search at level 1: Moving to Node #0,2 Current State: 36:[32, 39, 35], Operations: ['63-28=35'] Exploring Operation: 35-32=3, Resulting Numbers: [39, 3] Generated Node #0,2,0: 36:[39, 3] Operation: 35-32=3 Exploring Operation: 39-32=7, Resulting Numbers: [35, 7] Generated Node #0,2,1: 36:[35, 7] Operation: 39-32=7 Exploring Operation: 39-35=4, Resulting Numbers: [32, 4] Generated Node #0,2,2: 36:[32, 4] Operation: 39-35=4 Exploring Operation: 32+35=67, Resulting Numbers: [39, 67] Generated Node #0,2,3: 36:[39, 67] Operation: 32+35=67 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[35, 7], Operations: ['63-28=35', '39-32=7'] Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,36 unequal: No Solution Exploring Operation: 35+7=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 35*7=245, Resulting Numbers: [245] 245,36 unequal: No Solution No 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: 36:[39, 3], Operations: ['63-28=35', '35-32=3'] Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 39+3=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[63, 28, 32, 39], Operations: [] Exploring Operation: 63-28=35, Resulting Numbers: [32, 39, 35] Generated Node #0,2: 36:[32, 39, 35] Operation: 63-28=35 Moving to Node #0,2 Current State: 36:[32, 39, 35], Operations: ['63-28=35'] Exploring Operation: 35-32=3, Resulting Numbers: [39, 3] Generated Node #0,2,0: 36:[39, 3] Operation: 35-32=3 Moving to Node #0,2,0 Current State: 36:[39, 3], Operations: ['63-28=35', '35-32=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
mult_heuristic
[ 24, 31, 24, 19 ]
60
[ "24+31=55", "24-19=5", "55+5=60" ]
Current State: 60:[24, 31, 24, 19], Operations: [] Exploring Operation: 24+31=55, Resulting Numbers: [19, 55] Generated Node #2: [19, 55] from Operation: 24+31=55 Current State: 60:[19, 55], Operations: ['24+31=55'] Exploring Operation: 24-19=5, Resulting Numbers: [55, 5] Generated Node #3: [55, 5] from Operation: 24-19=5 Current State: 60:[55, 5], Operations: ['24+31=55', '24-19=5'] Exploring Operation: 55+5=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[24, 31, 24, 19], Operations: [] Exploring Operation: 24/24=1, Resulting Numbers: [31, 19, 1] Generated Node #0,0: 60:[31, 19, 1] Operation: 24/24=1 Moving to Node #0,0 Current State: 60:[31, 19, 1], Operations: ['24/24=1'] Exploring Operation: 31-19=12, Resulting Numbers: [1, 12] Generated Node #0,0,0: 60:[1, 12] Operation: 31-19=12 Moving to Node #0,0,0 Current State: 60:[1, 12], Operations: ['24/24=1', '31-19=12'] Exploring Operation: 1*12=12, Resulting Numbers: [12] 12,60 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 40, 36, 72, 26 ]
33
[ "40+26=66", "72/36=2", "66/2=33" ]
Current State: 33:[40, 36, 72, 26], Operations: [] Exploring Operation: 40+26=66, Resulting Numbers: [36, 72, 66] Generated Node #2: [36, 72, 66] from Operation: 40+26=66 Current State: 33:[36, 72, 66], Operations: ['40+26=66'] Exploring Operation: 72/36=2, Resulting Numbers: [66, 2] Generated Node #3: [66, 2] from Operation: 72/36=2 Current State: 33:[66, 2], Operations: ['40+26=66', '72/36=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,33 equal: Goal Reached
4
Current State: 33:[40, 36, 72, 26], Operations: [] Exploring Operation: 72/36=2, Resulting Numbers: [40, 26, 2] Generated Node #0,0: 33:[40, 26, 2] Operation: 72/36=2 Exploring Operation: 72-40=32, Resulting Numbers: [36, 26, 32] Generated Node #0,1: 33:[36, 26, 32] Operation: 72-40=32 Start Sub Search at level 1: Moving to Node #0,1 Current State: 33:[36, 26, 32], Operations: ['72-40=32'] Exploring Operation: 32-26=6, Resulting Numbers: [36, 6] Generated Node #0,1,0: 33:[36, 6] Operation: 32-26=6 Exploring Operation: 36-26=10, Resulting Numbers: [32, 10] Generated Node #0,1,1: 33:[32, 10] Operation: 36-26=10 Moving to Node #0,1,1 Current State: 33:[32, 10], Operations: ['72-40=32', '36-26=10'] Exploring Operation: 32-10=22, Resulting Numbers: [22] 22,33 unequal: No Solution Exploring Operation: 32+10=42, Resulting Numbers: [42] 42,33 unequal: No Solution Moving to Node #0,1,0 Current State: 33:[36, 6], Operations: ['72-40=32', '32-26=6'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,33 unequal: No Solution Exploring Operation: 36-6=30, Resulting Numbers: [30] 30,33 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 33:[40, 26, 2], Operations: ['72/36=2'] Exploring Operation: 40-26=14, Resulting Numbers: [2, 14] Generated Node #0,0,0: 33:[2, 14] Operation: 40-26=14 Exploring Operation: 26/2=13, Resulting Numbers: [40, 13] Generated Node #0,0,1: 33:[40, 13] Operation: 26/2=13 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 33:[2, 14], Operations: ['72/36=2', '40-26=14'] Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,33 unequal: No Solution Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 33:[40, 13], Operations: ['72/36=2', '26/2=13'] Exploring Operation: 40-13=27, Resulting Numbers: [27] 27,33 unequal: No Solution Exploring Operation: 40+13=53, Resulting Numbers: [53] 53,33 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 67, 65, 44, 54 ]
34
[ "67+65=132", "44+54=98", "132-98=34" ]
Current State: 34:[67, 65, 44, 54], Operations: [] Exploring Operation: 67+65=132, Resulting Numbers: [44, 54, 132] Generated Node #2: [44, 54, 132] from Operation: 67+65=132 Current State: 34:[44, 54, 132], Operations: ['67+65=132'] Exploring Operation: 44+54=98, Resulting Numbers: [132, 98] Generated Node #3: [132, 98] from Operation: 44+54=98 Current State: 34:[132, 98], Operations: ['67+65=132', '44+54=98'] Exploring Operation: 132-98=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
4
Current State: 34:[67, 65, 44, 54], Operations: [] Exploring Operation: 65-54=11, Resulting Numbers: [67, 44, 11] Generated Node #0,0: 34:[67, 44, 11] Operation: 65-54=11 Exploring Operation: 67-65=2, Resulting Numbers: [44, 54, 2] Generated Node #0,1: 34:[44, 54, 2] Operation: 67-65=2 Exploring Operation: 67-54=13, Resulting Numbers: [65, 44, 13] Generated Node #0,2: 34:[65, 44, 13] Operation: 67-54=13 Moving to Node #0,1 Current State: 34:[44, 54, 2], Operations: ['67-65=2'] Exploring Operation: 54/2=27, Resulting Numbers: [44, 27] Generated Node #0,1,0: 34:[44, 27] Operation: 54/2=27 Exploring Operation: 54-44=10, Resulting Numbers: [2, 10] Generated Node #0,1,1: 34:[2, 10] Operation: 54-44=10 Exploring Operation: 44/2=22, Resulting Numbers: [54, 22] Generated Node #0,1,2: 34:[54, 22] Operation: 44/2=22 Moving to Node #0,2 Current State: 34:[65, 44, 13], Operations: ['67-54=13'] Exploring Operation: 65/13=5, Resulting Numbers: [44, 5] Generated Node #0,2,0: 34:[44, 5] Operation: 65/13=5 Exploring Operation: 65-13=52, Resulting Numbers: [44, 52] Generated Node #0,2,1: 34:[44, 52] Operation: 65-13=52 Exploring Operation: 65-44=21, Resulting Numbers: [13, 21] Generated Node #0,2,2: 34:[13, 21] Operation: 65-44=21 Moving to Node #0,0 Current State: 34:[67, 44, 11], Operations: ['65-54=11'] Exploring Operation: 67-44=23, Resulting Numbers: [11, 23] Generated Node #0,0,0: 34:[11, 23] Operation: 67-44=23 Exploring Operation: 44-11=33, Resulting Numbers: [67, 33] Generated Node #0,0,1: 34:[67, 33] Operation: 44-11=33 Exploring Operation: 67-11=56, Resulting Numbers: [44, 56] Generated Node #0,0,2: 34:[44, 56] Operation: 67-11=56 Moving to Node #0,1,1 Current State: 34:[2, 10], Operations: ['67-65=2', '54-44=10'] Exploring Operation: 10/2=5, Resulting Numbers: [5] 5,34 unequal: No Solution Exploring Operation: 2*10=20, Resulting Numbers: [20] 20,34 unequal: No Solution Exploring Operation: 2+10=12, Resulting Numbers: [12] 12,34 unequal: No Solution Moving to Node #0,2,2 Current State: 34:[13, 21], Operations: ['67-54=13', '65-44=21'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,34 unequal: No Solution Exploring Operation: 13*21=273, Resulting Numbers: [273] 273,34 unequal: No Solution Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,34 equal: Goal Reached Moving to Node #0 Current State: 34:[67, 65, 44, 54], Operations: [] Exploring Operation: 67-54=13, Resulting Numbers: [65, 44, 13] Generated Node #0,2: 34:[65, 44, 13] Operation: 67-54=13 Moving to Node #0,2 Current State: 34:[65, 44, 13], Operations: ['67-54=13'] Exploring Operation: 65-44=21, Resulting Numbers: [13, 21] Generated Node #0,2,2: 34:[13, 21] Operation: 65-44=21 Moving to Node #0,2,2 Current State: 34:[13, 21], Operations: ['67-54=13', '65-44=21'] Exploring Operation: 13+21=34, Resulting Numbers: [34] 34,34 equal: Goal Reached
0.980903
hs_3
mult_heuristic
[ 3, 51, 71, 71 ]
16
[ "51/3=17", "71/71=1", "17-1=16" ]
Current State: 16:[3, 51, 71, 71], Operations: [] Exploring Operation: 51/3=17, Resulting Numbers: [71, 71, 17] Generated Node #2: [71, 71, 17] from Operation: 51/3=17 Current State: 16:[71, 71, 17], Operations: ['51/3=17'] Exploring Operation: 71/71=1, Resulting Numbers: [17, 1] Generated Node #3: [17, 1] from Operation: 71/71=1 Current State: 16:[17, 1], Operations: ['51/3=17', '71/71=1'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[3, 51, 71, 71], Operations: [] Exploring Operation: 71/71=1, Resulting Numbers: [3, 51, 1] Generated Node #0,0: 16:[3, 51, 1] Operation: 71/71=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[3, 51, 1], Operations: ['71/71=1'] Exploring Operation: 51/3=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 16:[1, 17] Operation: 51/3=17 Moving to Node #0,0,0 Current State: 16:[1, 17], Operations: ['71/71=1', '51/3=17'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[3, 51, 71, 71], Operations: [] Exploring Operation: 71/71=1, Resulting Numbers: [3, 51, 1] Generated Node #0,0: 16:[3, 51, 1] Operation: 71/71=1 Moving to Node #0,0 Current State: 16:[3, 51, 1], Operations: ['71/71=1'] Exploring Operation: 51/3=17, Resulting Numbers: [1, 17] Generated Node #0,0,0: 16:[1, 17] Operation: 51/3=17 Moving to Node #0,0,0 Current State: 16:[1, 17], Operations: ['71/71=1', '51/3=17'] Exploring Operation: 17-1=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 20, 3, 70, 72 ]
58
[ "20*3=60", "72-70=2", "60-2=58" ]
Current State: 58:[20, 3, 70, 72], Operations: [] Exploring Operation: 20*3=60, Resulting Numbers: [70, 72, 60] Generated Node #2: [70, 72, 60] from Operation: 20*3=60 Current State: 58:[70, 72, 60], Operations: ['20*3=60'] Exploring Operation: 72-70=2, Resulting Numbers: [60, 2] Generated Node #3: [60, 2] from Operation: 72-70=2 Current State: 58:[60, 2], Operations: ['20*3=60', '72-70=2'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[20, 3, 70, 72], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [20, 3, 2] Generated Node #0,0: 58:[20, 3, 2] Operation: 72-70=2 Moving to Node #0,0 Current State: 58:[20, 3, 2], Operations: ['72-70=2'] Exploring Operation: 20*3=60, Resulting Numbers: [2, 60] Generated Node #0,0,0: 58:[2, 60] Operation: 20*3=60 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[2, 60], Operations: ['72-70=2', '20*3=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[20, 3, 70, 72], Operations: [] Exploring Operation: 72-70=2, Resulting Numbers: [20, 3, 2] Generated Node #0,0: 58:[20, 3, 2] Operation: 72-70=2 Moving to Node #0,0 Current State: 58:[20, 3, 2], Operations: ['72-70=2'] Exploring Operation: 20*3=60, Resulting Numbers: [2, 60] Generated Node #0,0,0: 58:[2, 60] Operation: 20*3=60 Moving to Node #0,0,0 Current State: 58:[2, 60], Operations: ['72-70=2', '20*3=60'] Exploring Operation: 60-2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 85, 70, 42, 75 ]
40
[ "70*75=5250", "5250/42=125", "125-85=40" ]
Current State: 40:[85, 70, 42, 75], Operations: [] Exploring Operation: 70*75=5250, Resulting Numbers: [85, 42, 5250] Generated Node #2: [85, 42, 5250] from Operation: 70*75=5250 Current State: 40:[85, 42, 5250], Operations: ['70*75=5250'] Exploring Operation: 5250/42=125, Resulting Numbers: [85, 125] Generated Node #3: [85, 125] from Operation: 5250/42=125 Current State: 40:[85, 125], Operations: ['70*75=5250', '5250/42=125'] Exploring Operation: 125-85=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[85, 70, 42, 75], Operations: [] Exploring Operation: 85-75=10, Resulting Numbers: [70, 42, 10] Generated Node #0,0: 40:[70, 42, 10] Operation: 85-75=10 Exploring Operation: 75-70=5, Resulting Numbers: [85, 42, 5] Generated Node #0,1: 40:[85, 42, 5] Operation: 75-70=5 Exploring Operation: 85-70=15, Resulting Numbers: [42, 75, 15] Generated Node #0,2: 40:[42, 75, 15] Operation: 85-70=15 Exploring Operation: 85-42=43, Resulting Numbers: [70, 75, 43] Generated Node #0,3: 40:[70, 75, 43] Operation: 85-42=43 Moving to Node #0,0 Current State: 40:[70, 42, 10], Operations: ['85-75=10'] Exploring Operation: 70/10=7, Resulting Numbers: [42, 7] Generated Node #0,0,0: 40:[42, 7] Operation: 70/10=7 Exploring Operation: 42-10=32, Resulting Numbers: [70, 32] Generated Node #0,0,1: 40:[70, 32] Operation: 42-10=32 Exploring Operation: 70-10=60, Resulting Numbers: [42, 60] Generated Node #0,0,2: 40:[42, 60] Operation: 70-10=60 Exploring Operation: 70-42=28, Resulting Numbers: [10, 28] Generated Node #0,0,3: 40:[10, 28] Operation: 70-42=28 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 40:[42, 7], Operations: ['85-75=10', '70/10=7'] Exploring Operation: 42+7=49, Resulting Numbers: [49] 49,40 unequal: No Solution Exploring Operation: 42/7=6, Resulting Numbers: [6] 6,40 unequal: No Solution Exploring Operation: 42*7=294, Resulting Numbers: [294] 294,40 unequal: No Solution Exploring Operation: 42-7=35, Resulting Numbers: [35] 35,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 40:[10, 28], Operations: ['85-75=10', '70-42=28'] Exploring Operation: 10+28=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 28-10=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 10*28=280, Resulting Numbers: [280] 280,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 40:[42, 60], Operations: ['85-75=10', '70-10=60'] Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 42+60=102, Resulting Numbers: [102] 102,40 unequal: No Solution Exploring Operation: 42*60=2520, Resulting Numbers: [2520] 2520,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 40:[70, 32], Operations: ['85-75=10', '42-10=32'] Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 70*32=2240, Resulting Numbers: [2240] 2240,40 unequal: No Solution Exploring Operation: 70+32=102, Resulting Numbers: [102] 102,40 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: 40:[42, 75, 15], Operations: ['85-70=15'] Exploring Operation: 42-15=27, Resulting Numbers: [75, 27] Generated Node #0,2,0: 40:[75, 27] Operation: 42-15=27 Exploring Operation: 75-42=33, Resulting Numbers: [15, 33] Generated Node #0,2,1: 40:[15, 33] Operation: 75-42=33 Exploring Operation: 75/15=5, Resulting Numbers: [42, 5] Generated Node #0,2,2: 40:[42, 5] Operation: 75/15=5 Exploring Operation: 75-15=60, Resulting Numbers: [42, 60] Generated Node #0,2,3: 40:[42, 60] Operation: 75-15=60 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 40:[42, 5], Operations: ['85-70=15', '75/15=5'] Exploring Operation: 42+5=47, Resulting Numbers: [47] 47,40 unequal: No Solution Exploring Operation: 42-5=37, Resulting Numbers: [37] 37,40 unequal: No Solution Exploring Operation: 42*5=210, Resulting Numbers: [210] 210,40 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 #0,2,1 Current State: 40:[15, 33], Operations: ['85-70=15', '75-42=33'] Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,40 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,40 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 #0,2,3 Current State: 40:[42, 60], Operations: ['85-70=15', '75-15=60'] Exploring Operation: 60-42=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 42*60=2520, Resulting Numbers: [2520] 2520,40 unequal: No Solution Exploring Operation: 42+60=102, Resulting Numbers: [102] 102,40 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 #0,2,0 Current State: 40:[75, 27], Operations: ['85-70=15', '42-15=27'] Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,40 unequal: No Solution Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,40 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: 40:[85, 42, 5], Operations: ['75-70=5'] Exploring Operation: 42-5=37, Resulting Numbers: [85, 37] Generated Node #0,1,0: 40:[85, 37] Operation: 42-5=37 Exploring Operation: 85-5=80, Resulting Numbers: [42, 80] Generated Node #0,1,1: 40:[42, 80] Operation: 85-5=80 Exploring Operation: 85/5=17, Resulting Numbers: [42, 17] Generated Node #0,1,2: 40:[42, 17] Operation: 85/5=17 Exploring Operation: 85-42=43, Resulting Numbers: [5, 43] Generated Node #0,1,3: 40:[5, 43] Operation: 85-42=43 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 40:[5, 43], Operations: ['75-70=5', '85-42=43'] Exploring Operation: 5+43=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 5*43=215, Resulting Numbers: [215] 215,40 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 #0,1,2 Current State: 40:[42, 17], Operations: ['75-70=5', '85/5=17'] Exploring Operation: 42+17=59, Resulting Numbers: [59] 59,40 unequal: No Solution Exploring Operation: 42-17=25, Resulting Numbers: [25] 25,40 unequal: No Solution Exploring Operation: 42*17=714, Resulting Numbers: [714] 714,40 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 #0,1,1 Current State: 40:[42, 80], Operations: ['75-70=5', '85-5=80'] Exploring Operation: 42*80=3360, Resulting Numbers: [3360] 3360,40 unequal: No Solution Exploring Operation: 42+80=122, Resulting Numbers: [122] 122,40 unequal: No Solution Exploring Operation: 80-42=38, Resulting Numbers: [38] 38,40 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 #0,1,0 Current State: 40:[85, 37], Operations: ['75-70=5', '42-5=37'] Exploring Operation: 85*37=3145, Resulting Numbers: [3145] 3145,40 unequal: No Solution Exploring Operation: 85-37=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 85+37=122, Resulting Numbers: [122] 122,40 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: 40:[70, 75, 43], Operations: ['85-42=43'] Exploring Operation: 75-70=5, Resulting Numbers: [43, 5] Generated Node #0,3,0: 40:[43, 5] Operation: 75-70=5 Exploring Operation: 70+75=145, Resulting Numbers: [43, 145] Generated Node #0,3,1: 40:[43, 145] Operation: 70+75=145 Exploring Operation: 75-43=32, Resulting Numbers: [70, 32] Generated Node #0,3,2: 40:[70, 32] Operation: 75-43=32 Exploring Operation: 70-43=27, Resulting Numbers: [75, 27] Generated Node #0,3,3: 40:[75, 27] Operation: 70-43=27 Moving to Node #0,3,0 Current State: 40:[43, 5], Operations: ['85-42=43', '75-70=5'] Exploring Operation: 43-5=38, Resulting Numbers: [38] 38,40 unequal: No Solution Exploring Operation: 43+5=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 43*5=215, Resulting Numbers: [215] 215,40 unequal: No Solution Moving to Node #0,3,2 Current State: 40:[70, 32], Operations: ['85-42=43', '75-43=32'] Exploring Operation: 70+32=102, Resulting Numbers: [102] 102,40 unequal: No Solution Exploring Operation: 70*32=2240, Resulting Numbers: [2240] 2240,40 unequal: No Solution Exploring Operation: 70-32=38, Resulting Numbers: [38] 38,40 unequal: No Solution Moving to Node #0,3,3 Current State: 40:[75, 27], Operations: ['85-42=43', '70-43=27'] Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,40 unequal: No Solution Exploring Operation: 75*27=2025, Resulting Numbers: [2025] 2025,40 unequal: No Solution Exploring Operation: 75+27=102, Resulting Numbers: [102] 102,40 unequal: No Solution Moving to Node #0,3,1 Current State: 40:[43, 145], Operations: ['85-42=43', '70+75=145'] Exploring Operation: 43+145=188, Resulting Numbers: [188] 188,40 unequal: No Solution Exploring Operation: 145-43=102, Resulting Numbers: [102] 102,40 unequal: No Solution Exploring Operation: 43*145=6235, Resulting Numbers: [6235] 6235,40 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 51, 98, 68, 28 ]
77
[ "51*28=1428", "1428/68=21", "98-21=77" ]
Current State: 77:[51, 98, 68, 28], Operations: [] Exploring Operation: 51*28=1428, Resulting Numbers: [98, 68, 1428] Generated Node #2: [98, 68, 1428] from Operation: 51*28=1428 Current State: 77:[98, 68, 1428], Operations: ['51*28=1428'] Exploring Operation: 1428/68=21, Resulting Numbers: [98, 21] Generated Node #3: [98, 21] from Operation: 1428/68=21 Current State: 77:[98, 21], Operations: ['51*28=1428', '1428/68=21'] Exploring Operation: 98-21=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[51, 98, 68, 28], Operations: [] Exploring Operation: 51-28=23, Resulting Numbers: [98, 68, 23] Generated Node #0,0: 77:[98, 68, 23] Operation: 51-28=23 Exploring Operation: 51+28=79, Resulting Numbers: [98, 68, 79] Generated Node #0,1: 77:[98, 68, 79] Operation: 51+28=79 Moving to Node #0,1 Current State: 77:[98, 68, 79], Operations: ['51+28=79'] Exploring Operation: 98-68=30, Resulting Numbers: [79, 30] Generated Node #0,1,0: 77:[79, 30] Operation: 98-68=30 Exploring Operation: 98-79=19, Resulting Numbers: [68, 19] Generated Node #0,1,1: 77:[68, 19] Operation: 98-79=19 Moving to Node #0,0 Current State: 77:[98, 68, 23], Operations: ['51-28=23'] Exploring Operation: 98-23=75, Resulting Numbers: [68, 75] Generated Node #0,0,0: 77:[68, 75] Operation: 98-23=75 Exploring Operation: 98-68=30, Resulting Numbers: [23, 30] Generated Node #0,0,1: 77:[23, 30] Operation: 98-68=30 Moving to Node #0,0,0 Current State: 77:[68, 75], Operations: ['51-28=23', '98-23=75'] Exploring Operation: 75-68=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 68+75=143, Resulting Numbers: [143] 143,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[68, 19], Operations: ['51+28=79', '98-79=19'] Exploring Operation: 68-19=49, Resulting Numbers: [49] 49,77 unequal: No Solution Exploring Operation: 68+19=87, Resulting Numbers: [87] 87,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[79, 30], Operations: ['51+28=79', '98-68=30'] Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,77 unequal: No Solution Exploring Operation: 79+30=109, Resulting Numbers: [109] 109,77 unequal: No Solution Moving to Node #0,0,1 Current State: 77:[23, 30], Operations: ['51-28=23', '98-68=30'] Exploring Operation: 30-23=7, Resulting Numbers: [7] 7,77 unequal: No Solution Exploring Operation: 23+30=53, Resulting Numbers: [53] 53,77 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 77, 63, 39, 29 ]
72
[ "77+63=140", "39+29=68", "140-68=72" ]
Current State: 72:[77, 63, 39, 29], Operations: [] Exploring Operation: 77+63=140, Resulting Numbers: [39, 29, 140] Generated Node #2: [39, 29, 140] from Operation: 77+63=140 Current State: 72:[39, 29, 140], Operations: ['77+63=140'] Exploring Operation: 39+29=68, Resulting Numbers: [140, 68] Generated Node #3: [140, 68] from Operation: 39+29=68 Current State: 72:[140, 68], Operations: ['77+63=140', '39+29=68'] Exploring Operation: 140-68=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[77, 63, 39, 29], Operations: [] Exploring Operation: 77-63=14, Resulting Numbers: [39, 29, 14] Generated Node #0,0: 72:[39, 29, 14] Operation: 77-63=14 Exploring Operation: 63-39=24, Resulting Numbers: [77, 29, 24] Generated Node #0,1: 72:[77, 29, 24] Operation: 63-39=24 Moving to Node #0,0 Current State: 72:[39, 29, 14], Operations: ['77-63=14'] Exploring Operation: 39-29=10, Resulting Numbers: [14, 10] Generated Node #0,0,0: 72:[14, 10] Operation: 39-29=10 Exploring Operation: 39+29=68, Resulting Numbers: [14, 68] Generated Node #0,0,1: 72:[14, 68] Operation: 39+29=68 Moving to Node #0,1 Current State: 72:[77, 29, 24], Operations: ['63-39=24'] Exploring Operation: 77-29=48, Resulting Numbers: [24, 48] Generated Node #0,1,0: 72:[24, 48] Operation: 77-29=48 Exploring Operation: 29-24=5, Resulting Numbers: [77, 5] Generated Node #0,1,1: 72:[77, 5] Operation: 29-24=5 Moving to Node #0,0,0 Current State: 72:[14, 10], Operations: ['77-63=14', '39-29=10'] Exploring Operation: 14-10=4, Resulting Numbers: [4] 4,72 unequal: No Solution Exploring Operation: 14+10=24, Resulting Numbers: [24] 24,72 unequal: No Solution Moving to Node #0,1,1 Current State: 72:[77, 5], Operations: ['63-39=24', '29-24=5'] Exploring Operation: 77+5=82, Resulting Numbers: [82] 82,72 unequal: No Solution Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[77, 63, 39, 29], Operations: [] Exploring Operation: 63-39=24, Resulting Numbers: [77, 29, 24] Generated Node #0,1: 72:[77, 29, 24] Operation: 63-39=24 Moving to Node #0,1 Current State: 72:[77, 29, 24], Operations: ['63-39=24'] Exploring Operation: 29-24=5, Resulting Numbers: [77, 5] Generated Node #0,1,1: 72:[77, 5] Operation: 29-24=5 Moving to Node #0,1,1 Current State: 72:[77, 5], Operations: ['63-39=24', '29-24=5'] Exploring Operation: 77-5=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
0.987847
hs_2
mult_heuristic
[ 57, 54, 47, 59 ]
82
[ "57-54=3", "47*3=141", "141-59=82" ]
Current State: 82:[57, 54, 47, 59], Operations: [] Exploring Operation: 57-54=3, Resulting Numbers: [47, 59, 3] Generated Node #2: [47, 59, 3] from Operation: 57-54=3 Current State: 82:[47, 59, 3], Operations: ['57-54=3'] Exploring Operation: 47*3=141, Resulting Numbers: [59, 141] Generated Node #3: [59, 141] from Operation: 47*3=141 Current State: 82:[59, 141], Operations: ['57-54=3', '47*3=141'] Exploring Operation: 141-59=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[57, 54, 47, 59], Operations: [] Exploring Operation: 59-57=2, Resulting Numbers: [54, 47, 2] Generated Node #0,0: 82:[54, 47, 2] Operation: 59-57=2 Exploring Operation: 59-54=5, Resulting Numbers: [57, 47, 5] Generated Node #0,1: 82:[57, 47, 5] Operation: 59-54=5 Exploring Operation: 57-54=3, Resulting Numbers: [47, 59, 3] Generated Node #0,2: 82:[47, 59, 3] Operation: 57-54=3 Exploring Operation: 57-47=10, Resulting Numbers: [54, 59, 10] Generated Node #0,3: 82:[54, 59, 10] Operation: 57-47=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[54, 47, 2], Operations: ['59-57=2'] Exploring Operation: 54-47=7, Resulting Numbers: [2, 7] Generated Node #0,0,0: 82:[2, 7] Operation: 54-47=7 Exploring Operation: 47-2=45, Resulting Numbers: [54, 45] Generated Node #0,0,1: 82:[54, 45] Operation: 47-2=45 Exploring Operation: 54+47=101, Resulting Numbers: [2, 101] Generated Node #0,0,2: 82:[2, 101] Operation: 54+47=101 Exploring Operation: 54-2=52, Resulting Numbers: [47, 52] Generated Node #0,0,3: 82:[47, 52] Operation: 54-2=52 Moving to Node #0,0,0 Current State: 82:[2, 7], Operations: ['59-57=2', '54-47=7'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 2+7=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 2*7=14, Resulting Numbers: [14] 14,82 unequal: No Solution Moving to Node #0,0,3 Current State: 82:[47, 52], Operations: ['59-57=2', '54-2=52'] Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,82 unequal: No Solution Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[54, 45], Operations: ['59-57=2', '47-2=45'] Exploring Operation: 54*45=2430, Resulting Numbers: [2430] 2430,82 unequal: No Solution Exploring Operation: 54+45=99, Resulting Numbers: [99] 99,82 unequal: No Solution Exploring Operation: 54-45=9, Resulting Numbers: [9] 9,82 unequal: No Solution Moving to Node #0,0,2 Current State: 82:[2, 101], Operations: ['59-57=2', '54+47=101'] Exploring Operation: 2+101=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 101-2=99, Resulting Numbers: [99] 99,82 unequal: No Solution Exploring Operation: 2*101=202, Resulting Numbers: [202] 202,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[57, 47, 5], Operations: ['59-54=5'] Exploring Operation: 47-5=42, Resulting Numbers: [57, 42] Generated Node #0,1,0: 82:[57, 42] Operation: 47-5=42 Exploring Operation: 57+47=104, Resulting Numbers: [5, 104] Generated Node #0,1,1: 82:[5, 104] Operation: 57+47=104 Exploring Operation: 57-47=10, Resulting Numbers: [5, 10] Generated Node #0,1,2: 82:[5, 10] Operation: 57-47=10 Exploring Operation: 57-5=52, Resulting Numbers: [47, 52] Generated Node #0,1,3: 82:[47, 52] Operation: 57-5=52 Moving to Node #0,1,2 Current State: 82:[5, 10], Operations: ['59-54=5', '57-47=10'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 5*10=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 5+10=15, Resulting Numbers: [15] 15,82 unequal: No Solution Moving to Node #0,1,3 Current State: 82:[47, 52], Operations: ['59-54=5', '57-5=52'] Exploring Operation: 47+52=99, Resulting Numbers: [99] 99,82 unequal: No Solution Exploring Operation: 47*52=2444, Resulting Numbers: [2444] 2444,82 unequal: No Solution Exploring Operation: 52-47=5, Resulting Numbers: [5] 5,82 unequal: No Solution Moving to Node #0,1,0 Current State: 82:[57, 42], Operations: ['59-54=5', '47-5=42'] Exploring Operation: 57*42=2394, Resulting Numbers: [2394] 2394,82 unequal: No Solution Exploring Operation: 57+42=99, Resulting Numbers: [99] 99,82 unequal: No Solution Exploring Operation: 57-42=15, Resulting Numbers: [15] 15,82 unequal: No Solution Moving to Node #0,1,1 Current State: 82:[5, 104], Operations: ['59-54=5', '57+47=104'] Exploring Operation: 5+104=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 5*104=520, Resulting Numbers: [520] 520,82 unequal: No Solution Exploring Operation: 104-5=99, Resulting Numbers: [99] 99,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 82:[47, 59, 3], Operations: ['57-54=3'] Exploring Operation: 59-3=56, Resulting Numbers: [47, 56] Generated Node #0,2,0: 82:[47, 56] Operation: 59-3=56 Exploring Operation: 47+59=106, Resulting Numbers: [3, 106] Generated Node #0,2,1: 82:[3, 106] Operation: 47+59=106 Exploring Operation: 47-3=44, Resulting Numbers: [59, 44] Generated Node #0,2,2: 82:[59, 44] Operation: 47-3=44 Exploring Operation: 59-47=12, Resulting Numbers: [3, 12] Generated Node #0,2,3: 82:[3, 12] Operation: 59-47=12 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 82:[3, 12], Operations: ['57-54=3', '59-47=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,82 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,82 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,82 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 82:[47, 56], Operations: ['57-54=3', '59-3=56'] Exploring Operation: 47*56=2632, Resulting Numbers: [2632] 2632,82 unequal: No Solution Exploring Operation: 47+56=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 56-47=9, Resulting Numbers: [9] 9,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 82:[59, 44], Operations: ['57-54=3', '47-3=44'] Exploring Operation: 59+44=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 59*44=2596, Resulting Numbers: [2596] 2596,82 unequal: No Solution Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 82:[3, 106], Operations: ['57-54=3', '47+59=106'] Exploring Operation: 3*106=318, Resulting Numbers: [318] 318,82 unequal: No Solution Exploring Operation: 3+106=109, Resulting Numbers: [109] 109,82 unequal: No Solution Exploring Operation: 106-3=103, Resulting Numbers: [103] 103,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 82:[54, 59, 10], Operations: ['57-47=10'] Exploring Operation: 59-10=49, Resulting Numbers: [54, 49] Generated Node #0,3,0: 82:[54, 49] Operation: 59-10=49 Exploring Operation: 59-54=5, Resulting Numbers: [10, 5] Generated Node #0,3,1: 82:[10, 5] Operation: 59-54=5 Exploring Operation: 54-10=44, Resulting Numbers: [59, 44] Generated Node #0,3,2: 82:[59, 44] Operation: 54-10=44 Exploring Operation: 59+10=69, Resulting Numbers: [54, 69] Generated Node #0,3,3: 82:[54, 69] Operation: 59+10=69 Moving to Node #0,3,1 Current State: 82:[10, 5], Operations: ['57-47=10', '59-54=5'] Exploring Operation: 10-5=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 10/5=2, Resulting Numbers: [2] 2,82 unequal: No Solution Exploring Operation: 10*5=50, Resulting Numbers: [50] 50,82 unequal: No Solution Exploring Operation: 10+5=15, Resulting Numbers: [15] 15,82 unequal: No Solution Moving to Node #0,3,2 Current State: 82:[59, 44], Operations: ['57-47=10', '54-10=44'] Exploring Operation: 59+44=103, Resulting Numbers: [103] 103,82 unequal: No Solution Exploring Operation: 59-44=15, Resulting Numbers: [15] 15,82 unequal: No Solution Exploring Operation: 59*44=2596, Resulting Numbers: [2596] 2596,82 unequal: No Solution Moving to Node #0,3,0 Current State: 82:[54, 49], Operations: ['57-47=10', '59-10=49'] Exploring Operation: 54*49=2646, Resulting Numbers: [2646] 2646,82 unequal: No Solution Exploring Operation: 54-49=5, Resulting Numbers: [5] 5,82 unequal: No Solution Exploring Operation: 54+49=103, Resulting Numbers: [103] 103,82 unequal: No Solution Moving to Node #0,3,3 Current State: 82:[54, 69], Operations: ['57-47=10', '59+10=69'] Exploring Operation: 54+69=123, Resulting Numbers: [123] 123,82 unequal: No Solution Exploring Operation: 69-54=15, Resulting Numbers: [15] 15,82 unequal: No Solution Exploring Operation: 54*69=3726, Resulting Numbers: [3726] 3726,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 24, 57, 8, 25 ]
16
[ "57-24=33", "25-8=17", "33-17=16" ]
Current State: 16:[24, 57, 8, 25], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [8, 25, 33] Generated Node #2: [8, 25, 33] from Operation: 57-24=33 Current State: 16:[8, 25, 33], Operations: ['57-24=33'] Exploring Operation: 25-8=17, Resulting Numbers: [33, 17] Generated Node #3: [33, 17] from Operation: 25-8=17 Current State: 16:[33, 17], Operations: ['57-24=33', '25-8=17'] Exploring Operation: 33-17=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[24, 57, 8, 25], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [8, 25, 33] Generated Node #0,0: 16:[8, 25, 33] Operation: 57-24=33 Exploring Operation: 24-8=16, Resulting Numbers: [57, 25, 16] Generated Node #0,1: 16:[57, 25, 16] Operation: 24-8=16 Exploring Operation: 57-25=32, Resulting Numbers: [24, 8, 32] Generated Node #0,2: 16:[24, 8, 32] Operation: 57-25=32 Exploring Operation: 57-8=49, Resulting Numbers: [24, 25, 49] Generated Node #0,3: 16:[24, 25, 49] Operation: 57-8=49 Exploring Operation: 25-24=1, Resulting Numbers: [57, 8, 1] Generated Node #0,4: 16:[57, 8, 1] Operation: 25-24=1 Moving to Node #0,2 Current State: 16:[24, 8, 32], Operations: ['57-25=32'] Exploring Operation: 24/8=3, Resulting Numbers: [32, 3] Generated Node #0,2,0: 16:[32, 3] Operation: 24/8=3 Exploring Operation: 32-8=24, Resulting Numbers: [24, 24] Generated Node #0,2,1: 16:[24, 24] Operation: 32-8=24 Exploring Operation: 24-8=16, Resulting Numbers: [32, 16] Generated Node #0,2,2: 16:[32, 16] Operation: 24-8=16 Exploring Operation: 32-24=8, Resulting Numbers: [8, 8] Generated Node #0,2,3: 16:[8, 8] Operation: 32-24=8 Exploring Operation: 32/8=4, Resulting Numbers: [24, 4] Generated Node #0,2,4: 16:[24, 4] Operation: 32/8=4 Moving to Node #0,0 Current State: 16:[8, 25, 33], Operations: ['57-24=33'] Exploring Operation: 8+25=33, Resulting Numbers: [33, 33] Generated Node #0,0,0: 16:[33, 33] Operation: 8+25=33 Exploring Operation: 8+33=41, Resulting Numbers: [25, 41] Generated Node #0,0,1: 16:[25, 41] Operation: 8+33=41 Exploring Operation: 33-8=25, Resulting Numbers: [25, 25] Generated Node #0,0,2: 16:[25, 25] Operation: 33-8=25 Exploring Operation: 33-25=8, Resulting Numbers: [8, 8] Generated Node #0,0,3: 16:[8, 8] Operation: 33-25=8 Exploring Operation: 25-8=17, Resulting Numbers: [33, 17] Generated Node #0,0,4: 16:[33, 17] Operation: 25-8=17 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 16:[8, 8], Operations: ['57-24=33', '33-25=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[24, 57, 8, 25], Operations: [] Exploring Operation: 57-24=33, Resulting Numbers: [8, 25, 33] Generated Node #0,0: 16:[8, 25, 33] Operation: 57-24=33 Moving to Node #0,0 Current State: 16:[8, 25, 33], Operations: ['57-24=33'] Exploring Operation: 33-25=8, Resulting Numbers: [8, 8] Generated Node #0,0,3: 16:[8, 8] Operation: 33-25=8 Moving to Node #0,0,3 Current State: 16:[8, 8], Operations: ['57-24=33', '33-25=8'] Exploring Operation: 8+8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 23, 4, 9, 4 ]
99
[ "23+4=27", "4*27=108", "108-9=99" ]
Current State: 99:[23, 4, 9, 4], Operations: [] Exploring Operation: 23+4=27, Resulting Numbers: [9, 27] Generated Node #2: [9, 27] from Operation: 23+4=27 Current State: 99:[9, 27], Operations: ['23+4=27'] Exploring Operation: 4*27=108, Resulting Numbers: [9, 108] Generated Node #3: [9, 108] from Operation: 4*27=108 Current State: 99:[9, 108], Operations: ['23+4=27', '4*27=108'] Exploring Operation: 108-9=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[23, 4, 9, 4], Operations: [] Exploring Operation: 23+9=32, Resulting Numbers: [4, 4, 32] Generated Node #0,0: 99:[4, 4, 32] Operation: 23+9=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[4, 4, 32], Operations: ['23+9=32'] Exploring Operation: 4+4=8, Resulting Numbers: [32, 8] Generated Node #0,0,0: 99:[32, 8] Operation: 4+4=8 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[32, 8], Operations: ['23+9=32', '4+4=8'] Exploring Operation: 32/8=4, Resulting Numbers: [4] 4,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 11, 88, 33, 47 ]
43
[ "33-11=22", "88/22=4", "47-4=43" ]
Current State: 43:[11, 88, 33, 47], Operations: [] Exploring Operation: 33-11=22, Resulting Numbers: [88, 47, 22] Generated Node #2: [88, 47, 22] from Operation: 33-11=22 Current State: 43:[88, 47, 22], Operations: ['33-11=22'] Exploring Operation: 88/22=4, Resulting Numbers: [47, 4] Generated Node #3: [47, 4] from Operation: 88/22=4 Current State: 43:[47, 4], Operations: ['33-11=22', '88/22=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[11, 88, 33, 47], Operations: [] Exploring Operation: 88-33=55, Resulting Numbers: [11, 47, 55] Generated Node #0,0: 43:[11, 47, 55] Operation: 88-33=55 Exploring Operation: 88-11=77, Resulting Numbers: [33, 47, 77] Generated Node #0,1: 43:[33, 47, 77] Operation: 88-11=77 Exploring Operation: 88-47=41, Resulting Numbers: [11, 33, 41] Generated Node #0,2: 43:[11, 33, 41] Operation: 88-47=41 Exploring Operation: 88/11=8, Resulting Numbers: [33, 47, 8] Generated Node #0,3: 43:[33, 47, 8] Operation: 88/11=8 Start Sub Search at level 1: Moving to Node #0,2 Current State: 43:[11, 33, 41], Operations: ['88-47=41'] Exploring Operation: 41-11=30, Resulting Numbers: [33, 30] Generated Node #0,2,0: 43:[33, 30] Operation: 41-11=30 Exploring Operation: 33-11=22, Resulting Numbers: [41, 22] Generated Node #0,2,1: 43:[41, 22] Operation: 33-11=22 Exploring Operation: 11+41=52, Resulting Numbers: [33, 52] Generated Node #0,2,2: 43:[33, 52] Operation: 11+41=52 Exploring Operation: 11+33=44, Resulting Numbers: [41, 44] Generated Node #0,2,3: 43:[41, 44] Operation: 11+33=44 Moving to Node #0,2,3 Current State: 43:[41, 44], Operations: ['88-47=41', '11+33=44'] Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 41*44=1804, Resulting Numbers: [1804] 1804,43 unequal: No Solution Exploring Operation: 41+44=85, Resulting Numbers: [85] 85,43 unequal: No Solution Moving to Node #0,2,2 Current State: 43:[33, 52], Operations: ['88-47=41', '11+41=52'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,43 unequal: No Solution Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,43 unequal: No Solution Moving to Node #0,2,1 Current State: 43:[41, 22], Operations: ['88-47=41', '33-11=22'] Exploring Operation: 41+22=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 41*22=902, Resulting Numbers: [902] 902,43 unequal: No Solution Exploring Operation: 41-22=19, Resulting Numbers: [19] 19,43 unequal: No Solution Moving to Node #0,2,0 Current State: 43:[33, 30], Operations: ['88-47=41', '41-11=30'] Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,43 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,43 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 Current State: 43:[11, 47, 55], Operations: ['88-33=55'] Exploring Operation: 11+55=66, Resulting Numbers: [47, 66] Generated Node #0,0,0: 43:[47, 66] Operation: 11+55=66 Exploring Operation: 11+47=58, Resulting Numbers: [55, 58] Generated Node #0,0,1: 43:[55, 58] Operation: 11+47=58 Exploring Operation: 55-11=44, Resulting Numbers: [47, 44] Generated Node #0,0,2: 43:[47, 44] Operation: 55-11=44 Exploring Operation: 47-11=36, Resulting Numbers: [55, 36] Generated Node #0,0,3: 43:[55, 36] Operation: 47-11=36 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 43:[47, 44], Operations: ['88-33=55', '55-11=44'] Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,43 unequal: No Solution Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 43:[55, 36], Operations: ['88-33=55', '47-11=36'] Exploring Operation: 55*36=1980, Resulting Numbers: [1980] 1980,43 unequal: No Solution Exploring Operation: 55-36=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 55+36=91, Resulting Numbers: [91] 91,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[47, 66], Operations: ['88-33=55', '11+55=66'] Exploring Operation: 66-47=19, Resulting Numbers: [19] 19,43 unequal: No Solution Exploring Operation: 47+66=113, Resulting Numbers: [113] 113,43 unequal: No Solution Exploring Operation: 47*66=3102, Resulting Numbers: [3102] 3102,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 43:[55, 58], Operations: ['88-33=55', '11+47=58'] Exploring Operation: 55+58=113, Resulting Numbers: [113] 113,43 unequal: No Solution Exploring Operation: 58-55=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 55*58=3190, Resulting Numbers: [3190] 3190,43 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: 43:[33, 47, 77], Operations: ['88-11=77'] Exploring Operation: 77-47=30, Resulting Numbers: [33, 30] Generated Node #0,1,0: 43:[33, 30] Operation: 77-47=30 Exploring Operation: 47-33=14, Resulting Numbers: [77, 14] Generated Node #0,1,1: 43:[77, 14] Operation: 47-33=14 Exploring Operation: 77-33=44, Resulting Numbers: [47, 44] Generated Node #0,1,2: 43:[47, 44] Operation: 77-33=44 Exploring Operation: 33+47=80, Resulting Numbers: [77, 80] Generated Node #0,1,3: 43:[77, 80] Operation: 33+47=80 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 43:[47, 44], Operations: ['88-11=77', '77-33=44'] Exploring Operation: 47+44=91, Resulting Numbers: [91] 91,43 unequal: No Solution Exploring Operation: 47-44=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 47*44=2068, Resulting Numbers: [2068] 2068,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 43:[33, 30], Operations: ['88-11=77', '77-47=30'] Exploring Operation: 33*30=990, Resulting Numbers: [990] 990,43 unequal: No Solution Exploring Operation: 33+30=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 33-30=3, Resulting Numbers: [3] 3,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 43:[77, 14], Operations: ['88-11=77', '47-33=14'] Exploring Operation: 77*14=1078, Resulting Numbers: [1078] 1078,43 unequal: No Solution Exploring Operation: 77-14=63, Resulting Numbers: [63] 63,43 unequal: No Solution Exploring Operation: 77+14=91, Resulting Numbers: [91] 91,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 43:[77, 80], Operations: ['88-11=77', '33+47=80'] Exploring Operation: 77+80=157, Resulting Numbers: [157] 157,43 unequal: No Solution Exploring Operation: 80-77=3, Resulting Numbers: [3] 3,43 unequal: No Solution Exploring Operation: 77*80=6160, Resulting Numbers: [6160] 6160,43 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: 43:[33, 47, 8], Operations: ['88/11=8'] Exploring Operation: 47-8=39, Resulting Numbers: [33, 39] Generated Node #0,3,0: 43:[33, 39] Operation: 47-8=39 Exploring Operation: 33-8=25, Resulting Numbers: [47, 25] Generated Node #0,3,1: 43:[47, 25] Operation: 33-8=25 Exploring Operation: 33+8=41, Resulting Numbers: [47, 41] Generated Node #0,3,2: 43:[47, 41] Operation: 33+8=41 Exploring Operation: 47+8=55, Resulting Numbers: [33, 55] Generated Node #0,3,3: 43:[33, 55] Operation: 47+8=55 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 43:[47, 41], Operations: ['88/11=8', '33+8=41'] Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 47+41=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 47*41=1927, Resulting Numbers: [1927] 1927,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 43:[33, 39], Operations: ['88/11=8', '47-8=39'] Exploring Operation: 39-33=6, Resulting Numbers: [6] 6,43 unequal: No Solution Exploring Operation: 33+39=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 33*39=1287, Resulting Numbers: [1287] 1287,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 43:[47, 25], Operations: ['88/11=8', '33-8=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 47+25=72, Resulting Numbers: [72] 72,43 unequal: No Solution Exploring Operation: 47*25=1175, Resulting Numbers: [1175] 1175,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 43:[33, 55], Operations: ['88/11=8', '47+8=55'] Exploring Operation: 33+55=88, Resulting Numbers: [88] 88,43 unequal: No Solution Exploring Operation: 55-33=22, Resulting Numbers: [22] 22,43 unequal: No Solution Exploring Operation: 33*55=1815, Resulting Numbers: [1815] 1815,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 26, 4, 70, 24 ]
58
[ "26*4=104", "70-24=46", "104-46=58" ]
Current State: 58:[26, 4, 70, 24], Operations: [] Exploring Operation: 26*4=104, Resulting Numbers: [70, 24, 104] Generated Node #2: [70, 24, 104] from Operation: 26*4=104 Current State: 58:[70, 24, 104], Operations: ['26*4=104'] Exploring Operation: 70-24=46, Resulting Numbers: [104, 46] Generated Node #3: [104, 46] from Operation: 70-24=46 Current State: 58:[104, 46], Operations: ['26*4=104', '70-24=46'] Exploring Operation: 104-46=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[26, 4, 70, 24], Operations: [] Exploring Operation: 26-24=2, Resulting Numbers: [4, 70, 2] Generated Node #0,0: 58:[4, 70, 2] Operation: 26-24=2 Exploring Operation: 70-4=66, Resulting Numbers: [26, 24, 66] Generated Node #0,1: 58:[26, 24, 66] Operation: 70-4=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[4, 70, 2], Operations: ['26-24=2'] Exploring Operation: 70-4=66, Resulting Numbers: [2, 66] Generated Node #0,0,0: 58:[2, 66] Operation: 70-4=66 Exploring Operation: 70/2=35, Resulting Numbers: [4, 35] Generated Node #0,0,1: 58:[4, 35] Operation: 70/2=35 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[2, 66], Operations: ['26-24=2', '70-4=66'] Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,58 unequal: No Solution Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 58:[4, 35], Operations: ['26-24=2', '70/2=35'] Exploring Operation: 4+35=39, Resulting Numbers: [39] 39,58 unequal: No Solution Exploring Operation: 35-4=31, Resulting Numbers: [31] 31,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[26, 24, 66], Operations: ['70-4=66'] Exploring Operation: 26-24=2, Resulting Numbers: [66, 2] Generated Node #0,1,0: 58:[66, 2] Operation: 26-24=2 Exploring Operation: 26+24=50, Resulting Numbers: [66, 50] Generated Node #0,1,1: 58:[66, 50] Operation: 26+24=50 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[66, 2], Operations: ['70-4=66', '26-24=2'] Exploring Operation: 66/2=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 66-2=64, Resulting Numbers: [64] 64,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[66, 50], Operations: ['70-4=66', '26+24=50'] Exploring Operation: 66-50=16, Resulting Numbers: [16] 16,58 unequal: No Solution Exploring Operation: 66+50=116, Resulting Numbers: [116] 116,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 91, 61, 31, 59 ]
62
[ "91+61=152", "31+59=90", "152-90=62" ]
Current State: 62:[91, 61, 31, 59], Operations: [] Exploring Operation: 91+61=152, Resulting Numbers: [31, 59, 152] Generated Node #2: [31, 59, 152] from Operation: 91+61=152 Current State: 62:[31, 59, 152], Operations: ['91+61=152'] Exploring Operation: 31+59=90, Resulting Numbers: [152, 90] Generated Node #3: [152, 90] from Operation: 31+59=90 Current State: 62:[152, 90], Operations: ['91+61=152', '31+59=90'] Exploring Operation: 152-90=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[91, 61, 31, 59], Operations: [] Exploring Operation: 91-61=30, Resulting Numbers: [31, 59, 30] Generated Node #0,0: 62:[31, 59, 30] Operation: 91-61=30 Exploring Operation: 91-31=60, Resulting Numbers: [61, 59, 60] Generated Node #0,1: 62:[61, 59, 60] Operation: 91-31=60 Exploring Operation: 91-59=32, Resulting Numbers: [61, 31, 32] Generated Node #0,2: 62:[61, 31, 32] Operation: 91-59=32 Moving to Node #0,2 Current State: 62:[61, 31, 32], Operations: ['91-59=32'] Exploring Operation: 31+32=63, Resulting Numbers: [61, 63] Generated Node #0,2,0: 62:[61, 63] Operation: 31+32=63 Exploring Operation: 61-32=29, Resulting Numbers: [31, 29] Generated Node #0,2,1: 62:[31, 29] Operation: 61-32=29 Exploring Operation: 61-31=30, Resulting Numbers: [32, 30] Generated Node #0,2,2: 62:[32, 30] Operation: 61-31=30 Moving to Node #0,0 Current State: 62:[31, 59, 30], Operations: ['91-61=30'] Exploring Operation: 31+30=61, Resulting Numbers: [59, 61] Generated Node #0,0,0: 62:[59, 61] Operation: 31+30=61 Exploring Operation: 59-31=28, Resulting Numbers: [30, 28] Generated Node #0,0,1: 62:[30, 28] Operation: 59-31=28 Exploring Operation: 59-30=29, Resulting Numbers: [31, 29] Generated Node #0,0,2: 62:[31, 29] Operation: 59-30=29 Moving to Node #0,1 Current State: 62:[61, 59, 60], Operations: ['91-31=60'] Exploring Operation: 60-59=1, Resulting Numbers: [61, 1] Generated Node #0,1,0: 62:[61, 1] Operation: 60-59=1 Exploring Operation: 61-59=2, Resulting Numbers: [60, 2] Generated Node #0,1,1: 62:[60, 2] Operation: 61-59=2 Exploring Operation: 61-60=1, Resulting Numbers: [59, 1] Generated Node #0,1,2: 62:[59, 1] Operation: 61-60=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 62:[61, 1], Operations: ['91-31=60', '60-59=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[91, 61, 31, 59], Operations: [] Exploring Operation: 91-31=60, Resulting Numbers: [61, 59, 60] Generated Node #0,1: 62:[61, 59, 60] Operation: 91-31=60 Moving to Node #0,1 Current State: 62:[61, 59, 60], Operations: ['91-31=60'] Exploring Operation: 60-59=1, Resulting Numbers: [61, 1] Generated Node #0,1,0: 62:[61, 1] Operation: 60-59=1 Moving to Node #0,1,0 Current State: 62:[61, 1], Operations: ['91-31=60', '60-59=1'] Exploring Operation: 61+1=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 99, 1, 57, 50 ]
59
[ "99+1=100", "100/50=2", "57+2=59" ]
Current State: 59:[99, 1, 57, 50], Operations: [] Exploring Operation: 99+1=100, Resulting Numbers: [57, 50, 100] Generated Node #2: [57, 50, 100] from Operation: 99+1=100 Current State: 59:[57, 50, 100], Operations: ['99+1=100'] Exploring Operation: 100/50=2, Resulting Numbers: [57, 2] Generated Node #3: [57, 2] from Operation: 100/50=2 Current State: 59:[57, 2], Operations: ['99+1=100', '100/50=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[99, 1, 57, 50], Operations: [] Exploring Operation: 1+57=58, Resulting Numbers: [99, 50, 58] Generated Node #0,0: 59:[99, 50, 58] Operation: 1+57=58 Exploring Operation: 99-1=98, Resulting Numbers: [57, 50, 98] Generated Node #0,1: 59:[57, 50, 98] Operation: 99-1=98 Moving to Node #0,0 Current State: 59:[99, 50, 58], Operations: ['1+57=58'] Exploring Operation: 99-50=49, Resulting Numbers: [58, 49] Generated Node #0,0,0: 59:[58, 49] Operation: 99-50=49 Exploring Operation: 99-58=41, Resulting Numbers: [50, 41] Generated Node #0,0,1: 59:[50, 41] Operation: 99-58=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 59:[58, 49], Operations: ['1+57=58', '99-50=49'] Exploring Operation: 58-49=9, Resulting Numbers: [9] 9,59 unequal: No Solution Exploring Operation: 58+49=107, Resulting Numbers: [107] 107,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 59:[50, 41], Operations: ['1+57=58', '99-58=41'] Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,59 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: 59:[57, 50, 98], Operations: ['99-1=98'] Exploring Operation: 98-50=48, Resulting Numbers: [57, 48] Generated Node #0,1,0: 59:[57, 48] Operation: 98-50=48 Exploring Operation: 98-57=41, Resulting Numbers: [50, 41] Generated Node #0,1,1: 59:[50, 41] Operation: 98-57=41 Moving to Node #0,1,0 Current State: 59:[57, 48], Operations: ['99-1=98', '98-50=48'] Exploring Operation: 57+48=105, Resulting Numbers: [105] 105,59 unequal: No Solution Exploring Operation: 57-48=9, Resulting Numbers: [9] 9,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[50, 41], Operations: ['99-1=98', '98-57=41'] Exploring Operation: 50+41=91, Resulting Numbers: [91] 91,59 unequal: No Solution Exploring Operation: 50-41=9, Resulting Numbers: [9] 9,59 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 78, 54, 52, 55 ]
46
[ "78-55=23", "54-52=2", "23*2=46" ]
Current State: 46:[78, 54, 52, 55], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [54, 52, 23] Generated Node #2: [54, 52, 23] from Operation: 78-55=23 Current State: 46:[54, 52, 23], Operations: ['78-55=23'] Exploring Operation: 54-52=2, Resulting Numbers: [23, 2] Generated Node #3: [23, 2] from Operation: 54-52=2 Current State: 46:[23, 2], Operations: ['78-55=23', '54-52=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[78, 54, 52, 55], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [54, 52, 23] Generated Node #0,0: 46:[54, 52, 23] Operation: 78-55=23 Moving to Node #0,0 Current State: 46:[54, 52, 23], Operations: ['78-55=23'] Exploring Operation: 54-52=2, Resulting Numbers: [23, 2] Generated Node #0,0,0: 46:[23, 2] Operation: 54-52=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[23, 2], Operations: ['78-55=23', '54-52=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[78, 54, 52, 55], Operations: [] Exploring Operation: 78-55=23, Resulting Numbers: [54, 52, 23] Generated Node #0,0: 46:[54, 52, 23] Operation: 78-55=23 Moving to Node #0,0 Current State: 46:[54, 52, 23], Operations: ['78-55=23'] Exploring Operation: 54-52=2, Resulting Numbers: [23, 2] Generated Node #0,0,0: 46:[23, 2] Operation: 54-52=2 Moving to Node #0,0,0 Current State: 46:[23, 2], Operations: ['78-55=23', '54-52=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 2, 31, 49, 18 ]
49
[ "2*49=98", "31+18=49", "98-49=49" ]
Current State: 49:[2, 31, 49, 18], Operations: [] Exploring Operation: 2*49=98, Resulting Numbers: [31, 18, 98] Generated Node #2: [31, 18, 98] from Operation: 2*49=98 Current State: 49:[31, 18, 98], Operations: ['2*49=98'] Exploring Operation: 31+18=49, Resulting Numbers: [98, 49] Generated Node #3: [98, 49] from Operation: 31+18=49 Current State: 49:[98, 49], Operations: ['2*49=98', '31+18=49'] Exploring Operation: 98-49=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[2, 31, 49, 18], Operations: [] Exploring Operation: 2+31=33, Resulting Numbers: [49, 18, 33] Generated Node #0,0: 49:[49, 18, 33] Operation: 2+31=33 Exploring Operation: 31-18=13, Resulting Numbers: [2, 49, 13] Generated Node #0,1: 49:[2, 49, 13] Operation: 31-18=13 Exploring Operation: 2*31=62, Resulting Numbers: [49, 18, 62] Generated Node #0,2: 49:[49, 18, 62] Operation: 2*31=62 Exploring Operation: 18/2=9, Resulting Numbers: [31, 49, 9] Generated Node #0,3: 49:[31, 49, 9] Operation: 18/2=9 Exploring Operation: 31+18=49, Resulting Numbers: [2, 49, 49] Generated Node #0,4: 49:[2, 49, 49] Operation: 31+18=49 Start Sub Search at level 1: Moving to Node #0,4 Current State: 49:[2, 49, 49], Operations: ['31+18=49'] Exploring Operation: 2+49=51, Resulting Numbers: [49, 51] Generated Node #0,4,0: 49:[49, 51] Operation: 2+49=51 Exploring Operation: 49/49=1, Resulting Numbers: [2, 1] Generated Node #0,4,1: 49:[2, 1] Operation: 49/49=1 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,4,2: 49:[49, 47] Operation: 49-2=47 Exploring Operation: 2+49=51, Resulting Numbers: [49, 51] Generated Node #0,4,3: 49:[49, 51] Operation: 2+49=51 Exploring Operation: 49-2=47, Resulting Numbers: [49, 47] Generated Node #0,4,4: 49:[49, 47] Operation: 49-2=47 Moving to Node #0,4,0 Current State: 49:[49, 51], Operations: ['31+18=49', '2+49=51'] Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,49 unequal: No Solution Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,49 unequal: No Solution Moving to Node #0,4,3 Current State: 49:[49, 51], Operations: ['31+18=49', '2+49=51'] Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,49 unequal: No Solution Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,49 unequal: No Solution Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,49 unequal: No Solution Moving to Node #0,4,2 Current State: 49:[49, 47], Operations: ['31+18=49', '49-2=47'] Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,49 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,49 unequal: No Solution Moving to Node #0,4,4 Current State: 49:[49, 47], Operations: ['31+18=49', '49-2=47'] Exploring Operation: 49+47=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 49*47=2303, Resulting Numbers: [2303] 2303,49 unequal: No Solution Moving to Node #0,4,1 Current State: 49:[2, 1], Operations: ['31+18=49', '49/49=1'] Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 2-1=1, Resulting Numbers: [1] 1,49 unequal: No Solution Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 2+1=3, Resulting Numbers: [3] 3,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 49:[2, 49, 13], Operations: ['31-18=13'] Exploring Operation: 2+13=15, Resulting Numbers: [49, 15] Generated Node #0,1,0: 49:[49, 15] Operation: 2+13=15 Exploring Operation: 49+13=62, Resulting Numbers: [2, 62] Generated Node #0,1,1: 49:[2, 62] Operation: 49+13=62 Exploring Operation: 13-2=11, Resulting Numbers: [49, 11] Generated Node #0,1,2: 49:[49, 11] Operation: 13-2=11 Exploring Operation: 49-2=47, Resulting Numbers: [13, 47] Generated Node #0,1,3: 49:[13, 47] Operation: 49-2=47 Exploring Operation: 2+49=51, Resulting Numbers: [13, 51] Generated Node #0,1,4: 49:[13, 51] Operation: 2+49=51 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 49:[49, 11], Operations: ['31-18=13', '13-2=11'] Exploring Operation: 49*11=539, Resulting Numbers: [539] 539,49 unequal: No Solution Exploring Operation: 49-11=38, Resulting Numbers: [38] 38,49 unequal: No Solution Exploring Operation: 49+11=60, Resulting Numbers: [60] 60,49 unequal: No Solution No 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: 49:[49, 15], Operations: ['31-18=13', '2+13=15'] Exploring Operation: 49*15=735, Resulting Numbers: [735] 735,49 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 49+15=64, Resulting Numbers: [64] 64,49 unequal: No Solution No 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: 49:[13, 47], Operations: ['31-18=13', '49-2=47'] Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 13*47=611, Resulting Numbers: [611] 611,49 unequal: No Solution Exploring Operation: 13+47=60, Resulting Numbers: [60] 60,49 unequal: No Solution No 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: 49:[13, 51], Operations: ['31-18=13', '2+49=51'] Exploring Operation: 13+51=64, Resulting Numbers: [64] 64,49 unequal: No Solution Exploring Operation: 51-13=38, Resulting Numbers: [38] 38,49 unequal: No Solution Exploring Operation: 13*51=663, Resulting Numbers: [663] 663,49 unequal: No Solution No 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: 49:[2, 62], Operations: ['31-18=13', '49+13=62'] Exploring Operation: 2*62=124, Resulting Numbers: [124] 124,49 unequal: No Solution Exploring Operation: 62/2=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 62-2=60, Resulting Numbers: [60] 60,49 unequal: No Solution Exploring Operation: 2+62=64, Resulting Numbers: [64] 64,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 49:[31, 49, 9], Operations: ['18/2=9'] Exploring Operation: 49-31=18, Resulting Numbers: [9, 18] Generated Node #0,3,0: 49:[9, 18] Operation: 49-31=18 Exploring Operation: 31+9=40, Resulting Numbers: [49, 40] Generated Node #0,3,1: 49:[49, 40] Operation: 31+9=40 Exploring Operation: 31-9=22, Resulting Numbers: [49, 22] Generated Node #0,3,2: 49:[49, 22] Operation: 31-9=22 Exploring Operation: 49+9=58, Resulting Numbers: [31, 58] Generated Node #0,3,3: 49:[31, 58] Operation: 49+9=58 Exploring Operation: 49-9=40, Resulting Numbers: [31, 40] Generated Node #0,3,4: 49:[31, 40] Operation: 49-9=40 Moving to Node #0,3,1 Current State: 49:[49, 40], Operations: ['18/2=9', '31+9=40'] Exploring Operation: 49+40=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 49*40=1960, Resulting Numbers: [1960] 1960,49 unequal: No Solution Exploring Operation: 49-40=9, Resulting Numbers: [9] 9,49 unequal: No Solution Moving to Node #0,3,0 Current State: 49:[9, 18], Operations: ['18/2=9', '49-31=18'] Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,49 unequal: No Solution Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,49 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 9*18=162, Resulting Numbers: [162] 162,49 unequal: No Solution Moving to Node #0,3,2 Current State: 49:[49, 22], Operations: ['18/2=9', '31-9=22'] Exploring Operation: 49+22=71, Resulting Numbers: [71] 71,49 unequal: No Solution Exploring Operation: 49-22=27, Resulting Numbers: [27] 27,49 unequal: No Solution Exploring Operation: 49*22=1078, Resulting Numbers: [1078] 1078,49 unequal: No Solution Moving to Node #0,3,3 Current State: 49:[31, 58], Operations: ['18/2=9', '49+9=58'] Exploring Operation: 31+58=89, Resulting Numbers: [89] 89,49 unequal: No Solution Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,49 unequal: No Solution Exploring Operation: 31*58=1798, Resulting Numbers: [1798] 1798,49 unequal: No Solution Moving to Node #0,3,4 Current State: 49:[31, 40], Operations: ['18/2=9', '49-9=40'] Exploring Operation: 31*40=1240, Resulting Numbers: [1240] 1240,49 unequal: No Solution Exploring Operation: 31+40=71, Resulting Numbers: [71] 71,49 unequal: No Solution Exploring Operation: 40-31=9, Resulting Numbers: [9] 9,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[49, 18, 62], Operations: ['2*31=62'] Exploring Operation: 18+62=80, Resulting Numbers: [49, 80] Generated Node #0,2,0: 49:[49, 80] Operation: 18+62=80 Exploring Operation: 49-18=31, Resulting Numbers: [62, 31] Generated Node #0,2,1: 49:[62, 31] Operation: 49-18=31 Exploring Operation: 62-18=44, Resulting Numbers: [49, 44] Generated Node #0,2,2: 49:[49, 44] Operation: 62-18=44 Exploring Operation: 49+18=67, Resulting Numbers: [62, 67] Generated Node #0,2,3: 49:[62, 67] Operation: 49+18=67 Exploring Operation: 62-49=13, Resulting Numbers: [18, 13] Generated Node #0,2,4: 49:[18, 13] Operation: 62-49=13 Moving to Node #0,2,2 Current State: 49:[49, 44], Operations: ['2*31=62', '62-18=44'] Exploring Operation: 49-44=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 49*44=2156, Resulting Numbers: [2156] 2156,49 unequal: No Solution Exploring Operation: 49+44=93, Resulting Numbers: [93] 93,49 unequal: No Solution Moving to Node #0,2,4 Current State: 49:[18, 13], Operations: ['2*31=62', '62-49=13'] Exploring Operation: 18-13=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 18*13=234, Resulting Numbers: [234] 234,49 unequal: No Solution Exploring Operation: 18+13=31, Resulting Numbers: [31] 31,49 unequal: No Solution Moving to Node #0,2,0 Current State: 49:[49, 80], Operations: ['2*31=62', '18+62=80'] Exploring Operation: 49+80=129, Resulting Numbers: [129] 129,49 unequal: No Solution Exploring Operation: 49*80=3920, Resulting Numbers: [3920] 3920,49 unequal: No Solution Exploring Operation: 80-49=31, Resulting Numbers: [31] 31,49 unequal: No Solution Moving to Node #0,2,1 Current State: 49:[62, 31], Operations: ['2*31=62', '49-18=31'] Exploring Operation: 62/31=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 62-31=31, Resulting Numbers: [31] 31,49 unequal: No Solution Exploring Operation: 62+31=93, Resulting Numbers: [93] 93,49 unequal: No Solution Exploring Operation: 62*31=1922, Resulting Numbers: [1922] 1922,49 unequal: No Solution Moving to Node #0,2,3 Current State: 49:[62, 67], Operations: ['2*31=62', '49+18=67'] Exploring Operation: 62+67=129, Resulting Numbers: [129] 129,49 unequal: No Solution Exploring Operation: 67-62=5, Resulting Numbers: [5] 5,49 unequal: No Solution Exploring Operation: 62*67=4154, Resulting Numbers: [4154] 4154,49 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[49, 18, 33], Operations: ['2+31=33'] Exploring Operation: 49-18=31, Resulting Numbers: [33, 31] Generated Node #0,0,0: 49:[33, 31] Operation: 49-18=31 Exploring Operation: 33-18=15, Resulting Numbers: [49, 15] Generated Node #0,0,1: 49:[49, 15] Operation: 33-18=15 Exploring Operation: 18+33=51, Resulting Numbers: [49, 51] Generated Node #0,0,2: 49:[49, 51] Operation: 18+33=51 Exploring Operation: 49-33=16, Resulting Numbers: [18, 16] Generated Node #0,0,3: 49:[18, 16] Operation: 49-33=16 Exploring Operation: 49+18=67, Resulting Numbers: [33, 67] Generated Node #0,0,4: 49:[33, 67] Operation: 49+18=67 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 49:[49, 51], Operations: ['2+31=33', '18+33=51'] Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,49 unequal: No Solution Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,49 unequal: No Solution No 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: 49:[49, 15], Operations: ['2+31=33', '33-18=15'] Exploring Operation: 49*15=735, Resulting Numbers: [735] 735,49 unequal: No Solution Exploring Operation: 49-15=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 49+15=64, Resulting Numbers: [64] 64,49 unequal: No Solution No 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: 49:[18, 16], Operations: ['2+31=33', '49-33=16'] Exploring Operation: 18*16=288, Resulting Numbers: [288] 288,49 unequal: No Solution Exploring Operation: 18+16=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 18-16=2, Resulting Numbers: [2] 2,49 unequal: No Solution No 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: 49:[33, 31], Operations: ['2+31=33', '49-18=31'] Exploring Operation: 33-31=2, Resulting Numbers: [2] 2,49 unequal: No Solution Exploring Operation: 33+31=64, Resulting Numbers: [64] 64,49 unequal: No Solution Exploring Operation: 33*31=1023, Resulting Numbers: [1023] 1023,49 unequal: No Solution No 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: 49:[33, 67], Operations: ['2+31=33', '49+18=67'] Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,49 unequal: No Solution Exploring Operation: 33*67=2211, Resulting Numbers: [2211] 2211,49 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 28, 97, 55, 88 ]
18
[ "28+97=125", "55+88=143", "143-125=18" ]
Current State: 18:[28, 97, 55, 88], Operations: [] Exploring Operation: 28+97=125, Resulting Numbers: [55, 88, 125] Generated Node #2: [55, 88, 125] from Operation: 28+97=125 Current State: 18:[55, 88, 125], Operations: ['28+97=125'] Exploring Operation: 55+88=143, Resulting Numbers: [125, 143] Generated Node #3: [125, 143] from Operation: 55+88=143 Current State: 18:[125, 143], Operations: ['28+97=125', '55+88=143'] Exploring Operation: 143-125=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[28, 97, 55, 88], Operations: [] Exploring Operation: 97-55=42, Resulting Numbers: [28, 88, 42] Generated Node #0,0: 18:[28, 88, 42] Operation: 97-55=42 Exploring Operation: 97-28=69, Resulting Numbers: [55, 88, 69] Generated Node #0,1: 18:[55, 88, 69] Operation: 97-28=69 Exploring Operation: 97-88=9, Resulting Numbers: [28, 55, 9] Generated Node #0,2: 18:[28, 55, 9] Operation: 97-88=9 Exploring Operation: 88-55=33, Resulting Numbers: [28, 97, 33] Generated Node #0,3: 18:[28, 97, 33] Operation: 88-55=33 Moving to Node #0,2 Current State: 18:[28, 55, 9], Operations: ['97-88=9'] Exploring Operation: 28-9=19, Resulting Numbers: [55, 19] Generated Node #0,2,0: 18:[55, 19] Operation: 28-9=19 Exploring Operation: 55-28=27, Resulting Numbers: [9, 27] Generated Node #0,2,1: 18:[9, 27] Operation: 55-28=27 Exploring Operation: 28+9=37, Resulting Numbers: [55, 37] Generated Node #0,2,2: 18:[55, 37] Operation: 28+9=37 Exploring Operation: 55-9=46, Resulting Numbers: [28, 46] Generated Node #0,2,3: 18:[28, 46] Operation: 55-9=46 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[9, 27], Operations: ['97-88=9', '55-28=27'] Exploring Operation: 9+27=36, Resulting Numbers: [36] 36,18 unequal: No Solution Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[28, 97, 55, 88], Operations: [] Exploring Operation: 97-88=9, Resulting Numbers: [28, 55, 9] Generated Node #0,2: 18:[28, 55, 9] Operation: 97-88=9 Moving to Node #0,2 Current State: 18:[28, 55, 9], Operations: ['97-88=9'] Exploring Operation: 55-28=27, Resulting Numbers: [9, 27] Generated Node #0,2,1: 18:[9, 27] Operation: 55-28=27 Moving to Node #0,2,1 Current State: 18:[9, 27], Operations: ['97-88=9', '55-28=27'] Exploring Operation: 27-9=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic