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
[ 99, 42, 3, 94 ]
27
[ "99-94=5", "3*5=15", "42-15=27" ]
Current State: 27:[99, 42, 3, 94], Operations: [] Exploring Operation: 99-94=5, Resulting Numbers: [42, 3, 5] Generated Node #2: [42, 3, 5] from Operation: 99-94=5 Current State: 27:[42, 3, 5], Operations: ['99-94=5'] Exploring Operation: 3*5=15, Resulting Numbers: [42, 15] Generated Node #3: [42, 15] from Operation: 3*5=15 Current State: 27:[42, 15], Operations: ['99-94=5', '3*5=15'] Exploring Operation: 42-15=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[99, 42, 3, 94], Operations: [] Exploring Operation: 94-42=52, Resulting Numbers: [99, 3, 52] Generated Node #0,0: 27:[99, 3, 52] Operation: 94-42=52 Exploring Operation: 99-42=57, Resulting Numbers: [3, 94, 57] Generated Node #0,1: 27:[3, 94, 57] Operation: 99-42=57 Exploring Operation: 99-94=5, Resulting Numbers: [42, 3, 5] Generated Node #0,2: 27:[42, 3, 5] Operation: 99-94=5 Exploring Operation: 99/3=33, Resulting Numbers: [42, 94, 33] Generated Node #0,3: 27:[42, 94, 33] Operation: 99/3=33 Moving to Node #0,2 Current State: 27:[42, 3, 5], Operations: ['99-94=5'] Exploring Operation: 42/3=14, Resulting Numbers: [5, 14] Generated Node #0,2,0: 27:[5, 14] Operation: 42/3=14 Exploring Operation: 42-3=39, Resulting Numbers: [5, 39] Generated Node #0,2,1: 27:[5, 39] Operation: 42-3=39 Exploring Operation: 42-5=37, Resulting Numbers: [3, 37] Generated Node #0,2,2: 27:[3, 37] Operation: 42-5=37 Exploring Operation: 3+5=8, Resulting Numbers: [42, 8] Generated Node #0,2,3: 27:[42, 8] Operation: 3+5=8 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 27:[5, 14], Operations: ['99-94=5', '42/3=14'] Exploring Operation: 5+14=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 5*14=70, Resulting Numbers: [70] 70,27 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 27:[3, 37], Operations: ['99-94=5', '42-5=37'] Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 27:[5, 39], Operations: ['99-94=5', '42-3=39'] Exploring Operation: 5+39=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 39-5=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 5*39=195, Resulting Numbers: [195] 195,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 27:[42, 8], Operations: ['99-94=5', '3+5=8'] Exploring Operation: 42*8=336, Resulting Numbers: [336] 336,27 unequal: No Solution Exploring Operation: 42+8=50, Resulting Numbers: [50] 50,27 unequal: No Solution Exploring Operation: 42-8=34, Resulting Numbers: [34] 34,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 27:[42, 94, 33], Operations: ['99/3=33'] Exploring Operation: 42-33=9, Resulting Numbers: [94, 9] Generated Node #0,3,0: 27:[94, 9] Operation: 42-33=9 Exploring Operation: 94-42=52, Resulting Numbers: [33, 52] Generated Node #0,3,1: 27:[33, 52] Operation: 94-42=52 Exploring Operation: 94-33=61, Resulting Numbers: [42, 61] Generated Node #0,3,2: 27:[42, 61] Operation: 94-33=61 Exploring Operation: 42+94=136, Resulting Numbers: [33, 136] Generated Node #0,3,3: 27:[33, 136] Operation: 42+94=136 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 27:[33, 52], Operations: ['99/3=33', '94-42=52'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 33*52=1716, Resulting Numbers: [1716] 1716,27 unequal: No Solution Exploring Operation: 33+52=85, Resulting Numbers: [85] 85,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 27:[42, 61], Operations: ['99/3=33', '94-33=61'] Exploring Operation: 42+61=103, Resulting Numbers: [103] 103,27 unequal: No Solution Exploring Operation: 61-42=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 42*61=2562, Resulting Numbers: [2562] 2562,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 27:[94, 9], Operations: ['99/3=33', '42-33=9'] Exploring Operation: 94+9=103, Resulting Numbers: [103] 103,27 unequal: No Solution Exploring Operation: 94*9=846, Resulting Numbers: [846] 846,27 unequal: No Solution Exploring Operation: 94-9=85, Resulting Numbers: [85] 85,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 27:[33, 136], Operations: ['99/3=33', '42+94=136'] Exploring Operation: 33*136=4488, Resulting Numbers: [4488] 4488,27 unequal: No Solution Exploring Operation: 33+136=169, Resulting Numbers: [169] 169,27 unequal: No Solution Exploring Operation: 136-33=103, Resulting Numbers: [103] 103,27 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: 27:[3, 94, 57], Operations: ['99-42=57'] Exploring Operation: 57-3=54, Resulting Numbers: [94, 54] Generated Node #0,1,0: 27:[94, 54] Operation: 57-3=54 Exploring Operation: 57/3=19, Resulting Numbers: [94, 19] Generated Node #0,1,1: 27:[94, 19] Operation: 57/3=19 Exploring Operation: 94-3=91, Resulting Numbers: [57, 91] Generated Node #0,1,2: 27:[57, 91] Operation: 94-3=91 Exploring Operation: 94-57=37, Resulting Numbers: [3, 37] Generated Node #0,1,3: 27:[3, 37] Operation: 94-57=37 Moving to Node #0,0 Current State: 27:[99, 3, 52], Operations: ['94-42=52'] Exploring Operation: 99-52=47, Resulting Numbers: [3, 47] Generated Node #0,0,0: 27:[3, 47] Operation: 99-52=47 Exploring Operation: 52-3=49, Resulting Numbers: [99, 49] Generated Node #0,0,1: 27:[99, 49] Operation: 52-3=49 Exploring Operation: 99/3=33, Resulting Numbers: [52, 33] Generated Node #0,0,2: 27:[52, 33] Operation: 99/3=33 Exploring Operation: 99-3=96, Resulting Numbers: [52, 96] Generated Node #0,0,3: 27:[52, 96] Operation: 99-3=96 Moving to Node #0,1,3 Current State: 27:[3, 37], Operations: ['99-42=57', '94-57=37'] Exploring Operation: 3*37=111, Resulting Numbers: [111] 111,27 unequal: No Solution Exploring Operation: 3+37=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 37-3=34, Resulting Numbers: [34] 34,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[3, 47], Operations: ['94-42=52', '99-52=47'] Exploring Operation: 3*47=141, Resulting Numbers: [141] 141,27 unequal: No Solution Exploring Operation: 47-3=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 3+47=50, Resulting Numbers: [50] 50,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[52, 33], Operations: ['94-42=52', '99/3=33'] Exploring Operation: 52-33=19, Resulting Numbers: [19] 19,27 unequal: No Solution Exploring Operation: 52+33=85, Resulting Numbers: [85] 85,27 unequal: No Solution Exploring Operation: 52*33=1716, Resulting Numbers: [1716] 1716,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[94, 19], Operations: ['99-42=57', '57/3=19'] Exploring Operation: 94-19=75, Resulting Numbers: [75] 75,27 unequal: No Solution Exploring Operation: 94*19=1786, Resulting Numbers: [1786] 1786,27 unequal: No Solution Exploring Operation: 94+19=113, Resulting Numbers: [113] 113,27 unequal: No Solution Moving to Node #0,1,0 Current State: 27:[94, 54], Operations: ['99-42=57', '57-3=54'] Exploring Operation: 94*54=5076, Resulting Numbers: [5076] 5076,27 unequal: No Solution Exploring Operation: 94-54=40, Resulting Numbers: [40] 40,27 unequal: No Solution Exploring Operation: 94+54=148, Resulting Numbers: [148] 148,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[99, 49], Operations: ['94-42=52', '52-3=49'] Exploring Operation: 99+49=148, Resulting Numbers: [148] 148,27 unequal: No Solution Exploring Operation: 99*49=4851, Resulting Numbers: [4851] 4851,27 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,27 unequal: No Solution Moving to Node #0,0,3 Current State: 27:[52, 96], Operations: ['94-42=52', '99-3=96'] Exploring Operation: 52*96=4992, Resulting Numbers: [4992] 4992,27 unequal: No Solution Exploring Operation: 96-52=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 52+96=148, Resulting Numbers: [148] 148,27 unequal: No Solution Moving to Node #0,1,2 Current State: 27:[57, 91], Operations: ['99-42=57', '94-3=91'] Exploring Operation: 57+91=148, Resulting Numbers: [148] 148,27 unequal: No Solution Exploring Operation: 91-57=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 57*91=5187, Resulting Numbers: [5187] 5187,27 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 62, 81, 11, 83 ]
42
[ "83-81=2", "62/2=31", "11+31=42" ]
Current State: 42:[62, 81, 11, 83], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [62, 11, 2] Generated Node #2: [62, 11, 2] from Operation: 83-81=2 Current State: 42:[62, 11, 2], Operations: ['83-81=2'] Exploring Operation: 62/2=31, Resulting Numbers: [11, 31] Generated Node #3: [11, 31] from Operation: 62/2=31 Current State: 42:[11, 31], Operations: ['83-81=2', '62/2=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[62, 81, 11, 83], Operations: [] Exploring Operation: 83-62=21, Resulting Numbers: [81, 11, 21] Generated Node #0,0: 42:[81, 11, 21] Operation: 83-62=21 Exploring Operation: 81-62=19, Resulting Numbers: [11, 83, 19] Generated Node #0,1: 42:[11, 83, 19] Operation: 81-62=19 Exploring Operation: 83-81=2, Resulting Numbers: [62, 11, 2] Generated Node #0,2: 42:[62, 11, 2] Operation: 83-81=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[62, 11, 2], Operations: ['83-81=2'] Exploring Operation: 62/2=31, Resulting Numbers: [11, 31] Generated Node #0,2,0: 42:[11, 31] Operation: 62/2=31 Exploring Operation: 62-11=51, Resulting Numbers: [2, 51] Generated Node #0,2,1: 42:[2, 51] Operation: 62-11=51 Exploring Operation: 62-2=60, Resulting Numbers: [11, 60] Generated Node #0,2,2: 42:[11, 60] Operation: 62-2=60 Moving to Node #0,2,1 Current State: 42:[2, 51], Operations: ['83-81=2', '62-11=51'] Exploring Operation: 2+51=53, Resulting Numbers: [53] 53,42 unequal: No Solution Exploring Operation: 51-2=49, Resulting Numbers: [49] 49,42 unequal: No Solution Exploring Operation: 2*51=102, Resulting Numbers: [102] 102,42 unequal: No Solution Moving to Node #0,2,0 Current State: 42:[11, 31], Operations: ['83-81=2', '62/2=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,42 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[62, 81, 11, 83], Operations: [] Exploring Operation: 83-81=2, Resulting Numbers: [62, 11, 2] Generated Node #0,2: 42:[62, 11, 2] Operation: 83-81=2 Moving to Node #0,2 Current State: 42:[62, 11, 2], Operations: ['83-81=2'] Exploring Operation: 62/2=31, Resulting Numbers: [11, 31] Generated Node #0,2,0: 42:[11, 31] Operation: 62/2=31 Moving to Node #0,2,0 Current State: 42:[11, 31], Operations: ['83-81=2', '62/2=31'] Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_3
sum_heuristic
[ 94, 15, 34, 20 ]
80
[ "94-34=60", "60/15=4", "20*4=80" ]
Current State: 80:[94, 15, 34, 20], Operations: [] Exploring Operation: 94-34=60, Resulting Numbers: [15, 20, 60] Generated Node #2: [15, 20, 60] from Operation: 94-34=60 Current State: 80:[15, 20, 60], Operations: ['94-34=60'] Exploring Operation: 60/15=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 60/15=4 Current State: 80:[20, 4], Operations: ['94-34=60', '60/15=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[94, 15, 34, 20], Operations: [] Exploring Operation: 94-20=74, Resulting Numbers: [15, 34, 74] Generated Node #0,0: 80:[15, 34, 74] Operation: 94-20=74 Exploring Operation: 94-15=79, Resulting Numbers: [34, 20, 79] Generated Node #0,1: 80:[34, 20, 79] Operation: 94-15=79 Exploring Operation: 34-15=19, Resulting Numbers: [94, 20, 19] Generated Node #0,2: 80:[94, 20, 19] Operation: 34-15=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[34, 20, 79], Operations: ['94-15=79'] Exploring Operation: 34+20=54, Resulting Numbers: [79, 54] Generated Node #0,1,0: 80:[79, 54] Operation: 34+20=54 Exploring Operation: 34-20=14, Resulting Numbers: [79, 14] Generated Node #0,1,1: 80:[79, 14] Operation: 34-20=14 Exploring Operation: 79-34=45, Resulting Numbers: [20, 45] Generated Node #0,1,2: 80:[20, 45] Operation: 79-34=45 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[79, 14], Operations: ['94-15=79', '34-20=14'] Exploring Operation: 79+14=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 79-14=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 79*14=1106, Resulting Numbers: [1106] 1106,80 unequal: No Solution No 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: 80:[20, 45], Operations: ['94-15=79', '79-34=45'] Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,80 unequal: No Solution Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,80 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,80 unequal: No Solution No 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: 80:[79, 54], Operations: ['94-15=79', '34+20=54'] Exploring Operation: 79+54=133, Resulting Numbers: [133] 133,80 unequal: No Solution Exploring Operation: 79-54=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 79*54=4266, Resulting Numbers: [4266] 4266,80 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: 80:[15, 34, 74], Operations: ['94-20=74'] Exploring Operation: 74-34=40, Resulting Numbers: [15, 40] Generated Node #0,0,0: 80:[15, 40] Operation: 74-34=40 Exploring Operation: 34-15=19, Resulting Numbers: [74, 19] Generated Node #0,0,1: 80:[74, 19] Operation: 34-15=19 Exploring Operation: 15+34=49, Resulting Numbers: [74, 49] Generated Node #0,0,2: 80:[74, 49] Operation: 15+34=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[15, 40], Operations: ['94-20=74', '74-34=40'] Exploring Operation: 15+40=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 40-15=25, Resulting Numbers: [25] 25,80 unequal: No Solution Exploring Operation: 15*40=600, Resulting Numbers: [600] 600,80 unequal: No Solution No 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: 80:[74, 19], Operations: ['94-20=74', '34-15=19'] Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,80 unequal: No Solution Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,80 unequal: No Solution No 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: 80:[74, 49], Operations: ['94-20=74', '15+34=49'] Exploring Operation: 74+49=123, Resulting Numbers: [123] 123,80 unequal: No Solution Exploring Operation: 74*49=3626, Resulting Numbers: [3626] 3626,80 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,80 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: 80:[94, 20, 19], Operations: ['34-15=19'] Exploring Operation: 20+19=39, Resulting Numbers: [94, 39] Generated Node #0,2,0: 80:[94, 39] Operation: 20+19=39 Exploring Operation: 94-19=75, Resulting Numbers: [20, 75] Generated Node #0,2,1: 80:[20, 75] Operation: 94-19=75 Exploring Operation: 94-20=74, Resulting Numbers: [19, 74] Generated Node #0,2,2: 80:[19, 74] Operation: 94-20=74 Moving to Node #0,2,1 Current State: 80:[20, 75], Operations: ['34-15=19', '94-19=75'] Exploring Operation: 20*75=1500, Resulting Numbers: [1500] 1500,80 unequal: No Solution Exploring Operation: 20+75=95, Resulting Numbers: [95] 95,80 unequal: No Solution Exploring Operation: 75-20=55, Resulting Numbers: [55] 55,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[19, 74], Operations: ['34-15=19', '94-20=74'] Exploring Operation: 19+74=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 19*74=1406, Resulting Numbers: [1406] 1406,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[94, 39], Operations: ['34-15=19', '20+19=39'] Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,80 unequal: No Solution Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 33, 35, 34, 2 ]
19
[ "35-33=2", "34/2=17", "2+17=19" ]
Current State: 19:[33, 35, 34, 2], Operations: [] Exploring Operation: 35-33=2, Resulting Numbers: [34, 2, 2] Generated Node #2: [34, 2, 2] from Operation: 35-33=2 Current State: 19:[34, 2, 2], Operations: ['35-33=2'] Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,19 equal: Goal Reached Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[33, 35, 34, 2], Operations: [] Exploring Operation: 35-2=33, Resulting Numbers: [33, 34, 33] Generated Node #0,0: 19:[33, 34, 33] Operation: 35-2=33 Exploring Operation: 34-2=32, Resulting Numbers: [33, 35, 32] Generated Node #0,1: 19:[33, 35, 32] Operation: 34-2=32 Exploring Operation: 34/2=17, Resulting Numbers: [33, 35, 17] Generated Node #0,2: 19:[33, 35, 17] Operation: 34/2=17 Exploring Operation: 33-2=31, Resulting Numbers: [35, 34, 31] Generated Node #0,3: 19:[35, 34, 31] Operation: 33-2=31 Exploring Operation: 33+2=35, Resulting Numbers: [35, 34, 35] Generated Node #0,4: 19:[35, 34, 35] Operation: 33+2=35 Moving to Node #0,2 Current State: 19:[33, 35, 17], Operations: ['34/2=17'] Exploring Operation: 33+17=50, Resulting Numbers: [35, 50] Generated Node #0,2,0: 19:[35, 50] Operation: 33+17=50 Exploring Operation: 33-17=16, Resulting Numbers: [35, 16] Generated Node #0,2,1: 19:[35, 16] Operation: 33-17=16 Exploring Operation: 35-17=18, Resulting Numbers: [33, 18] Generated Node #0,2,2: 19:[33, 18] Operation: 35-17=18 Exploring Operation: 35+17=52, Resulting Numbers: [33, 52] Generated Node #0,2,3: 19:[33, 52] Operation: 35+17=52 Exploring Operation: 35-33=2, Resulting Numbers: [17, 2] Generated Node #0,2,4: 19:[17, 2] Operation: 35-33=2 Moving to Node #0,1 Current State: 19:[33, 35, 32], Operations: ['34-2=32'] Exploring Operation: 33+32=65, Resulting Numbers: [35, 65] Generated Node #0,1,0: 19:[35, 65] Operation: 33+32=65 Exploring Operation: 33-32=1, Resulting Numbers: [35, 1] Generated Node #0,1,1: 19:[35, 1] Operation: 33-32=1 Exploring Operation: 35-32=3, Resulting Numbers: [33, 3] Generated Node #0,1,2: 19:[33, 3] Operation: 35-32=3 Exploring Operation: 35-33=2, Resulting Numbers: [32, 2] Generated Node #0,1,3: 19:[32, 2] Operation: 35-33=2 Exploring Operation: 33+35=68, Resulting Numbers: [32, 68] Generated Node #0,1,4: 19:[32, 68] Operation: 33+35=68 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 19:[33, 3], Operations: ['34-2=32', '35-32=3'] Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,19 unequal: No Solution Exploring Operation: 33*3=99, Resulting Numbers: [99] 99,19 unequal: No Solution Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,19 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:[32, 2], Operations: ['34-2=32', '35-33=2'] Exploring Operation: 32-2=30, Resulting Numbers: [30] 30,19 unequal: No Solution Exploring Operation: 32+2=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 32*2=64, Resulting Numbers: [64] 64,19 unequal: No Solution Exploring Operation: 32/2=16, Resulting Numbers: [16] 16,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 19:[35, 1], Operations: ['34-2=32', '33-32=1'] Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 19:[35, 65], Operations: ['34-2=32', '33+32=65'] Exploring Operation: 35*65=2275, Resulting Numbers: [2275] 2275,19 unequal: No Solution Exploring Operation: 35+65=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 65-35=30, Resulting Numbers: [30] 30,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 19:[32, 68], Operations: ['34-2=32', '33+35=68'] Exploring Operation: 68-32=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 32+68=100, Resulting Numbers: [100] 100,19 unequal: No Solution Exploring Operation: 32*68=2176, Resulting Numbers: [2176] 2176,19 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:[33, 34, 33], Operations: ['35-2=33'] Exploring Operation: 34-33=1, Resulting Numbers: [33, 1] Generated Node #0,0,0: 19:[33, 1] Operation: 34-33=1 Exploring Operation: 33-33=0, Resulting Numbers: [34, 0] Generated Node #0,0,1: 19:[34, 0] Operation: 33-33=0 Exploring Operation: 34-33=1, Resulting Numbers: [33, 1] Generated Node #0,0,2: 19:[33, 1] Operation: 34-33=1 Exploring Operation: 33+34=67, Resulting Numbers: [33, 67] Generated Node #0,0,3: 19:[33, 67] Operation: 33+34=67 Exploring Operation: 33/33=1, Resulting Numbers: [34, 1] Generated Node #0,0,4: 19:[34, 1] Operation: 33/33=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 19:[33, 1], Operations: ['35-2=33', '34-33=1'] Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,19 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,19 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 #0,0,2 Current State: 19:[33, 1], Operations: ['35-2=33', '34-33=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,19 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 #0,0,4 Current State: 19:[34, 1], Operations: ['35-2=33', '33/33=1'] Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,19 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 #0,0,1 Current State: 19:[34, 0], Operations: ['35-2=33', '33-33=0'] Exploring Operation: 34*0=0, Resulting Numbers: [0] 0,19 unequal: No Solution Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34-0=34, Resulting Numbers: [34] 34,19 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 #0,0,3 Current State: 19:[33, 67], Operations: ['35-2=33', '33+34=67'] Exploring Operation: 33*67=2211, Resulting Numbers: [2211] 2211,19 unequal: No Solution Exploring Operation: 67-33=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 33+67=100, Resulting Numbers: [100] 100,19 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: 19:[35, 34, 31], Operations: ['33-2=31'] Exploring Operation: 35-34=1, Resulting Numbers: [31, 1] Generated Node #0,3,0: 19:[31, 1] Operation: 35-34=1 Exploring Operation: 35-31=4, Resulting Numbers: [34, 4] Generated Node #0,3,1: 19:[34, 4] Operation: 35-31=4 Exploring Operation: 35+31=66, Resulting Numbers: [34, 66] Generated Node #0,3,2: 19:[34, 66] Operation: 35+31=66 Exploring Operation: 34-31=3, Resulting Numbers: [35, 3] Generated Node #0,3,3: 19:[35, 3] Operation: 34-31=3 Exploring Operation: 35+34=69, Resulting Numbers: [31, 69] Generated Node #0,3,4: 19:[31, 69] Operation: 35+34=69 Moving to Node #0,4 Current State: 19:[35, 34, 35], Operations: ['33+2=35'] Exploring Operation: 35/35=1, Resulting Numbers: [34, 1] Generated Node #0,4,0: 19:[34, 1] Operation: 35/35=1 Exploring Operation: 35+34=69, Resulting Numbers: [35, 69] Generated Node #0,4,1: 19:[35, 69] Operation: 35+34=69 Exploring Operation: 35-34=1, Resulting Numbers: [35, 1] Generated Node #0,4,2: 19:[35, 1] Operation: 35-34=1 Exploring Operation: 35-35=0, Resulting Numbers: [34, 0] Generated Node #0,4,3: 19:[34, 0] Operation: 35-35=0 Exploring Operation: 35-34=1, Resulting Numbers: [35, 1] Generated Node #0,4,4: 19:[35, 1] Operation: 35-34=1 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 19:[34, 1], Operations: ['33+2=35', '35/35=1'] Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,19 unequal: No Solution Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,19 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 #0,4,2 Current State: 19:[35, 1], Operations: ['33+2=35', '35-34=1'] Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,19 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 #0,4,3 Current State: 19:[34, 0], Operations: ['33+2=35', '35-35=0'] Exploring Operation: 34+0=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34-0=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 34*0=0, Resulting Numbers: [0] 0,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 19:[35, 1], Operations: ['33+2=35', '35-34=1'] Exploring Operation: 35*1=35, Resulting Numbers: [35] 35,19 unequal: No Solution Exploring Operation: 35-1=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 35+1=36, Resulting Numbers: [36] 36,19 unequal: No Solution Exploring Operation: 35/1=35, Resulting Numbers: [35] 35,19 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 #0,4,1 Current State: 19:[35, 69], Operations: ['33+2=35', '35+34=69'] Exploring Operation: 35+69=104, Resulting Numbers: [104] 104,19 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,19 unequal: No Solution Exploring Operation: 35*69=2415, Resulting Numbers: [2415] 2415,19 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 19:[33, 18], Operations: ['34/2=17', '35-17=18'] Exploring Operation: 33+18=51, Resulting Numbers: [51] 51,19 unequal: No Solution Exploring Operation: 33*18=594, Resulting Numbers: [594] 594,19 unequal: No Solution Exploring Operation: 33-18=15, Resulting Numbers: [15] 15,19 unequal: No Solution Moving to Node #0,2,4 Current State: 19:[17, 2], Operations: ['34/2=17', '35-33=2'] Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,19 unequal: No Solution Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached Moving to Node #0 Current State: 19:[33, 35, 34, 2], Operations: [] Exploring Operation: 34/2=17, Resulting Numbers: [33, 35, 17] Generated Node #0,2: 19:[33, 35, 17] Operation: 34/2=17 Moving to Node #0,2 Current State: 19:[33, 35, 17], Operations: ['34/2=17'] Exploring Operation: 35-33=2, Resulting Numbers: [17, 2] Generated Node #0,2,4: 19:[17, 2] Operation: 35-33=2 Moving to Node #0,2,4 Current State: 19:[17, 2], Operations: ['34/2=17', '35-33=2'] Exploring Operation: 17+2=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
0.919271
hs_5
mult_heuristic
[ 32, 10, 12, 13 ]
77
[ "12-10=2", "32*2=64", "13+64=77" ]
Current State: 77:[32, 10, 12, 13], Operations: [] Exploring Operation: 12-10=2, Resulting Numbers: [32, 13, 2] Generated Node #2: [32, 13, 2] from Operation: 12-10=2 Current State: 77:[32, 13, 2], Operations: ['12-10=2'] Exploring Operation: 32*2=64, Resulting Numbers: [13, 64] Generated Node #3: [13, 64] from Operation: 32*2=64 Current State: 77:[13, 64], Operations: ['12-10=2', '32*2=64'] Exploring Operation: 13+64=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[32, 10, 12, 13], Operations: [] Exploring Operation: 32-10=22, Resulting Numbers: [12, 13, 22] Generated Node #0,0: 77:[12, 13, 22] Operation: 32-10=22 Exploring Operation: 32-12=20, Resulting Numbers: [10, 13, 20] Generated Node #0,1: 77:[10, 13, 20] Operation: 32-12=20 Exploring Operation: 32-13=19, Resulting Numbers: [10, 12, 19] Generated Node #0,2: 77:[10, 12, 19] Operation: 32-13=19 Exploring Operation: 13-10=3, Resulting Numbers: [32, 12, 3] Generated Node #0,3: 77:[32, 12, 3] Operation: 13-10=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 77:[10, 12, 19], Operations: ['32-13=19'] Exploring Operation: 10+12=22, Resulting Numbers: [19, 22] Generated Node #0,2,0: 77:[19, 22] Operation: 10+12=22 Exploring Operation: 19-12=7, Resulting Numbers: [10, 7] Generated Node #0,2,1: 77:[10, 7] Operation: 19-12=7 Exploring Operation: 12-10=2, Resulting Numbers: [19, 2] Generated Node #0,2,2: 77:[19, 2] Operation: 12-10=2 Exploring Operation: 19-10=9, Resulting Numbers: [12, 9] Generated Node #0,2,3: 77:[12, 9] Operation: 19-10=9 Moving to Node #0,2,1 Current State: 77:[10, 7], Operations: ['32-13=19', '19-12=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,2,3 Current State: 77:[12, 9], Operations: ['32-13=19', '19-10=9'] Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,77 unequal: No Solution Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,77 unequal: No Solution Moving to Node #0,2,2 Current State: 77:[19, 2], Operations: ['32-13=19', '12-10=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,77 unequal: No Solution Moving to Node #0,2,0 Current State: 77:[19, 22], Operations: ['32-13=19', '10+12=22'] Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,77 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 77:[10, 13, 20], Operations: ['32-12=20'] Exploring Operation: 20-10=10, Resulting Numbers: [13, 10] Generated Node #0,1,0: 77:[13, 10] Operation: 20-10=10 Exploring Operation: 20-13=7, Resulting Numbers: [10, 7] Generated Node #0,1,1: 77:[10, 7] Operation: 20-13=7 Exploring Operation: 13-10=3, Resulting Numbers: [20, 3] Generated Node #0,1,2: 77:[20, 3] Operation: 13-10=3 Exploring Operation: 20/10=2, Resulting Numbers: [13, 2] Generated Node #0,1,3: 77:[13, 2] Operation: 20/10=2 Moving to Node #0,1,1 Current State: 77:[10, 7], Operations: ['32-12=20', '20-13=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,77 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[13, 10], Operations: ['32-12=20', '20-10=10'] Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,77 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,77 unequal: No Solution Moving to Node #0,1,3 Current State: 77:[13, 2], Operations: ['32-12=20', '20/10=2'] Exploring Operation: 13+2=15, Resulting Numbers: [15] 15,77 unequal: No Solution Exploring Operation: 13*2=26, Resulting Numbers: [26] 26,77 unequal: No Solution Exploring Operation: 13-2=11, Resulting Numbers: [11] 11,77 unequal: No Solution Moving to Node #0,1,2 Current State: 77:[20, 3], Operations: ['32-12=20', '13-10=3'] Exploring Operation: 20*3=60, Resulting Numbers: [60] 60,77 unequal: No Solution Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 77:[12, 13, 22], Operations: ['32-10=22'] Exploring Operation: 13-12=1, Resulting Numbers: [22, 1] Generated Node #0,0,0: 77:[22, 1] Operation: 13-12=1 Exploring Operation: 22-12=10, Resulting Numbers: [13, 10] Generated Node #0,0,1: 77:[13, 10] Operation: 22-12=10 Exploring Operation: 22-13=9, Resulting Numbers: [12, 9] Generated Node #0,0,2: 77:[12, 9] Operation: 22-13=9 Exploring Operation: 12+13=25, Resulting Numbers: [22, 25] Generated Node #0,0,3: 77:[22, 25] Operation: 12+13=25 Moving to Node #0,0,1 Current State: 77:[13, 10], Operations: ['32-10=22', '22-12=10'] Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,77 unequal: No Solution Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,77 unequal: No Solution Moving to Node #0,0,2 Current State: 77:[12, 9], Operations: ['32-10=22', '22-13=9'] Exploring Operation: 12-9=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 12+9=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 12*9=108, Resulting Numbers: [108] 108,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[22, 1], Operations: ['32-10=22', '13-12=1'] Exploring Operation: 22+1=23, Resulting Numbers: [23] 23,77 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,77 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,77 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,77 unequal: No Solution Moving to Node #0,0,3 Current State: 77:[22, 25], Operations: ['32-10=22', '12+13=25'] Exploring Operation: 25-22=3, Resulting Numbers: [3] 3,77 unequal: No Solution Exploring Operation: 22+25=47, Resulting Numbers: [47] 47,77 unequal: No Solution Exploring Operation: 22*25=550, Resulting Numbers: [550] 550,77 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 77:[32, 12, 3], Operations: ['13-10=3'] Exploring Operation: 32-12=20, Resulting Numbers: [3, 20] Generated Node #0,3,0: 77:[3, 20] Operation: 32-12=20 Exploring Operation: 32-3=29, Resulting Numbers: [12, 29] Generated Node #0,3,1: 77:[12, 29] Operation: 32-3=29 Exploring Operation: 32*3=96, Resulting Numbers: [12, 96] Generated Node #0,3,2: 77:[12, 96] Operation: 32*3=96 Exploring Operation: 12-3=9, Resulting Numbers: [32, 9] Generated Node #0,3,3: 77:[32, 9] Operation: 12-3=9 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 77:[3, 20], Operations: ['13-10=3', '32-12=20'] Exploring Operation: 20-3=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 3*20=60, Resulting Numbers: [60] 60,77 unequal: No Solution Exploring Operation: 3+20=23, Resulting Numbers: [23] 23,77 unequal: No Solution No 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: 77:[12, 29], Operations: ['13-10=3', '32-3=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,77 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,77 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,77 unequal: No Solution No 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: 77:[12, 96], Operations: ['13-10=3', '32*3=96'] Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,77 unequal: No Solution Exploring Operation: 12*96=1152, Resulting Numbers: [1152] 1152,77 unequal: No Solution Exploring Operation: 12+96=108, Resulting Numbers: [108] 108,77 unequal: No Solution Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,77 unequal: No Solution No 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: 77:[32, 9], Operations: ['13-10=3', '12-3=9'] Exploring Operation: 32*9=288, Resulting Numbers: [288] 288,77 unequal: No Solution Exploring Operation: 32+9=41, Resulting Numbers: [41] 41,77 unequal: No Solution Exploring Operation: 32-9=23, Resulting Numbers: [23] 23,77 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 59, 45, 78, 3 ]
89
[ "59-45=14", "78-3=75", "14+75=89" ]
Current State: 89:[59, 45, 78, 3], Operations: [] Exploring Operation: 59-45=14, Resulting Numbers: [78, 3, 14] Generated Node #2: [78, 3, 14] from Operation: 59-45=14 Current State: 89:[78, 3, 14], Operations: ['59-45=14'] Exploring Operation: 78-3=75, Resulting Numbers: [14, 75] Generated Node #3: [14, 75] from Operation: 78-3=75 Current State: 89:[14, 75], Operations: ['59-45=14', '78-3=75'] Exploring Operation: 14+75=89, Resulting Numbers: [89] 89,89 equal: Goal Reached
4
Current State: 89:[59, 45, 78, 3], Operations: [] Exploring Operation: 59+3=62, Resulting Numbers: [45, 78, 62] Generated Node #0,0: 89:[45, 78, 62] Operation: 59+3=62 Exploring Operation: 45+3=48, Resulting Numbers: [59, 78, 48] Generated Node #0,1: 89:[59, 78, 48] Operation: 45+3=48 Exploring Operation: 78+3=81, Resulting Numbers: [59, 45, 81] Generated Node #0,2: 89:[59, 45, 81] Operation: 78+3=81 Moving to Node #0,0 Current State: 89:[45, 78, 62], Operations: ['59+3=62'] Exploring Operation: 45+78=123, Resulting Numbers: [62, 123] Generated Node #0,0,0: 89:[62, 123] Operation: 45+78=123 Exploring Operation: 78-45=33, Resulting Numbers: [62, 33] Generated Node #0,0,1: 89:[62, 33] Operation: 78-45=33 Exploring Operation: 45+62=107, Resulting Numbers: [78, 107] Generated Node #0,0,2: 89:[78, 107] Operation: 45+62=107 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 89:[78, 107], Operations: ['59+3=62', '45+62=107'] Exploring Operation: 78+107=185, Resulting Numbers: [185] 185,89 unequal: No Solution Exploring Operation: 107-78=29, Resulting Numbers: [29] 29,89 unequal: No Solution Exploring Operation: 78*107=8346, Resulting Numbers: [8346] 8346,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 89:[62, 123], Operations: ['59+3=62', '45+78=123'] Exploring Operation: 62*123=7626, Resulting Numbers: [7626] 7626,89 unequal: No Solution Exploring Operation: 123-62=61, Resulting Numbers: [61] 61,89 unequal: No Solution Exploring Operation: 62+123=185, Resulting Numbers: [185] 185,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 89:[62, 33], Operations: ['59+3=62', '78-45=33'] Exploring Operation: 62+33=95, Resulting Numbers: [95] 95,89 unequal: No Solution Exploring Operation: 62-33=29, Resulting Numbers: [29] 29,89 unequal: No Solution Exploring Operation: 62*33=2046, Resulting Numbers: [2046] 2046,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 89:[59, 78, 48], Operations: ['45+3=48'] Exploring Operation: 78+48=126, Resulting Numbers: [59, 126] Generated Node #0,1,0: 89:[59, 126] Operation: 78+48=126 Exploring Operation: 59+48=107, Resulting Numbers: [78, 107] Generated Node #0,1,1: 89:[78, 107] Operation: 59+48=107 Exploring Operation: 59+78=137, Resulting Numbers: [48, 137] Generated Node #0,1,2: 89:[48, 137] Operation: 59+78=137 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 89:[78, 107], Operations: ['45+3=48', '59+48=107'] Exploring Operation: 78*107=8346, Resulting Numbers: [8346] 8346,89 unequal: No Solution Exploring Operation: 78+107=185, Resulting Numbers: [185] 185,89 unequal: No Solution Exploring Operation: 107-78=29, Resulting Numbers: [29] 29,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 89:[59, 126], Operations: ['45+3=48', '78+48=126'] Exploring Operation: 59+126=185, Resulting Numbers: [185] 185,89 unequal: No Solution Exploring Operation: 126-59=67, Resulting Numbers: [67] 67,89 unequal: No Solution Exploring Operation: 59*126=7434, Resulting Numbers: [7434] 7434,89 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 89:[48, 137], Operations: ['45+3=48', '59+78=137'] Exploring Operation: 137-48=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Moving to Node #0 Current State: 89:[59, 45, 78, 3], Operations: [] Exploring Operation: 45+3=48, Resulting Numbers: [59, 78, 48] Generated Node #0,1: 89:[59, 78, 48] Operation: 45+3=48 Moving to Node #0,1 Current State: 89:[59, 78, 48], Operations: ['45+3=48'] Exploring Operation: 59+78=137, Resulting Numbers: [48, 137] Generated Node #0,1,2: 89:[48, 137] Operation: 59+78=137 Moving to Node #0,1,2 Current State: 89:[48, 137], Operations: ['45+3=48', '59+78=137'] Exploring Operation: 137-48=89, Resulting Numbers: [89] 89,89 equal: Goal Reached Exit Sub Search at level 1
0.974826
hs_3
mult_heuristic
[ 76, 15, 26, 48 ]
30
[ "76-26=50", "50-48=2", "15*2=30" ]
Current State: 30:[76, 15, 26, 48], Operations: [] Exploring Operation: 76-26=50, Resulting Numbers: [15, 48, 50] Generated Node #2: [15, 48, 50] from Operation: 76-26=50 Current State: 30:[15, 48, 50], Operations: ['76-26=50'] Exploring Operation: 50-48=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 50-48=2 Current State: 30:[15, 2], Operations: ['76-26=50', '50-48=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[76, 15, 26, 48], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [15, 26, 28] Generated Node #0,0: 30:[15, 26, 28] Operation: 76-48=28 Moving to Node #0,0 Current State: 30:[15, 26, 28], Operations: ['76-48=28'] Exploring Operation: 28-26=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 30:[15, 2] Operation: 28-26=2 Moving to Node #0,0,0 Current State: 30:[15, 2], Operations: ['76-48=28', '28-26=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[76, 15, 26, 48], Operations: [] Exploring Operation: 76-48=28, Resulting Numbers: [15, 26, 28] Generated Node #0,0: 30:[15, 26, 28] Operation: 76-48=28 Moving to Node #0,0 Current State: 30:[15, 26, 28], Operations: ['76-48=28'] Exploring Operation: 28-26=2, Resulting Numbers: [15, 2] Generated Node #0,0,0: 30:[15, 2] Operation: 28-26=2 Moving to Node #0,0,0 Current State: 30:[15, 2], Operations: ['76-48=28', '28-26=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 47, 11, 22, 2 ]
80
[ "47-11=36", "22*2=44", "36+44=80" ]
Current State: 80:[47, 11, 22, 2], Operations: [] Exploring Operation: 47-11=36, Resulting Numbers: [22, 2, 36] Generated Node #2: [22, 2, 36] from Operation: 47-11=36 Current State: 80:[22, 2, 36], Operations: ['47-11=36'] Exploring Operation: 22*2=44, Resulting Numbers: [36, 44] Generated Node #3: [36, 44] from Operation: 22*2=44 Current State: 80:[36, 44], Operations: ['47-11=36', '22*2=44'] Exploring Operation: 36+44=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[47, 11, 22, 2], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [47, 2, 2] Generated Node #0,0: 80:[47, 2, 2] Operation: 22/11=2 Exploring Operation: 47-11=36, Resulting Numbers: [22, 2, 36] Generated Node #0,1: 80:[22, 2, 36] Operation: 47-11=36 Exploring Operation: 47-22=25, Resulting Numbers: [11, 2, 25] Generated Node #0,2: 80:[11, 2, 25] Operation: 47-22=25 Moving to Node #0,1 Current State: 80:[22, 2, 36], Operations: ['47-11=36'] Exploring Operation: 22-2=20, Resulting Numbers: [36, 20] Generated Node #0,1,0: 80:[36, 20] Operation: 22-2=20 Exploring Operation: 36-22=14, Resulting Numbers: [2, 14] Generated Node #0,1,1: 80:[2, 14] Operation: 36-22=14 Exploring Operation: 2+36=38, Resulting Numbers: [22, 38] Generated Node #0,1,2: 80:[22, 38] Operation: 2+36=38 Moving to Node #0,2 Current State: 80:[11, 2, 25], Operations: ['47-22=25'] Exploring Operation: 25-11=14, Resulting Numbers: [2, 14] Generated Node #0,2,0: 80:[2, 14] Operation: 25-11=14 Exploring Operation: 11+25=36, Resulting Numbers: [2, 36] Generated Node #0,2,1: 80:[2, 36] Operation: 11+25=36 Exploring Operation: 25-2=23, Resulting Numbers: [11, 23] Generated Node #0,2,2: 80:[11, 23] Operation: 25-2=23 Moving to Node #0,0 Current State: 80:[47, 2, 2], Operations: ['22/11=2'] Exploring Operation: 2+2=4, Resulting Numbers: [47, 4] Generated Node #0,0,0: 80:[47, 4] Operation: 2+2=4 Exploring Operation: 47-2=45, Resulting Numbers: [2, 45] Generated Node #0,0,1: 80:[2, 45] Operation: 47-2=45 Exploring Operation: 47-2=45, Resulting Numbers: [2, 45] Generated Node #0,0,2: 80:[2, 45] Operation: 47-2=45 Moving to Node #0,1,1 Current State: 80:[2, 14], Operations: ['47-11=36', '36-22=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,80 unequal: No Solution Moving to Node #0,2,0 Current State: 80:[2, 14], Operations: ['47-22=25', '25-11=14'] Exploring Operation: 14/2=7, Resulting Numbers: [7] 7,80 unequal: No Solution Exploring Operation: 14-2=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 2+14=16, Resulting Numbers: [16] 16,80 unequal: No Solution Moving to Node #0,1,2 Current State: 80:[22, 38], Operations: ['47-11=36', '2+36=38'] Exploring Operation: 22+38=60, Resulting Numbers: [60] 60,80 unequal: No Solution Exploring Operation: 22*38=836, Resulting Numbers: [836] 836,80 unequal: No Solution Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,80 unequal: No Solution Moving to Node #0,2,2 Current State: 80:[11, 23], Operations: ['47-22=25', '25-2=23'] Exploring Operation: 11*23=253, Resulting Numbers: [253] 253,80 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,80 unequal: No Solution Exploring Operation: 11+23=34, Resulting Numbers: [34] 34,80 unequal: No Solution Moving to Node #0,2,1 Current State: 80:[2, 36], Operations: ['47-22=25', '11+25=36'] Exploring Operation: 2+36=38, Resulting Numbers: [38] 38,80 unequal: No Solution Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,80 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,80 unequal: No Solution Moving to Node #0,1,0 Current State: 80:[36, 20], Operations: ['47-11=36', '22-2=20'] Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,80 unequal: No Solution Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,80 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[2, 45], Operations: ['22/11=2', '47-2=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,80 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[2, 45], Operations: ['22/11=2', '47-2=45'] Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 2+45=47, Resulting Numbers: [47] 47,80 unequal: No Solution Exploring Operation: 2*45=90, Resulting Numbers: [90] 90,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[47, 4], Operations: ['22/11=2', '2+2=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,80 unequal: No Solution Exploring Operation: 47+4=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 47*4=188, Resulting Numbers: [188] 188,80 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 68, 3, 70, 56 ]
74
[ "68-56=12", "12/3=4", "70+4=74" ]
Current State: 74:[68, 3, 70, 56], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [3, 70, 12] Generated Node #2: [3, 70, 12] from Operation: 68-56=12 Current State: 74:[3, 70, 12], Operations: ['68-56=12'] Exploring Operation: 12/3=4, Resulting Numbers: [70, 4] Generated Node #3: [70, 4] from Operation: 12/3=4 Current State: 74:[70, 4], Operations: ['68-56=12', '12/3=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[68, 3, 70, 56], Operations: [] Exploring Operation: 70-68=2, Resulting Numbers: [3, 56, 2] Generated Node #0,0: 74:[3, 56, 2] Operation: 70-68=2 Exploring Operation: 68-56=12, Resulting Numbers: [3, 70, 12] Generated Node #0,1: 74:[3, 70, 12] Operation: 68-56=12 Exploring Operation: 68+3=71, Resulting Numbers: [70, 56, 71] Generated Node #0,2: 74:[70, 56, 71] Operation: 68+3=71 Exploring Operation: 70-56=14, Resulting Numbers: [68, 3, 14] Generated Node #0,3: 74:[68, 3, 14] Operation: 70-56=14 Moving to Node #0,1 Current State: 74:[3, 70, 12], Operations: ['68-56=12'] Exploring Operation: 70+12=82, Resulting Numbers: [3, 82] Generated Node #0,1,0: 74:[3, 82] Operation: 70+12=82 Exploring Operation: 12/3=4, Resulting Numbers: [70, 4] Generated Node #0,1,1: 74:[70, 4] Operation: 12/3=4 Exploring Operation: 3*12=36, Resulting Numbers: [70, 36] Generated Node #0,1,2: 74:[70, 36] Operation: 3*12=36 Exploring Operation: 3+70=73, Resulting Numbers: [12, 73] Generated Node #0,1,3: 74:[12, 73] Operation: 3+70=73 Moving to Node #0,3 Current State: 74:[68, 3, 14], Operations: ['70-56=14'] Exploring Operation: 68+14=82, Resulting Numbers: [3, 82] Generated Node #0,3,0: 74:[3, 82] Operation: 68+14=82 Exploring Operation: 3*14=42, Resulting Numbers: [68, 42] Generated Node #0,3,1: 74:[68, 42] Operation: 3*14=42 Exploring Operation: 14-3=11, Resulting Numbers: [68, 11] Generated Node #0,3,2: 74:[68, 11] Operation: 14-3=11 Exploring Operation: 68+3=71, Resulting Numbers: [14, 71] Generated Node #0,3,3: 74:[14, 71] Operation: 68+3=71 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 74:[3, 82], Operations: ['70-56=14', '68+14=82'] Exploring Operation: 3+82=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 3*82=246, Resulting Numbers: [246] 246,74 unequal: No Solution Exploring Operation: 82-3=79, Resulting Numbers: [79] 79,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[68, 42], Operations: ['70-56=14', '3*14=42'] Exploring Operation: 68+42=110, Resulting Numbers: [110] 110,74 unequal: No Solution Exploring Operation: 68-42=26, Resulting Numbers: [26] 26,74 unequal: No Solution Exploring Operation: 68*42=2856, Resulting Numbers: [2856] 2856,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[68, 11], Operations: ['70-56=14', '14-3=11'] Exploring Operation: 68*11=748, Resulting Numbers: [748] 748,74 unequal: No Solution Exploring Operation: 68-11=57, Resulting Numbers: [57] 57,74 unequal: No Solution Exploring Operation: 68+11=79, Resulting Numbers: [79] 79,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[14, 71], Operations: ['70-56=14', '68+3=71'] Exploring Operation: 14+71=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,74 unequal: No Solution Exploring Operation: 14*71=994, Resulting Numbers: [994] 994,74 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: 74:[3, 56, 2], Operations: ['70-68=2'] Exploring Operation: 56/2=28, Resulting Numbers: [3, 28] Generated Node #0,0,0: 74:[3, 28] Operation: 56/2=28 Exploring Operation: 3+56=59, Resulting Numbers: [2, 59] Generated Node #0,0,1: 74:[2, 59] Operation: 3+56=59 Exploring Operation: 56+2=58, Resulting Numbers: [3, 58] Generated Node #0,0,2: 74:[3, 58] Operation: 56+2=58 Exploring Operation: 56-3=53, Resulting Numbers: [2, 53] Generated Node #0,0,3: 74:[2, 53] Operation: 56-3=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 74:[3, 28], Operations: ['70-68=2', '56/2=28'] Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,74 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,74 unequal: No Solution Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 74:[2, 59], Operations: ['70-68=2', '3+56=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,74 unequal: No Solution Exploring Operation: 2*59=118, Resulting Numbers: [118] 118,74 unequal: No Solution Exploring Operation: 2+59=61, Resulting Numbers: [61] 61,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 74:[2, 53], Operations: ['70-68=2', '56-3=53'] Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,74 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 74:[3, 58], Operations: ['70-68=2', '56+2=58'] Exploring Operation: 3+58=61, Resulting Numbers: [61] 61,74 unequal: No Solution Exploring Operation: 3*58=174, Resulting Numbers: [174] 174,74 unequal: No Solution Exploring Operation: 58-3=55, Resulting Numbers: [55] 55,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 74:[70, 56, 71], Operations: ['68+3=71'] Exploring Operation: 71-70=1, Resulting Numbers: [56, 1] Generated Node #0,2,0: 74:[56, 1] Operation: 71-70=1 Exploring Operation: 71-56=15, Resulting Numbers: [70, 15] Generated Node #0,2,1: 74:[70, 15] Operation: 71-56=15 Exploring Operation: 70-56=14, Resulting Numbers: [71, 14] Generated Node #0,2,2: 74:[71, 14] Operation: 70-56=14 Exploring Operation: 70+56=126, Resulting Numbers: [71, 126] Generated Node #0,2,3: 74:[71, 126] Operation: 70+56=126 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 74:[71, 14], Operations: ['68+3=71', '70-56=14'] Exploring Operation: 71+14=85, Resulting Numbers: [85] 85,74 unequal: No Solution Exploring Operation: 71-14=57, Resulting Numbers: [57] 57,74 unequal: No Solution Exploring Operation: 71*14=994, Resulting Numbers: [994] 994,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 74:[70, 15], Operations: ['68+3=71', '71-56=15'] Exploring Operation: 70*15=1050, Resulting Numbers: [1050] 1050,74 unequal: No Solution Exploring Operation: 70-15=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 70+15=85, Resulting Numbers: [85] 85,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 74:[56, 1], Operations: ['68+3=71', '71-70=1'] Exploring Operation: 56-1=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,74 unequal: No Solution Exploring Operation: 56/1=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 56*1=56, Resulting Numbers: [56] 56,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 74:[71, 126], Operations: ['68+3=71', '70+56=126'] Exploring Operation: 126-71=55, Resulting Numbers: [55] 55,74 unequal: No Solution Exploring Operation: 71*126=8946, Resulting Numbers: [8946] 8946,74 unequal: No Solution Exploring Operation: 71+126=197, Resulting Numbers: [197] 197,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,2 Current State: 74:[70, 36], Operations: ['68-56=12', '3*12=36'] Exploring Operation: 70+36=106, Resulting Numbers: [106] 106,74 unequal: No Solution Exploring Operation: 70*36=2520, Resulting Numbers: [2520] 2520,74 unequal: No Solution Exploring Operation: 70-36=34, Resulting Numbers: [34] 34,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[70, 4], Operations: ['68-56=12', '12/3=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,74 unequal: No Solution Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,74 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[68, 3, 70, 56], Operations: [] Exploring Operation: 68-56=12, Resulting Numbers: [3, 70, 12] Generated Node #0,1: 74:[3, 70, 12] Operation: 68-56=12 Moving to Node #0,1 Current State: 74:[3, 70, 12], Operations: ['68-56=12'] Exploring Operation: 12/3=4, Resulting Numbers: [70, 4] Generated Node #0,1,1: 74:[70, 4] Operation: 12/3=4 Moving to Node #0,1,1 Current State: 74:[70, 4], Operations: ['68-56=12', '12/3=4'] Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
0.94184
hs_4
sum_heuristic
[ 21, 84, 2, 97 ]
29
[ "84-21=63", "2*63=126", "126-97=29" ]
Current State: 29:[21, 84, 2, 97], Operations: [] Exploring Operation: 84-21=63, Resulting Numbers: [2, 97, 63] Generated Node #2: [2, 97, 63] from Operation: 84-21=63 Current State: 29:[2, 97, 63], Operations: ['84-21=63'] Exploring Operation: 2*63=126, Resulting Numbers: [97, 126] Generated Node #3: [97, 126] from Operation: 2*63=126 Current State: 29:[97, 126], Operations: ['84-21=63', '2*63=126'] Exploring Operation: 126-97=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[21, 84, 2, 97], Operations: [] Exploring Operation: 84/21=4, Resulting Numbers: [2, 97, 4] Generated Node #0,0: 29:[2, 97, 4] Operation: 84/21=4 Exploring Operation: 21+2=23, Resulting Numbers: [84, 97, 23] Generated Node #0,1: 29:[84, 97, 23] Operation: 21+2=23 Exploring Operation: 84-21=63, Resulting Numbers: [2, 97, 63] Generated Node #0,2: 29:[2, 97, 63] Operation: 84-21=63 Exploring Operation: 97-84=13, Resulting Numbers: [21, 2, 13] Generated Node #0,3: 29:[21, 2, 13] Operation: 97-84=13 Exploring Operation: 84/2=42, Resulting Numbers: [21, 97, 42] Generated Node #0,4: 29:[21, 97, 42] Operation: 84/2=42 Start Sub Search at level 1: Moving to Node #0,3 Current State: 29:[21, 2, 13], Operations: ['97-84=13'] Exploring Operation: 13-2=11, Resulting Numbers: [21, 11] Generated Node #0,3,0: 29:[21, 11] Operation: 13-2=11 Exploring Operation: 2+13=15, Resulting Numbers: [21, 15] Generated Node #0,3,1: 29:[21, 15] Operation: 2+13=15 Exploring Operation: 21-2=19, Resulting Numbers: [13, 19] Generated Node #0,3,2: 29:[13, 19] Operation: 21-2=19 Exploring Operation: 2*13=26, Resulting Numbers: [21, 26] Generated Node #0,3,3: 29:[21, 26] Operation: 2*13=26 Exploring Operation: 21+2=23, Resulting Numbers: [13, 23] Generated Node #0,3,4: 29:[13, 23] Operation: 21+2=23 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 29:[21, 26], Operations: ['97-84=13', '2*13=26'] Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,29 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,29 unequal: No Solution Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 29:[21, 15], Operations: ['97-84=13', '2+13=15'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,29 unequal: No Solution Exploring Operation: 21*15=315, Resulting Numbers: [315] 315,29 unequal: No Solution Exploring Operation: 21+15=36, Resulting Numbers: [36] 36,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 29:[13, 23], Operations: ['97-84=13', '21+2=23'] Exploring Operation: 13+23=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 13*23=299, Resulting Numbers: [299] 299,29 unequal: No Solution Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 29:[21, 11], Operations: ['97-84=13', '13-2=11'] Exploring Operation: 21-11=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 21+11=32, Resulting Numbers: [32] 32,29 unequal: No Solution Exploring Operation: 21*11=231, Resulting Numbers: [231] 231,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 29:[13, 19], Operations: ['97-84=13', '21-2=19'] Exploring Operation: 13*19=247, Resulting Numbers: [247] 247,29 unequal: No Solution Exploring Operation: 13+19=32, Resulting Numbers: [32] 32,29 unequal: No Solution Exploring Operation: 19-13=6, Resulting Numbers: [6] 6,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 29:[21, 97, 42], Operations: ['84/2=42'] Exploring Operation: 42/21=2, Resulting Numbers: [97, 2] Generated Node #0,4,0: 29:[97, 2] Operation: 42/21=2 Exploring Operation: 42-21=21, Resulting Numbers: [97, 21] Generated Node #0,4,1: 29:[97, 21] Operation: 42-21=21 Exploring Operation: 97-42=55, Resulting Numbers: [21, 55] Generated Node #0,4,2: 29:[21, 55] Operation: 97-42=55 Exploring Operation: 97-21=76, Resulting Numbers: [42, 76] Generated Node #0,4,3: 29:[42, 76] Operation: 97-21=76 Exploring Operation: 21+97=118, Resulting Numbers: [42, 118] Generated Node #0,4,4: 29:[42, 118] Operation: 21+97=118 Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 29:[21, 55], Operations: ['84/2=42', '97-42=55'] Exploring Operation: 21+55=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 21*55=1155, Resulting Numbers: [1155] 1155,29 unequal: No Solution Exploring Operation: 55-21=34, Resulting Numbers: [34] 34,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 29:[42, 76], Operations: ['84/2=42', '97-21=76'] Exploring Operation: 42*76=3192, Resulting Numbers: [3192] 3192,29 unequal: No Solution Exploring Operation: 42+76=118, Resulting Numbers: [118] 118,29 unequal: No Solution Exploring Operation: 76-42=34, Resulting Numbers: [34] 34,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 29:[97, 21], Operations: ['84/2=42', '42-21=21'] Exploring Operation: 97*21=2037, Resulting Numbers: [2037] 2037,29 unequal: No Solution Exploring Operation: 97-21=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 97+21=118, Resulting Numbers: [118] 118,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 29:[97, 2], Operations: ['84/2=42', '42/21=2'] Exploring Operation: 97-2=95, Resulting Numbers: [95] 95,29 unequal: No Solution Exploring Operation: 97*2=194, Resulting Numbers: [194] 194,29 unequal: No Solution Exploring Operation: 97+2=99, Resulting Numbers: [99] 99,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 29:[42, 118], Operations: ['84/2=42', '21+97=118'] Exploring Operation: 42+118=160, Resulting Numbers: [160] 160,29 unequal: No Solution Exploring Operation: 118-42=76, Resulting Numbers: [76] 76,29 unequal: No Solution Exploring Operation: 42*118=4956, Resulting Numbers: [4956] 4956,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[2, 97, 4], Operations: ['84/21=4'] Exploring Operation: 97-2=95, Resulting Numbers: [4, 95] Generated Node #0,0,0: 29:[4, 95] Operation: 97-2=95 Exploring Operation: 2+4=6, Resulting Numbers: [97, 6] Generated Node #0,0,1: 29:[97, 6] Operation: 2+4=6 Exploring Operation: 2*4=8, Resulting Numbers: [97, 8] Generated Node #0,0,2: 29:[97, 8] Operation: 2*4=8 Exploring Operation: 2+97=99, Resulting Numbers: [4, 99] Generated Node #0,0,3: 29:[4, 99] Operation: 2+97=99 Exploring Operation: 97-4=93, Resulting Numbers: [2, 93] Generated Node #0,0,4: 29:[2, 93] Operation: 97-4=93 Moving to Node #0,0,2 Current State: 29:[97, 8], Operations: ['84/21=4', '2*4=8'] Exploring Operation: 97+8=105, Resulting Numbers: [105] 105,29 unequal: No Solution Exploring Operation: 97-8=89, Resulting Numbers: [89] 89,29 unequal: No Solution Exploring Operation: 97*8=776, Resulting Numbers: [776] 776,29 unequal: No Solution Moving to Node #0,0,1 Current State: 29:[97, 6], Operations: ['84/21=4', '2+4=6'] Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,29 unequal: No Solution Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,29 unequal: No Solution Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,29 unequal: No Solution Moving to Node #0,0,0 Current State: 29:[4, 95], Operations: ['84/21=4', '97-2=95'] Exploring Operation: 4*95=380, Resulting Numbers: [380] 380,29 unequal: No Solution Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,29 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,29 unequal: No Solution Moving to Node #0,0,4 Current State: 29:[2, 93], Operations: ['84/21=4', '97-4=93'] Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,29 unequal: No Solution Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,29 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,29 unequal: No Solution Moving to Node #0,0,3 Current State: 29:[4, 99], Operations: ['84/21=4', '2+97=99'] Exploring Operation: 4*99=396, Resulting Numbers: [396] 396,29 unequal: No Solution Exploring Operation: 99-4=95, Resulting Numbers: [95] 95,29 unequal: No Solution Exploring Operation: 4+99=103, Resulting Numbers: [103] 103,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[84, 97, 23], Operations: ['21+2=23'] Exploring Operation: 97+23=120, Resulting Numbers: [84, 120] Generated Node #0,1,0: 29:[84, 120] Operation: 97+23=120 Exploring Operation: 97-84=13, Resulting Numbers: [23, 13] Generated Node #0,1,1: 29:[23, 13] Operation: 97-84=13 Exploring Operation: 84-23=61, Resulting Numbers: [97, 61] Generated Node #0,1,2: 29:[97, 61] Operation: 84-23=61 Exploring Operation: 97-23=74, Resulting Numbers: [84, 74] Generated Node #0,1,3: 29:[84, 74] Operation: 97-23=74 Exploring Operation: 84+23=107, Resulting Numbers: [97, 107] Generated Node #0,1,4: 29:[97, 107] Operation: 84+23=107 Moving to Node #0,1,1 Current State: 29:[23, 13], Operations: ['21+2=23', '97-84=13'] Exploring Operation: 23-13=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 23*13=299, Resulting Numbers: [299] 299,29 unequal: No Solution Exploring Operation: 23+13=36, Resulting Numbers: [36] 36,29 unequal: No Solution Moving to Node #0,1,3 Current State: 29:[84, 74], Operations: ['21+2=23', '97-23=74'] Exploring Operation: 84-74=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 84*74=6216, Resulting Numbers: [6216] 6216,29 unequal: No Solution Exploring Operation: 84+74=158, Resulting Numbers: [158] 158,29 unequal: No Solution Moving to Node #0,1,2 Current State: 29:[97, 61], Operations: ['21+2=23', '84-23=61'] Exploring Operation: 97*61=5917, Resulting Numbers: [5917] 5917,29 unequal: No Solution Exploring Operation: 97+61=158, Resulting Numbers: [158] 158,29 unequal: No Solution Exploring Operation: 97-61=36, Resulting Numbers: [36] 36,29 unequal: No Solution Moving to Node #0,1,0 Current State: 29:[84, 120], Operations: ['21+2=23', '97+23=120'] Exploring Operation: 84*120=10080, Resulting Numbers: [10080] 10080,29 unequal: No Solution Exploring Operation: 120-84=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 84+120=204, Resulting Numbers: [204] 204,29 unequal: No Solution Moving to Node #0,1,4 Current State: 29:[97, 107], Operations: ['21+2=23', '84+23=107'] Exploring Operation: 107-97=10, Resulting Numbers: [10] 10,29 unequal: No Solution Exploring Operation: 97*107=10379, Resulting Numbers: [10379] 10379,29 unequal: No Solution Exploring Operation: 97+107=204, Resulting Numbers: [204] 204,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 29:[2, 97, 63], Operations: ['84-21=63'] Exploring Operation: 63-2=61, Resulting Numbers: [97, 61] Generated Node #0,2,0: 29:[97, 61] Operation: 63-2=61 Exploring Operation: 97-2=95, Resulting Numbers: [63, 95] Generated Node #0,2,1: 29:[63, 95] Operation: 97-2=95 Exploring Operation: 97-63=34, Resulting Numbers: [2, 34] Generated Node #0,2,2: 29:[2, 34] Operation: 97-63=34 Exploring Operation: 2+63=65, Resulting Numbers: [97, 65] Generated Node #0,2,3: 29:[97, 65] Operation: 2+63=65 Exploring Operation: 2+97=99, Resulting Numbers: [63, 99] Generated Node #0,2,4: 29:[63, 99] Operation: 2+97=99 Moving to Node #0,2,2 Current State: 29:[2, 34], Operations: ['84-21=63', '97-63=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,29 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,2,1 Current State: 29:[63, 95], Operations: ['84-21=63', '97-2=95'] Exploring Operation: 63*95=5985, Resulting Numbers: [5985] 5985,29 unequal: No Solution Exploring Operation: 63+95=158, Resulting Numbers: [158] 158,29 unequal: No Solution Exploring Operation: 95-63=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,2,0 Current State: 29:[97, 61], Operations: ['84-21=63', '63-2=61'] Exploring Operation: 97*61=5917, Resulting Numbers: [5917] 5917,29 unequal: No Solution Exploring Operation: 97+61=158, Resulting Numbers: [158] 158,29 unequal: No Solution Exploring Operation: 97-61=36, Resulting Numbers: [36] 36,29 unequal: No Solution Moving to Node #0,2,3 Current State: 29:[97, 65], Operations: ['84-21=63', '2+63=65'] Exploring Operation: 97*65=6305, Resulting Numbers: [6305] 6305,29 unequal: No Solution Exploring Operation: 97+65=162, Resulting Numbers: [162] 162,29 unequal: No Solution Exploring Operation: 97-65=32, Resulting Numbers: [32] 32,29 unequal: No Solution Moving to Node #0,2,4 Current State: 29:[63, 99], Operations: ['84-21=63', '2+97=99'] Exploring Operation: 63*99=6237, Resulting Numbers: [6237] 6237,29 unequal: No Solution Exploring Operation: 99-63=36, Resulting Numbers: [36] 36,29 unequal: No Solution Exploring Operation: 63+99=162, Resulting Numbers: [162] 162,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 17, 74, 99, 18 ]
60
[ "74-17=57", "99+18=117", "117-57=60" ]
Current State: 60:[17, 74, 99, 18], Operations: [] Exploring Operation: 74-17=57, Resulting Numbers: [99, 18, 57] Generated Node #2: [99, 18, 57] from Operation: 74-17=57 Current State: 60:[99, 18, 57], Operations: ['74-17=57'] Exploring Operation: 99+18=117, Resulting Numbers: [57, 117] Generated Node #3: [57, 117] from Operation: 99+18=117 Current State: 60:[57, 117], Operations: ['74-17=57', '99+18=117'] Exploring Operation: 117-57=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[17, 74, 99, 18], Operations: [] Exploring Operation: 99-74=25, Resulting Numbers: [17, 18, 25] Generated Node #0,0: 60:[17, 18, 25] Operation: 99-74=25 Exploring Operation: 99-18=81, Resulting Numbers: [17, 74, 81] Generated Node #0,1: 60:[17, 74, 81] Operation: 99-18=81 Exploring Operation: 74-17=57, Resulting Numbers: [99, 18, 57] Generated Node #0,2: 60:[99, 18, 57] Operation: 74-17=57 Exploring Operation: 74-18=56, Resulting Numbers: [17, 99, 56] Generated Node #0,3: 60:[17, 99, 56] Operation: 74-18=56 Exploring Operation: 99-17=82, Resulting Numbers: [74, 18, 82] Generated Node #0,4: 60:[74, 18, 82] Operation: 99-17=82 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[17, 18, 25], Operations: ['99-74=25'] Exploring Operation: 25-17=8, Resulting Numbers: [18, 8] Generated Node #0,0,0: 60:[18, 8] Operation: 25-17=8 Exploring Operation: 17+25=42, Resulting Numbers: [18, 42] Generated Node #0,0,1: 60:[18, 42] Operation: 17+25=42 Exploring Operation: 17+18=35, Resulting Numbers: [25, 35] Generated Node #0,0,2: 60:[25, 35] Operation: 17+18=35 Exploring Operation: 18-17=1, Resulting Numbers: [25, 1] Generated Node #0,0,3: 60:[25, 1] Operation: 18-17=1 Exploring Operation: 25-18=7, Resulting Numbers: [17, 7] Generated Node #0,0,4: 60:[17, 7] Operation: 25-18=7 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 60:[17, 7], Operations: ['99-74=25', '25-18=7'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 17+7=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 17*7=119, Resulting Numbers: [119] 119,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[18, 8], Operations: ['99-74=25', '25-17=8'] Exploring Operation: 18-8=10, Resulting Numbers: [10] 10,60 unequal: No Solution Exploring Operation: 18+8=26, Resulting Numbers: [26] 26,60 unequal: No Solution Exploring Operation: 18*8=144, Resulting Numbers: [144] 144,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 60:[25, 1], Operations: ['99-74=25', '18-17=1'] Exploring Operation: 25-1=24, Resulting Numbers: [24] 24,60 unequal: No Solution Exploring Operation: 25/1=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 25*1=25, Resulting Numbers: [25] 25,60 unequal: No Solution Exploring Operation: 25+1=26, Resulting Numbers: [26] 26,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 60:[25, 35], Operations: ['99-74=25', '17+18=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[17, 74, 99, 18], Operations: [] Exploring Operation: 99-74=25, Resulting Numbers: [17, 18, 25] Generated Node #0,0: 60:[17, 18, 25] Operation: 99-74=25 Moving to Node #0,0 Current State: 60:[17, 18, 25], Operations: ['99-74=25'] Exploring Operation: 17+18=35, Resulting Numbers: [25, 35] Generated Node #0,0,2: 60:[25, 35] Operation: 17+18=35 Moving to Node #0,0,2 Current State: 60:[25, 35], Operations: ['99-74=25', '17+18=35'] Exploring Operation: 25+35=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.978299
hs_5
sum_heuristic
[ 21, 22, 4, 12 ]
91
[ "21+22=43", "4*12=48", "43+48=91" ]
Current State: 91:[21, 22, 4, 12], Operations: [] Exploring Operation: 21+22=43, Resulting Numbers: [4, 12, 43] Generated Node #2: [4, 12, 43] from Operation: 21+22=43 Current State: 91:[4, 12, 43], Operations: ['21+22=43'] Exploring Operation: 4*12=48, Resulting Numbers: [43, 48] Generated Node #3: [43, 48] from Operation: 4*12=48 Current State: 91:[43, 48], Operations: ['21+22=43', '4*12=48'] Exploring Operation: 43+48=91, Resulting Numbers: [91] 91,91 equal: Goal Reached
4
Current State: 91:[21, 22, 4, 12], Operations: [] Exploring Operation: 22-21=1, Resulting Numbers: [4, 12, 1] Generated Node #0,0: 91:[4, 12, 1] Operation: 22-21=1 Moving to Node #0,0 Current State: 91:[4, 12, 1], Operations: ['22-21=1'] Exploring Operation: 4+1=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 91:[12, 5] Operation: 4+1=5 Moving to Node #0,0,0 Current State: 91:[12, 5], Operations: ['22-21=1', '4+1=5'] Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,91 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 7, 31, 66, 65 ]
37
[ "7+31=38", "66-65=1", "38-1=37" ]
Current State: 37:[7, 31, 66, 65], Operations: [] Exploring Operation: 7+31=38, Resulting Numbers: [66, 65, 38] Generated Node #2: [66, 65, 38] from Operation: 7+31=38 Current State: 37:[66, 65, 38], Operations: ['7+31=38'] Exploring Operation: 66-65=1, Resulting Numbers: [38, 1] Generated Node #3: [38, 1] from Operation: 66-65=1 Current State: 37:[38, 1], Operations: ['7+31=38', '66-65=1'] Exploring Operation: 38-1=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[7, 31, 66, 65], Operations: [] Exploring Operation: 65-7=58, Resulting Numbers: [31, 66, 58] Generated Node #0,0: 37:[31, 66, 58] Operation: 65-7=58 Exploring Operation: 66-7=59, Resulting Numbers: [31, 65, 59] Generated Node #0,1: 37:[31, 65, 59] Operation: 66-7=59 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[31, 66, 58], Operations: ['65-7=58'] Exploring Operation: 66-58=8, Resulting Numbers: [31, 8] Generated Node #0,0,0: 37:[31, 8] Operation: 66-58=8 Exploring Operation: 66-31=35, Resulting Numbers: [58, 35] Generated Node #0,0,1: 37:[58, 35] Operation: 66-31=35 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[58, 35], Operations: ['65-7=58', '66-31=35'] Exploring Operation: 58-35=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 58+35=93, Resulting Numbers: [93] 93,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[31, 8], Operations: ['65-7=58', '66-58=8'] Exploring Operation: 31-8=23, Resulting Numbers: [23] 23,37 unequal: No Solution Exploring Operation: 31+8=39, Resulting Numbers: [39] 39,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[31, 65, 59], Operations: ['66-7=59'] Exploring Operation: 65-31=34, Resulting Numbers: [59, 34] Generated Node #0,1,0: 37:[59, 34] Operation: 65-31=34 Exploring Operation: 59-31=28, Resulting Numbers: [65, 28] Generated Node #0,1,1: 37:[65, 28] Operation: 59-31=28 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[59, 34], Operations: ['66-7=59', '65-31=34'] Exploring Operation: 59-34=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 59+34=93, Resulting Numbers: [93] 93,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[65, 28], Operations: ['66-7=59', '59-31=28'] Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,37 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[7, 31, 66, 65], Operations: [] Exploring Operation: 66-7=59, Resulting Numbers: [31, 65, 59] Generated Node #0,1: 37:[31, 65, 59] Operation: 66-7=59 Moving to Node #0,1 Current State: 37:[31, 65, 59], Operations: ['66-7=59'] Exploring Operation: 59-31=28, Resulting Numbers: [65, 28] Generated Node #0,1,1: 37:[65, 28] Operation: 59-31=28 Moving to Node #0,1,1 Current State: 37:[65, 28], Operations: ['66-7=59', '59-31=28'] Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_2
mult_heuristic
[ 18, 30, 50, 60 ]
54
[ "18*30=540", "60-50=10", "540/10=54" ]
Current State: 54:[18, 30, 50, 60], Operations: [] Exploring Operation: 18*30=540, Resulting Numbers: [50, 60, 540] Generated Node #2: [50, 60, 540] from Operation: 18*30=540 Current State: 54:[50, 60, 540], Operations: ['18*30=540'] Exploring Operation: 60-50=10, Resulting Numbers: [540, 10] Generated Node #3: [540, 10] from Operation: 60-50=10 Current State: 54:[540, 10], Operations: ['18*30=540', '60-50=10'] Exploring Operation: 540/10=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[18, 30, 50, 60], Operations: [] Exploring Operation: 60-50=10, Resulting Numbers: [18, 30, 10] Generated Node #0,0: 54:[18, 30, 10] Operation: 60-50=10 Exploring Operation: 60-30=30, Resulting Numbers: [18, 50, 30] Generated Node #0,1: 54:[18, 50, 30] Operation: 60-30=30 Exploring Operation: 30-18=12, Resulting Numbers: [50, 60, 12] Generated Node #0,2: 54:[50, 60, 12] Operation: 30-18=12 Exploring Operation: 50-30=20, Resulting Numbers: [18, 60, 20] Generated Node #0,3: 54:[18, 60, 20] Operation: 50-30=20 Exploring Operation: 60/30=2, Resulting Numbers: [18, 50, 2] Generated Node #0,4: 54:[18, 50, 2] Operation: 60/30=2 Moving to Node #0,0 Current State: 54:[18, 30, 10], Operations: ['60-50=10'] Exploring Operation: 18-10=8, Resulting Numbers: [30, 8] Generated Node #0,0,0: 54:[30, 8] Operation: 18-10=8 Exploring Operation: 30/10=3, Resulting Numbers: [18, 3] Generated Node #0,0,1: 54:[18, 3] Operation: 30/10=3 Exploring Operation: 18+10=28, Resulting Numbers: [30, 28] Generated Node #0,0,2: 54:[30, 28] Operation: 18+10=28 Exploring Operation: 30-10=20, Resulting Numbers: [18, 20] Generated Node #0,0,3: 54:[18, 20] Operation: 30-10=20 Exploring Operation: 30-18=12, Resulting Numbers: [10, 12] Generated Node #0,0,4: 54:[10, 12] Operation: 30-18=12 Moving to Node #0,4 Current State: 54:[18, 50, 2], Operations: ['60/30=2'] Exploring Operation: 50-18=32, Resulting Numbers: [2, 32] Generated Node #0,4,0: 54:[2, 32] Operation: 50-18=32 Exploring Operation: 50/2=25, Resulting Numbers: [18, 25] Generated Node #0,4,1: 54:[18, 25] Operation: 50/2=25 Exploring Operation: 50+2=52, Resulting Numbers: [18, 52] Generated Node #0,4,2: 54:[18, 52] Operation: 50+2=52 Exploring Operation: 18+2=20, Resulting Numbers: [50, 20] Generated Node #0,4,3: 54:[50, 20] Operation: 18+2=20 Exploring Operation: 18/2=9, Resulting Numbers: [50, 9] Generated Node #0,4,4: 54:[50, 9] Operation: 18/2=9 Moving to Node #0,1 Current State: 54:[18, 50, 30], Operations: ['60-30=30'] Exploring Operation: 50-30=20, Resulting Numbers: [18, 20] Generated Node #0,1,0: 54:[18, 20] Operation: 50-30=20 Exploring Operation: 18+30=48, Resulting Numbers: [50, 48] Generated Node #0,1,1: 54:[50, 48] Operation: 18+30=48 Exploring Operation: 50-18=32, Resulting Numbers: [30, 32] Generated Node #0,1,2: 54:[30, 32] Operation: 50-18=32 Exploring Operation: 18+50=68, Resulting Numbers: [30, 68] Generated Node #0,1,3: 54:[30, 68] Operation: 18+50=68 Exploring Operation: 30-18=12, Resulting Numbers: [50, 12] Generated Node #0,1,4: 54:[50, 12] Operation: 30-18=12 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[18, 20], Operations: ['60-30=30', '50-30=20'] Exploring Operation: 18+20=38, Resulting Numbers: [38] 38,54 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 18*20=360, Resulting Numbers: [360] 360,54 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 #0,1,4 Current State: 54:[50, 12], Operations: ['60-30=30', '30-18=12'] Exploring Operation: 50*12=600, Resulting Numbers: [600] 600,54 unequal: No Solution Exploring Operation: 50+12=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 50-12=38, Resulting Numbers: [38] 38,54 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 #0,1,2 Current State: 54:[30, 32], Operations: ['60-30=30', '50-18=32'] Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,54 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,54 unequal: No Solution Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,54 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:[50, 48], Operations: ['60-30=30', '18+30=48'] Exploring Operation: 50+48=98, Resulting Numbers: [98] 98,54 unequal: No Solution Exploring Operation: 50*48=2400, Resulting Numbers: [2400] 2400,54 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,54 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 #0,1,3 Current State: 54:[30, 68], Operations: ['60-30=30', '18+50=68'] Exploring Operation: 68-30=38, Resulting Numbers: [38] 38,54 unequal: No Solution Exploring Operation: 30+68=98, Resulting Numbers: [98] 98,54 unequal: No Solution Exploring Operation: 30*68=2040, Resulting Numbers: [2040] 2040,54 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: 54:[18, 60, 20], Operations: ['50-30=20'] Exploring Operation: 60/20=3, Resulting Numbers: [18, 3] Generated Node #0,3,0: 54:[18, 3] Operation: 60/20=3 Exploring Operation: 20-18=2, Resulting Numbers: [60, 2] Generated Node #0,3,1: 54:[60, 2] Operation: 20-18=2 Exploring Operation: 60-18=42, Resulting Numbers: [20, 42] Generated Node #0,3,2: 54:[20, 42] Operation: 60-18=42 Exploring Operation: 18+20=38, Resulting Numbers: [60, 38] Generated Node #0,3,3: 54:[60, 38] Operation: 18+20=38 Exploring Operation: 60-20=40, Resulting Numbers: [18, 40] Generated Node #0,3,4: 54:[18, 40] Operation: 60-20=40 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 54:[18, 3], Operations: ['50-30=20', '60/20=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[18, 30, 50, 60], Operations: [] Exploring Operation: 50-30=20, Resulting Numbers: [18, 60, 20] Generated Node #0,3: 54:[18, 60, 20] Operation: 50-30=20 Moving to Node #0,3 Current State: 54:[18, 60, 20], Operations: ['50-30=20'] Exploring Operation: 60/20=3, Resulting Numbers: [18, 3] Generated Node #0,3,0: 54:[18, 3] Operation: 60/20=3 Moving to Node #0,3,0 Current State: 54:[18, 3], Operations: ['50-30=20', '60/20=3'] Exploring Operation: 18*3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.960938
hs_5
mult_heuristic
[ 94, 85, 13, 15 ]
18
[ "94-85=9", "15-13=2", "9*2=18" ]
Current State: 18:[94, 85, 13, 15], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [13, 15, 9] Generated Node #2: [13, 15, 9] from Operation: 94-85=9 Current State: 18:[13, 15, 9], Operations: ['94-85=9'] Exploring Operation: 15-13=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 15-13=2 Current State: 18:[9, 2], Operations: ['94-85=9', '15-13=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[94, 85, 13, 15], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [13, 15, 9] Generated Node #0,0: 18:[13, 15, 9] Operation: 94-85=9 Moving to Node #0,0 Current State: 18:[13, 15, 9], Operations: ['94-85=9'] Exploring Operation: 15-13=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 18:[9, 2] Operation: 15-13=2 Moving to Node #0,0,0 Current State: 18:[9, 2], Operations: ['94-85=9', '15-13=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[94, 85, 13, 15], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [13, 15, 9] Generated Node #0,0: 18:[13, 15, 9] Operation: 94-85=9 Moving to Node #0,0 Current State: 18:[13, 15, 9], Operations: ['94-85=9'] Exploring Operation: 15-13=2, Resulting Numbers: [9, 2] Generated Node #0,0,0: 18:[9, 2] Operation: 15-13=2 Moving to Node #0,0,0 Current State: 18:[9, 2], Operations: ['94-85=9', '15-13=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 80, 44, 34, 8 ]
17
[ "80+8=88", "44*34=1496", "1496/88=17" ]
Current State: 17:[80, 44, 34, 8], Operations: [] Exploring Operation: 80+8=88, Resulting Numbers: [44, 34, 88] Generated Node #2: [44, 34, 88] from Operation: 80+8=88 Current State: 17:[44, 34, 88], Operations: ['80+8=88'] Exploring Operation: 44*34=1496, Resulting Numbers: [88, 1496] Generated Node #3: [88, 1496] from Operation: 44*34=1496 Current State: 17:[88, 1496], Operations: ['80+8=88', '44*34=1496'] Exploring Operation: 1496/88=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[80, 44, 34, 8], Operations: [] Exploring Operation: 80-44=36, Resulting Numbers: [34, 8, 36] Generated Node #0,0: 17:[34, 8, 36] Operation: 80-44=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[34, 8, 36], Operations: ['80-44=36'] Exploring Operation: 36-34=2, Resulting Numbers: [8, 2] Generated Node #0,0,0: 17:[8, 2] Operation: 36-34=2 Moving to Node #0,0,0 Current State: 17:[8, 2], Operations: ['80-44=36', '36-34=2'] Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,17 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
[ 3, 93, 12, 14 ]
99
[ "14-12=2", "3*2=6", "93+6=99" ]
Current State: 99:[3, 93, 12, 14], Operations: [] Exploring Operation: 14-12=2, Resulting Numbers: [3, 93, 2] Generated Node #2: [3, 93, 2] from Operation: 14-12=2 Current State: 99:[3, 93, 2], Operations: ['14-12=2'] Exploring Operation: 3*2=6, Resulting Numbers: [93, 6] Generated Node #3: [93, 6] from Operation: 3*2=6 Current State: 99:[93, 6], Operations: ['14-12=2', '3*2=6'] Exploring Operation: 93+6=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[3, 93, 12, 14], Operations: [] Exploring Operation: 3+93=96, Resulting Numbers: [12, 14, 96] Generated Node #0,0: 99:[12, 14, 96] Operation: 3+93=96 Exploring Operation: 14-3=11, Resulting Numbers: [93, 12, 11] Generated Node #0,1: 99:[93, 12, 11] Operation: 14-3=11 Exploring Operation: 93/3=31, Resulting Numbers: [12, 14, 31] Generated Node #0,2: 99:[12, 14, 31] Operation: 93/3=31 Exploring Operation: 14-12=2, Resulting Numbers: [3, 93, 2] Generated Node #0,3: 99:[3, 93, 2] Operation: 14-12=2 Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[12, 14, 31], Operations: ['93/3=31'] Exploring Operation: 14-12=2, Resulting Numbers: [31, 2] Generated Node #0,2,0: 99:[31, 2] Operation: 14-12=2 Exploring Operation: 31-14=17, Resulting Numbers: [12, 17] Generated Node #0,2,1: 99:[12, 17] Operation: 31-14=17 Exploring Operation: 31-12=19, Resulting Numbers: [14, 19] Generated Node #0,2,2: 99:[14, 19] Operation: 31-12=19 Exploring Operation: 12+14=26, Resulting Numbers: [31, 26] Generated Node #0,2,3: 99:[31, 26] Operation: 12+14=26 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[31, 2], Operations: ['93/3=31', '14-12=2'] Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 31+2=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 31*2=62, Resulting Numbers: [62] 62,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[12, 17], Operations: ['93/3=31', '31-14=17'] Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,99 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 99:[31, 26], Operations: ['93/3=31', '12+14=26'] Exploring Operation: 31+26=57, Resulting Numbers: [57] 57,99 unequal: No Solution Exploring Operation: 31*26=806, Resulting Numbers: [806] 806,99 unequal: No Solution Exploring Operation: 31-26=5, Resulting Numbers: [5] 5,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[14, 19], Operations: ['93/3=31', '31-12=19'] Exploring Operation: 14+19=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 14*19=266, Resulting Numbers: [266] 266,99 unequal: No Solution Exploring Operation: 19-14=5, Resulting Numbers: [5] 5,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[12, 14, 96], Operations: ['3+93=96'] Exploring Operation: 14-12=2, Resulting Numbers: [96, 2] Generated Node #0,0,0: 99:[96, 2] Operation: 14-12=2 Exploring Operation: 12+96=108, Resulting Numbers: [14, 108] Generated Node #0,0,1: 99:[14, 108] Operation: 12+96=108 Exploring Operation: 96/12=8, Resulting Numbers: [14, 8] Generated Node #0,0,2: 99:[14, 8] Operation: 96/12=8 Exploring Operation: 12+14=26, Resulting Numbers: [96, 26] Generated Node #0,0,3: 99:[96, 26] Operation: 12+14=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 99:[96, 2], Operations: ['3+93=96', '14-12=2'] Exploring Operation: 96*2=192, Resulting Numbers: [192] 192,99 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 99:[14, 8], Operations: ['3+93=96', '96/12=8'] Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,99 unequal: No Solution Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,99 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 99:[96, 26], Operations: ['3+93=96', '12+14=26'] Exploring Operation: 96*26=2496, Resulting Numbers: [2496] 2496,99 unequal: No Solution Exploring Operation: 96+26=122, Resulting Numbers: [122] 122,99 unequal: No Solution Exploring Operation: 96-26=70, Resulting Numbers: [70] 70,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 99:[14, 108], Operations: ['3+93=96', '12+96=108'] Exploring Operation: 108-14=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 14+108=122, Resulting Numbers: [122] 122,99 unequal: No Solution Exploring Operation: 14*108=1512, Resulting Numbers: [1512] 1512,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[93, 12, 11], Operations: ['14-3=11'] Exploring Operation: 12-11=1, Resulting Numbers: [93, 1] Generated Node #0,1,0: 99:[93, 1] Operation: 12-11=1 Exploring Operation: 93+11=104, Resulting Numbers: [12, 104] Generated Node #0,1,1: 99:[12, 104] Operation: 93+11=104 Exploring Operation: 93+12=105, Resulting Numbers: [11, 105] Generated Node #0,1,2: 99:[11, 105] Operation: 93+12=105 Exploring Operation: 12+11=23, Resulting Numbers: [93, 23] Generated Node #0,1,3: 99:[93, 23] Operation: 12+11=23 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 99:[12, 104], Operations: ['14-3=11', '93+11=104'] Exploring Operation: 12+104=116, Resulting Numbers: [116] 116,99 unequal: No Solution Exploring Operation: 104-12=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 12*104=1248, Resulting Numbers: [1248] 1248,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 99:[11, 105], Operations: ['14-3=11', '93+12=105'] Exploring Operation: 11*105=1155, Resulting Numbers: [1155] 1155,99 unequal: No Solution Exploring Operation: 105-11=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 11+105=116, Resulting Numbers: [116] 116,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 99:[93, 1], Operations: ['14-3=11', '12-11=1'] Exploring Operation: 93+1=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 93-1=92, Resulting Numbers: [92] 92,99 unequal: No Solution Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,99 unequal: No Solution Exploring Operation: 93/1=93, Resulting Numbers: [93] 93,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 99:[93, 23], Operations: ['14-3=11', '12+11=23'] Exploring Operation: 93-23=70, Resulting Numbers: [70] 70,99 unequal: No Solution Exploring Operation: 93*23=2139, Resulting Numbers: [2139] 2139,99 unequal: No Solution Exploring Operation: 93+23=116, Resulting Numbers: [116] 116,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 99:[3, 93, 2], Operations: ['14-12=2'] Exploring Operation: 93+2=95, Resulting Numbers: [3, 95] Generated Node #0,3,0: 99:[3, 95] Operation: 93+2=95 Exploring Operation: 3+93=96, Resulting Numbers: [2, 96] Generated Node #0,3,1: 99:[2, 96] Operation: 3+93=96 Exploring Operation: 93/3=31, Resulting Numbers: [2, 31] Generated Node #0,3,2: 99:[2, 31] Operation: 93/3=31 Exploring Operation: 3+2=5, Resulting Numbers: [93, 5] Generated Node #0,3,3: 99:[93, 5] Operation: 3+2=5 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 99:[2, 31], Operations: ['14-12=2', '93/3=31'] Exploring Operation: 2+31=33, Resulting Numbers: [33] 33,99 unequal: No Solution Exploring Operation: 31-2=29, Resulting Numbers: [29] 29,99 unequal: No Solution Exploring Operation: 2*31=62, Resulting Numbers: [62] 62,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 99:[3, 95], Operations: ['14-12=2', '93+2=95'] Exploring Operation: 3+95=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 3*95=285, Resulting Numbers: [285] 285,99 unequal: No Solution Exploring Operation: 95-3=92, Resulting Numbers: [92] 92,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 99:[2, 96], Operations: ['14-12=2', '3+93=96'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 2+96=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 2*96=192, Resulting Numbers: [192] 192,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 99:[93, 5], Operations: ['14-12=2', '3+2=5'] Exploring Operation: 93*5=465, Resulting Numbers: [465] 465,99 unequal: No Solution Exploring Operation: 93+5=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 93-5=88, Resulting Numbers: [88] 88,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 77, 1, 51, 70 ]
58
[ "77*1=77", "70-51=19", "77-19=58" ]
Current State: 58:[77, 1, 51, 70], Operations: [] Exploring Operation: 77*1=77, Resulting Numbers: [51, 70, 77] Generated Node #2: [51, 70, 77] from Operation: 77*1=77 Current State: 58:[51, 70, 77], Operations: ['77*1=77'] Exploring Operation: 70-51=19, Resulting Numbers: [77, 19] Generated Node #3: [77, 19] from Operation: 70-51=19 Current State: 58:[77, 19], Operations: ['77*1=77', '70-51=19'] Exploring Operation: 77-19=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[77, 1, 51, 70], Operations: [] Exploring Operation: 77-51=26, Resulting Numbers: [1, 70, 26] Generated Node #0,0: 58:[1, 70, 26] Operation: 77-51=26 Exploring Operation: 77-70=7, Resulting Numbers: [1, 51, 7] Generated Node #0,1: 58:[1, 51, 7] Operation: 77-70=7 Moving to Node #0,1 Current State: 58:[1, 51, 7], Operations: ['77-70=7'] Exploring Operation: 51+7=58, Resulting Numbers: [1, 58] Generated Node #0,1,0: 58:[1, 58] Operation: 51+7=58 Exploring Operation: 1+51=52, Resulting Numbers: [7, 52] Generated Node #0,1,1: 58:[7, 52] Operation: 1+51=52 Moving to Node #0,0 Current State: 58:[1, 70, 26], Operations: ['77-51=26'] Exploring Operation: 1+26=27, Resulting Numbers: [70, 27] Generated Node #0,0,0: 58:[70, 27] Operation: 1+26=27 Exploring Operation: 70-1=69, Resulting Numbers: [26, 69] Generated Node #0,0,1: 58:[26, 69] Operation: 70-1=69 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 58:[70, 27], Operations: ['77-51=26', '1+26=27'] Exploring Operation: 70+27=97, Resulting Numbers: [97] 97,58 unequal: No Solution Exploring Operation: 70-27=43, Resulting Numbers: [43] 43,58 unequal: No Solution No 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: 58:[26, 69], Operations: ['77-51=26', '70-1=69'] Exploring Operation: 26+69=95, Resulting Numbers: [95] 95,58 unequal: No Solution Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,58 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: 58:[1, 58], Operations: ['77-70=7', '51+7=58'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[77, 1, 51, 70], Operations: [] Exploring Operation: 77-70=7, Resulting Numbers: [1, 51, 7] Generated Node #0,1: 58:[1, 51, 7] Operation: 77-70=7 Moving to Node #0,1 Current State: 58:[1, 51, 7], Operations: ['77-70=7'] Exploring Operation: 51+7=58, Resulting Numbers: [1, 58] Generated Node #0,1,0: 58:[1, 58] Operation: 51+7=58 Moving to Node #0,1,0 Current State: 58:[1, 58], Operations: ['77-70=7', '51+7=58'] Exploring Operation: 58/1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 15, 32, 21, 90 ]
52
[ "32-15=17", "90-21=69", "69-17=52" ]
Current State: 52:[15, 32, 21, 90], Operations: [] Exploring Operation: 32-15=17, Resulting Numbers: [21, 90, 17] Generated Node #2: [21, 90, 17] from Operation: 32-15=17 Current State: 52:[21, 90, 17], Operations: ['32-15=17'] Exploring Operation: 90-21=69, Resulting Numbers: [17, 69] Generated Node #3: [17, 69] from Operation: 90-21=69 Current State: 52:[17, 69], Operations: ['32-15=17', '90-21=69'] Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[15, 32, 21, 90], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [32, 21, 6] Generated Node #0,0: 52:[32, 21, 6] Operation: 90/15=6 Exploring Operation: 32+21=53, Resulting Numbers: [15, 90, 53] Generated Node #0,1: 52:[15, 90, 53] Operation: 32+21=53 Exploring Operation: 90-32=58, Resulting Numbers: [15, 21, 58] Generated Node #0,2: 52:[15, 21, 58] Operation: 90-32=58 Exploring Operation: 90-15=75, Resulting Numbers: [32, 21, 75] Generated Node #0,3: 52:[32, 21, 75] Operation: 90-15=75 Exploring Operation: 90-21=69, Resulting Numbers: [15, 32, 69] Generated Node #0,4: 52:[15, 32, 69] Operation: 90-21=69 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[32, 21, 6], Operations: ['90/15=6'] Exploring Operation: 21+6=27, Resulting Numbers: [32, 27] Generated Node #0,0,0: 52:[32, 27] Operation: 21+6=27 Exploring Operation: 32-6=26, Resulting Numbers: [21, 26] Generated Node #0,0,1: 52:[21, 26] Operation: 32-6=26 Exploring Operation: 32-21=11, Resulting Numbers: [6, 11] Generated Node #0,0,2: 52:[6, 11] Operation: 32-21=11 Exploring Operation: 32+21=53, Resulting Numbers: [6, 53] Generated Node #0,0,3: 52:[6, 53] Operation: 32+21=53 Exploring Operation: 21-6=15, Resulting Numbers: [32, 15] Generated Node #0,0,4: 52:[32, 15] Operation: 21-6=15 Moving to Node #0,0,3 Current State: 52:[6, 53], Operations: ['90/15=6', '32+21=53'] Exploring Operation: 6+53=59, Resulting Numbers: [59] 59,52 unequal: No Solution Exploring Operation: 6*53=318, Resulting Numbers: [318] 318,52 unequal: No Solution Exploring Operation: 53-6=47, Resulting Numbers: [47] 47,52 unequal: No Solution Moving to Node #0,0,2 Current State: 52:[6, 11], Operations: ['90/15=6', '32-21=11'] Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,52 unequal: No Solution Exploring Operation: 6+11=17, Resulting Numbers: [17] 17,52 unequal: No Solution Moving to Node #0,0,1 Current State: 52:[21, 26], Operations: ['90/15=6', '32-6=26'] Exploring Operation: 21*26=546, Resulting Numbers: [546] 546,52 unequal: No Solution Exploring Operation: 21+26=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 26-21=5, Resulting Numbers: [5] 5,52 unequal: No Solution Moving to Node #0,0,0 Current State: 52:[32, 27], Operations: ['90/15=6', '21+6=27'] Exploring Operation: 32*27=864, Resulting Numbers: [864] 864,52 unequal: No Solution Exploring Operation: 32-27=5, Resulting Numbers: [5] 5,52 unequal: No Solution Exploring Operation: 32+27=59, Resulting Numbers: [59] 59,52 unequal: No Solution Moving to Node #0,0,4 Current State: 52:[32, 15], Operations: ['90/15=6', '21-6=15'] Exploring Operation: 32-15=17, Resulting Numbers: [17] 17,52 unequal: No Solution Exploring Operation: 32+15=47, Resulting Numbers: [47] 47,52 unequal: No Solution Exploring Operation: 32*15=480, Resulting Numbers: [480] 480,52 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 #0,2 Current State: 52:[15, 21, 58], Operations: ['90-32=58'] Exploring Operation: 15+21=36, Resulting Numbers: [58, 36] Generated Node #0,2,0: 52:[58, 36] Operation: 15+21=36 Exploring Operation: 21-15=6, Resulting Numbers: [58, 6] Generated Node #0,2,1: 52:[58, 6] Operation: 21-15=6 Exploring Operation: 58-21=37, Resulting Numbers: [15, 37] Generated Node #0,2,2: 52:[15, 37] Operation: 58-21=37 Exploring Operation: 15+58=73, Resulting Numbers: [21, 73] Generated Node #0,2,3: 52:[21, 73] Operation: 15+58=73 Exploring Operation: 58-15=43, Resulting Numbers: [21, 43] Generated Node #0,2,4: 52:[21, 43] Operation: 58-15=43 Moving to Node #0,2,1 Current State: 52:[58, 6], Operations: ['90-32=58', '21-15=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[15, 32, 21, 90], Operations: [] Exploring Operation: 90-32=58, Resulting Numbers: [15, 21, 58] Generated Node #0,2: 52:[15, 21, 58] Operation: 90-32=58 Moving to Node #0,2 Current State: 52:[15, 21, 58], Operations: ['90-32=58'] Exploring Operation: 21-15=6, Resulting Numbers: [58, 6] Generated Node #0,2,1: 52:[58, 6] Operation: 21-15=6 Moving to Node #0,2,1 Current State: 52:[58, 6], Operations: ['90-32=58', '21-15=6'] Exploring Operation: 58-6=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 1
0.969618
hs_5
mult_heuristic
[ 3, 70, 35, 36 ]
71
[ "3*35=105", "70-36=34", "105-34=71" ]
Current State: 71:[3, 70, 35, 36], Operations: [] Exploring Operation: 3*35=105, Resulting Numbers: [70, 36, 105] Generated Node #2: [70, 36, 105] from Operation: 3*35=105 Current State: 71:[70, 36, 105], Operations: ['3*35=105'] Exploring Operation: 70-36=34, Resulting Numbers: [105, 34] Generated Node #3: [105, 34] from Operation: 70-36=34 Current State: 71:[105, 34], Operations: ['3*35=105', '70-36=34'] Exploring Operation: 105-34=71, Resulting Numbers: [71] 71,71 equal: Goal Reached
4
Current State: 71:[3, 70, 35, 36], Operations: [] Exploring Operation: 35+36=71, Resulting Numbers: [3, 70, 71] Generated Node #0,0: 71:[3, 70, 71] Operation: 35+36=71 Exploring Operation: 3+35=38, Resulting Numbers: [70, 36, 38] Generated Node #0,1: 71:[70, 36, 38] Operation: 3+35=38 Exploring Operation: 3+36=39, Resulting Numbers: [70, 35, 39] Generated Node #0,2: 71:[70, 35, 39] Operation: 3+36=39 Exploring Operation: 3*35=105, Resulting Numbers: [70, 36, 105] Generated Node #0,3: 71:[70, 36, 105] Operation: 3*35=105 Start Sub Search at level 1: Moving to Node #0,0 Current State: 71:[3, 70, 71], Operations: ['35+36=71'] Exploring Operation: 71-3=68, Resulting Numbers: [70, 68] Generated Node #0,0,0: 71:[70, 68] Operation: 71-3=68 Exploring Operation: 70-3=67, Resulting Numbers: [71, 67] Generated Node #0,0,1: 71:[71, 67] Operation: 70-3=67 Exploring Operation: 3+71=74, Resulting Numbers: [70, 74] Generated Node #0,0,2: 71:[70, 74] Operation: 3+71=74 Exploring Operation: 3+70=73, Resulting Numbers: [71, 73] Generated Node #0,0,3: 71:[71, 73] Operation: 3+70=73 Moving to Node #0,0,3 Current State: 71:[71, 73], Operations: ['35+36=71', '3+70=73'] Exploring Operation: 71*73=5183, Resulting Numbers: [5183] 5183,71 unequal: No Solution Exploring Operation: 71+73=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 73-71=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,0,1 Current State: 71:[71, 67], Operations: ['35+36=71', '70-3=67'] Exploring Operation: 71-67=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 71+67=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 71*67=4757, Resulting Numbers: [4757] 4757,71 unequal: No Solution Moving to Node #0,0,0 Current State: 71:[70, 68], Operations: ['35+36=71', '71-3=68'] Exploring Operation: 70*68=4760, Resulting Numbers: [4760] 4760,71 unequal: No Solution Exploring Operation: 70+68=138, Resulting Numbers: [138] 138,71 unequal: No Solution Exploring Operation: 70-68=2, Resulting Numbers: [2] 2,71 unequal: No Solution Moving to Node #0,0,2 Current State: 71:[70, 74], Operations: ['35+36=71', '3+71=74'] Exploring Operation: 70+74=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 70*74=5180, Resulting Numbers: [5180] 5180,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 71:[70, 36, 38], Operations: ['3+35=38'] Exploring Operation: 70+36=106, Resulting Numbers: [38, 106] Generated Node #0,1,0: 71:[38, 106] Operation: 70+36=106 Exploring Operation: 38-36=2, Resulting Numbers: [70, 2] Generated Node #0,1,1: 71:[70, 2] Operation: 38-36=2 Exploring Operation: 36+38=74, Resulting Numbers: [70, 74] Generated Node #0,1,2: 71:[70, 74] Operation: 36+38=74 Exploring Operation: 70-36=34, Resulting Numbers: [38, 34] Generated Node #0,1,3: 71:[38, 34] Operation: 70-36=34 Moving to Node #0,1,2 Current State: 71:[70, 74], Operations: ['3+35=38', '36+38=74'] Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 70*74=5180, Resulting Numbers: [5180] 5180,71 unequal: No Solution Exploring Operation: 70+74=144, Resulting Numbers: [144] 144,71 unequal: No Solution Moving to Node #0,1,0 Current State: 71:[38, 106], Operations: ['3+35=38', '70+36=106'] Exploring Operation: 38+106=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 38*106=4028, Resulting Numbers: [4028] 4028,71 unequal: No Solution Exploring Operation: 106-38=68, Resulting Numbers: [68] 68,71 unequal: No Solution Moving to Node #0,1,3 Current State: 71:[38, 34], Operations: ['3+35=38', '70-36=34'] Exploring Operation: 38+34=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 38*34=1292, Resulting Numbers: [1292] 1292,71 unequal: No Solution Exploring Operation: 38-34=4, Resulting Numbers: [4] 4,71 unequal: No Solution Moving to Node #0,1,1 Current State: 71:[70, 2], Operations: ['3+35=38', '38-36=2'] Exploring Operation: 70/2=35, Resulting Numbers: [35] 35,71 unequal: No Solution Exploring Operation: 70*2=140, Resulting Numbers: [140] 140,71 unequal: No Solution Exploring Operation: 70+2=72, Resulting Numbers: [72] 72,71 unequal: No Solution Exploring Operation: 70-2=68, Resulting Numbers: [68] 68,71 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 71:[70, 35, 39], Operations: ['3+36=39'] Exploring Operation: 70-35=35, Resulting Numbers: [39, 35] Generated Node #0,2,0: 71:[39, 35] Operation: 70-35=35 Exploring Operation: 35+39=74, Resulting Numbers: [70, 74] Generated Node #0,2,1: 71:[70, 74] Operation: 35+39=74 Exploring Operation: 70+35=105, Resulting Numbers: [39, 105] Generated Node #0,2,2: 71:[39, 105] Operation: 70+35=105 Exploring Operation: 39-35=4, Resulting Numbers: [70, 4] Generated Node #0,2,3: 71:[70, 4] Operation: 39-35=4 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 71:[70, 74], Operations: ['3+36=39', '35+39=74'] Exploring Operation: 74-70=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 70*74=5180, Resulting Numbers: [5180] 5180,71 unequal: No Solution Exploring Operation: 70+74=144, Resulting Numbers: [144] 144,71 unequal: No Solution No 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: 71:[39, 105], Operations: ['3+36=39', '70+35=105'] Exploring Operation: 39+105=144, Resulting Numbers: [144] 144,71 unequal: No Solution Exploring Operation: 105-39=66, Resulting Numbers: [66] 66,71 unequal: No Solution Exploring Operation: 39*105=4095, Resulting Numbers: [4095] 4095,71 unequal: No Solution No 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: 71:[39, 35], Operations: ['3+36=39', '70-35=35'] Exploring Operation: 39-35=4, Resulting Numbers: [4] 4,71 unequal: No Solution Exploring Operation: 39+35=74, Resulting Numbers: [74] 74,71 unequal: No Solution Exploring Operation: 39*35=1365, Resulting Numbers: [1365] 1365,71 unequal: No Solution No 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: 71:[70, 4], Operations: ['3+36=39', '39-35=4'] Exploring Operation: 70-4=66, Resulting Numbers: [66] 66,71 unequal: No Solution Exploring Operation: 70+4=74, Resulting Numbers: [74] 74,71 unequal: No Solution Exploring Operation: 70*4=280, Resulting Numbers: [280] 280,71 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: 71:[70, 36, 105], Operations: ['3*35=105'] Exploring Operation: 70-36=34, Resulting Numbers: [105, 34] Generated Node #0,3,0: 71:[105, 34] Operation: 70-36=34 Exploring Operation: 105-70=35, Resulting Numbers: [36, 35] Generated Node #0,3,1: 71:[36, 35] Operation: 105-70=35 Exploring Operation: 105-36=69, Resulting Numbers: [70, 69] Generated Node #0,3,2: 71:[70, 69] Operation: 105-36=69 Exploring Operation: 70+36=106, Resulting Numbers: [105, 106] Generated Node #0,3,3: 71:[105, 106] Operation: 70+36=106 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 71:[70, 69], Operations: ['3*35=105', '105-36=69'] Exploring Operation: 70*69=4830, Resulting Numbers: [4830] 4830,71 unequal: No Solution Exploring Operation: 70+69=139, Resulting Numbers: [139] 139,71 unequal: No Solution Exploring Operation: 70-69=1, Resulting Numbers: [1] 1,71 unequal: No Solution No 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: 71:[105, 106], Operations: ['3*35=105', '70+36=106'] Exploring Operation: 105+106=211, Resulting Numbers: [211] 211,71 unequal: No Solution Exploring Operation: 105*106=11130, Resulting Numbers: [11130] 11130,71 unequal: No Solution Exploring Operation: 106-105=1, Resulting Numbers: [1] 1,71 unequal: No Solution No 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: 71:[105, 34], Operations: ['3*35=105', '70-36=34'] Exploring Operation: 105-34=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Moving to Node #0 Current State: 71:[3, 70, 35, 36], Operations: [] Exploring Operation: 3*35=105, Resulting Numbers: [70, 36, 105] Generated Node #0,3: 71:[70, 36, 105] Operation: 3*35=105 Moving to Node #0,3 Current State: 71:[70, 36, 105], Operations: ['3*35=105'] Exploring Operation: 70-36=34, Resulting Numbers: [105, 34] Generated Node #0,3,0: 71:[105, 34] Operation: 70-36=34 Moving to Node #0,3,0 Current State: 71:[105, 34], Operations: ['3*35=105', '70-36=34'] Exploring Operation: 105-34=71, Resulting Numbers: [71] 71,71 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 8, 56, 15, 32 ]
10
[ "56-8=48", "15*32=480", "480/48=10" ]
Current State: 10:[8, 56, 15, 32], Operations: [] Exploring Operation: 56-8=48, Resulting Numbers: [15, 32, 48] Generated Node #2: [15, 32, 48] from Operation: 56-8=48 Current State: 10:[15, 32, 48], Operations: ['56-8=48'] Exploring Operation: 15*32=480, Resulting Numbers: [48, 480] Generated Node #3: [48, 480] from Operation: 15*32=480 Current State: 10:[48, 480], Operations: ['56-8=48', '15*32=480'] Exploring Operation: 480/48=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[8, 56, 15, 32], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [15, 32, 7] Generated Node #0,0: 10:[15, 32, 7] Operation: 56/8=7 Exploring Operation: 56-32=24, Resulting Numbers: [8, 15, 24] Generated Node #0,1: 10:[8, 15, 24] Operation: 56-32=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[8, 15, 24], Operations: ['56-32=24'] Exploring Operation: 24/8=3, Resulting Numbers: [15, 3] Generated Node #0,1,0: 10:[15, 3] Operation: 24/8=3 Exploring Operation: 24-15=9, Resulting Numbers: [8, 9] Generated Node #0,1,1: 10:[8, 9] Operation: 24-15=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[8, 9], Operations: ['56-32=24', '24-15=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,10 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[15, 3], Operations: ['56-32=24', '24/8=3'] Exploring Operation: 15-3=12, Resulting Numbers: [12] 12,10 unequal: No Solution Exploring Operation: 15/3=5, Resulting Numbers: [5] 5,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[15, 32, 7], Operations: ['56/8=7'] Exploring Operation: 32-7=25, Resulting Numbers: [15, 25] Generated Node #0,0,0: 10:[15, 25] Operation: 32-7=25 Exploring Operation: 32-15=17, Resulting Numbers: [7, 17] Generated Node #0,0,1: 10:[7, 17] Operation: 32-15=17 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[7, 17], Operations: ['56/8=7', '32-15=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[8, 56, 15, 32], Operations: [] Exploring Operation: 56/8=7, Resulting Numbers: [15, 32, 7] Generated Node #0,0: 10:[15, 32, 7] Operation: 56/8=7 Moving to Node #0,0 Current State: 10:[15, 32, 7], Operations: ['56/8=7'] Exploring Operation: 32-15=17, Resulting Numbers: [7, 17] Generated Node #0,0,1: 10:[7, 17] Operation: 32-15=17 Moving to Node #0,0,1 Current State: 10:[7, 17], Operations: ['56/8=7', '32-15=17'] Exploring Operation: 17-7=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 12, 56, 54, 13 ]
46
[ "12*13=156", "56+54=110", "156-110=46" ]
Current State: 46:[12, 56, 54, 13], Operations: [] Exploring Operation: 12*13=156, Resulting Numbers: [56, 54, 156] Generated Node #2: [56, 54, 156] from Operation: 12*13=156 Current State: 46:[56, 54, 156], Operations: ['12*13=156'] Exploring Operation: 56+54=110, Resulting Numbers: [156, 110] Generated Node #3: [156, 110] from Operation: 56+54=110 Current State: 46:[156, 110], Operations: ['12*13=156', '56+54=110'] Exploring Operation: 156-110=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[12, 56, 54, 13], Operations: [] Exploring Operation: 13-12=1, Resulting Numbers: [56, 54, 1] Generated Node #0,0: 46:[56, 54, 1] Operation: 13-12=1 Exploring Operation: 12+13=25, Resulting Numbers: [56, 54, 25] Generated Node #0,1: 46:[56, 54, 25] Operation: 12+13=25 Exploring Operation: 56-12=44, Resulting Numbers: [54, 13, 44] Generated Node #0,2: 46:[54, 13, 44] Operation: 56-12=44 Moving to Node #0,0 Current State: 46:[56, 54, 1], Operations: ['13-12=1'] Exploring Operation: 54-1=53, Resulting Numbers: [56, 53] Generated Node #0,0,0: 46:[56, 53] Operation: 54-1=53 Exploring Operation: 56-1=55, Resulting Numbers: [54, 55] Generated Node #0,0,1: 46:[54, 55] Operation: 56-1=55 Exploring Operation: 56-54=2, Resulting Numbers: [1, 2] Generated Node #0,0,2: 46:[1, 2] Operation: 56-54=2 Moving to Node #0,1 Current State: 46:[56, 54, 25], Operations: ['12+13=25'] Exploring Operation: 54-25=29, Resulting Numbers: [56, 29] Generated Node #0,1,0: 46:[56, 29] Operation: 54-25=29 Exploring Operation: 56-25=31, Resulting Numbers: [54, 31] Generated Node #0,1,1: 46:[54, 31] Operation: 56-25=31 Exploring Operation: 56-54=2, Resulting Numbers: [25, 2] Generated Node #0,1,2: 46:[25, 2] Operation: 56-54=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 46:[25, 2], Operations: ['12+13=25', '56-54=2'] Exploring Operation: 25*2=50, Resulting Numbers: [50] 50,46 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 25+2=27, Resulting Numbers: [27] 27,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 46:[56, 29], Operations: ['12+13=25', '54-25=29'] Exploring Operation: 56+29=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 56*29=1624, Resulting Numbers: [1624] 1624,46 unequal: No Solution Exploring Operation: 56-29=27, Resulting Numbers: [27] 27,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 46:[54, 31], Operations: ['12+13=25', '56-25=31'] Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 54*31=1674, Resulting Numbers: [1674] 1674,46 unequal: No Solution Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,46 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 46:[54, 13, 44], Operations: ['56-12=44'] Exploring Operation: 44-13=31, Resulting Numbers: [54, 31] Generated Node #0,2,0: 46:[54, 31] Operation: 44-13=31 Exploring Operation: 54-44=10, Resulting Numbers: [13, 10] Generated Node #0,2,1: 46:[13, 10] Operation: 54-44=10 Exploring Operation: 54-13=41, Resulting Numbers: [44, 41] Generated Node #0,2,2: 46:[44, 41] Operation: 54-13=41 Moving to Node #0,0,2 Current State: 46:[1, 2], Operations: ['13-12=1', '56-54=2'] Exploring Operation: 1+2=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 2/1=2, Resulting Numbers: [2] 2,46 unequal: No Solution Exploring Operation: 1*2=2, Resulting Numbers: [2] 2,46 unequal: No Solution Moving to Node #0,2,2 Current State: 46:[44, 41], Operations: ['56-12=44', '54-13=41'] Exploring Operation: 44+41=85, Resulting Numbers: [85] 85,46 unequal: No Solution Exploring Operation: 44*41=1804, Resulting Numbers: [1804] 1804,46 unequal: No Solution Exploring Operation: 44-41=3, Resulting Numbers: [3] 3,46 unequal: No Solution Moving to Node #0,2,0 Current State: 46:[54, 31], Operations: ['56-12=44', '44-13=31'] Exploring Operation: 54-31=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 54*31=1674, Resulting Numbers: [1674] 1674,46 unequal: No Solution Exploring Operation: 54+31=85, Resulting Numbers: [85] 85,46 unequal: No Solution Moving to Node #0,0,1 Current State: 46:[54, 55], Operations: ['13-12=1', '56-1=55'] Exploring Operation: 54+55=109, Resulting Numbers: [109] 109,46 unequal: No Solution Exploring Operation: 54*55=2970, Resulting Numbers: [2970] 2970,46 unequal: No Solution Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,46 unequal: No Solution Moving to Node #0,0,0 Current State: 46:[56, 53], Operations: ['13-12=1', '54-1=53'] Exploring Operation: 56-53=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 56*53=2968, Resulting Numbers: [2968] 2968,46 unequal: No Solution Exploring Operation: 56+53=109, Resulting Numbers: [109] 109,46 unequal: No Solution Moving to Node #0,2,1 Current State: 46:[13, 10], Operations: ['56-12=44', '54-44=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,46 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,46 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,46 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 51, 11, 13, 85 ]
58
[ "51-11=40", "13+85=98", "98-40=58" ]
Current State: 58:[51, 11, 13, 85], Operations: [] Exploring Operation: 51-11=40, Resulting Numbers: [13, 85, 40] Generated Node #2: [13, 85, 40] from Operation: 51-11=40 Current State: 58:[13, 85, 40], Operations: ['51-11=40'] Exploring Operation: 13+85=98, Resulting Numbers: [40, 98] Generated Node #3: [40, 98] from Operation: 13+85=98 Current State: 58:[40, 98], Operations: ['51-11=40', '13+85=98'] Exploring Operation: 98-40=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[51, 11, 13, 85], Operations: [] Exploring Operation: 85-51=34, Resulting Numbers: [11, 13, 34] Generated Node #0,0: 58:[11, 13, 34] Operation: 85-51=34 Moving to Node #0,0 Current State: 58:[11, 13, 34], Operations: ['85-51=34'] Exploring Operation: 13-11=2, Resulting Numbers: [34, 2] Generated Node #0,0,0: 58:[34, 2] Operation: 13-11=2 Moving to Node #0,0,0 Current State: 58:[34, 2], Operations: ['85-51=34', '13-11=2'] Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,58 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 27, 26, 91, 71 ]
73
[ "27+26=53", "91-71=20", "53+20=73" ]
Current State: 73:[27, 26, 91, 71], Operations: [] Exploring Operation: 27+26=53, Resulting Numbers: [91, 71, 53] Generated Node #2: [91, 71, 53] from Operation: 27+26=53 Current State: 73:[91, 71, 53], Operations: ['27+26=53'] Exploring Operation: 91-71=20, Resulting Numbers: [53, 20] Generated Node #3: [53, 20] from Operation: 91-71=20 Current State: 73:[53, 20], Operations: ['27+26=53', '91-71=20'] Exploring Operation: 53+20=73, Resulting Numbers: [73] 73,73 equal: Goal Reached
4
Current State: 73:[27, 26, 91, 71], Operations: [] Exploring Operation: 27+26=53, Resulting Numbers: [91, 71, 53] Generated Node #0,0: 73:[91, 71, 53] Operation: 27+26=53 Exploring Operation: 91-27=64, Resulting Numbers: [26, 71, 64] Generated Node #0,1: 73:[26, 71, 64] Operation: 91-27=64 Exploring Operation: 27+71=98, Resulting Numbers: [26, 91, 98] Generated Node #0,2: 73:[26, 91, 98] Operation: 27+71=98 Exploring Operation: 91-26=65, Resulting Numbers: [27, 71, 65] Generated Node #0,3: 73:[27, 71, 65] Operation: 91-26=65 Exploring Operation: 26+71=97, Resulting Numbers: [27, 91, 97] Generated Node #0,4: 73:[27, 91, 97] Operation: 26+71=97 Start Sub Search at level 1: Moving to Node #0,0 Current State: 73:[91, 71, 53], Operations: ['27+26=53'] Exploring Operation: 71+53=124, Resulting Numbers: [91, 124] Generated Node #0,0,0: 73:[91, 124] Operation: 71+53=124 Exploring Operation: 91-71=20, Resulting Numbers: [53, 20] Generated Node #0,0,1: 73:[53, 20] Operation: 91-71=20 Exploring Operation: 91-53=38, Resulting Numbers: [71, 38] Generated Node #0,0,2: 73:[71, 38] Operation: 91-53=38 Exploring Operation: 71-53=18, Resulting Numbers: [91, 18] Generated Node #0,0,3: 73:[91, 18] Operation: 71-53=18 Exploring Operation: 91+53=144, Resulting Numbers: [71, 144] Generated Node #0,0,4: 73:[71, 144] Operation: 91+53=144 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 73:[71, 38], Operations: ['27+26=53', '91-53=38'] Exploring Operation: 71-38=33, Resulting Numbers: [33] 33,73 unequal: No Solution Exploring Operation: 71*38=2698, Resulting Numbers: [2698] 2698,73 unequal: No Solution Exploring Operation: 71+38=109, Resulting Numbers: [109] 109,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 73:[91, 124], Operations: ['27+26=53', '71+53=124'] Exploring Operation: 124-91=33, Resulting Numbers: [33] 33,73 unequal: No Solution Exploring Operation: 91*124=11284, Resulting Numbers: [11284] 11284,73 unequal: No Solution Exploring Operation: 91+124=215, Resulting Numbers: [215] 215,73 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 73:[53, 20], Operations: ['27+26=53', '91-71=20'] Exploring Operation: 53+20=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Moving to Node #0 Current State: 73:[27, 26, 91, 71], Operations: [] Exploring Operation: 27+26=53, Resulting Numbers: [91, 71, 53] Generated Node #0,0: 73:[91, 71, 53] Operation: 27+26=53 Moving to Node #0,0 Current State: 73:[91, 71, 53], Operations: ['27+26=53'] Exploring Operation: 91-71=20, Resulting Numbers: [53, 20] Generated Node #0,0,1: 73:[53, 20] Operation: 91-71=20 Moving to Node #0,0,1 Current State: 73:[53, 20], Operations: ['27+26=53', '91-71=20'] Exploring Operation: 53+20=73, Resulting Numbers: [73] 73,73 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 40, 26, 45, 61 ]
65
[ "40*26=1040", "61-45=16", "1040/16=65" ]
Current State: 65:[40, 26, 45, 61], Operations: [] Exploring Operation: 40*26=1040, Resulting Numbers: [45, 61, 1040] Generated Node #2: [45, 61, 1040] from Operation: 40*26=1040 Current State: 65:[45, 61, 1040], Operations: ['40*26=1040'] Exploring Operation: 61-45=16, Resulting Numbers: [1040, 16] Generated Node #3: [1040, 16] from Operation: 61-45=16 Current State: 65:[1040, 16], Operations: ['40*26=1040', '61-45=16'] Exploring Operation: 1040/16=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[40, 26, 45, 61], Operations: [] Exploring Operation: 26+45=71, Resulting Numbers: [40, 61, 71] Generated Node #0,0: 65:[40, 61, 71] Operation: 26+45=71 Exploring Operation: 45-40=5, Resulting Numbers: [26, 61, 5] Generated Node #0,1: 65:[26, 61, 5] Operation: 45-40=5 Exploring Operation: 40-26=14, Resulting Numbers: [45, 61, 14] Generated Node #0,2: 65:[45, 61, 14] Operation: 40-26=14 Exploring Operation: 40+26=66, Resulting Numbers: [45, 61, 66] Generated Node #0,3: 65:[45, 61, 66] Operation: 40+26=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[26, 61, 5], Operations: ['45-40=5'] Exploring Operation: 61-26=35, Resulting Numbers: [5, 35] Generated Node #0,1,0: 65:[5, 35] Operation: 61-26=35 Exploring Operation: 26+61=87, Resulting Numbers: [5, 87] Generated Node #0,1,1: 65:[5, 87] Operation: 26+61=87 Exploring Operation: 61+5=66, Resulting Numbers: [26, 66] Generated Node #0,1,2: 65:[26, 66] Operation: 61+5=66 Exploring Operation: 26-5=21, Resulting Numbers: [61, 21] Generated Node #0,1,3: 65:[61, 21] Operation: 26-5=21 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 65:[61, 21], Operations: ['45-40=5', '26-5=21'] Exploring Operation: 61*21=1281, Resulting Numbers: [1281] 1281,65 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 65:[26, 66], Operations: ['45-40=5', '61+5=66'] Exploring Operation: 66-26=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 26+66=92, Resulting Numbers: [92] 92,65 unequal: No Solution Exploring Operation: 26*66=1716, Resulting Numbers: [1716] 1716,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[5, 35], Operations: ['45-40=5', '61-26=35'] Exploring Operation: 35/5=7, Resulting Numbers: [7] 7,65 unequal: No Solution Exploring Operation: 5+35=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 5*35=175, Resulting Numbers: [175] 175,65 unequal: No Solution Exploring Operation: 35-5=30, Resulting Numbers: [30] 30,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 65:[5, 87], Operations: ['45-40=5', '26+61=87'] Exploring Operation: 5+87=92, Resulting Numbers: [92] 92,65 unequal: No Solution Exploring Operation: 5*87=435, Resulting Numbers: [435] 435,65 unequal: No Solution Exploring Operation: 87-5=82, Resulting Numbers: [82] 82,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 65:[45, 61, 14], Operations: ['40-26=14'] Exploring Operation: 45+14=59, Resulting Numbers: [61, 59] Generated Node #0,2,0: 65:[61, 59] Operation: 45+14=59 Exploring Operation: 61+14=75, Resulting Numbers: [45, 75] Generated Node #0,2,1: 65:[45, 75] Operation: 61+14=75 Exploring Operation: 45-14=31, Resulting Numbers: [61, 31] Generated Node #0,2,2: 65:[61, 31] Operation: 45-14=31 Exploring Operation: 61-45=16, Resulting Numbers: [14, 16] Generated Node #0,2,3: 65:[14, 16] Operation: 61-45=16 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 65:[14, 16], Operations: ['40-26=14', '61-45=16'] Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 14+16=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 14*16=224, Resulting Numbers: [224] 224,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 65:[61, 59], Operations: ['40-26=14', '45+14=59'] Exploring Operation: 61*59=3599, Resulting Numbers: [3599] 3599,65 unequal: No Solution Exploring Operation: 61-59=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 61+59=120, Resulting Numbers: [120] 120,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 65:[61, 31], Operations: ['40-26=14', '45-14=31'] Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,65 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 65:[45, 75], Operations: ['40-26=14', '61+14=75'] Exploring Operation: 75-45=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 45+75=120, Resulting Numbers: [120] 120,65 unequal: No Solution Exploring Operation: 45*75=3375, Resulting Numbers: [3375] 3375,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 65:[45, 61, 66], Operations: ['40+26=66'] Exploring Operation: 45+61=106, Resulting Numbers: [66, 106] Generated Node #0,3,0: 65:[66, 106] Operation: 45+61=106 Exploring Operation: 61-45=16, Resulting Numbers: [66, 16] Generated Node #0,3,1: 65:[66, 16] Operation: 61-45=16 Exploring Operation: 66-61=5, Resulting Numbers: [45, 5] Generated Node #0,3,2: 65:[45, 5] Operation: 66-61=5 Exploring Operation: 66-45=21, Resulting Numbers: [61, 21] Generated Node #0,3,3: 65:[61, 21] Operation: 66-45=21 Moving to Node #0,3,1 Current State: 65:[66, 16], Operations: ['40+26=66', '61-45=16'] Exploring Operation: 66*16=1056, Resulting Numbers: [1056] 1056,65 unequal: No Solution Exploring Operation: 66-16=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 66+16=82, Resulting Numbers: [82] 82,65 unequal: No Solution Moving to Node #0,3,3 Current State: 65:[61, 21], Operations: ['40+26=66', '66-45=21'] Exploring Operation: 61*21=1281, Resulting Numbers: [1281] 1281,65 unequal: No Solution Exploring Operation: 61-21=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 61+21=82, Resulting Numbers: [82] 82,65 unequal: No Solution Moving to Node #0,3,2 Current State: 65:[45, 5], Operations: ['40+26=66', '66-61=5'] Exploring Operation: 45/5=9, Resulting Numbers: [9] 9,65 unequal: No Solution Exploring Operation: 45*5=225, Resulting Numbers: [225] 225,65 unequal: No Solution Exploring Operation: 45-5=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 45+5=50, Resulting Numbers: [50] 50,65 unequal: No Solution Moving to Node #0,3,0 Current State: 65:[66, 106], Operations: ['40+26=66', '45+61=106'] Exploring Operation: 66+106=172, Resulting Numbers: [172] 172,65 unequal: No Solution Exploring Operation: 106-66=40, Resulting Numbers: [40] 40,65 unequal: No Solution Exploring Operation: 66*106=6996, Resulting Numbers: [6996] 6996,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 65:[40, 61, 71], Operations: ['26+45=71'] Exploring Operation: 61-40=21, Resulting Numbers: [71, 21] Generated Node #0,0,0: 65:[71, 21] Operation: 61-40=21 Exploring Operation: 40+61=101, Resulting Numbers: [71, 101] Generated Node #0,0,1: 65:[71, 101] Operation: 40+61=101 Exploring Operation: 71-40=31, Resulting Numbers: [61, 31] Generated Node #0,0,2: 65:[61, 31] Operation: 71-40=31 Exploring Operation: 71-61=10, Resulting Numbers: [40, 10] Generated Node #0,0,3: 65:[40, 10] Operation: 71-61=10 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 65:[71, 21], Operations: ['26+45=71', '61-40=21'] Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,65 unequal: No Solution Exploring Operation: 71*21=1491, Resulting Numbers: [1491] 1491,65 unequal: No Solution Exploring Operation: 71+21=92, Resulting Numbers: [92] 92,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 65:[61, 31], Operations: ['26+45=71', '71-40=31'] Exploring Operation: 61+31=92, Resulting Numbers: [92] 92,65 unequal: No Solution Exploring Operation: 61-31=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 61*31=1891, Resulting Numbers: [1891] 1891,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 65:[40, 10], Operations: ['26+45=71', '71-61=10'] Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 40*10=400, Resulting Numbers: [400] 400,65 unequal: No Solution Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,65 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 65:[71, 101], Operations: ['26+45=71', '40+61=101'] Exploring Operation: 71+101=172, Resulting Numbers: [172] 172,65 unequal: No Solution Exploring Operation: 71*101=7171, Resulting Numbers: [7171] 7171,65 unequal: No Solution Exploring Operation: 101-71=30, Resulting Numbers: [30] 30,65 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 95, 14, 5, 67 ]
100
[ "95/5=19", "14+67=81", "19+81=100" ]
Current State: 100:[95, 14, 5, 67], Operations: [] Exploring Operation: 95/5=19, Resulting Numbers: [14, 67, 19] Generated Node #2: [14, 67, 19] from Operation: 95/5=19 Current State: 100:[14, 67, 19], Operations: ['95/5=19'] Exploring Operation: 14+67=81, Resulting Numbers: [19, 81] Generated Node #3: [19, 81] from Operation: 14+67=81 Current State: 100:[19, 81], Operations: ['95/5=19', '14+67=81'] Exploring Operation: 19+81=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[95, 14, 5, 67], Operations: [] Exploring Operation: 67-14=53, Resulting Numbers: [95, 5, 53] Generated Node #0,0: 100:[95, 5, 53] Operation: 67-14=53 Exploring Operation: 95-67=28, Resulting Numbers: [14, 5, 28] Generated Node #0,1: 100:[14, 5, 28] Operation: 95-67=28 Moving to Node #0,1 Current State: 100:[14, 5, 28], Operations: ['95-67=28'] Exploring Operation: 28/14=2, Resulting Numbers: [5, 2] Generated Node #0,1,0: 100:[5, 2] Operation: 28/14=2 Exploring Operation: 14+5=19, Resulting Numbers: [28, 19] Generated Node #0,1,1: 100:[28, 19] Operation: 14+5=19 Moving to Node #0,0 Current State: 100:[95, 5, 53], Operations: ['67-14=53'] Exploring Operation: 95+5=100, Resulting Numbers: [53, 100] Generated Node #0,0,0: 100:[53, 100] Operation: 95+5=100 Exploring Operation: 95/5=19, Resulting Numbers: [53, 19] Generated Node #0,0,1: 100:[53, 19] Operation: 95/5=19 Moving to Node #0,1,0 Current State: 100:[5, 2], Operations: ['95-67=28', '28/14=2'] Exploring Operation: 5*2=10, Resulting Numbers: [10] 10,100 unequal: No Solution Exploring Operation: 5-2=3, Resulting Numbers: [3] 3,100 unequal: No Solution Moving to Node #0,0,0 Current State: 100:[53, 100], Operations: ['67-14=53', '95+5=100'] Exploring Operation: 53+100=153, Resulting Numbers: [153] 153,100 unequal: No Solution Exploring Operation: 100-53=47, Resulting Numbers: [47] 47,100 unequal: No Solution Moving to Node #0,1,1 Current State: 100:[28, 19], Operations: ['95-67=28', '14+5=19'] Exploring Operation: 28+19=47, Resulting Numbers: [47] 47,100 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,100 unequal: No Solution Moving to Node #0,0,1 Current State: 100:[53, 19], Operations: ['67-14=53', '95/5=19'] Exploring Operation: 53+19=72, Resulting Numbers: [72] 72,100 unequal: No Solution Exploring Operation: 53-19=34, Resulting Numbers: [34] 34,100 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 88, 96, 33, 55 ]
80
[ "96-88=8", "33+55=88", "88-8=80" ]
Current State: 80:[88, 96, 33, 55], Operations: [] Exploring Operation: 96-88=8, Resulting Numbers: [33, 55, 8] Generated Node #2: [33, 55, 8] from Operation: 96-88=8 Current State: 80:[33, 55, 8], Operations: ['96-88=8'] Exploring Operation: 33+55=88, Resulting Numbers: [8, 88] Generated Node #3: [8, 88] from Operation: 33+55=88 Current State: 80:[8, 88], Operations: ['96-88=8', '33+55=88'] Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[88, 96, 33, 55], Operations: [] Exploring Operation: 55-33=22, Resulting Numbers: [88, 96, 22] Generated Node #0,0: 80:[88, 96, 22] Operation: 55-33=22 Exploring Operation: 96-88=8, Resulting Numbers: [33, 55, 8] Generated Node #0,1: 80:[33, 55, 8] Operation: 96-88=8 Exploring Operation: 96-55=41, Resulting Numbers: [88, 33, 41] Generated Node #0,2: 80:[88, 33, 41] Operation: 96-55=41 Exploring Operation: 88-55=33, Resulting Numbers: [96, 33, 33] Generated Node #0,3: 80:[96, 33, 33] Operation: 88-55=33 Exploring Operation: 33+55=88, Resulting Numbers: [88, 96, 88] Generated Node #0,4: 80:[88, 96, 88] Operation: 33+55=88 Moving to Node #0,2 Current State: 80:[88, 33, 41], Operations: ['96-55=41'] Exploring Operation: 88-33=55, Resulting Numbers: [41, 55] Generated Node #0,2,0: 80:[41, 55] Operation: 88-33=55 Exploring Operation: 88-41=47, Resulting Numbers: [33, 47] Generated Node #0,2,1: 80:[33, 47] Operation: 88-41=47 Exploring Operation: 88+33=121, Resulting Numbers: [41, 121] Generated Node #0,2,2: 80:[41, 121] Operation: 88+33=121 Exploring Operation: 41-33=8, Resulting Numbers: [88, 8] Generated Node #0,2,3: 80:[88, 8] Operation: 41-33=8 Exploring Operation: 33+41=74, Resulting Numbers: [88, 74] Generated Node #0,2,4: 80:[88, 74] Operation: 33+41=74 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[88, 8], Operations: ['96-55=41', '41-33=8'] Exploring Operation: 88*8=704, Resulting Numbers: [704] 704,80 unequal: No Solution Exploring Operation: 88+8=96, Resulting Numbers: [96] 96,80 unequal: No Solution Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[88, 96, 33, 55], Operations: [] Exploring Operation: 96-55=41, Resulting Numbers: [88, 33, 41] Generated Node #0,2: 80:[88, 33, 41] Operation: 96-55=41 Moving to Node #0,2 Current State: 80:[88, 33, 41], Operations: ['96-55=41'] Exploring Operation: 41-33=8, Resulting Numbers: [88, 8] Generated Node #0,2,3: 80:[88, 8] Operation: 41-33=8 Moving to Node #0,2,3 Current State: 80:[88, 8], Operations: ['96-55=41', '41-33=8'] Exploring Operation: 88-8=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 76, 19, 73, 53 ]
37
[ "76-19=57", "73-53=20", "57-20=37" ]
Current State: 37:[76, 19, 73, 53], Operations: [] Exploring Operation: 76-19=57, Resulting Numbers: [73, 53, 57] Generated Node #2: [73, 53, 57] from Operation: 76-19=57 Current State: 37:[73, 53, 57], Operations: ['76-19=57'] Exploring Operation: 73-53=20, Resulting Numbers: [57, 20] Generated Node #3: [57, 20] from Operation: 73-53=20 Current State: 37:[57, 20], Operations: ['76-19=57', '73-53=20'] Exploring Operation: 57-20=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[76, 19, 73, 53], Operations: [] Exploring Operation: 76-19=57, Resulting Numbers: [73, 53, 57] Generated Node #0,0: 37:[73, 53, 57] Operation: 76-19=57 Exploring Operation: 76-73=3, Resulting Numbers: [19, 53, 3] Generated Node #0,1: 37:[19, 53, 3] Operation: 76-73=3 Exploring Operation: 73-19=54, Resulting Numbers: [76, 53, 54] Generated Node #0,2: 37:[76, 53, 54] Operation: 73-19=54 Exploring Operation: 76-53=23, Resulting Numbers: [19, 73, 23] Generated Node #0,3: 37:[19, 73, 23] Operation: 76-53=23 Exploring Operation: 73-53=20, Resulting Numbers: [76, 19, 20] Generated Node #0,4: 37:[76, 19, 20] Operation: 73-53=20 Moving to Node #0,1 Current State: 37:[19, 53, 3], Operations: ['76-73=3'] Exploring Operation: 19*3=57, Resulting Numbers: [53, 57] Generated Node #0,1,0: 37:[53, 57] Operation: 19*3=57 Exploring Operation: 19-3=16, Resulting Numbers: [53, 16] Generated Node #0,1,1: 37:[53, 16] Operation: 19-3=16 Exploring Operation: 19+3=22, Resulting Numbers: [53, 22] Generated Node #0,1,2: 37:[53, 22] Operation: 19+3=22 Exploring Operation: 53-3=50, Resulting Numbers: [19, 50] Generated Node #0,1,3: 37:[19, 50] Operation: 53-3=50 Exploring Operation: 53-19=34, Resulting Numbers: [3, 34] Generated Node #0,1,4: 37:[3, 34] Operation: 53-19=34 Moving to Node #0,3 Current State: 37:[19, 73, 23], Operations: ['76-53=23'] Exploring Operation: 73-23=50, Resulting Numbers: [19, 50] Generated Node #0,3,0: 37:[19, 50] Operation: 73-23=50 Exploring Operation: 23-19=4, Resulting Numbers: [73, 4] Generated Node #0,3,1: 37:[73, 4] Operation: 23-19=4 Exploring Operation: 19+23=42, Resulting Numbers: [73, 42] Generated Node #0,3,2: 37:[73, 42] Operation: 19+23=42 Exploring Operation: 73-19=54, Resulting Numbers: [23, 54] Generated Node #0,3,3: 37:[23, 54] Operation: 73-19=54 Exploring Operation: 19+73=92, Resulting Numbers: [23, 92] Generated Node #0,3,4: 37:[23, 92] Operation: 19+73=92 Moving to Node #0,0 Current State: 37:[73, 53, 57], Operations: ['76-19=57'] Exploring Operation: 73+53=126, Resulting Numbers: [57, 126] Generated Node #0,0,0: 37:[57, 126] Operation: 73+53=126 Exploring Operation: 73+57=130, Resulting Numbers: [53, 130] Generated Node #0,0,1: 37:[53, 130] Operation: 73+57=130 Exploring Operation: 57-53=4, Resulting Numbers: [73, 4] Generated Node #0,0,2: 37:[73, 4] Operation: 57-53=4 Exploring Operation: 73-57=16, Resulting Numbers: [53, 16] Generated Node #0,0,3: 37:[53, 16] Operation: 73-57=16 Exploring Operation: 73-53=20, Resulting Numbers: [57, 20] Generated Node #0,0,4: 37:[57, 20] Operation: 73-53=20 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[53, 16], Operations: ['76-19=57', '73-57=16'] Exploring Operation: 53+16=69, Resulting Numbers: [69] 69,37 unequal: No Solution Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[76, 19, 73, 53], Operations: [] Exploring Operation: 76-19=57, Resulting Numbers: [73, 53, 57] Generated Node #0,0: 37:[73, 53, 57] Operation: 76-19=57 Moving to Node #0,0 Current State: 37:[73, 53, 57], Operations: ['76-19=57'] Exploring Operation: 73-57=16, Resulting Numbers: [53, 16] Generated Node #0,0,3: 37:[53, 16] Operation: 73-57=16 Moving to Node #0,0,3 Current State: 37:[53, 16], Operations: ['76-19=57', '73-57=16'] Exploring Operation: 53-16=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_5
mult_heuristic
[ 96, 21, 68, 24 ]
18
[ "96-68=28", "21*24=504", "504/28=18" ]
Current State: 18:[96, 21, 68, 24], Operations: [] Exploring Operation: 96-68=28, Resulting Numbers: [21, 24, 28] Generated Node #2: [21, 24, 28] from Operation: 96-68=28 Current State: 18:[21, 24, 28], Operations: ['96-68=28'] Exploring Operation: 21*24=504, Resulting Numbers: [28, 504] Generated Node #3: [28, 504] from Operation: 21*24=504 Current State: 18:[28, 504], Operations: ['96-68=28', '21*24=504'] Exploring Operation: 504/28=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[96, 21, 68, 24], Operations: [] Exploring Operation: 96-24=72, Resulting Numbers: [21, 68, 72] Generated Node #0,0: 18:[21, 68, 72] Operation: 96-24=72 Exploring Operation: 96/24=4, Resulting Numbers: [21, 68, 4] Generated Node #0,1: 18:[21, 68, 4] Operation: 96/24=4 Exploring Operation: 96-68=28, Resulting Numbers: [21, 24, 28] Generated Node #0,2: 18:[21, 24, 28] Operation: 96-68=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 18:[21, 24, 28], Operations: ['96-68=28'] Exploring Operation: 28-21=7, Resulting Numbers: [24, 7] Generated Node #0,2,0: 18:[24, 7] Operation: 28-21=7 Exploring Operation: 28-24=4, Resulting Numbers: [21, 4] Generated Node #0,2,1: 18:[21, 4] Operation: 28-24=4 Exploring Operation: 24-21=3, Resulting Numbers: [28, 3] Generated Node #0,2,2: 18:[28, 3] Operation: 24-21=3 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 18:[21, 4], Operations: ['96-68=28', '28-24=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 18:[24, 7], Operations: ['96-68=28', '28-21=7'] Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 18:[28, 3], Operations: ['96-68=28', '24-21=3'] Exploring Operation: 28+3=31, Resulting Numbers: [31] 31,18 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 28*3=84, Resulting Numbers: [84] 84,18 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 18:[21, 68, 4], Operations: ['96/24=4'] Exploring Operation: 68-21=47, Resulting Numbers: [4, 47] Generated Node #0,1,0: 18:[4, 47] Operation: 68-21=47 Exploring Operation: 68/4=17, Resulting Numbers: [21, 17] Generated Node #0,1,1: 18:[21, 17] Operation: 68/4=17 Exploring Operation: 68-4=64, Resulting Numbers: [21, 64] Generated Node #0,1,2: 18:[21, 64] Operation: 68-4=64 Moving to Node #0,1,1 Current State: 18:[21, 17], Operations: ['96/24=4', '68/4=17'] Exploring Operation: 21*17=357, Resulting Numbers: [357] 357,18 unequal: No Solution Exploring Operation: 21+17=38, Resulting Numbers: [38] 38,18 unequal: No Solution Exploring Operation: 21-17=4, Resulting Numbers: [4] 4,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[4, 47], Operations: ['96/24=4', '68-21=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,18 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[21, 64], Operations: ['96/24=4', '68-4=64'] Exploring Operation: 21+64=85, Resulting Numbers: [85] 85,18 unequal: No Solution Exploring Operation: 64-21=43, Resulting Numbers: [43] 43,18 unequal: No Solution Exploring Operation: 21*64=1344, Resulting Numbers: [1344] 1344,18 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:[21, 68, 72], Operations: ['96-24=72'] Exploring Operation: 72-21=51, Resulting Numbers: [68, 51] Generated Node #0,0,0: 18:[68, 51] Operation: 72-21=51 Exploring Operation: 68-21=47, Resulting Numbers: [72, 47] Generated Node #0,0,1: 18:[72, 47] Operation: 68-21=47 Exploring Operation: 72-68=4, Resulting Numbers: [21, 4] Generated Node #0,0,2: 18:[21, 4] Operation: 72-68=4 Moving to Node #0,0,2 Current State: 18:[21, 4], Operations: ['96-24=72', '72-68=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 21*4=84, Resulting Numbers: [84] 84,18 unequal: No Solution Exploring Operation: 21+4=25, Resulting Numbers: [25] 25,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[68, 51], Operations: ['96-24=72', '72-21=51'] Exploring Operation: 68-51=17, Resulting Numbers: [17] 17,18 unequal: No Solution Exploring Operation: 68+51=119, Resulting Numbers: [119] 119,18 unequal: No Solution Exploring Operation: 68*51=3468, Resulting Numbers: [3468] 3468,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[72, 47], Operations: ['96-24=72', '68-21=47'] Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,18 unequal: No Solution Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,18 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
[ 27, 69, 64, 59 ]
29
[ "69+59=128", "128/64=2", "27+2=29" ]
Current State: 29:[27, 69, 64, 59], Operations: [] Exploring Operation: 69+59=128, Resulting Numbers: [27, 64, 128] Generated Node #2: [27, 64, 128] from Operation: 69+59=128 Current State: 29:[27, 64, 128], Operations: ['69+59=128'] Exploring Operation: 128/64=2, Resulting Numbers: [27, 2] Generated Node #3: [27, 2] from Operation: 128/64=2 Current State: 29:[27, 2], Operations: ['69+59=128', '128/64=2'] Exploring Operation: 27+2=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[27, 69, 64, 59], Operations: [] Exploring Operation: 69-64=5, Resulting Numbers: [27, 59, 5] Generated Node #0,0: 29:[27, 59, 5] Operation: 69-64=5 Moving to Node #0,0 Current State: 29:[27, 59, 5], Operations: ['69-64=5'] Exploring Operation: 59-27=32, Resulting Numbers: [5, 32] Generated Node #0,0,0: 29:[5, 32] Operation: 59-27=32 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[5, 32], Operations: ['69-64=5', '59-27=32'] Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 89, 69, 9, 45 ]
74
[ "89-69=20", "9+45=54", "20+54=74" ]
Current State: 74:[89, 69, 9, 45], Operations: [] Exploring Operation: 89-69=20, Resulting Numbers: [9, 45, 20] Generated Node #2: [9, 45, 20] from Operation: 89-69=20 Current State: 74:[9, 45, 20], Operations: ['89-69=20'] Exploring Operation: 9+45=54, Resulting Numbers: [20, 54] Generated Node #3: [20, 54] from Operation: 9+45=54 Current State: 74:[20, 54], Operations: ['89-69=20', '9+45=54'] Exploring Operation: 20+54=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[89, 69, 9, 45], Operations: [] Exploring Operation: 89-45=44, Resulting Numbers: [69, 9, 44] Generated Node #0,0: 74:[69, 9, 44] Operation: 89-45=44 Exploring Operation: 89-9=80, Resulting Numbers: [69, 45, 80] Generated Node #0,1: 74:[69, 45, 80] Operation: 89-9=80 Exploring Operation: 45-9=36, Resulting Numbers: [89, 69, 36] Generated Node #0,2: 74:[89, 69, 36] Operation: 45-9=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 74:[69, 9, 44], Operations: ['89-45=44'] Exploring Operation: 69-44=25, Resulting Numbers: [9, 25] Generated Node #0,0,0: 74:[9, 25] Operation: 69-44=25 Exploring Operation: 44-9=35, Resulting Numbers: [69, 35] Generated Node #0,0,1: 74:[69, 35] Operation: 44-9=35 Exploring Operation: 69+9=78, Resulting Numbers: [44, 78] Generated Node #0,0,2: 74:[44, 78] Operation: 69+9=78 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 74:[69, 35], Operations: ['89-45=44', '44-9=35'] Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,74 unequal: No Solution Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,74 unequal: No Solution No 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: 74:[44, 78], Operations: ['89-45=44', '69+9=78'] Exploring Operation: 44+78=122, Resulting Numbers: [122] 122,74 unequal: No Solution Exploring Operation: 78-44=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 44*78=3432, Resulting Numbers: [3432] 3432,74 unequal: No Solution No 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: 74:[9, 25], Operations: ['89-45=44', '69-44=25'] Exploring Operation: 9*25=225, Resulting Numbers: [225] 225,74 unequal: No Solution Exploring Operation: 25-9=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 9+25=34, Resulting Numbers: [34] 34,74 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: 74:[69, 45, 80], Operations: ['89-9=80'] Exploring Operation: 69-45=24, Resulting Numbers: [80, 24] Generated Node #0,1,0: 74:[80, 24] Operation: 69-45=24 Exploring Operation: 80-69=11, Resulting Numbers: [45, 11] Generated Node #0,1,1: 74:[45, 11] Operation: 80-69=11 Exploring Operation: 80-45=35, Resulting Numbers: [69, 35] Generated Node #0,1,2: 74:[69, 35] Operation: 80-45=35 Moving to Node #0,1,2 Current State: 74:[69, 35], Operations: ['89-9=80', '80-45=35'] Exploring Operation: 69-35=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 69+35=104, Resulting Numbers: [104] 104,74 unequal: No Solution Exploring Operation: 69*35=2415, Resulting Numbers: [2415] 2415,74 unequal: No Solution Moving to Node #0,1,1 Current State: 74:[45, 11], Operations: ['89-9=80', '80-69=11'] Exploring Operation: 45-11=34, Resulting Numbers: [34] 34,74 unequal: No Solution Exploring Operation: 45+11=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 45*11=495, Resulting Numbers: [495] 495,74 unequal: No Solution Moving to Node #0,1,0 Current State: 74:[80, 24], Operations: ['89-9=80', '69-45=24'] Exploring Operation: 80-24=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 80*24=1920, Resulting Numbers: [1920] 1920,74 unequal: No Solution Exploring Operation: 80+24=104, Resulting Numbers: [104] 104,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[89, 69, 36], Operations: ['45-9=36'] Exploring Operation: 89-69=20, Resulting Numbers: [36, 20] Generated Node #0,2,0: 74:[36, 20] Operation: 89-69=20 Exploring Operation: 69-36=33, Resulting Numbers: [89, 33] Generated Node #0,2,1: 74:[89, 33] Operation: 69-36=33 Exploring Operation: 89-36=53, Resulting Numbers: [69, 53] Generated Node #0,2,2: 74:[69, 53] Operation: 89-36=53 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 74:[36, 20], Operations: ['45-9=36', '89-69=20'] Exploring Operation: 36*20=720, Resulting Numbers: [720] 720,74 unequal: No Solution Exploring Operation: 36-20=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 36+20=56, Resulting Numbers: [56] 56,74 unequal: No Solution No 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: 74:[89, 33], Operations: ['45-9=36', '69-36=33'] Exploring Operation: 89*33=2937, Resulting Numbers: [2937] 2937,74 unequal: No Solution Exploring Operation: 89-33=56, Resulting Numbers: [56] 56,74 unequal: No Solution Exploring Operation: 89+33=122, Resulting Numbers: [122] 122,74 unequal: No Solution No 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: 74:[69, 53], Operations: ['45-9=36', '89-36=53'] Exploring Operation: 69*53=3657, Resulting Numbers: [3657] 3657,74 unequal: No Solution Exploring Operation: 69-53=16, Resulting Numbers: [16] 16,74 unequal: No Solution Exploring Operation: 69+53=122, Resulting Numbers: [122] 122,74 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 85, 9, 7, 88 ]
36
[ "85+7=92", "92-88=4", "9*4=36" ]
Current State: 36:[85, 9, 7, 88], Operations: [] Exploring Operation: 85+7=92, Resulting Numbers: [9, 88, 92] Generated Node #2: [9, 88, 92] from Operation: 85+7=92 Current State: 36:[9, 88, 92], Operations: ['85+7=92'] Exploring Operation: 92-88=4, Resulting Numbers: [9, 4] Generated Node #3: [9, 4] from Operation: 92-88=4 Current State: 36:[9, 4], Operations: ['85+7=92', '92-88=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[85, 9, 7, 88], Operations: [] Exploring Operation: 85-9=76, Resulting Numbers: [7, 88, 76] Generated Node #0,0: 36:[7, 88, 76] Operation: 85-9=76 Exploring Operation: 88-85=3, Resulting Numbers: [9, 7, 3] Generated Node #0,1: 36:[9, 7, 3] Operation: 88-85=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[9, 7, 3], Operations: ['88-85=3'] Exploring Operation: 7-3=4, Resulting Numbers: [9, 4] Generated Node #0,1,0: 36:[9, 4] Operation: 7-3=4 Exploring Operation: 9-7=2, Resulting Numbers: [3, 2] Generated Node #0,1,1: 36:[3, 2] Operation: 9-7=2 Moving to Node #0,1,0 Current State: 36:[9, 4], Operations: ['88-85=3', '7-3=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[85, 9, 7, 88], Operations: [] Exploring Operation: 88-85=3, Resulting Numbers: [9, 7, 3] Generated Node #0,1: 36:[9, 7, 3] Operation: 88-85=3 Moving to Node #0,1 Current State: 36:[9, 7, 3], Operations: ['88-85=3'] Exploring Operation: 7-3=4, Resulting Numbers: [9, 4] Generated Node #0,1,0: 36:[9, 4] Operation: 7-3=4 Moving to Node #0,1,0 Current State: 36:[9, 4], Operations: ['88-85=3', '7-3=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 72, 26, 2, 78 ]
38
[ "78-72=6", "2*6=12", "26+12=38" ]
Current State: 38:[72, 26, 2, 78], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [26, 2, 6] Generated Node #2: [26, 2, 6] from Operation: 78-72=6 Current State: 38:[26, 2, 6], Operations: ['78-72=6'] Exploring Operation: 2*6=12, Resulting Numbers: [26, 12] Generated Node #3: [26, 12] from Operation: 2*6=12 Current State: 38:[26, 12], Operations: ['78-72=6', '2*6=12'] Exploring Operation: 26+12=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[72, 26, 2, 78], Operations: [] Exploring Operation: 78-72=6, Resulting Numbers: [26, 2, 6] Generated Node #0,0: 38:[26, 2, 6] Operation: 78-72=6 Moving to Node #0,0 Current State: 38:[26, 2, 6], Operations: ['78-72=6'] Exploring Operation: 26-6=20, Resulting Numbers: [2, 20] Generated Node #0,0,0: 38:[2, 20] Operation: 26-6=20 Moving to Node #0,0,0 Current State: 38:[2, 20], Operations: ['78-72=6', '26-6=20'] Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,38 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 30, 2, 67, 86 ]
54
[ "30+67=97", "86/2=43", "97-43=54" ]
Current State: 54:[30, 2, 67, 86], Operations: [] Exploring Operation: 30+67=97, Resulting Numbers: [2, 86, 97] Generated Node #2: [2, 86, 97] from Operation: 30+67=97 Current State: 54:[2, 86, 97], Operations: ['30+67=97'] Exploring Operation: 86/2=43, Resulting Numbers: [97, 43] Generated Node #3: [97, 43] from Operation: 86/2=43 Current State: 54:[97, 43], Operations: ['30+67=97', '86/2=43'] Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[30, 2, 67, 86], Operations: [] Exploring Operation: 67-30=37, Resulting Numbers: [2, 86, 37] Generated Node #0,0: 54:[2, 86, 37] Operation: 67-30=37 Exploring Operation: 86-30=56, Resulting Numbers: [2, 67, 56] Generated Node #0,1: 54:[2, 67, 56] Operation: 86-30=56 Exploring Operation: 86-67=19, Resulting Numbers: [30, 2, 19] Generated Node #0,2: 54:[30, 2, 19] Operation: 86-67=19 Exploring Operation: 86/2=43, Resulting Numbers: [30, 67, 43] Generated Node #0,3: 54:[30, 67, 43] Operation: 86/2=43 Start Sub Search at level 1: Moving to Node #0,2 Current State: 54:[30, 2, 19], Operations: ['86-67=19'] Exploring Operation: 30-19=11, Resulting Numbers: [2, 11] Generated Node #0,2,0: 54:[2, 11] Operation: 30-19=11 Exploring Operation: 30-2=28, Resulting Numbers: [19, 28] Generated Node #0,2,1: 54:[19, 28] Operation: 30-2=28 Exploring Operation: 19-2=17, Resulting Numbers: [30, 17] Generated Node #0,2,2: 54:[30, 17] Operation: 19-2=17 Exploring Operation: 30/2=15, Resulting Numbers: [19, 15] Generated Node #0,2,3: 54:[19, 15] Operation: 30/2=15 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[2, 11], Operations: ['86-67=19', '30-19=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,54 unequal: No Solution No 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: 54:[19, 28], Operations: ['86-67=19', '30-2=28'] Exploring Operation: 19*28=532, Resulting Numbers: [532] 532,54 unequal: No Solution Exploring Operation: 28-19=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 19+28=47, Resulting Numbers: [47] 47,54 unequal: No Solution No 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: 54:[30, 17], Operations: ['86-67=19', '19-2=17'] Exploring Operation: 30+17=47, Resulting Numbers: [47] 47,54 unequal: No Solution Exploring Operation: 30*17=510, Resulting Numbers: [510] 510,54 unequal: No Solution Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,54 unequal: No Solution No 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: 54:[19, 15], Operations: ['86-67=19', '30/2=15'] Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,54 unequal: No Solution Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,54 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,54 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: 54:[2, 67, 56], Operations: ['86-30=56'] Exploring Operation: 56/2=28, Resulting Numbers: [67, 28] Generated Node #0,1,0: 54:[67, 28] Operation: 56/2=28 Exploring Operation: 67-56=11, Resulting Numbers: [2, 11] Generated Node #0,1,1: 54:[2, 11] Operation: 67-56=11 Exploring Operation: 56-2=54, Resulting Numbers: [67, 54] Generated Node #0,1,2: 54:[67, 54] Operation: 56-2=54 Exploring Operation: 67-2=65, Resulting Numbers: [56, 65] Generated Node #0,1,3: 54:[56, 65] Operation: 67-2=65 Moving to Node #0,1,1 Current State: 54:[2, 11], Operations: ['86-30=56', '67-56=11'] Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,54 unequal: No Solution Moving to Node #0,1,3 Current State: 54:[56, 65], Operations: ['86-30=56', '67-2=65'] Exploring Operation: 56*65=3640, Resulting Numbers: [3640] 3640,54 unequal: No Solution Exploring Operation: 65-56=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 56+65=121, Resulting Numbers: [121] 121,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[67, 54], Operations: ['86-30=56', '56-2=54'] Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,54 unequal: No Solution Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,54 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[67, 28], Operations: ['86-30=56', '56/2=28'] Exploring Operation: 67*28=1876, Resulting Numbers: [1876] 1876,54 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,54 unequal: No Solution Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 54:[30, 67, 43], Operations: ['86/2=43'] Exploring Operation: 43-30=13, Resulting Numbers: [67, 13] Generated Node #0,3,0: 54:[67, 13] Operation: 43-30=13 Exploring Operation: 30+43=73, Resulting Numbers: [67, 73] Generated Node #0,3,1: 54:[67, 73] Operation: 30+43=73 Exploring Operation: 67-30=37, Resulting Numbers: [43, 37] Generated Node #0,3,2: 54:[43, 37] Operation: 67-30=37 Exploring Operation: 67-43=24, Resulting Numbers: [30, 24] Generated Node #0,3,3: 54:[30, 24] Operation: 67-43=24 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 54:[30, 24], Operations: ['86/2=43', '67-43=24'] Exploring Operation: 30*24=720, Resulting Numbers: [720] 720,54 unequal: No Solution Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[30, 2, 67, 86], Operations: [] Exploring Operation: 86/2=43, Resulting Numbers: [30, 67, 43] Generated Node #0,3: 54:[30, 67, 43] Operation: 86/2=43 Moving to Node #0,3 Current State: 54:[30, 67, 43], Operations: ['86/2=43'] Exploring Operation: 67-43=24, Resulting Numbers: [30, 24] Generated Node #0,3,3: 54:[30, 24] Operation: 67-43=24 Moving to Node #0,3,3 Current State: 54:[30, 24], Operations: ['86/2=43', '67-43=24'] Exploring Operation: 30+24=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_4
mult_heuristic
[ 10, 82, 55, 20 ]
70
[ "82-55=27", "27-20=7", "10*7=70" ]
Current State: 70:[10, 82, 55, 20], Operations: [] Exploring Operation: 82-55=27, Resulting Numbers: [10, 20, 27] Generated Node #2: [10, 20, 27] from Operation: 82-55=27 Current State: 70:[10, 20, 27], Operations: ['82-55=27'] Exploring Operation: 27-20=7, Resulting Numbers: [10, 7] Generated Node #3: [10, 7] from Operation: 27-20=7 Current State: 70:[10, 7], Operations: ['82-55=27', '27-20=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[10, 82, 55, 20], Operations: [] Exploring Operation: 82-10=72, Resulting Numbers: [55, 20, 72] Generated Node #0,0: 70:[55, 20, 72] Operation: 82-10=72 Exploring Operation: 55+20=75, Resulting Numbers: [10, 82, 75] Generated Node #0,1: 70:[10, 82, 75] Operation: 55+20=75 Exploring Operation: 55-20=35, Resulting Numbers: [10, 82, 35] Generated Node #0,2: 70:[10, 82, 35] Operation: 55-20=35 Exploring Operation: 82-55=27, Resulting Numbers: [10, 20, 27] Generated Node #0,3: 70:[10, 20, 27] Operation: 82-55=27 Moving to Node #0,2 Current State: 70:[10, 82, 35], Operations: ['55-20=35'] Exploring Operation: 82-35=47, Resulting Numbers: [10, 47] Generated Node #0,2,0: 70:[10, 47] Operation: 82-35=47 Exploring Operation: 10+82=92, Resulting Numbers: [35, 92] Generated Node #0,2,1: 70:[35, 92] Operation: 10+82=92 Exploring Operation: 10+35=45, Resulting Numbers: [82, 45] Generated Node #0,2,2: 70:[82, 45] Operation: 10+35=45 Exploring Operation: 82-10=72, Resulting Numbers: [35, 72] Generated Node #0,2,3: 70:[35, 72] Operation: 82-10=72 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 70:[35, 72], Operations: ['55-20=35', '82-10=72'] Exploring Operation: 35+72=107, Resulting Numbers: [107] 107,70 unequal: No Solution Exploring Operation: 35*72=2520, Resulting Numbers: [2520] 2520,70 unequal: No Solution Exploring Operation: 72-35=37, Resulting Numbers: [37] 37,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 70:[10, 47], Operations: ['55-20=35', '82-35=47'] Exploring Operation: 47-10=37, Resulting Numbers: [37] 37,70 unequal: No Solution Exploring Operation: 10+47=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 10*47=470, Resulting Numbers: [470] 470,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 70:[35, 92], Operations: ['55-20=35', '10+82=92'] Exploring Operation: 92-35=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 35+92=127, Resulting Numbers: [127] 127,70 unequal: No Solution Exploring Operation: 35*92=3220, Resulting Numbers: [3220] 3220,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 70:[82, 45], Operations: ['55-20=35', '10+35=45'] Exploring Operation: 82+45=127, Resulting Numbers: [127] 127,70 unequal: No Solution Exploring Operation: 82*45=3690, Resulting Numbers: [3690] 3690,70 unequal: No Solution Exploring Operation: 82-45=37, Resulting Numbers: [37] 37,70 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: 70:[10, 20, 27], Operations: ['82-55=27'] Exploring Operation: 10+27=37, Resulting Numbers: [20, 37] Generated Node #0,3,0: 70:[20, 37] Operation: 10+27=37 Exploring Operation: 27-20=7, Resulting Numbers: [10, 7] Generated Node #0,3,1: 70:[10, 7] Operation: 27-20=7 Exploring Operation: 20/10=2, Resulting Numbers: [27, 2] Generated Node #0,3,2: 70:[27, 2] Operation: 20/10=2 Exploring Operation: 20-10=10, Resulting Numbers: [27, 10] Generated Node #0,3,3: 70:[27, 10] Operation: 20-10=10 Moving to Node #0,1 Current State: 70:[10, 82, 75], Operations: ['55+20=75'] Exploring Operation: 82-75=7, Resulting Numbers: [10, 7] Generated Node #0,1,0: 70:[10, 7] Operation: 82-75=7 Exploring Operation: 75-10=65, Resulting Numbers: [82, 65] Generated Node #0,1,1: 70:[82, 65] Operation: 75-10=65 Exploring Operation: 10+82=92, Resulting Numbers: [75, 92] Generated Node #0,1,2: 70:[75, 92] Operation: 10+82=92 Exploring Operation: 82-10=72, Resulting Numbers: [75, 72] Generated Node #0,1,3: 70:[75, 72] Operation: 82-10=72 Moving to Node #0,0 Current State: 70:[55, 20, 72], Operations: ['82-10=72'] Exploring Operation: 72-20=52, Resulting Numbers: [55, 52] Generated Node #0,0,0: 70:[55, 52] Operation: 72-20=52 Exploring Operation: 72-55=17, Resulting Numbers: [20, 17] Generated Node #0,0,1: 70:[20, 17] Operation: 72-55=17 Exploring Operation: 55-20=35, Resulting Numbers: [72, 35] Generated Node #0,0,2: 70:[72, 35] Operation: 55-20=35 Exploring Operation: 55+20=75, Resulting Numbers: [72, 75] Generated Node #0,0,3: 70:[72, 75] Operation: 55+20=75 Moving to Node #0,3,1 Current State: 70:[10, 7], Operations: ['82-55=27', '27-20=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[10, 82, 55, 20], Operations: [] Exploring Operation: 82-55=27, Resulting Numbers: [10, 20, 27] Generated Node #0,3: 70:[10, 20, 27] Operation: 82-55=27 Moving to Node #0,3 Current State: 70:[10, 20, 27], Operations: ['82-55=27'] Exploring Operation: 27-20=7, Resulting Numbers: [10, 7] Generated Node #0,3,1: 70:[10, 7] Operation: 27-20=7 Moving to Node #0,3,1 Current State: 70:[10, 7], Operations: ['82-55=27', '27-20=7'] Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.966146
hs_4
sum_heuristic
[ 53, 69, 72, 20 ]
90
[ "69-53=16", "72*20=1440", "1440/16=90" ]
Current State: 90:[53, 69, 72, 20], Operations: [] Exploring Operation: 69-53=16, Resulting Numbers: [72, 20, 16] Generated Node #2: [72, 20, 16] from Operation: 69-53=16 Current State: 90:[72, 20, 16], Operations: ['69-53=16'] Exploring Operation: 72*20=1440, Resulting Numbers: [16, 1440] Generated Node #3: [16, 1440] from Operation: 72*20=1440 Current State: 90:[16, 1440], Operations: ['69-53=16', '72*20=1440'] Exploring Operation: 1440/16=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[53, 69, 72, 20], Operations: [] Exploring Operation: 69-53=16, Resulting Numbers: [72, 20, 16] Generated Node #0,0: 90:[72, 20, 16] Operation: 69-53=16 Exploring Operation: 72-69=3, Resulting Numbers: [53, 20, 3] Generated Node #0,1: 90:[53, 20, 3] Operation: 72-69=3 Moving to Node #0,1 Current State: 90:[53, 20, 3], Operations: ['72-69=3'] Exploring Operation: 53-3=50, Resulting Numbers: [20, 50] Generated Node #0,1,0: 90:[20, 50] Operation: 53-3=50 Exploring Operation: 53-20=33, Resulting Numbers: [3, 33] Generated Node #0,1,1: 90:[3, 33] Operation: 53-20=33 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 90:[3, 33], Operations: ['72-69=3', '53-20=33'] Exploring Operation: 33-3=30, Resulting Numbers: [30] 30,90 unequal: No Solution Exploring Operation: 33/3=11, Resulting Numbers: [11] 11,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 90:[20, 50], Operations: ['72-69=3', '53-3=50'] Exploring Operation: 20+50=70, Resulting Numbers: [70] 70,90 unequal: No Solution Exploring Operation: 50-20=30, Resulting Numbers: [30] 30,90 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:[72, 20, 16], Operations: ['69-53=16'] Exploring Operation: 72+20=92, Resulting Numbers: [16, 92] Generated Node #0,0,0: 90:[16, 92] Operation: 72+20=92 Exploring Operation: 72+16=88, Resulting Numbers: [20, 88] Generated Node #0,0,1: 90:[20, 88] Operation: 72+16=88 Moving to Node #0,0,0 Current State: 90:[16, 92], Operations: ['69-53=16', '72+20=92'] Exploring Operation: 92-16=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 16+92=108, Resulting Numbers: [108] 108,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[20, 88], Operations: ['69-53=16', '72+16=88'] Exploring Operation: 20+88=108, Resulting Numbers: [108] 108,90 unequal: No Solution Exploring Operation: 88-20=68, Resulting Numbers: [68] 68,90 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 15, 24, 3, 15 ]
54
[ "24-15=9", "3*15=45", "9+45=54" ]
Current State: 54:[15, 24, 3, 15], Operations: [] Exploring Operation: 24-15=9, Resulting Numbers: [3, 9] Generated Node #2: [3, 9] from Operation: 24-15=9 Current State: 54:[3, 9], Operations: ['24-15=9'] Exploring Operation: 3*15=45, Resulting Numbers: [9, 45] Generated Node #3: [9, 45] from Operation: 3*15=45 Current State: 54:[9, 45], Operations: ['24-15=9', '3*15=45'] Exploring Operation: 9+45=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[15, 24, 3, 15], Operations: [] Exploring Operation: 24-15=9, Resulting Numbers: [3, 15, 9] Generated Node #0,0: 54:[3, 15, 9] Operation: 24-15=9 Exploring Operation: 15/15=1, Resulting Numbers: [24, 3, 1] Generated Node #0,1: 54:[24, 3, 1] Operation: 15/15=1 Exploring Operation: 24-15=9, Resulting Numbers: [15, 3, 9] Generated Node #0,2: 54:[15, 3, 9] Operation: 24-15=9 Moving to Node #0,0 Current State: 54:[3, 15, 9], Operations: ['24-15=9'] Exploring Operation: 15-9=6, Resulting Numbers: [3, 6] Generated Node #0,0,0: 54:[3, 6] Operation: 15-9=6 Exploring Operation: 15/3=5, Resulting Numbers: [9, 5] Generated Node #0,0,1: 54:[9, 5] Operation: 15/3=5 Exploring Operation: 3+15=18, Resulting Numbers: [9, 18] Generated Node #0,0,2: 54:[9, 18] Operation: 3+15=18 Moving to Node #0,2 Current State: 54:[15, 3, 9], Operations: ['24-15=9'] Exploring Operation: 15+3=18, Resulting Numbers: [9, 18] Generated Node #0,2,0: 54:[9, 18] Operation: 15+3=18 Exploring Operation: 15-9=6, Resulting Numbers: [3, 6] Generated Node #0,2,1: 54:[3, 6] Operation: 15-9=6 Exploring Operation: 15/3=5, Resulting Numbers: [9, 5] Generated Node #0,2,2: 54:[9, 5] Operation: 15/3=5 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[9, 18], Operations: ['24-15=9', '15+3=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,54 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 #0,2,1 Current State: 54:[3, 6], Operations: ['24-15=9', '15-9=6'] Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 54:[9, 5], Operations: ['24-15=9', '15/3=5'] Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 54:[24, 3, 1], Operations: ['15/15=1'] Exploring Operation: 24+1=25, Resulting Numbers: [3, 25] Generated Node #0,1,0: 54:[3, 25] Operation: 24+1=25 Exploring Operation: 24/3=8, Resulting Numbers: [1, 8] Generated Node #0,1,1: 54:[1, 8] Operation: 24/3=8 Exploring Operation: 24+3=27, Resulting Numbers: [1, 27] Generated Node #0,1,2: 54:[1, 27] Operation: 24+3=27 Moving to Node #0,0,0 Current State: 54:[3, 6], Operations: ['24-15=9', '15-9=6'] Exploring Operation: 6-3=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 3+6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 3*6=18, Resulting Numbers: [18] 18,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[9, 18], Operations: ['24-15=9', '3+15=18'] Exploring Operation: 9+18=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 18-9=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 18/9=2, Resulting Numbers: [2] 2,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[9, 5], Operations: ['24-15=9', '15/3=5'] Exploring Operation: 9*5=45, Resulting Numbers: [45] 45,54 unequal: No Solution Exploring Operation: 9+5=14, Resulting Numbers: [14] 14,54 unequal: No Solution Exploring Operation: 9-5=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,1,2 Current State: 54:[1, 27], Operations: ['15/15=1', '24+3=27'] Exploring Operation: 1+27=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 1*27=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 27/1=27, Resulting Numbers: [27] 27,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[1, 8], Operations: ['15/15=1', '24/3=8'] Exploring Operation: 1*8=8, Resulting Numbers: [8] 8,54 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,54 unequal: No Solution Exploring Operation: 1+8=9, Resulting Numbers: [9] 9,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[3, 25], Operations: ['15/15=1', '24+1=25'] Exploring Operation: 3+25=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 25-3=22, Resulting Numbers: [22] 22,54 unequal: No Solution Exploring Operation: 3*25=75, Resulting Numbers: [75] 75,54 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 60, 94, 85, 83 ]
14
[ "60+94=154", "85+83=168", "168-154=14" ]
Current State: 14:[60, 94, 85, 83], Operations: [] Exploring Operation: 60+94=154, Resulting Numbers: [85, 83, 154] Generated Node #2: [85, 83, 154] from Operation: 60+94=154 Current State: 14:[85, 83, 154], Operations: ['60+94=154'] Exploring Operation: 85+83=168, Resulting Numbers: [154, 168] Generated Node #3: [154, 168] from Operation: 85+83=168 Current State: 14:[154, 168], Operations: ['60+94=154', '85+83=168'] Exploring Operation: 168-154=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[60, 94, 85, 83], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [60, 83, 9] Generated Node #0,0: 14:[60, 83, 9] Operation: 94-85=9 Exploring Operation: 94-83=11, Resulting Numbers: [60, 85, 11] Generated Node #0,1: 14:[60, 85, 11] Operation: 94-83=11 Exploring Operation: 85-83=2, Resulting Numbers: [60, 94, 2] Generated Node #0,2: 14:[60, 94, 2] Operation: 85-83=2 Exploring Operation: 94-60=34, Resulting Numbers: [85, 83, 34] Generated Node #0,3: 14:[85, 83, 34] Operation: 94-60=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 14:[60, 83, 9], Operations: ['94-85=9'] Exploring Operation: 83-60=23, Resulting Numbers: [9, 23] Generated Node #0,0,0: 14:[9, 23] Operation: 83-60=23 Exploring Operation: 60-9=51, Resulting Numbers: [83, 51] Generated Node #0,0,1: 14:[83, 51] Operation: 60-9=51 Exploring Operation: 83-9=74, Resulting Numbers: [60, 74] Generated Node #0,0,2: 14:[60, 74] Operation: 83-9=74 Exploring Operation: 60+9=69, Resulting Numbers: [83, 69] Generated Node #0,0,3: 14:[83, 69] Operation: 60+9=69 Moving to Node #0,0,0 Current State: 14:[9, 23], Operations: ['94-85=9', '83-60=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Moving to Node #0 Current State: 14:[60, 94, 85, 83], Operations: [] Exploring Operation: 94-85=9, Resulting Numbers: [60, 83, 9] Generated Node #0,0: 14:[60, 83, 9] Operation: 94-85=9 Moving to Node #0,0 Current State: 14:[60, 83, 9], Operations: ['94-85=9'] Exploring Operation: 83-60=23, Resulting Numbers: [9, 23] Generated Node #0,0,0: 14:[9, 23] Operation: 83-60=23 Moving to Node #0,0,0 Current State: 14:[9, 23], Operations: ['94-85=9', '83-60=23'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_4
mult_heuristic
[ 2, 58, 13, 9 ]
41
[ "2*13=26", "58+9=67", "67-26=41" ]
Current State: 41:[2, 58, 13, 9], Operations: [] Exploring Operation: 2*13=26, Resulting Numbers: [58, 9, 26] Generated Node #2: [58, 9, 26] from Operation: 2*13=26 Current State: 41:[58, 9, 26], Operations: ['2*13=26'] Exploring Operation: 58+9=67, Resulting Numbers: [26, 67] Generated Node #3: [26, 67] from Operation: 58+9=67 Current State: 41:[26, 67], Operations: ['2*13=26', '58+9=67'] Exploring Operation: 67-26=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[2, 58, 13, 9], Operations: [] Exploring Operation: 2*13=26, Resulting Numbers: [58, 9, 26] Generated Node #0,0: 41:[58, 9, 26] Operation: 2*13=26 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[58, 9, 26], Operations: ['2*13=26'] Exploring Operation: 58-9=49, Resulting Numbers: [26, 49] Generated Node #0,0,0: 41:[26, 49] Operation: 58-9=49 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[26, 49], Operations: ['2*13=26', '58-9=49'] Exploring Operation: 49-26=23, Resulting Numbers: [23] 23,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 58, 44, 46, 43 ]
30
[ "58-43=15", "46-44=2", "15*2=30" ]
Current State: 30:[58, 44, 46, 43], Operations: [] Exploring Operation: 58-43=15, Resulting Numbers: [44, 46, 15] Generated Node #2: [44, 46, 15] from Operation: 58-43=15 Current State: 30:[44, 46, 15], Operations: ['58-43=15'] Exploring Operation: 46-44=2, Resulting Numbers: [15, 2] Generated Node #3: [15, 2] from Operation: 46-44=2 Current State: 30:[15, 2], Operations: ['58-43=15', '46-44=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[58, 44, 46, 43], Operations: [] Exploring Operation: 58-46=12, Resulting Numbers: [44, 43, 12] Generated Node #0,0: 30:[44, 43, 12] Operation: 58-46=12 Exploring Operation: 46-43=3, Resulting Numbers: [58, 44, 3] Generated Node #0,1: 30:[58, 44, 3] Operation: 46-43=3 Exploring Operation: 58-43=15, Resulting Numbers: [44, 46, 15] Generated Node #0,2: 30:[44, 46, 15] Operation: 58-43=15 Exploring Operation: 58-44=14, Resulting Numbers: [46, 43, 14] Generated Node #0,3: 30:[46, 43, 14] Operation: 58-44=14 Exploring Operation: 46-44=2, Resulting Numbers: [58, 43, 2] Generated Node #0,4: 30:[58, 43, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 30:[44, 43, 12], Operations: ['58-46=12'] Exploring Operation: 44-12=32, Resulting Numbers: [43, 32] Generated Node #0,0,0: 30:[43, 32] Operation: 44-12=32 Exploring Operation: 43-12=31, Resulting Numbers: [44, 31] Generated Node #0,0,1: 30:[44, 31] Operation: 43-12=31 Exploring Operation: 44+12=56, Resulting Numbers: [43, 56] Generated Node #0,0,2: 30:[43, 56] Operation: 44+12=56 Exploring Operation: 44-43=1, Resulting Numbers: [12, 1] Generated Node #0,0,3: 30:[12, 1] Operation: 44-43=1 Exploring Operation: 43+12=55, Resulting Numbers: [44, 55] Generated Node #0,0,4: 30:[44, 55] Operation: 43+12=55 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 30:[12, 1], Operations: ['58-46=12', '44-43=1'] Exploring Operation: 12*1=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 12+1=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 12/1=12, Resulting Numbers: [12] 12,30 unequal: No Solution Exploring Operation: 12-1=11, Resulting Numbers: [11] 11,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 30:[43, 32], Operations: ['58-46=12', '44-12=32'] Exploring Operation: 43+32=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 43*32=1376, Resulting Numbers: [1376] 1376,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 30:[44, 31], Operations: ['58-46=12', '43-12=31'] Exploring Operation: 44+31=75, Resulting Numbers: [75] 75,30 unequal: No Solution Exploring Operation: 44*31=1364, Resulting Numbers: [1364] 1364,30 unequal: No Solution Exploring Operation: 44-31=13, Resulting Numbers: [13] 13,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 30:[43, 56], Operations: ['58-46=12', '44+12=56'] Exploring Operation: 43+56=99, Resulting Numbers: [99] 99,30 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 43*56=2408, Resulting Numbers: [2408] 2408,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 30:[44, 55], Operations: ['58-46=12', '43+12=55'] Exploring Operation: 44*55=2420, Resulting Numbers: [2420] 2420,30 unequal: No Solution Exploring Operation: 55-44=11, Resulting Numbers: [11] 11,30 unequal: No Solution Exploring Operation: 44+55=99, Resulting Numbers: [99] 99,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 30:[44, 46, 15], Operations: ['58-43=15'] Exploring Operation: 44-15=29, Resulting Numbers: [46, 29] Generated Node #0,2,0: 30:[46, 29] Operation: 44-15=29 Exploring Operation: 44+15=59, Resulting Numbers: [46, 59] Generated Node #0,2,1: 30:[46, 59] Operation: 44+15=59 Exploring Operation: 46-15=31, Resulting Numbers: [44, 31] Generated Node #0,2,2: 30:[44, 31] Operation: 46-15=31 Exploring Operation: 46+15=61, Resulting Numbers: [44, 61] Generated Node #0,2,3: 30:[44, 61] Operation: 46+15=61 Exploring Operation: 46-44=2, Resulting Numbers: [15, 2] Generated Node #0,2,4: 30:[15, 2] Operation: 46-44=2 Moving to Node #0,2,4 Current State: 30:[15, 2], Operations: ['58-43=15', '46-44=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,30 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[58, 44, 46, 43], Operations: [] Exploring Operation: 58-43=15, Resulting Numbers: [44, 46, 15] Generated Node #0,2: 30:[44, 46, 15] Operation: 58-43=15 Moving to Node #0,2 Current State: 30:[44, 46, 15], Operations: ['58-43=15'] Exploring Operation: 46-44=2, Resulting Numbers: [15, 2] Generated Node #0,2,4: 30:[15, 2] Operation: 46-44=2 Moving to Node #0,2,4 Current State: 30:[15, 2], Operations: ['58-43=15', '46-44=2'] Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 69, 7, 9, 54 ]
82
[ "69+7=76", "54/9=6", "76+6=82" ]
Current State: 82:[69, 7, 9, 54], Operations: [] Exploring Operation: 69+7=76, Resulting Numbers: [9, 54, 76] Generated Node #2: [9, 54, 76] from Operation: 69+7=76 Current State: 82:[9, 54, 76], Operations: ['69+7=76'] Exploring Operation: 54/9=6, Resulting Numbers: [76, 6] Generated Node #3: [76, 6] from Operation: 54/9=6 Current State: 82:[76, 6], Operations: ['69+7=76', '54/9=6'] Exploring Operation: 76+6=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[69, 7, 9, 54], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [69, 7, 6] Generated Node #0,0: 82:[69, 7, 6] Operation: 54/9=6 Exploring Operation: 54-9=45, Resulting Numbers: [69, 7, 45] Generated Node #0,1: 82:[69, 7, 45] Operation: 54-9=45 Exploring Operation: 69+9=78, Resulting Numbers: [7, 54, 78] Generated Node #0,2: 82:[7, 54, 78] Operation: 69+9=78 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[69, 7, 6], Operations: ['54/9=6'] Exploring Operation: 69+7=76, Resulting Numbers: [6, 76] Generated Node #0,0,0: 82:[6, 76] Operation: 69+7=76 Exploring Operation: 69+6=75, Resulting Numbers: [7, 75] Generated Node #0,0,1: 82:[7, 75] Operation: 69+6=75 Exploring Operation: 7*6=42, Resulting Numbers: [69, 42] Generated Node #0,0,2: 82:[69, 42] Operation: 7*6=42 Moving to Node #0,0,0 Current State: 82:[6, 76], Operations: ['54/9=6', '69+7=76'] Exploring Operation: 6*76=456, Resulting Numbers: [456] 456,82 unequal: No Solution Exploring Operation: 76-6=70, Resulting Numbers: [70] 70,82 unequal: No Solution Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[69, 7, 9, 54], Operations: [] Exploring Operation: 54/9=6, Resulting Numbers: [69, 7, 6] Generated Node #0,0: 82:[69, 7, 6] Operation: 54/9=6 Moving to Node #0,0 Current State: 82:[69, 7, 6], Operations: ['54/9=6'] Exploring Operation: 69+7=76, Resulting Numbers: [6, 76] Generated Node #0,0,0: 82:[6, 76] Operation: 69+7=76 Moving to Node #0,0,0 Current State: 82:[6, 76], Operations: ['54/9=6', '69+7=76'] Exploring Operation: 6+76=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 31, 21, 45, 42 ]
97
[ "31-21=10", "45+42=87", "10+87=97" ]
Current State: 97:[31, 21, 45, 42], Operations: [] Exploring Operation: 31-21=10, Resulting Numbers: [45, 42, 10] Generated Node #2: [45, 42, 10] from Operation: 31-21=10 Current State: 97:[45, 42, 10], Operations: ['31-21=10'] Exploring Operation: 45+42=87, Resulting Numbers: [10, 87] Generated Node #3: [10, 87] from Operation: 45+42=87 Current State: 97:[10, 87], Operations: ['31-21=10', '45+42=87'] Exploring Operation: 10+87=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[31, 21, 45, 42], Operations: [] Exploring Operation: 31+21=52, Resulting Numbers: [45, 42, 52] Generated Node #0,0: 97:[45, 42, 52] Operation: 31+21=52 Moving to Node #0,0 Current State: 97:[45, 42, 52], Operations: ['31+21=52'] Exploring Operation: 45+42=87, Resulting Numbers: [52, 87] Generated Node #0,0,0: 97:[52, 87] Operation: 45+42=87 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[52, 87], Operations: ['31+21=52', '45+42=87'] Exploring Operation: 52+87=139, Resulting Numbers: [139] 139,97 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 21, 88, 74, 18 ]
53
[ "21+88=109", "74-18=56", "109-56=53" ]
Current State: 53:[21, 88, 74, 18], Operations: [] Exploring Operation: 21+88=109, Resulting Numbers: [74, 18, 109] Generated Node #2: [74, 18, 109] from Operation: 21+88=109 Current State: 53:[74, 18, 109], Operations: ['21+88=109'] Exploring Operation: 74-18=56, Resulting Numbers: [109, 56] Generated Node #3: [109, 56] from Operation: 74-18=56 Current State: 53:[109, 56], Operations: ['21+88=109', '74-18=56'] Exploring Operation: 109-56=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[21, 88, 74, 18], Operations: [] Exploring Operation: 88-21=67, Resulting Numbers: [74, 18, 67] Generated Node #0,0: 53:[74, 18, 67] Operation: 88-21=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[74, 18, 67], Operations: ['88-21=67'] Exploring Operation: 74-18=56, Resulting Numbers: [67, 56] Generated Node #0,0,0: 53:[67, 56] Operation: 74-18=56 Moving to Node #0,0,0 Current State: 53:[67, 56], Operations: ['88-21=67', '74-18=56'] Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,53 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
[ 95, 2, 70, 42 ]
87
[ "95-42=53", "2*70=140", "140-53=87" ]
Current State: 87:[95, 2, 70, 42], Operations: [] Exploring Operation: 95-42=53, Resulting Numbers: [2, 70, 53] Generated Node #2: [2, 70, 53] from Operation: 95-42=53 Current State: 87:[2, 70, 53], Operations: ['95-42=53'] Exploring Operation: 2*70=140, Resulting Numbers: [53, 140] Generated Node #3: [53, 140] from Operation: 2*70=140 Current State: 87:[53, 140], Operations: ['95-42=53', '2*70=140'] Exploring Operation: 140-53=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[95, 2, 70, 42], Operations: [] Exploring Operation: 70/2=35, Resulting Numbers: [95, 42, 35] Generated Node #0,0: 87:[95, 42, 35] Operation: 70/2=35 Exploring Operation: 70-42=28, Resulting Numbers: [95, 2, 28] Generated Node #0,1: 87:[95, 2, 28] Operation: 70-42=28 Exploring Operation: 95-70=25, Resulting Numbers: [2, 42, 25] Generated Node #0,2: 87:[2, 42, 25] Operation: 95-70=25 Moving to Node #0,1 Current State: 87:[95, 2, 28], Operations: ['70-42=28'] Exploring Operation: 95+2=97, Resulting Numbers: [28, 97] Generated Node #0,1,0: 87:[28, 97] Operation: 95+2=97 Exploring Operation: 95-2=93, Resulting Numbers: [28, 93] Generated Node #0,1,1: 87:[28, 93] Operation: 95-2=93 Exploring Operation: 2+28=30, Resulting Numbers: [95, 30] Generated Node #0,1,2: 87:[95, 30] Operation: 2+28=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 87:[28, 93], Operations: ['70-42=28', '95-2=93'] Exploring Operation: 28+93=121, Resulting Numbers: [121] 121,87 unequal: No Solution Exploring Operation: 28*93=2604, Resulting Numbers: [2604] 2604,87 unequal: No Solution Exploring Operation: 93-28=65, Resulting Numbers: [65] 65,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 87:[95, 30], Operations: ['70-42=28', '2+28=30'] Exploring Operation: 95*30=2850, Resulting Numbers: [2850] 2850,87 unequal: No Solution Exploring Operation: 95-30=65, Resulting Numbers: [65] 65,87 unequal: No Solution Exploring Operation: 95+30=125, Resulting Numbers: [125] 125,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 87:[28, 97], Operations: ['70-42=28', '95+2=97'] Exploring Operation: 28*97=2716, Resulting Numbers: [2716] 2716,87 unequal: No Solution Exploring Operation: 97-28=69, Resulting Numbers: [69] 69,87 unequal: No Solution Exploring Operation: 28+97=125, Resulting Numbers: [125] 125,87 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: 87:[2, 42, 25], Operations: ['95-70=25'] Exploring Operation: 2*42=84, Resulting Numbers: [25, 84] Generated Node #0,2,0: 87:[25, 84] Operation: 2*42=84 Exploring Operation: 42-25=17, Resulting Numbers: [2, 17] Generated Node #0,2,1: 87:[2, 17] Operation: 42-25=17 Exploring Operation: 42/2=21, Resulting Numbers: [25, 21] Generated Node #0,2,2: 87:[25, 21] Operation: 42/2=21 Moving to Node #0,0 Current State: 87:[95, 42, 35], Operations: ['70/2=35'] Exploring Operation: 42-35=7, Resulting Numbers: [95, 7] Generated Node #0,0,0: 87:[95, 7] Operation: 42-35=7 Exploring Operation: 42+35=77, Resulting Numbers: [95, 77] Generated Node #0,0,1: 87:[95, 77] Operation: 42+35=77 Exploring Operation: 95-42=53, Resulting Numbers: [35, 53] Generated Node #0,0,2: 87:[35, 53] Operation: 95-42=53 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 87:[95, 7], Operations: ['70/2=35', '42-35=7'] Exploring Operation: 95-7=88, Resulting Numbers: [88] 88,87 unequal: No Solution Exploring Operation: 95+7=102, Resulting Numbers: [102] 102,87 unequal: No Solution Exploring Operation: 95*7=665, Resulting Numbers: [665] 665,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 87:[95, 77], Operations: ['70/2=35', '42+35=77'] Exploring Operation: 95+77=172, Resulting Numbers: [172] 172,87 unequal: No Solution Exploring Operation: 95-77=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 95*77=7315, Resulting Numbers: [7315] 7315,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 87:[35, 53], Operations: ['70/2=35', '95-42=53'] Exploring Operation: 35*53=1855, Resulting Numbers: [1855] 1855,87 unequal: No Solution Exploring Operation: 53-35=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 35+53=88, Resulting Numbers: [88] 88,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 87:[25, 84], Operations: ['95-70=25', '2*42=84'] Exploring Operation: 84-25=59, Resulting Numbers: [59] 59,87 unequal: No Solution Exploring Operation: 25+84=109, Resulting Numbers: [109] 109,87 unequal: No Solution Exploring Operation: 25*84=2100, Resulting Numbers: [2100] 2100,87 unequal: No Solution Moving to Node #0,2,2 Current State: 87:[25, 21], Operations: ['95-70=25', '42/2=21'] Exploring Operation: 25+21=46, Resulting Numbers: [46] 46,87 unequal: No Solution Exploring Operation: 25-21=4, Resulting Numbers: [4] 4,87 unequal: No Solution Exploring Operation: 25*21=525, Resulting Numbers: [525] 525,87 unequal: No Solution Moving to Node #0,2,1 Current State: 87:[2, 17], Operations: ['95-70=25', '42-25=17'] Exploring Operation: 2+17=19, Resulting Numbers: [19] 19,87 unequal: No Solution Exploring Operation: 17-2=15, Resulting Numbers: [15] 15,87 unequal: No Solution Exploring Operation: 2*17=34, Resulting Numbers: [34] 34,87 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 44, 26, 90, 54 ]
74
[ "44+26=70", "90+54=144", "144-70=74" ]
Current State: 74:[44, 26, 90, 54], Operations: [] Exploring Operation: 44+26=70, Resulting Numbers: [90, 54, 70] Generated Node #2: [90, 54, 70] from Operation: 44+26=70 Current State: 74:[90, 54, 70], Operations: ['44+26=70'] Exploring Operation: 90+54=144, Resulting Numbers: [70, 144] Generated Node #3: [70, 144] from Operation: 90+54=144 Current State: 74:[70, 144], Operations: ['44+26=70', '90+54=144'] Exploring Operation: 144-70=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[44, 26, 90, 54], Operations: [] Exploring Operation: 90-54=36, Resulting Numbers: [44, 26, 36] Generated Node #0,0: 74:[44, 26, 36] Operation: 90-54=36 Exploring Operation: 90-26=64, Resulting Numbers: [44, 54, 64] Generated Node #0,1: 74:[44, 54, 64] Operation: 90-26=64 Exploring Operation: 26+54=80, Resulting Numbers: [44, 90, 80] Generated Node #0,2: 74:[44, 90, 80] Operation: 26+54=80 Exploring Operation: 54-44=10, Resulting Numbers: [26, 90, 10] Generated Node #0,3: 74:[26, 90, 10] Operation: 54-44=10 Exploring Operation: 54-26=28, Resulting Numbers: [44, 90, 28] Generated Node #0,4: 74:[44, 90, 28] Operation: 54-26=28 Moving to Node #0,0 Current State: 74:[44, 26, 36], Operations: ['90-54=36'] Exploring Operation: 44+26=70, Resulting Numbers: [36, 70] Generated Node #0,0,0: 74:[36, 70] Operation: 44+26=70 Exploring Operation: 44+36=80, Resulting Numbers: [26, 80] Generated Node #0,0,1: 74:[26, 80] Operation: 44+36=80 Exploring Operation: 36-26=10, Resulting Numbers: [44, 10] Generated Node #0,0,2: 74:[44, 10] Operation: 36-26=10 Exploring Operation: 44-26=18, Resulting Numbers: [36, 18] Generated Node #0,0,3: 74:[36, 18] Operation: 44-26=18 Exploring Operation: 44-36=8, Resulting Numbers: [26, 8] Generated Node #0,0,4: 74:[26, 8] Operation: 44-36=8 Moving to Node #0,2 Current State: 74:[44, 90, 80], Operations: ['26+54=80'] Exploring Operation: 90-80=10, Resulting Numbers: [44, 10] Generated Node #0,2,0: 74:[44, 10] Operation: 90-80=10 Exploring Operation: 44+80=124, Resulting Numbers: [90, 124] Generated Node #0,2,1: 74:[90, 124] Operation: 44+80=124 Exploring Operation: 90-44=46, Resulting Numbers: [80, 46] Generated Node #0,2,2: 74:[80, 46] Operation: 90-44=46 Exploring Operation: 80-44=36, Resulting Numbers: [90, 36] Generated Node #0,2,3: 74:[90, 36] Operation: 80-44=36 Exploring Operation: 44+90=134, Resulting Numbers: [80, 134] Generated Node #0,2,4: 74:[80, 134] Operation: 44+90=134 Moving to Node #0,4 Current State: 74:[44, 90, 28], Operations: ['54-26=28'] Exploring Operation: 90-44=46, Resulting Numbers: [28, 46] Generated Node #0,4,0: 74:[28, 46] Operation: 90-44=46 Exploring Operation: 90-28=62, Resulting Numbers: [44, 62] Generated Node #0,4,1: 74:[44, 62] Operation: 90-28=62 Exploring Operation: 44-28=16, Resulting Numbers: [90, 16] Generated Node #0,4,2: 74:[90, 16] Operation: 44-28=16 Exploring Operation: 44+28=72, Resulting Numbers: [90, 72] Generated Node #0,4,3: 74:[90, 72] Operation: 44+28=72 Exploring Operation: 90+28=118, Resulting Numbers: [44, 118] Generated Node #0,4,4: 74:[44, 118] Operation: 90+28=118 Moving to Node #0,1 Current State: 74:[44, 54, 64], Operations: ['90-26=64'] Exploring Operation: 54-44=10, Resulting Numbers: [64, 10] Generated Node #0,1,0: 74:[64, 10] Operation: 54-44=10 Exploring Operation: 44+54=98, Resulting Numbers: [64, 98] Generated Node #0,1,1: 74:[64, 98] Operation: 44+54=98 Exploring Operation: 44+64=108, Resulting Numbers: [54, 108] Generated Node #0,1,2: 74:[54, 108] Operation: 44+64=108 Exploring Operation: 64-54=10, Resulting Numbers: [44, 10] Generated Node #0,1,3: 74:[44, 10] Operation: 64-54=10 Exploring Operation: 64-44=20, Resulting Numbers: [54, 20] Generated Node #0,1,4: 74:[54, 20] Operation: 64-44=20 Moving to Node #0,3 Current State: 74:[26, 90, 10], Operations: ['54-44=10'] Exploring Operation: 26-10=16, Resulting Numbers: [90, 16] Generated Node #0,3,0: 74:[90, 16] Operation: 26-10=16 Exploring Operation: 26+10=36, Resulting Numbers: [90, 36] Generated Node #0,3,1: 74:[90, 36] Operation: 26+10=36 Exploring Operation: 90-10=80, Resulting Numbers: [26, 80] Generated Node #0,3,2: 74:[26, 80] Operation: 90-10=80 Exploring Operation: 90-26=64, Resulting Numbers: [10, 64] Generated Node #0,3,3: 74:[10, 64] Operation: 90-26=64 Exploring Operation: 90/10=9, Resulting Numbers: [26, 9] Generated Node #0,3,4: 74:[26, 9] Operation: 90/10=9 Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 74:[90, 36], Operations: ['54-44=10', '26+10=36'] Exploring Operation: 90-36=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 90*36=3240, Resulting Numbers: [3240] 3240,74 unequal: No Solution Exploring Operation: 90+36=126, Resulting Numbers: [126] 126,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 74:[26, 80], Operations: ['54-44=10', '90-10=80'] Exploring Operation: 26*80=2080, Resulting Numbers: [2080] 2080,74 unequal: No Solution Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,74 unequal: No Solution Exploring Operation: 26+80=106, Resulting Numbers: [106] 106,74 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 74:[10, 64], Operations: ['54-44=10', '90-26=64'] Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[44, 26, 90, 54], Operations: [] Exploring Operation: 54-44=10, Resulting Numbers: [26, 90, 10] Generated Node #0,3: 74:[26, 90, 10] Operation: 54-44=10 Moving to Node #0,3 Current State: 74:[26, 90, 10], Operations: ['54-44=10'] Exploring Operation: 90-26=64, Resulting Numbers: [10, 64] Generated Node #0,3,3: 74:[10, 64] Operation: 90-26=64 Moving to Node #0,3,3 Current State: 74:[10, 64], Operations: ['54-44=10', '90-26=64'] Exploring Operation: 10+64=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 59, 56, 51, 79 ]
84
[ "59-56=3", "79-51=28", "3*28=84" ]
Current State: 84:[59, 56, 51, 79], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [51, 79, 3] Generated Node #2: [51, 79, 3] from Operation: 59-56=3 Current State: 84:[51, 79, 3], Operations: ['59-56=3'] Exploring Operation: 79-51=28, Resulting Numbers: [3, 28] Generated Node #3: [3, 28] from Operation: 79-51=28 Current State: 84:[3, 28], Operations: ['59-56=3', '79-51=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[59, 56, 51, 79], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [56, 79, 8] Generated Node #0,0: 84:[56, 79, 8] Operation: 59-51=8 Exploring Operation: 79-59=20, Resulting Numbers: [56, 51, 20] Generated Node #0,1: 84:[56, 51, 20] Operation: 79-59=20 Exploring Operation: 56-51=5, Resulting Numbers: [59, 79, 5] Generated Node #0,2: 84:[59, 79, 5] Operation: 56-51=5 Exploring Operation: 59-56=3, Resulting Numbers: [51, 79, 3] Generated Node #0,3: 84:[51, 79, 3] Operation: 59-56=3 Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[51, 79, 3], Operations: ['59-56=3'] Exploring Operation: 79-51=28, Resulting Numbers: [3, 28] Generated Node #0,3,0: 84:[3, 28] Operation: 79-51=28 Exploring Operation: 51/3=17, Resulting Numbers: [79, 17] Generated Node #0,3,1: 84:[79, 17] Operation: 51/3=17 Exploring Operation: 79+3=82, Resulting Numbers: [51, 82] Generated Node #0,3,2: 84:[51, 82] Operation: 79+3=82 Exploring Operation: 51-3=48, Resulting Numbers: [79, 48] Generated Node #0,3,3: 84:[79, 48] Operation: 51-3=48 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 84:[3, 28], Operations: ['59-56=3', '79-51=28'] Exploring Operation: 3+28=31, Resulting Numbers: [31] 31,84 unequal: No Solution Exploring Operation: 28-3=25, Resulting Numbers: [25] 25,84 unequal: No Solution Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[59, 56, 51, 79], Operations: [] Exploring Operation: 59-56=3, Resulting Numbers: [51, 79, 3] Generated Node #0,3: 84:[51, 79, 3] Operation: 59-56=3 Moving to Node #0,3 Current State: 84:[51, 79, 3], Operations: ['59-56=3'] Exploring Operation: 79-51=28, Resulting Numbers: [3, 28] Generated Node #0,3,0: 84:[3, 28] Operation: 79-51=28 Moving to Node #0,3,0 Current State: 84:[3, 28], Operations: ['59-56=3', '79-51=28'] Exploring Operation: 3*28=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
mult_heuristic
[ 50, 60, 30, 59 ]
18
[ "59-50=9", "60/30=2", "9*2=18" ]
Current State: 18:[50, 60, 30, 59], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [60, 30, 9] Generated Node #2: [60, 30, 9] from Operation: 59-50=9 Current State: 18:[60, 30, 9], Operations: ['59-50=9'] Exploring Operation: 60/30=2, Resulting Numbers: [9, 2] Generated Node #3: [9, 2] from Operation: 60/30=2 Current State: 18:[9, 2], Operations: ['59-50=9', '60/30=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[50, 60, 30, 59], Operations: [] Exploring Operation: 60-59=1, Resulting Numbers: [50, 30, 1] Generated Node #0,0: 18:[50, 30, 1] Operation: 60-59=1 Exploring Operation: 59-50=9, Resulting Numbers: [60, 30, 9] Generated Node #0,1: 18:[60, 30, 9] Operation: 59-50=9 Exploring Operation: 50-30=20, Resulting Numbers: [60, 59, 20] Generated Node #0,2: 18:[60, 59, 20] Operation: 50-30=20 Exploring Operation: 60/30=2, Resulting Numbers: [50, 59, 2] Generated Node #0,3: 18:[50, 59, 2] Operation: 60/30=2 Exploring Operation: 60-50=10, Resulting Numbers: [30, 59, 10] Generated Node #0,4: 18:[30, 59, 10] Operation: 60-50=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 18:[50, 30, 1], Operations: ['60-59=1'] Exploring Operation: 50-1=49, Resulting Numbers: [30, 49] Generated Node #0,0,0: 18:[30, 49] Operation: 50-1=49 Exploring Operation: 50*1=50, Resulting Numbers: [30, 50] Generated Node #0,0,1: 18:[30, 50] Operation: 50*1=50 Exploring Operation: 50-30=20, Resulting Numbers: [1, 20] Generated Node #0,0,2: 18:[1, 20] Operation: 50-30=20 Exploring Operation: 50/1=50, Resulting Numbers: [30, 50] Generated Node #0,0,3: 18:[30, 50] Operation: 50/1=50 Exploring Operation: 30-1=29, Resulting Numbers: [50, 29] Generated Node #0,0,4: 18:[50, 29] Operation: 30-1=29 Moving to Node #0,0,2 Current State: 18:[1, 20], Operations: ['60-59=1', '50-30=20'] Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,18 unequal: No Solution Moving to Node #0,0,4 Current State: 18:[50, 29], Operations: ['60-59=1', '30-1=29'] Exploring Operation: 50-29=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 50+29=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 50*29=1450, Resulting Numbers: [1450] 1450,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[30, 49], Operations: ['60-59=1', '50-1=49'] Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,18 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,18 unequal: No Solution Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,18 unequal: No Solution Moving to Node #0,0,1 Current State: 18:[30, 50], Operations: ['60-59=1', '50*1=50'] Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,18 unequal: No Solution Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,18 unequal: No Solution Moving to Node #0,0,3 Current State: 18:[30, 50], Operations: ['60-59=1', '50/1=50'] Exploring Operation: 50-30=20, Resulting Numbers: [20] 20,18 unequal: No Solution Exploring Operation: 30*50=1500, Resulting Numbers: [1500] 1500,18 unequal: No Solution Exploring Operation: 30+50=80, Resulting Numbers: [80] 80,18 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:[60, 30, 9], Operations: ['59-50=9'] Exploring Operation: 30-9=21, Resulting Numbers: [60, 21] Generated Node #0,1,0: 18:[60, 21] Operation: 30-9=21 Exploring Operation: 60-30=30, Resulting Numbers: [9, 30] Generated Node #0,1,1: 18:[9, 30] Operation: 60-30=30 Exploring Operation: 60/30=2, Resulting Numbers: [9, 2] Generated Node #0,1,2: 18:[9, 2] Operation: 60/30=2 Exploring Operation: 60-9=51, Resulting Numbers: [30, 51] Generated Node #0,1,3: 18:[30, 51] Operation: 60-9=51 Exploring Operation: 60+9=69, Resulting Numbers: [30, 69] Generated Node #0,1,4: 18:[30, 69] Operation: 60+9=69 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 18:[9, 2], Operations: ['59-50=9', '60/30=2'] Exploring Operation: 9-2=7, Resulting Numbers: [7] 7,18 unequal: No Solution Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Moving to Node #0 Current State: 18:[50, 60, 30, 59], Operations: [] Exploring Operation: 59-50=9, Resulting Numbers: [60, 30, 9] Generated Node #0,1: 18:[60, 30, 9] Operation: 59-50=9 Moving to Node #0,1 Current State: 18:[60, 30, 9], Operations: ['59-50=9'] Exploring Operation: 60/30=2, Resulting Numbers: [9, 2] Generated Node #0,1,2: 18:[9, 2] Operation: 60/30=2 Moving to Node #0,1,2 Current State: 18:[9, 2], Operations: ['59-50=9', '60/30=2'] Exploring Operation: 9*2=18, Resulting Numbers: [18] 18,18 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_5
sum_heuristic
[ 90, 5, 97, 48 ]
46
[ "90+5=95", "97-48=49", "95-49=46" ]
Current State: 46:[90, 5, 97, 48], Operations: [] Exploring Operation: 90+5=95, Resulting Numbers: [97, 48, 95] Generated Node #2: [97, 48, 95] from Operation: 90+5=95 Current State: 46:[97, 48, 95], Operations: ['90+5=95'] Exploring Operation: 97-48=49, Resulting Numbers: [95, 49] Generated Node #3: [95, 49] from Operation: 97-48=49 Current State: 46:[95, 49], Operations: ['90+5=95', '97-48=49'] Exploring Operation: 95-49=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[90, 5, 97, 48], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [5, 48, 7] Generated Node #0,0: 46:[5, 48, 7] Operation: 97-90=7 Exploring Operation: 97-48=49, Resulting Numbers: [90, 5, 49] Generated Node #0,1: 46:[90, 5, 49] Operation: 97-48=49 Moving to Node #0,0 Current State: 46:[5, 48, 7], Operations: ['97-90=7'] Exploring Operation: 7-5=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 46:[48, 2] Operation: 7-5=2 Exploring Operation: 48-5=43, Resulting Numbers: [7, 43] Generated Node #0,0,1: 46:[7, 43] Operation: 48-5=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 46:[48, 2], Operations: ['97-90=7', '7-5=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Moving to Node #0 Current State: 46:[90, 5, 97, 48], Operations: [] Exploring Operation: 97-90=7, Resulting Numbers: [5, 48, 7] Generated Node #0,0: 46:[5, 48, 7] Operation: 97-90=7 Moving to Node #0,0 Current State: 46:[5, 48, 7], Operations: ['97-90=7'] Exploring Operation: 7-5=2, Resulting Numbers: [48, 2] Generated Node #0,0,0: 46:[48, 2] Operation: 7-5=2 Moving to Node #0,0,0 Current State: 46:[48, 2], Operations: ['97-90=7', '7-5=2'] Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,46 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 4, 13, 64, 12 ]
25
[ "12/4=3", "13*3=39", "64-39=25" ]
Current State: 25:[4, 13, 64, 12], Operations: [] Exploring Operation: 12/4=3, Resulting Numbers: [13, 64, 3] Generated Node #2: [13, 64, 3] from Operation: 12/4=3 Current State: 25:[13, 64, 3], Operations: ['12/4=3'] Exploring Operation: 13*3=39, Resulting Numbers: [64, 39] Generated Node #3: [64, 39] from Operation: 13*3=39 Current State: 25:[64, 39], Operations: ['12/4=3', '13*3=39'] Exploring Operation: 64-39=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[4, 13, 64, 12], Operations: [] Exploring Operation: 64/4=16, Resulting Numbers: [13, 12, 16] Generated Node #0,0: 25:[13, 12, 16] Operation: 64/4=16 Exploring Operation: 64-13=51, Resulting Numbers: [4, 12, 51] Generated Node #0,1: 25:[4, 12, 51] Operation: 64-13=51 Exploring Operation: 13+12=25, Resulting Numbers: [4, 64, 25] Generated Node #0,2: 25:[4, 64, 25] Operation: 13+12=25 Exploring Operation: 64-12=52, Resulting Numbers: [4, 13, 52] Generated Node #0,3: 25:[4, 13, 52] Operation: 64-12=52 Exploring Operation: 13-12=1, Resulting Numbers: [4, 64, 1] Generated Node #0,4: 25:[4, 64, 1] Operation: 13-12=1 Moving to Node #0,0 Current State: 25:[13, 12, 16], Operations: ['64/4=16'] Exploring Operation: 12+16=28, Resulting Numbers: [13, 28] Generated Node #0,0,0: 25:[13, 28] Operation: 12+16=28 Exploring Operation: 13+12=25, Resulting Numbers: [16, 25] Generated Node #0,0,1: 25:[16, 25] Operation: 13+12=25 Exploring Operation: 13+16=29, Resulting Numbers: [12, 29] Generated Node #0,0,2: 25:[12, 29] Operation: 13+16=29 Exploring Operation: 16-13=3, Resulting Numbers: [12, 3] Generated Node #0,0,3: 25:[12, 3] Operation: 16-13=3 Exploring Operation: 16-12=4, Resulting Numbers: [13, 4] Generated Node #0,0,4: 25:[13, 4] Operation: 16-12=4 Moving to Node #0,1 Current State: 25:[4, 12, 51], Operations: ['64-13=51'] Exploring Operation: 4+12=16, Resulting Numbers: [51, 16] Generated Node #0,1,0: 25:[51, 16] Operation: 4+12=16 Exploring Operation: 51-12=39, Resulting Numbers: [4, 39] Generated Node #0,1,1: 25:[4, 39] Operation: 51-12=39 Exploring Operation: 12-4=8, Resulting Numbers: [51, 8] Generated Node #0,1,2: 25:[51, 8] Operation: 12-4=8 Exploring Operation: 12/4=3, Resulting Numbers: [51, 3] Generated Node #0,1,3: 25:[51, 3] Operation: 12/4=3 Exploring Operation: 51-4=47, Resulting Numbers: [12, 47] Generated Node #0,1,4: 25:[12, 47] Operation: 51-4=47 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 25:[4, 39], Operations: ['64-13=51', '51-12=39'] Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 25:[51, 3], Operations: ['64-13=51', '12/4=3'] Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,25 unequal: No Solution Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,25 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 25:[51, 8], Operations: ['64-13=51', '12-4=8'] Exploring Operation: 51-8=43, Resulting Numbers: [43] 43,25 unequal: No Solution Exploring Operation: 51*8=408, Resulting Numbers: [408] 408,25 unequal: No Solution Exploring Operation: 51+8=59, Resulting Numbers: [59] 59,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 25:[12, 47], Operations: ['64-13=51', '51-4=47'] Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,25 unequal: No Solution Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,25 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[51, 16], Operations: ['64-13=51', '4+12=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 51*16=816, Resulting Numbers: [816] 816,25 unequal: No Solution Exploring Operation: 51-16=35, Resulting Numbers: [35] 35,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 25:[4, 13, 52], Operations: ['64-12=52'] Exploring Operation: 52-4=48, Resulting Numbers: [13, 48] Generated Node #0,3,0: 25:[13, 48] Operation: 52-4=48 Exploring Operation: 52/4=13, Resulting Numbers: [13, 13] Generated Node #0,3,1: 25:[13, 13] Operation: 52/4=13 Exploring Operation: 52-13=39, Resulting Numbers: [4, 39] Generated Node #0,3,2: 25:[4, 39] Operation: 52-13=39 Exploring Operation: 13-4=9, Resulting Numbers: [52, 9] Generated Node #0,3,3: 25:[52, 9] Operation: 13-4=9 Exploring Operation: 52/13=4, Resulting Numbers: [4, 4] Generated Node #0,3,4: 25:[4, 4] Operation: 52/13=4 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 25:[4, 4], Operations: ['64-12=52', '52/13=4'] Exploring Operation: 4/4=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 4+4=8, Resulting Numbers: [8] 8,25 unequal: No Solution Exploring Operation: 4-4=0, Resulting Numbers: [0] 0,25 unequal: No Solution Exploring Operation: 4*4=16, Resulting Numbers: [16] 16,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 25:[4, 39], Operations: ['64-12=52', '52-13=39'] Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,25 unequal: No Solution Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 25:[13, 13], Operations: ['64-12=52', '52/4=13'] Exploring Operation: 13/13=1, Resulting Numbers: [1] 1,25 unequal: No Solution Exploring Operation: 13+13=26, Resulting Numbers: [26] 26,25 unequal: No Solution Exploring Operation: 13*13=169, Resulting Numbers: [169] 169,25 unequal: No Solution Exploring Operation: 13-13=0, Resulting Numbers: [0] 0,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 25:[13, 48], Operations: ['64-12=52', '52-4=48'] Exploring Operation: 48-13=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 13*48=624, Resulting Numbers: [624] 624,25 unequal: No Solution Exploring Operation: 13+48=61, Resulting Numbers: [61] 61,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 25:[52, 9], Operations: ['64-12=52', '13-4=9'] Exploring Operation: 52-9=43, Resulting Numbers: [43] 43,25 unequal: No Solution Exploring Operation: 52+9=61, Resulting Numbers: [61] 61,25 unequal: No Solution Exploring Operation: 52*9=468, Resulting Numbers: [468] 468,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 25:[4, 64, 25], Operations: ['13+12=25'] Exploring Operation: 4+64=68, Resulting Numbers: [25, 68] Generated Node #0,2,0: 25:[25, 68] Operation: 4+64=68 Exploring Operation: 64/4=16, Resulting Numbers: [25, 16] Generated Node #0,2,1: 25:[25, 16] Operation: 64/4=16 Exploring Operation: 64-25=39, Resulting Numbers: [4, 39] Generated Node #0,2,2: 25:[4, 39] Operation: 64-25=39 Exploring Operation: 4+25=29, Resulting Numbers: [64, 29] Generated Node #0,2,3: 25:[64, 29] Operation: 4+25=29 Exploring Operation: 64-4=60, Resulting Numbers: [25, 60] Generated Node #0,2,4: 25:[25, 60] Operation: 64-4=60 Moving to Node #0,4 Current State: 25:[4, 64, 1], Operations: ['13-12=1'] Exploring Operation: 64/4=16, Resulting Numbers: [1, 16] Generated Node #0,4,0: 25:[1, 16] Operation: 64/4=16 Exploring Operation: 4+1=5, Resulting Numbers: [64, 5] Generated Node #0,4,1: 25:[64, 5] Operation: 4+1=5 Exploring Operation: 64-4=60, Resulting Numbers: [1, 60] Generated Node #0,4,2: 25:[1, 60] Operation: 64-4=60 Exploring Operation: 4*1=4, Resulting Numbers: [64, 4] Generated Node #0,4,3: 25:[64, 4] Operation: 4*1=4 Exploring Operation: 64-1=63, Resulting Numbers: [4, 63] Generated Node #0,4,4: 25:[4, 63] Operation: 64-1=63 Moving to Node #0,0,1 Current State: 25:[16, 25], Operations: ['64/4=16', '13+12=25'] Exploring Operation: 16+25=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 16*25=400, Resulting Numbers: [400] 400,25 unequal: No Solution Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,25 unequal: No Solution Moving to Node #0,0,4 Current State: 25:[13, 4], Operations: ['64/4=16', '16-12=4'] Exploring Operation: 13*4=52, Resulting Numbers: [52] 52,25 unequal: No Solution Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 13+4=17, Resulting Numbers: [17] 17,25 unequal: No Solution Moving to Node #0,2,1 Current State: 25:[25, 16], Operations: ['13+12=25', '64/4=16'] Exploring Operation: 25-16=9, Resulting Numbers: [9] 9,25 unequal: No Solution Exploring Operation: 25+16=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 25*16=400, Resulting Numbers: [400] 400,25 unequal: No Solution Moving to Node #0,0,3 Current State: 25:[12, 3], Operations: ['64/4=16', '16-13=3'] Exploring Operation: 12+3=15, Resulting Numbers: [15] 15,25 unequal: No Solution Exploring Operation: 12*3=36, Resulting Numbers: [36] 36,25 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,25 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,25 unequal: No Solution Moving to Node #0,0,2 Current State: 25:[12, 29], Operations: ['64/4=16', '13+16=29'] Exploring Operation: 29-12=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 12*29=348, Resulting Numbers: [348] 348,25 unequal: No Solution Exploring Operation: 12+29=41, Resulting Numbers: [41] 41,25 unequal: No Solution Moving to Node #0,0,0 Current State: 25:[13, 28], Operations: ['64/4=16', '12+16=28'] Exploring Operation: 13*28=364, Resulting Numbers: [364] 364,25 unequal: No Solution Exploring Operation: 13+28=41, Resulting Numbers: [41] 41,25 unequal: No Solution Exploring Operation: 28-13=15, Resulting Numbers: [15] 15,25 unequal: No Solution Moving to Node #0,4,0 Current State: 25:[1, 16], Operations: ['13-12=1', '64/4=16'] Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,25 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,25 unequal: No Solution Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,25 unequal: No Solution Moving to Node #0,2,2 Current State: 25:[4, 39], Operations: ['13+12=25', '64-25=39'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 4+39=43, Resulting Numbers: [43] 43,25 unequal: No Solution Exploring Operation: 4*39=156, Resulting Numbers: [156] 156,25 unequal: No Solution Moving to Node #0,2,4 Current State: 25:[25, 60], Operations: ['13+12=25', '64-4=60'] Exploring Operation: 25+60=85, Resulting Numbers: [85] 85,25 unequal: No Solution Exploring Operation: 60-25=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 25*60=1500, Resulting Numbers: [1500] 1500,25 unequal: No Solution Moving to Node #0,4,4 Current State: 25:[4, 63], Operations: ['13-12=1', '64-1=63'] Exploring Operation: 4+63=67, Resulting Numbers: [67] 67,25 unequal: No Solution Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,25 unequal: No Solution Exploring Operation: 4*63=252, Resulting Numbers: [252] 252,25 unequal: No Solution Moving to Node #0,4,2 Current State: 25:[1, 60], Operations: ['13-12=1', '64-4=60'] Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,25 unequal: No Solution Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,25 unequal: No Solution Exploring Operation: 1+60=61, Resulting Numbers: [61] 61,25 unequal: No Solution Moving to Node #0,4,1 Current State: 25:[64, 5], Operations: ['13-12=1', '4+1=5'] Exploring Operation: 64-5=59, Resulting Numbers: [59] 59,25 unequal: No Solution Exploring Operation: 64*5=320, Resulting Numbers: [320] 320,25 unequal: No Solution Exploring Operation: 64+5=69, Resulting Numbers: [69] 69,25 unequal: No Solution Moving to Node #0,4,3 Current State: 25:[64, 4], Operations: ['13-12=1', '4*1=4'] Exploring Operation: 64*4=256, Resulting Numbers: [256] 256,25 unequal: No Solution Exploring Operation: 64/4=16, Resulting Numbers: [16] 16,25 unequal: No Solution Exploring Operation: 64+4=68, Resulting Numbers: [68] 68,25 unequal: No Solution Exploring Operation: 64-4=60, Resulting Numbers: [60] 60,25 unequal: No Solution Moving to Node #0,2,3 Current State: 25:[64, 29], Operations: ['13+12=25', '4+25=29'] Exploring Operation: 64*29=1856, Resulting Numbers: [1856] 1856,25 unequal: No Solution Exploring Operation: 64-29=35, Resulting Numbers: [35] 35,25 unequal: No Solution Exploring Operation: 64+29=93, Resulting Numbers: [93] 93,25 unequal: No Solution Moving to Node #0,2,0 Current State: 25:[25, 68], Operations: ['13+12=25', '4+64=68'] Exploring Operation: 25+68=93, Resulting Numbers: [93] 93,25 unequal: No Solution Exploring Operation: 25*68=1700, Resulting Numbers: [1700] 1700,25 unequal: No Solution Exploring Operation: 68-25=43, Resulting Numbers: [43] 43,25 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 62, 6, 8, 36 ]
24
[ "62+6=68", "8+36=44", "68-44=24" ]
Current State: 24:[62, 6, 8, 36], Operations: [] Exploring Operation: 62+6=68, Resulting Numbers: [8, 36, 68] Generated Node #2: [8, 36, 68] from Operation: 62+6=68 Current State: 24:[8, 36, 68], Operations: ['62+6=68'] Exploring Operation: 8+36=44, Resulting Numbers: [68, 44] Generated Node #3: [68, 44] from Operation: 8+36=44 Current State: 24:[68, 44], Operations: ['62+6=68', '8+36=44'] Exploring Operation: 68-44=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[62, 6, 8, 36], Operations: [] Exploring Operation: 36/6=6, Resulting Numbers: [62, 8, 6] Generated Node #0,0: 24:[62, 8, 6] Operation: 36/6=6 Exploring Operation: 62-8=54, Resulting Numbers: [6, 36, 54] Generated Node #0,1: 24:[6, 36, 54] Operation: 62-8=54 Exploring Operation: 62-36=26, Resulting Numbers: [6, 8, 26] Generated Node #0,2: 24:[6, 8, 26] Operation: 62-36=26 Moving to Node #0,2 Current State: 24:[6, 8, 26], Operations: ['62-36=26'] Exploring Operation: 8-6=2, Resulting Numbers: [26, 2] Generated Node #0,2,0: 24:[26, 2] Operation: 8-6=2 Exploring Operation: 6+8=14, Resulting Numbers: [26, 14] Generated Node #0,2,1: 24:[26, 14] Operation: 6+8=14 Exploring Operation: 26-6=20, Resulting Numbers: [8, 20] Generated Node #0,2,2: 24:[8, 20] Operation: 26-6=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 24:[26, 2], Operations: ['62-36=26', '8-6=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,24 unequal: No Solution Exploring Operation: 26+2=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[62, 6, 8, 36], Operations: [] Exploring Operation: 62-36=26, Resulting Numbers: [6, 8, 26] Generated Node #0,2: 24:[6, 8, 26] Operation: 62-36=26 Moving to Node #0,2 Current State: 24:[6, 8, 26], Operations: ['62-36=26'] Exploring Operation: 8-6=2, Resulting Numbers: [26, 2] Generated Node #0,2,0: 24:[26, 2] Operation: 8-6=2 Moving to Node #0,2,0 Current State: 24:[26, 2], Operations: ['62-36=26', '8-6=2'] Exploring Operation: 26-2=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 44, 56, 97, 88 ]
82
[ "88/44=2", "97-56=41", "2*41=82" ]
Current State: 82:[44, 56, 97, 88], Operations: [] Exploring Operation: 88/44=2, Resulting Numbers: [56, 97, 2] Generated Node #2: [56, 97, 2] from Operation: 88/44=2 Current State: 82:[56, 97, 2], Operations: ['88/44=2'] Exploring Operation: 97-56=41, Resulting Numbers: [2, 41] Generated Node #3: [2, 41] from Operation: 97-56=41 Current State: 82:[2, 41], Operations: ['88/44=2', '97-56=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[44, 56, 97, 88], Operations: [] Exploring Operation: 97-56=41, Resulting Numbers: [44, 88, 41] Generated Node #0,0: 82:[44, 88, 41] Operation: 97-56=41 Exploring Operation: 97-88=9, Resulting Numbers: [44, 56, 9] Generated Node #0,1: 82:[44, 56, 9] Operation: 97-88=9 Exploring Operation: 88/44=2, Resulting Numbers: [56, 97, 2] Generated Node #0,2: 82:[56, 97, 2] Operation: 88/44=2 Exploring Operation: 88-56=32, Resulting Numbers: [44, 97, 32] Generated Node #0,3: 82:[44, 97, 32] Operation: 88-56=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[44, 88, 41], Operations: ['97-56=41'] Exploring Operation: 44-41=3, Resulting Numbers: [88, 3] Generated Node #0,0,0: 82:[88, 3] Operation: 44-41=3 Exploring Operation: 44+41=85, Resulting Numbers: [88, 85] Generated Node #0,0,1: 82:[88, 85] Operation: 44+41=85 Exploring Operation: 88/44=2, Resulting Numbers: [41, 2] Generated Node #0,0,2: 82:[41, 2] Operation: 88/44=2 Exploring Operation: 88-44=44, Resulting Numbers: [41, 44] Generated Node #0,0,3: 82:[41, 44] Operation: 88-44=44 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 82:[41, 2], Operations: ['97-56=41', '88/44=2'] Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,82 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,82 unequal: No Solution Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Moving to Node #0 Current State: 82:[44, 56, 97, 88], Operations: [] Exploring Operation: 97-56=41, Resulting Numbers: [44, 88, 41] Generated Node #0,0: 82:[44, 88, 41] Operation: 97-56=41 Moving to Node #0,0 Current State: 82:[44, 88, 41], Operations: ['97-56=41'] Exploring Operation: 88/44=2, Resulting Numbers: [41, 2] Generated Node #0,0,2: 82:[41, 2] Operation: 88/44=2 Moving to Node #0,0,2 Current State: 82:[41, 2], Operations: ['97-56=41', '88/44=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,82 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 98, 51, 49, 97 ]
23
[ "98/49=2", "97-51=46", "46/2=23" ]
Current State: 23:[98, 51, 49, 97], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [51, 97, 2] Generated Node #2: [51, 97, 2] from Operation: 98/49=2 Current State: 23:[51, 97, 2], Operations: ['98/49=2'] Exploring Operation: 97-51=46, Resulting Numbers: [2, 46] Generated Node #3: [2, 46] from Operation: 97-51=46 Current State: 23:[2, 46], Operations: ['98/49=2', '97-51=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[98, 51, 49, 97], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [51, 97, 2] Generated Node #0,0: 23:[51, 97, 2] Operation: 98/49=2 Exploring Operation: 98-51=47, Resulting Numbers: [49, 97, 47] Generated Node #0,1: 23:[49, 97, 47] Operation: 98-51=47 Exploring Operation: 97-51=46, Resulting Numbers: [98, 49, 46] Generated Node #0,2: 23:[98, 49, 46] Operation: 97-51=46 Exploring Operation: 98-97=1, Resulting Numbers: [51, 49, 1] Generated Node #0,3: 23:[51, 49, 1] Operation: 98-97=1 Moving to Node #0,3 Current State: 23:[51, 49, 1], Operations: ['98-97=1'] Exploring Operation: 49-1=48, Resulting Numbers: [51, 48] Generated Node #0,3,0: 23:[51, 48] Operation: 49-1=48 Exploring Operation: 51*1=51, Resulting Numbers: [49, 51] Generated Node #0,3,1: 23:[49, 51] Operation: 51*1=51 Exploring Operation: 51-1=50, Resulting Numbers: [49, 50] Generated Node #0,3,2: 23:[49, 50] Operation: 51-1=50 Exploring Operation: 51-49=2, Resulting Numbers: [1, 2] Generated Node #0,3,3: 23:[1, 2] Operation: 51-49=2 Moving to Node #0,0 Current State: 23:[51, 97, 2], Operations: ['98/49=2'] Exploring Operation: 51-2=49, Resulting Numbers: [97, 49] Generated Node #0,0,0: 23:[97, 49] Operation: 51-2=49 Exploring Operation: 51+2=53, Resulting Numbers: [97, 53] Generated Node #0,0,1: 23:[97, 53] Operation: 51+2=53 Exploring Operation: 97-2=95, Resulting Numbers: [51, 95] Generated Node #0,0,2: 23:[51, 95] Operation: 97-2=95 Exploring Operation: 97-51=46, Resulting Numbers: [2, 46] Generated Node #0,0,3: 23:[2, 46] Operation: 97-51=46 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 23:[2, 46], Operations: ['98/49=2', '97-51=46'] Exploring Operation: 2+46=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 2*46=92, Resulting Numbers: [92] 92,23 unequal: No Solution Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[98, 51, 49, 97], Operations: [] Exploring Operation: 98/49=2, Resulting Numbers: [51, 97, 2] Generated Node #0,0: 23:[51, 97, 2] Operation: 98/49=2 Moving to Node #0,0 Current State: 23:[51, 97, 2], Operations: ['98/49=2'] Exploring Operation: 97-51=46, Resulting Numbers: [2, 46] Generated Node #0,0,3: 23:[2, 46] Operation: 97-51=46 Moving to Node #0,0,3 Current State: 23:[2, 46], Operations: ['98/49=2', '97-51=46'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_4
sum_heuristic
[ 11, 50, 78, 22 ]
30
[ "22/11=2", "78-50=28", "2+28=30" ]
Current State: 30:[11, 50, 78, 22], Operations: [] Exploring Operation: 22/11=2, Resulting Numbers: [50, 78, 2] Generated Node #2: [50, 78, 2] from Operation: 22/11=2 Current State: 30:[50, 78, 2], Operations: ['22/11=2'] Exploring Operation: 78-50=28, Resulting Numbers: [2, 28] Generated Node #3: [2, 28] from Operation: 78-50=28 Current State: 30:[2, 28], Operations: ['22/11=2', '78-50=28'] Exploring Operation: 2+28=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[11, 50, 78, 22], Operations: [] Exploring Operation: 50-11=39, Resulting Numbers: [78, 22, 39] Generated Node #0,0: 30:[78, 22, 39] Operation: 50-11=39 Exploring Operation: 78-11=67, Resulting Numbers: [50, 22, 67] Generated Node #0,1: 30:[50, 22, 67] Operation: 78-11=67 Exploring Operation: 78-22=56, Resulting Numbers: [11, 50, 56] Generated Node #0,2: 30:[11, 50, 56] Operation: 78-22=56 Exploring Operation: 78-50=28, Resulting Numbers: [11, 22, 28] Generated Node #0,3: 30:[11, 22, 28] Operation: 78-50=28 Exploring Operation: 50-22=28, Resulting Numbers: [11, 78, 28] Generated Node #0,4: 30:[11, 78, 28] Operation: 50-22=28 Start Sub Search at level 1: Moving to Node #0,3 Current State: 30:[11, 22, 28], Operations: ['78-50=28'] Exploring Operation: 22-11=11, Resulting Numbers: [28, 11] Generated Node #0,3,0: 30:[28, 11] Operation: 22-11=11 Exploring Operation: 28-11=17, Resulting Numbers: [22, 17] Generated Node #0,3,1: 30:[22, 17] Operation: 28-11=17 Exploring Operation: 28-22=6, Resulting Numbers: [11, 6] Generated Node #0,3,2: 30:[11, 6] Operation: 28-22=6 Exploring Operation: 11+22=33, Resulting Numbers: [28, 33] Generated Node #0,3,3: 30:[28, 33] Operation: 11+22=33 Exploring Operation: 22/11=2, Resulting Numbers: [28, 2] Generated Node #0,3,4: 30:[28, 2] Operation: 22/11=2 Moving to Node #0,3,2 Current State: 30:[11, 6], Operations: ['78-50=28', '28-22=6'] Exploring Operation: 11*6=66, Resulting Numbers: [66] 66,30 unequal: No Solution Exploring Operation: 11+6=17, Resulting Numbers: [17] 17,30 unequal: No Solution Exploring Operation: 11-6=5, Resulting Numbers: [5] 5,30 unequal: No Solution Moving to Node #0,3,4 Current State: 30:[28, 2], Operations: ['78-50=28', '22/11=2'] Exploring Operation: 28*2=56, Resulting Numbers: [56] 56,30 unequal: No Solution Exploring Operation: 28/2=14, Resulting Numbers: [14] 14,30 unequal: No Solution Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[11, 50, 78, 22], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [11, 22, 28] Generated Node #0,3: 30:[11, 22, 28] Operation: 78-50=28 Moving to Node #0,3 Current State: 30:[11, 22, 28], Operations: ['78-50=28'] Exploring Operation: 22/11=2, Resulting Numbers: [28, 2] Generated Node #0,3,4: 30:[28, 2] Operation: 22/11=2 Moving to Node #0,3,4 Current State: 30:[28, 2], Operations: ['78-50=28', '22/11=2'] Exploring Operation: 28+2=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 1
0.982639
hs_5
sum_heuristic
[ 65, 46, 99, 96 ]
37
[ "65+46=111", "99-96=3", "111/3=37" ]
Current State: 37:[65, 46, 99, 96], Operations: [] Exploring Operation: 65+46=111, Resulting Numbers: [99, 96, 111] Generated Node #2: [99, 96, 111] from Operation: 65+46=111 Current State: 37:[99, 96, 111], Operations: ['65+46=111'] Exploring Operation: 99-96=3, Resulting Numbers: [111, 3] Generated Node #3: [111, 3] from Operation: 99-96=3 Current State: 37:[111, 3], Operations: ['65+46=111', '99-96=3'] Exploring Operation: 111/3=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[65, 46, 99, 96], Operations: [] Exploring Operation: 96-65=31, Resulting Numbers: [46, 99, 31] Generated Node #0,0: 37:[46, 99, 31] Operation: 96-65=31 Exploring Operation: 99-65=34, Resulting Numbers: [46, 96, 34] Generated Node #0,1: 37:[46, 96, 34] Operation: 99-65=34 Exploring Operation: 99-96=3, Resulting Numbers: [65, 46, 3] Generated Node #0,2: 37:[65, 46, 3] Operation: 99-96=3 Exploring Operation: 99-46=53, Resulting Numbers: [65, 96, 53] Generated Node #0,3: 37:[65, 96, 53] Operation: 99-46=53 Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[46, 96, 34], Operations: ['99-65=34'] Exploring Operation: 46-34=12, Resulting Numbers: [96, 12] Generated Node #0,1,0: 37:[96, 12] Operation: 46-34=12 Exploring Operation: 46+34=80, Resulting Numbers: [96, 80] Generated Node #0,1,1: 37:[96, 80] Operation: 46+34=80 Exploring Operation: 96-46=50, Resulting Numbers: [34, 50] Generated Node #0,1,2: 37:[34, 50] Operation: 96-46=50 Exploring Operation: 96-34=62, Resulting Numbers: [46, 62] Generated Node #0,1,3: 37:[46, 62] Operation: 96-34=62 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[34, 50], Operations: ['99-65=34', '96-46=50'] Exploring Operation: 34*50=1700, Resulting Numbers: [1700] 1700,37 unequal: No Solution Exploring Operation: 34+50=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 50-34=16, Resulting Numbers: [16] 16,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 37:[46, 62], Operations: ['99-65=34', '96-34=62'] Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,37 unequal: No Solution Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[96, 12], Operations: ['99-65=34', '46-34=12'] Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 96*12=1152, Resulting Numbers: [1152] 1152,37 unequal: No Solution Exploring Operation: 96+12=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[96, 80], Operations: ['99-65=34', '46+34=80'] Exploring Operation: 96-80=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 96*80=7680, Resulting Numbers: [7680] 7680,37 unequal: No Solution Exploring Operation: 96+80=176, Resulting Numbers: [176] 176,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[65, 46, 3], Operations: ['99-96=3'] Exploring Operation: 65+3=68, Resulting Numbers: [46, 68] Generated Node #0,2,0: 37:[46, 68] Operation: 65+3=68 Exploring Operation: 65-3=62, Resulting Numbers: [46, 62] Generated Node #0,2,1: 37:[46, 62] Operation: 65-3=62 Exploring Operation: 46+3=49, Resulting Numbers: [65, 49] Generated Node #0,2,2: 37:[65, 49] Operation: 46+3=49 Exploring Operation: 46-3=43, Resulting Numbers: [65, 43] Generated Node #0,2,3: 37:[65, 43] Operation: 46-3=43 Moving to Node #0,2,1 Current State: 37:[46, 62], Operations: ['99-96=3', '65-3=62'] Exploring Operation: 62-46=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 46*62=2852, Resulting Numbers: [2852] 2852,37 unequal: No Solution Exploring Operation: 46+62=108, Resulting Numbers: [108] 108,37 unequal: No Solution Moving to Node #0,2,3 Current State: 37:[65, 43], Operations: ['99-96=3', '46-3=43'] Exploring Operation: 65*43=2795, Resulting Numbers: [2795] 2795,37 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 65+43=108, Resulting Numbers: [108] 108,37 unequal: No Solution Moving to Node #0,2,2 Current State: 37:[65, 49], Operations: ['99-96=3', '46+3=49'] Exploring Operation: 65*49=3185, Resulting Numbers: [3185] 3185,37 unequal: No Solution Exploring Operation: 65-49=16, Resulting Numbers: [16] 16,37 unequal: No Solution Exploring Operation: 65+49=114, Resulting Numbers: [114] 114,37 unequal: No Solution Moving to Node #0,2,0 Current State: 37:[46, 68], Operations: ['99-96=3', '65+3=68'] Exploring Operation: 46*68=3128, Resulting Numbers: [3128] 3128,37 unequal: No Solution Exploring Operation: 46+68=114, Resulting Numbers: [114] 114,37 unequal: No Solution Exploring Operation: 68-46=22, Resulting Numbers: [22] 22,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[46, 99, 31], Operations: ['96-65=31'] Exploring Operation: 99-46=53, Resulting Numbers: [31, 53] Generated Node #0,0,0: 37:[31, 53] Operation: 99-46=53 Exploring Operation: 46+31=77, Resulting Numbers: [99, 77] Generated Node #0,0,1: 37:[99, 77] Operation: 46+31=77 Exploring Operation: 46-31=15, Resulting Numbers: [99, 15] Generated Node #0,0,2: 37:[99, 15] Operation: 46-31=15 Exploring Operation: 99-31=68, Resulting Numbers: [46, 68] Generated Node #0,0,3: 37:[46, 68] Operation: 99-31=68 Moving to Node #0,0,0 Current State: 37:[31, 53], Operations: ['96-65=31', '99-46=53'] Exploring Operation: 31+53=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 31*53=1643, Resulting Numbers: [1643] 1643,37 unequal: No Solution Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,37 unequal: No Solution Moving to Node #0,0,3 Current State: 37:[46, 68], Operations: ['96-65=31', '99-31=68'] Exploring Operation: 68-46=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 46+68=114, Resulting Numbers: [114] 114,37 unequal: No Solution Exploring Operation: 46*68=3128, Resulting Numbers: [3128] 3128,37 unequal: No Solution Moving to Node #0,0,2 Current State: 37:[99, 15], Operations: ['96-65=31', '46-31=15'] Exploring Operation: 99*15=1485, Resulting Numbers: [1485] 1485,37 unequal: No Solution Exploring Operation: 99-15=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 99+15=114, Resulting Numbers: [114] 114,37 unequal: No Solution Moving to Node #0,0,1 Current State: 37:[99, 77], Operations: ['96-65=31', '46+31=77'] Exploring Operation: 99*77=7623, Resulting Numbers: [7623] 7623,37 unequal: No Solution Exploring Operation: 99-77=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 99+77=176, Resulting Numbers: [176] 176,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[65, 96, 53], Operations: ['99-46=53'] Exploring Operation: 65-53=12, Resulting Numbers: [96, 12] Generated Node #0,3,0: 37:[96, 12] Operation: 65-53=12 Exploring Operation: 65+96=161, Resulting Numbers: [53, 161] Generated Node #0,3,1: 37:[53, 161] Operation: 65+96=161 Exploring Operation: 96-65=31, Resulting Numbers: [53, 31] Generated Node #0,3,2: 37:[53, 31] Operation: 96-65=31 Exploring Operation: 96-53=43, Resulting Numbers: [65, 43] Generated Node #0,3,3: 37:[65, 43] Operation: 96-53=43 Moving to Node #0,3,2 Current State: 37:[53, 31], Operations: ['99-46=53', '96-65=31'] Exploring Operation: 53-31=22, Resulting Numbers: [22] 22,37 unequal: No Solution Exploring Operation: 53+31=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 53*31=1643, Resulting Numbers: [1643] 1643,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[65, 43], Operations: ['99-46=53', '96-53=43'] Exploring Operation: 65+43=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 65*43=2795, Resulting Numbers: [2795] 2795,37 unequal: No Solution Exploring Operation: 65-43=22, Resulting Numbers: [22] 22,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[96, 12], Operations: ['99-46=53', '65-53=12'] Exploring Operation: 96-12=84, Resulting Numbers: [84] 84,37 unequal: No Solution Exploring Operation: 96+12=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 96/12=8, Resulting Numbers: [8] 8,37 unequal: No Solution Exploring Operation: 96*12=1152, Resulting Numbers: [1152] 1152,37 unequal: No Solution Moving to Node #0,3,1 Current State: 37:[53, 161], Operations: ['99-46=53', '65+96=161'] Exploring Operation: 53*161=8533, Resulting Numbers: [8533] 8533,37 unequal: No Solution Exploring Operation: 161-53=108, Resulting Numbers: [108] 108,37 unequal: No Solution Exploring Operation: 53+161=214, Resulting Numbers: [214] 214,37 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
[ 8, 81, 84, 62 ]
68
[ "81-62=19", "8*19=152", "152-84=68" ]
Current State: 68:[8, 81, 84, 62], Operations: [] Exploring Operation: 81-62=19, Resulting Numbers: [8, 84, 19] Generated Node #2: [8, 84, 19] from Operation: 81-62=19 Current State: 68:[8, 84, 19], Operations: ['81-62=19'] Exploring Operation: 8*19=152, Resulting Numbers: [84, 152] Generated Node #3: [84, 152] from Operation: 8*19=152 Current State: 68:[84, 152], Operations: ['81-62=19', '8*19=152'] Exploring Operation: 152-84=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[8, 81, 84, 62], Operations: [] Exploring Operation: 81-62=19, Resulting Numbers: [8, 84, 19] Generated Node #0,0: 68:[8, 84, 19] Operation: 81-62=19 Exploring Operation: 84-81=3, Resulting Numbers: [8, 62, 3] Generated Node #0,1: 68:[8, 62, 3] Operation: 84-81=3 Exploring Operation: 84-62=22, Resulting Numbers: [8, 81, 22] Generated Node #0,2: 68:[8, 81, 22] Operation: 84-62=22 Moving to Node #0,1 Current State: 68:[8, 62, 3], Operations: ['84-81=3'] Exploring Operation: 8+62=70, Resulting Numbers: [3, 70] Generated Node #0,1,0: 68:[3, 70] Operation: 8+62=70 Exploring Operation: 62+3=65, Resulting Numbers: [8, 65] Generated Node #0,1,1: 68:[8, 65] Operation: 62+3=65 Exploring Operation: 8-3=5, Resulting Numbers: [62, 5] Generated Node #0,1,2: 68:[62, 5] Operation: 8-3=5 Moving to Node #0,0 Current State: 68:[8, 84, 19], Operations: ['81-62=19'] Exploring Operation: 84-19=65, Resulting Numbers: [8, 65] Generated Node #0,0,0: 68:[8, 65] Operation: 84-19=65 Exploring Operation: 84-8=76, Resulting Numbers: [19, 76] Generated Node #0,0,1: 68:[19, 76] Operation: 84-8=76 Exploring Operation: 19-8=11, Resulting Numbers: [84, 11] Generated Node #0,0,2: 68:[84, 11] Operation: 19-8=11 Moving to Node #0,2 Current State: 68:[8, 81, 22], Operations: ['84-62=22'] Exploring Operation: 81-8=73, Resulting Numbers: [22, 73] Generated Node #0,2,0: 68:[22, 73] Operation: 81-8=73 Exploring Operation: 81-22=59, Resulting Numbers: [8, 59] Generated Node #0,2,1: 68:[8, 59] Operation: 81-22=59 Exploring Operation: 22-8=14, Resulting Numbers: [81, 14] Generated Node #0,2,2: 68:[81, 14] Operation: 22-8=14 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 68:[22, 73], Operations: ['84-62=22', '81-8=73'] Exploring Operation: 73-22=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 22*73=1606, Resulting Numbers: [1606] 1606,68 unequal: No Solution Exploring Operation: 22+73=95, Resulting Numbers: [95] 95,68 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 #0,2,1 Current State: 68:[8, 59], Operations: ['84-62=22', '81-22=59'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,68 unequal: No Solution Exploring Operation: 8*59=472, Resulting Numbers: [472] 472,68 unequal: No Solution Exploring Operation: 8+59=67, Resulting Numbers: [67] 67,68 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:[81, 14], Operations: ['84-62=22', '22-8=14'] Exploring Operation: 81*14=1134, Resulting Numbers: [1134] 1134,68 unequal: No Solution Exploring Operation: 81+14=95, Resulting Numbers: [95] 95,68 unequal: No Solution Exploring Operation: 81-14=67, Resulting Numbers: [67] 67,68 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: 68:[3, 70], Operations: ['84-81=3', '8+62=70'] Exploring Operation: 70-3=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 3+70=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 3*70=210, Resulting Numbers: [210] 210,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[62, 5], Operations: ['84-81=3', '8-3=5'] Exploring Operation: 62+5=67, Resulting Numbers: [67] 67,68 unequal: No Solution Exploring Operation: 62*5=310, Resulting Numbers: [310] 310,68 unequal: No Solution Exploring Operation: 62-5=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,1,1 Current State: 68:[8, 65], Operations: ['84-81=3', '62+3=65'] Exploring Operation: 8*65=520, Resulting Numbers: [520] 520,68 unequal: No Solution Exploring Operation: 8+65=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,0,0 Current State: 68:[8, 65], Operations: ['81-62=19', '84-19=65'] Exploring Operation: 8*65=520, Resulting Numbers: [520] 520,68 unequal: No Solution Exploring Operation: 8+65=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 65-8=57, Resulting Numbers: [57] 57,68 unequal: No Solution Moving to Node #0,0,1 Current State: 68:[19, 76], Operations: ['81-62=19', '84-8=76'] Exploring Operation: 76-19=57, Resulting Numbers: [57] 57,68 unequal: No Solution Exploring Operation: 19+76=95, Resulting Numbers: [95] 95,68 unequal: No Solution Exploring Operation: 76/19=4, Resulting Numbers: [4] 4,68 unequal: No Solution Moving to Node #0,0,2 Current State: 68:[84, 11], Operations: ['81-62=19', '19-8=11'] Exploring Operation: 84-11=73, Resulting Numbers: [73] 73,68 unequal: No Solution Exploring Operation: 84+11=95, Resulting Numbers: [95] 95,68 unequal: No Solution Exploring Operation: 84*11=924, Resulting Numbers: [924] 924,68 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 73, 22, 48, 87 ]
56
[ "73+22=95", "87-48=39", "95-39=56" ]
Current State: 56:[73, 22, 48, 87], Operations: [] Exploring Operation: 73+22=95, Resulting Numbers: [48, 87, 95] Generated Node #2: [48, 87, 95] from Operation: 73+22=95 Current State: 56:[48, 87, 95], Operations: ['73+22=95'] Exploring Operation: 87-48=39, Resulting Numbers: [95, 39] Generated Node #3: [95, 39] from Operation: 87-48=39 Current State: 56:[95, 39], Operations: ['73+22=95', '87-48=39'] Exploring Operation: 95-39=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[73, 22, 48, 87], Operations: [] Exploring Operation: 87-22=65, Resulting Numbers: [73, 48, 65] Generated Node #0,0: 56:[73, 48, 65] Operation: 87-22=65 Exploring Operation: 87-73=14, Resulting Numbers: [22, 48, 14] Generated Node #0,1: 56:[22, 48, 14] Operation: 87-73=14 Start Sub Search at level 1: Moving to Node #0,1 Current State: 56:[22, 48, 14], Operations: ['87-73=14'] Exploring Operation: 48-22=26, Resulting Numbers: [14, 26] Generated Node #0,1,0: 56:[14, 26] Operation: 48-22=26 Exploring Operation: 22-14=8, Resulting Numbers: [48, 8] Generated Node #0,1,1: 56:[48, 8] Operation: 22-14=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 56:[14, 26], Operations: ['87-73=14', '48-22=26'] Exploring Operation: 14+26=40, Resulting Numbers: [40] 40,56 unequal: No Solution Exploring Operation: 26-14=12, Resulting Numbers: [12] 12,56 unequal: No Solution No 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: 56:[48, 8], Operations: ['87-73=14', '22-14=8'] Exploring Operation: 48/8=6, Resulting Numbers: [6] 6,56 unequal: No Solution Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[73, 22, 48, 87], Operations: [] Exploring Operation: 87-73=14, Resulting Numbers: [22, 48, 14] Generated Node #0,1: 56:[22, 48, 14] Operation: 87-73=14 Moving to Node #0,1 Current State: 56:[22, 48, 14], Operations: ['87-73=14'] Exploring Operation: 22-14=8, Resulting Numbers: [48, 8] Generated Node #0,1,1: 56:[48, 8] Operation: 22-14=8 Moving to Node #0,1,1 Current State: 56:[48, 8], Operations: ['87-73=14', '22-14=8'] Exploring Operation: 48+8=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 83, 66, 4, 2 ]
41
[ "66-4=62", "2*62=124", "124-83=41" ]
Current State: 41:[83, 66, 4, 2], Operations: [] Exploring Operation: 66-4=62, Resulting Numbers: [83, 2, 62] Generated Node #2: [83, 2, 62] from Operation: 66-4=62 Current State: 41:[83, 2, 62], Operations: ['66-4=62'] Exploring Operation: 2*62=124, Resulting Numbers: [83, 124] Generated Node #3: [83, 124] from Operation: 2*62=124 Current State: 41:[83, 124], Operations: ['66-4=62', '2*62=124'] Exploring Operation: 124-83=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[83, 66, 4, 2], Operations: [] Exploring Operation: 66/2=33, Resulting Numbers: [83, 4, 33] Generated Node #0,0: 41:[83, 4, 33] Operation: 66/2=33 Exploring Operation: 83-66=17, Resulting Numbers: [4, 2, 17] Generated Node #0,1: 41:[4, 2, 17] Operation: 83-66=17 Exploring Operation: 83-4=79, Resulting Numbers: [66, 2, 79] Generated Node #0,2: 41:[66, 2, 79] Operation: 83-4=79 Exploring Operation: 83-2=81, Resulting Numbers: [66, 4, 81] Generated Node #0,3: 41:[66, 4, 81] Operation: 83-2=81 Exploring Operation: 4*2=8, Resulting Numbers: [83, 66, 8] Generated Node #0,4: 41:[83, 66, 8] Operation: 4*2=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[83, 4, 33], Operations: ['66/2=33'] Exploring Operation: 4+33=37, Resulting Numbers: [83, 37] Generated Node #0,0,0: 41:[83, 37] Operation: 4+33=37 Exploring Operation: 83-33=50, Resulting Numbers: [4, 50] Generated Node #0,0,1: 41:[4, 50] Operation: 83-33=50 Exploring Operation: 83+4=87, Resulting Numbers: [33, 87] Generated Node #0,0,2: 41:[33, 87] Operation: 83+4=87 Exploring Operation: 33-4=29, Resulting Numbers: [83, 29] Generated Node #0,0,3: 41:[83, 29] Operation: 33-4=29 Exploring Operation: 83-4=79, Resulting Numbers: [33, 79] Generated Node #0,0,4: 41:[33, 79] Operation: 83-4=79 Moving to Node #0,0,0 Current State: 41:[83, 37], Operations: ['66/2=33', '4+33=37'] Exploring Operation: 83*37=3071, Resulting Numbers: [3071] 3071,41 unequal: No Solution Exploring Operation: 83-37=46, Resulting Numbers: [46] 46,41 unequal: No Solution Exploring Operation: 83+37=120, Resulting Numbers: [120] 120,41 unequal: No Solution Moving to Node #0,0,4 Current State: 41:[33, 79], Operations: ['66/2=33', '83-4=79'] Exploring Operation: 33*79=2607, Resulting Numbers: [2607] 2607,41 unequal: No Solution Exploring Operation: 33+79=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,41 unequal: No Solution Moving to Node #0,0,1 Current State: 41:[4, 50], Operations: ['66/2=33', '83-33=50'] Exploring Operation: 4+50=54, Resulting Numbers: [54] 54,41 unequal: No Solution Exploring Operation: 4*50=200, Resulting Numbers: [200] 200,41 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,41 unequal: No Solution Moving to Node #0,0,2 Current State: 41:[33, 87], Operations: ['66/2=33', '83+4=87'] Exploring Operation: 33*87=2871, Resulting Numbers: [2871] 2871,41 unequal: No Solution Exploring Operation: 33+87=120, Resulting Numbers: [120] 120,41 unequal: No Solution Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,41 unequal: No Solution Moving to Node #0,0,3 Current State: 41:[83, 29], Operations: ['66/2=33', '33-4=29'] Exploring Operation: 83+29=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 83*29=2407, Resulting Numbers: [2407] 2407,41 unequal: No Solution Exploring Operation: 83-29=54, Resulting Numbers: [54] 54,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[4, 2, 17], Operations: ['83-66=17'] Exploring Operation: 4+17=21, Resulting Numbers: [2, 21] Generated Node #0,1,0: 41:[2, 21] Operation: 4+17=21 Exploring Operation: 4*2=8, Resulting Numbers: [17, 8] Generated Node #0,1,1: 41:[17, 8] Operation: 4*2=8 Exploring Operation: 4+2=6, Resulting Numbers: [17, 6] Generated Node #0,1,2: 41:[17, 6] Operation: 4+2=6 Exploring Operation: 2*17=34, Resulting Numbers: [4, 34] Generated Node #0,1,3: 41:[4, 34] Operation: 2*17=34 Exploring Operation: 2+17=19, Resulting Numbers: [4, 19] Generated Node #0,1,4: 41:[4, 19] Operation: 2+17=19 Moving to Node #0,1,3 Current State: 41:[4, 34], Operations: ['83-66=17', '2*17=34'] Exploring Operation: 34-4=30, Resulting Numbers: [30] 30,41 unequal: No Solution Exploring Operation: 4*34=136, Resulting Numbers: [136] 136,41 unequal: No Solution Exploring Operation: 4+34=38, Resulting Numbers: [38] 38,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[17, 8], Operations: ['83-66=17', '4*2=8'] Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 17+8=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 17*8=136, Resulting Numbers: [136] 136,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[2, 21], Operations: ['83-66=17', '4+17=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,41 unequal: No Solution Exploring Operation: 2+21=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[17, 6], Operations: ['83-66=17', '4+2=6'] Exploring Operation: 17+6=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 17-6=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 17*6=102, Resulting Numbers: [102] 102,41 unequal: No Solution Moving to Node #0,1,4 Current State: 41:[4, 19], Operations: ['83-66=17', '2+17=19'] Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,41 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,41 unequal: No Solution Exploring Operation: 19-4=15, Resulting Numbers: [15] 15,41 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 #0,4 Current State: 41:[83, 66, 8], Operations: ['4*2=8'] Exploring Operation: 83+8=91, Resulting Numbers: [66, 91] Generated Node #0,4,0: 41:[66, 91] Operation: 83+8=91 Exploring Operation: 83-8=75, Resulting Numbers: [66, 75] Generated Node #0,4,1: 41:[66, 75] Operation: 83-8=75 Exploring Operation: 66+8=74, Resulting Numbers: [83, 74] Generated Node #0,4,2: 41:[83, 74] Operation: 66+8=74 Exploring Operation: 83-66=17, Resulting Numbers: [8, 17] Generated Node #0,4,3: 41:[8, 17] Operation: 83-66=17 Exploring Operation: 66-8=58, Resulting Numbers: [83, 58] Generated Node #0,4,4: 41:[83, 58] Operation: 66-8=58 Moving to Node #0,4,3 Current State: 41:[8, 17], Operations: ['4*2=8', '83-66=17'] Exploring Operation: 8+17=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 17-8=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 8*17=136, Resulting Numbers: [136] 136,41 unequal: No Solution Moving to Node #0,4,4 Current State: 41:[83, 58], Operations: ['4*2=8', '66-8=58'] Exploring Operation: 83-58=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 83*58=4814, Resulting Numbers: [4814] 4814,41 unequal: No Solution Exploring Operation: 83+58=141, Resulting Numbers: [141] 141,41 unequal: No Solution Moving to Node #0,4,1 Current State: 41:[66, 75], Operations: ['4*2=8', '83-8=75'] Exploring Operation: 66+75=141, Resulting Numbers: [141] 141,41 unequal: No Solution Exploring Operation: 75-66=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 66*75=4950, Resulting Numbers: [4950] 4950,41 unequal: No Solution Moving to Node #0,4,0 Current State: 41:[66, 91], Operations: ['4*2=8', '83+8=91'] Exploring Operation: 66+91=157, Resulting Numbers: [157] 157,41 unequal: No Solution Exploring Operation: 91-66=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 66*91=6006, Resulting Numbers: [6006] 6006,41 unequal: No Solution Moving to Node #0,4,2 Current State: 41:[83, 74], Operations: ['4*2=8', '66+8=74'] Exploring Operation: 83*74=6142, Resulting Numbers: [6142] 6142,41 unequal: No Solution Exploring Operation: 83-74=9, Resulting Numbers: [9] 9,41 unequal: No Solution Exploring Operation: 83+74=157, Resulting Numbers: [157] 157,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[66, 2, 79], Operations: ['83-4=79'] Exploring Operation: 66/2=33, Resulting Numbers: [79, 33] Generated Node #0,2,0: 41:[79, 33] Operation: 66/2=33 Exploring Operation: 66-2=64, Resulting Numbers: [79, 64] Generated Node #0,2,1: 41:[79, 64] Operation: 66-2=64 Exploring Operation: 79-2=77, Resulting Numbers: [66, 77] Generated Node #0,2,2: 41:[66, 77] Operation: 79-2=77 Exploring Operation: 66+2=68, Resulting Numbers: [79, 68] Generated Node #0,2,3: 41:[79, 68] Operation: 66+2=68 Exploring Operation: 2+79=81, Resulting Numbers: [66, 81] Generated Node #0,2,4: 41:[66, 81] Operation: 2+79=81 Moving to Node #0,2,0 Current State: 41:[79, 33], Operations: ['83-4=79', '66/2=33'] Exploring Operation: 79*33=2607, Resulting Numbers: [2607] 2607,41 unequal: No Solution Exploring Operation: 79+33=112, Resulting Numbers: [112] 112,41 unequal: No Solution Exploring Operation: 79-33=46, Resulting Numbers: [46] 46,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[66, 77], Operations: ['83-4=79', '79-2=77'] Exploring Operation: 66*77=5082, Resulting Numbers: [5082] 5082,41 unequal: No Solution Exploring Operation: 66+77=143, Resulting Numbers: [143] 143,41 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[79, 64], Operations: ['83-4=79', '66-2=64'] Exploring Operation: 79-64=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 79+64=143, Resulting Numbers: [143] 143,41 unequal: No Solution Exploring Operation: 79*64=5056, Resulting Numbers: [5056] 5056,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[79, 68], Operations: ['83-4=79', '66+2=68'] Exploring Operation: 79-68=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 79+68=147, Resulting Numbers: [147] 147,41 unequal: No Solution Exploring Operation: 79*68=5372, Resulting Numbers: [5372] 5372,41 unequal: No Solution Moving to Node #0,2,4 Current State: 41:[66, 81], Operations: ['83-4=79', '2+79=81'] Exploring Operation: 81-66=15, Resulting Numbers: [15] 15,41 unequal: No Solution Exploring Operation: 66+81=147, Resulting Numbers: [147] 147,41 unequal: No Solution Exploring Operation: 66*81=5346, Resulting Numbers: [5346] 5346,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[66, 4, 81], Operations: ['83-2=81'] Exploring Operation: 4+81=85, Resulting Numbers: [66, 85] Generated Node #0,3,0: 41:[66, 85] Operation: 4+81=85 Exploring Operation: 81-4=77, Resulting Numbers: [66, 77] Generated Node #0,3,1: 41:[66, 77] Operation: 81-4=77 Exploring Operation: 66+4=70, Resulting Numbers: [81, 70] Generated Node #0,3,2: 41:[81, 70] Operation: 66+4=70 Exploring Operation: 81-66=15, Resulting Numbers: [4, 15] Generated Node #0,3,3: 41:[4, 15] Operation: 81-66=15 Exploring Operation: 66-4=62, Resulting Numbers: [81, 62] Generated Node #0,3,4: 41:[81, 62] Operation: 66-4=62 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 41:[66, 77], Operations: ['83-2=81', '81-4=77'] Exploring Operation: 66*77=5082, Resulting Numbers: [5082] 5082,41 unequal: No Solution Exploring Operation: 66+77=143, Resulting Numbers: [143] 143,41 unequal: No Solution Exploring Operation: 77-66=11, Resulting Numbers: [11] 11,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 41:[81, 62], Operations: ['83-2=81', '66-4=62'] Exploring Operation: 81+62=143, Resulting Numbers: [143] 143,41 unequal: No Solution Exploring Operation: 81-62=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 81*62=5022, Resulting Numbers: [5022] 5022,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 41:[4, 15], Operations: ['83-2=81', '81-66=15'] Exploring Operation: 15-4=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 4+15=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 4*15=60, Resulting Numbers: [60] 60,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 41:[66, 85], Operations: ['83-2=81', '4+81=85'] Exploring Operation: 85-66=19, Resulting Numbers: [19] 19,41 unequal: No Solution Exploring Operation: 66+85=151, Resulting Numbers: [151] 151,41 unequal: No Solution Exploring Operation: 66*85=5610, Resulting Numbers: [5610] 5610,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 41:[81, 70], Operations: ['83-2=81', '66+4=70'] Exploring Operation: 81-70=11, Resulting Numbers: [11] 11,41 unequal: No Solution Exploring Operation: 81+70=151, Resulting Numbers: [151] 151,41 unequal: No Solution Exploring Operation: 81*70=5670, Resulting Numbers: [5670] 5670,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 31, 90, 85, 87 ]
28
[ "87-85=2", "31*2=62", "90-62=28" ]
Current State: 28:[31, 90, 85, 87], Operations: [] Exploring Operation: 87-85=2, Resulting Numbers: [31, 90, 2] Generated Node #2: [31, 90, 2] from Operation: 87-85=2 Current State: 28:[31, 90, 2], Operations: ['87-85=2'] Exploring Operation: 31*2=62, Resulting Numbers: [90, 62] Generated Node #3: [90, 62] from Operation: 31*2=62 Current State: 28:[90, 62], Operations: ['87-85=2', '31*2=62'] Exploring Operation: 90-62=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[31, 90, 85, 87], Operations: [] Exploring Operation: 90-87=3, Resulting Numbers: [31, 85, 3] Generated Node #0,0: 28:[31, 85, 3] Operation: 90-87=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[31, 85, 3], Operations: ['90-87=3'] Exploring Operation: 85-31=54, Resulting Numbers: [3, 54] Generated Node #0,0,0: 28:[3, 54] Operation: 85-31=54 Moving to Node #0,0,0 Current State: 28:[3, 54], Operations: ['90-87=3', '85-31=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,28 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 19, 84, 11, 72 ]
42
[ "19+84=103", "72-11=61", "103-61=42" ]
Current State: 42:[19, 84, 11, 72], Operations: [] Exploring Operation: 19+84=103, Resulting Numbers: [11, 72, 103] Generated Node #2: [11, 72, 103] from Operation: 19+84=103 Current State: 42:[11, 72, 103], Operations: ['19+84=103'] Exploring Operation: 72-11=61, Resulting Numbers: [103, 61] Generated Node #3: [103, 61] from Operation: 72-11=61 Current State: 42:[103, 61], Operations: ['19+84=103', '72-11=61'] Exploring Operation: 103-61=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[19, 84, 11, 72], Operations: [] Exploring Operation: 84-72=12, Resulting Numbers: [19, 11, 12] Generated Node #0,0: 42:[19, 11, 12] Operation: 84-72=12 Moving to Node #0,0 Current State: 42:[19, 11, 12], Operations: ['84-72=12'] Exploring Operation: 19-11=8, Resulting Numbers: [12, 8] Generated Node #0,0,0: 42:[12, 8] Operation: 19-11=8 Moving to Node #0,0,0 Current State: 42:[12, 8], Operations: ['84-72=12', '19-11=8'] Exploring Operation: 12+8=20, Resulting Numbers: [20] 20,42 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 78, 87, 24, 75 ]
76
[ "87-75=12", "24/12=2", "78-2=76" ]
Current State: 76:[78, 87, 24, 75], Operations: [] Exploring Operation: 87-75=12, Resulting Numbers: [78, 24, 12] Generated Node #2: [78, 24, 12] from Operation: 87-75=12 Current State: 76:[78, 24, 12], Operations: ['87-75=12'] Exploring Operation: 24/12=2, Resulting Numbers: [78, 2] Generated Node #3: [78, 2] from Operation: 24/12=2 Current State: 76:[78, 2], Operations: ['87-75=12', '24/12=2'] Exploring Operation: 78-2=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[78, 87, 24, 75], Operations: [] Exploring Operation: 87-78=9, Resulting Numbers: [24, 75, 9] Generated Node #0,0: 76:[24, 75, 9] Operation: 87-78=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[24, 75, 9], Operations: ['87-78=9'] Exploring Operation: 24-9=15, Resulting Numbers: [75, 15] Generated Node #0,0,0: 76:[75, 15] Operation: 24-9=15 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[75, 15], Operations: ['87-78=9', '24-9=15'] Exploring Operation: 75/15=5, Resulting Numbers: [5] 5,76 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
[ 25, 2, 12, 94 ]
94
[ "2*12=24", "25-24=1", "94*1=94" ]
Current State: 94:[25, 2, 12, 94], Operations: [] Exploring Operation: 2*12=24, Resulting Numbers: [25, 94, 24] Generated Node #2: [25, 94, 24] from Operation: 2*12=24 Current State: 94:[25, 94, 24], Operations: ['2*12=24'] Exploring Operation: 25-24=1, Resulting Numbers: [94, 1] Generated Node #3: [94, 1] from Operation: 25-24=1 Current State: 94:[94, 1], Operations: ['2*12=24', '25-24=1'] Exploring Operation: 94*1=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[25, 2, 12, 94], Operations: [] Exploring Operation: 25+2=27, Resulting Numbers: [12, 94, 27] Generated Node #0,0: 94:[12, 94, 27] Operation: 25+2=27 Exploring Operation: 12/2=6, Resulting Numbers: [25, 94, 6] Generated Node #0,1: 94:[25, 94, 6] Operation: 12/2=6 Exploring Operation: 25*2=50, Resulting Numbers: [12, 94, 50] Generated Node #0,2: 94:[12, 94, 50] Operation: 25*2=50 Exploring Operation: 25-12=13, Resulting Numbers: [2, 94, 13] Generated Node #0,3: 94:[2, 94, 13] Operation: 25-12=13 Exploring Operation: 25+12=37, Resulting Numbers: [2, 94, 37] Generated Node #0,4: 94:[2, 94, 37] Operation: 25+12=37 Start Sub Search at level 1: Moving to Node #0,4 Current State: 94:[2, 94, 37], Operations: ['25+12=37'] Exploring Operation: 94/2=47, Resulting Numbers: [37, 47] Generated Node #0,4,0: 94:[37, 47] Operation: 94/2=47 Exploring Operation: 2+37=39, Resulting Numbers: [94, 39] Generated Node #0,4,1: 94:[94, 39] Operation: 2+37=39 Exploring Operation: 94-37=57, Resulting Numbers: [2, 57] Generated Node #0,4,2: 94:[2, 57] Operation: 94-37=57 Exploring Operation: 2+94=96, Resulting Numbers: [37, 96] Generated Node #0,4,3: 94:[37, 96] Operation: 2+94=96 Exploring Operation: 94-2=92, Resulting Numbers: [37, 92] Generated Node #0,4,4: 94:[37, 92] Operation: 94-2=92 Moving to Node #0,4,1 Current State: 94:[94, 39], Operations: ['25+12=37', '2+37=39'] Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,94 unequal: No Solution Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,94 unequal: No Solution Moving to Node #0,4,2 Current State: 94:[2, 57], Operations: ['25+12=37', '94-37=57'] Exploring Operation: 2+57=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 57-2=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 2*57=114, Resulting Numbers: [114] 114,94 unequal: No Solution Moving to Node #0,4,0 Current State: 94:[37, 47], Operations: ['25+12=37', '94/2=47'] Exploring Operation: 47-37=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 37+47=84, Resulting Numbers: [84] 84,94 unequal: No Solution Exploring Operation: 37*47=1739, Resulting Numbers: [1739] 1739,94 unequal: No Solution Moving to Node #0,4,3 Current State: 94:[37, 96], Operations: ['25+12=37', '2+94=96'] Exploring Operation: 37*96=3552, Resulting Numbers: [3552] 3552,94 unequal: No Solution Exploring Operation: 37+96=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 96-37=59, Resulting Numbers: [59] 59,94 unequal: No Solution Moving to Node #0,4,4 Current State: 94:[37, 92], Operations: ['25+12=37', '94-2=92'] Exploring Operation: 37*92=3404, Resulting Numbers: [3404] 3404,94 unequal: No Solution Exploring Operation: 37+92=129, Resulting Numbers: [129] 129,94 unequal: No Solution Exploring Operation: 92-37=55, Resulting Numbers: [55] 55,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[2, 94, 13], Operations: ['25-12=13'] Exploring Operation: 94-2=92, Resulting Numbers: [13, 92] Generated Node #0,3,0: 94:[13, 92] Operation: 94-2=92 Exploring Operation: 2+94=96, Resulting Numbers: [13, 96] Generated Node #0,3,1: 94:[13, 96] Operation: 2+94=96 Exploring Operation: 94/2=47, Resulting Numbers: [13, 47] Generated Node #0,3,2: 94:[13, 47] Operation: 94/2=47 Exploring Operation: 13-2=11, Resulting Numbers: [94, 11] Generated Node #0,3,3: 94:[94, 11] Operation: 13-2=11 Exploring Operation: 2+13=15, Resulting Numbers: [94, 15] Generated Node #0,3,4: 94:[94, 15] Operation: 2+13=15 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 94:[94, 11], Operations: ['25-12=13', '13-2=11'] Exploring Operation: 94*11=1034, Resulting Numbers: [1034] 1034,94 unequal: No Solution Exploring Operation: 94+11=105, Resulting Numbers: [105] 105,94 unequal: No Solution Exploring Operation: 94-11=83, Resulting Numbers: [83] 83,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 94:[13, 47], Operations: ['25-12=13', '94/2=47'] Exploring Operation: 13*47=611, Resulting Numbers: [611] 611,94 unequal: No Solution Exploring Operation: 47-13=34, Resulting Numbers: [34] 34,94 unequal: No Solution Exploring Operation: 13+47=60, Resulting Numbers: [60] 60,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 94:[13, 92], Operations: ['25-12=13', '94-2=92'] Exploring Operation: 13*92=1196, Resulting Numbers: [1196] 1196,94 unequal: No Solution Exploring Operation: 92-13=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 13+92=105, Resulting Numbers: [105] 105,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 94:[13, 96], Operations: ['25-12=13', '2+94=96'] Exploring Operation: 13+96=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 13*96=1248, Resulting Numbers: [1248] 1248,94 unequal: No Solution Exploring Operation: 96-13=83, Resulting Numbers: [83] 83,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 94:[94, 15], Operations: ['25-12=13', '2+13=15'] Exploring Operation: 94+15=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 94*15=1410, Resulting Numbers: [1410] 1410,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[12, 94, 50], Operations: ['25*2=50'] Exploring Operation: 50-12=38, Resulting Numbers: [94, 38] Generated Node #0,2,0: 94:[94, 38] Operation: 50-12=38 Exploring Operation: 12+50=62, Resulting Numbers: [94, 62] Generated Node #0,2,1: 94:[94, 62] Operation: 12+50=62 Exploring Operation: 94-12=82, Resulting Numbers: [50, 82] Generated Node #0,2,2: 94:[50, 82] Operation: 94-12=82 Exploring Operation: 94-50=44, Resulting Numbers: [12, 44] Generated Node #0,2,3: 94:[12, 44] Operation: 94-50=44 Exploring Operation: 12+94=106, Resulting Numbers: [50, 106] Generated Node #0,2,4: 94:[50, 106] Operation: 12+94=106 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 94:[94, 38], Operations: ['25*2=50', '50-12=38'] Exploring Operation: 94+38=132, Resulting Numbers: [132] 132,94 unequal: No Solution Exploring Operation: 94-38=56, Resulting Numbers: [56] 56,94 unequal: No Solution Exploring Operation: 94*38=3572, Resulting Numbers: [3572] 3572,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 94:[12, 44], Operations: ['25*2=50', '94-50=44'] Exploring Operation: 12*44=528, Resulting Numbers: [528] 528,94 unequal: No Solution Exploring Operation: 44-12=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 12+44=56, Resulting Numbers: [56] 56,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 94:[94, 62], Operations: ['25*2=50', '12+50=62'] Exploring Operation: 94*62=5828, Resulting Numbers: [5828] 5828,94 unequal: No Solution Exploring Operation: 94+62=156, Resulting Numbers: [156] 156,94 unequal: No Solution Exploring Operation: 94-62=32, Resulting Numbers: [32] 32,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 94:[50, 82], Operations: ['25*2=50', '94-12=82'] Exploring Operation: 82-50=32, Resulting Numbers: [32] 32,94 unequal: No Solution Exploring Operation: 50+82=132, Resulting Numbers: [132] 132,94 unequal: No Solution Exploring Operation: 50*82=4100, Resulting Numbers: [4100] 4100,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 94:[50, 106], Operations: ['25*2=50', '12+94=106'] Exploring Operation: 50+106=156, Resulting Numbers: [156] 156,94 unequal: No Solution Exploring Operation: 50*106=5300, Resulting Numbers: [5300] 5300,94 unequal: No Solution Exploring Operation: 106-50=56, Resulting Numbers: [56] 56,94 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 94:[25, 94, 6], Operations: ['12/2=6'] Exploring Operation: 25+6=31, Resulting Numbers: [94, 31] Generated Node #0,1,0: 94:[94, 31] Operation: 25+6=31 Exploring Operation: 25-6=19, Resulting Numbers: [94, 19] Generated Node #0,1,1: 94:[94, 19] Operation: 25-6=19 Exploring Operation: 94+6=100, Resulting Numbers: [25, 100] Generated Node #0,1,2: 94:[25, 100] Operation: 94+6=100 Exploring Operation: 94-25=69, Resulting Numbers: [6, 69] Generated Node #0,1,3: 94:[6, 69] Operation: 94-25=69 Exploring Operation: 94-6=88, Resulting Numbers: [25, 88] Generated Node #0,1,4: 94:[25, 88] Operation: 94-6=88 Moving to Node #0,1,0 Current State: 94:[94, 31], Operations: ['12/2=6', '25+6=31'] Exploring Operation: 94*31=2914, Resulting Numbers: [2914] 2914,94 unequal: No Solution Exploring Operation: 94+31=125, Resulting Numbers: [125] 125,94 unequal: No Solution Exploring Operation: 94-31=63, Resulting Numbers: [63] 63,94 unequal: No Solution Moving to Node #0,1,1 Current State: 94:[94, 19], Operations: ['12/2=6', '25-6=19'] Exploring Operation: 94-19=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 94*19=1786, Resulting Numbers: [1786] 1786,94 unequal: No Solution Exploring Operation: 94+19=113, Resulting Numbers: [113] 113,94 unequal: No Solution Moving to Node #0,1,3 Current State: 94:[6, 69], Operations: ['12/2=6', '94-25=69'] Exploring Operation: 6+69=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 6*69=414, Resulting Numbers: [414] 414,94 unequal: No Solution Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,94 unequal: No Solution Moving to Node #0,1,2 Current State: 94:[25, 100], Operations: ['12/2=6', '94+6=100'] Exploring Operation: 100/25=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 25+100=125, Resulting Numbers: [125] 125,94 unequal: No Solution Exploring Operation: 100-25=75, Resulting Numbers: [75] 75,94 unequal: No Solution Exploring Operation: 25*100=2500, Resulting Numbers: [2500] 2500,94 unequal: No Solution Moving to Node #0,1,4 Current State: 94:[25, 88], Operations: ['12/2=6', '94-6=88'] Exploring Operation: 25*88=2200, Resulting Numbers: [2200] 2200,94 unequal: No Solution Exploring Operation: 88-25=63, Resulting Numbers: [63] 63,94 unequal: No Solution Exploring Operation: 25+88=113, Resulting Numbers: [113] 113,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[12, 94, 27], Operations: ['25+2=27'] Exploring Operation: 94-12=82, Resulting Numbers: [27, 82] Generated Node #0,0,0: 94:[27, 82] Operation: 94-12=82 Exploring Operation: 12+27=39, Resulting Numbers: [94, 39] Generated Node #0,0,1: 94:[94, 39] Operation: 12+27=39 Exploring Operation: 27-12=15, Resulting Numbers: [94, 15] Generated Node #0,0,2: 94:[94, 15] Operation: 27-12=15 Exploring Operation: 12+94=106, Resulting Numbers: [27, 106] Generated Node #0,0,3: 94:[27, 106] Operation: 12+94=106 Exploring Operation: 94-27=67, Resulting Numbers: [12, 67] Generated Node #0,0,4: 94:[12, 67] Operation: 94-27=67 Moving to Node #0,0,1 Current State: 94:[94, 39], Operations: ['25+2=27', '12+27=39'] Exploring Operation: 94+39=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 94*39=3666, Resulting Numbers: [3666] 3666,94 unequal: No Solution Exploring Operation: 94-39=55, Resulting Numbers: [55] 55,94 unequal: No Solution Moving to Node #0,0,2 Current State: 94:[94, 15], Operations: ['25+2=27', '27-12=15'] Exploring Operation: 94*15=1410, Resulting Numbers: [1410] 1410,94 unequal: No Solution Exploring Operation: 94+15=109, Resulting Numbers: [109] 109,94 unequal: No Solution Exploring Operation: 94-15=79, Resulting Numbers: [79] 79,94 unequal: No Solution Moving to Node #0,0,4 Current State: 94:[12, 67], Operations: ['25+2=27', '94-27=67'] Exploring Operation: 12+67=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 67-12=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 12*67=804, Resulting Numbers: [804] 804,94 unequal: No Solution Moving to Node #0,0,0 Current State: 94:[27, 82], Operations: ['25+2=27', '94-12=82'] Exploring Operation: 27*82=2214, Resulting Numbers: [2214] 2214,94 unequal: No Solution Exploring Operation: 82-27=55, Resulting Numbers: [55] 55,94 unequal: No Solution Exploring Operation: 27+82=109, Resulting Numbers: [109] 109,94 unequal: No Solution Moving to Node #0,0,3 Current State: 94:[27, 106], Operations: ['25+2=27', '12+94=106'] Exploring Operation: 27+106=133, Resulting Numbers: [133] 133,94 unequal: No Solution Exploring Operation: 106-27=79, Resulting Numbers: [79] 79,94 unequal: No Solution Exploring Operation: 27*106=2862, Resulting Numbers: [2862] 2862,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 57, 36, 51, 38 ]
27
[ "36*38=1368", "1368/57=24", "51-24=27" ]
Current State: 27:[57, 36, 51, 38], Operations: [] Exploring Operation: 36*38=1368, Resulting Numbers: [57, 51, 1368] Generated Node #2: [57, 51, 1368] from Operation: 36*38=1368 Current State: 27:[57, 51, 1368], Operations: ['36*38=1368'] Exploring Operation: 1368/57=24, Resulting Numbers: [51, 24] Generated Node #3: [51, 24] from Operation: 1368/57=24 Current State: 27:[51, 24], Operations: ['36*38=1368', '1368/57=24'] Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[57, 36, 51, 38], Operations: [] Exploring Operation: 57-51=6, Resulting Numbers: [36, 38, 6] Generated Node #0,0: 27:[36, 38, 6] Operation: 57-51=6 Exploring Operation: 57-38=19, Resulting Numbers: [36, 51, 19] Generated Node #0,1: 27:[36, 51, 19] Operation: 57-38=19 Exploring Operation: 57-36=21, Resulting Numbers: [51, 38, 21] Generated Node #0,2: 27:[51, 38, 21] Operation: 57-36=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[36, 38, 6], Operations: ['57-51=6'] Exploring Operation: 36-6=30, Resulting Numbers: [38, 30] Generated Node #0,0,0: 27:[38, 30] Operation: 36-6=30 Exploring Operation: 36/6=6, Resulting Numbers: [38, 6] Generated Node #0,0,1: 27:[38, 6] Operation: 36/6=6 Exploring Operation: 38-36=2, Resulting Numbers: [6, 2] Generated Node #0,0,2: 27:[6, 2] Operation: 38-36=2 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 27:[6, 2], Operations: ['57-51=6', '38-36=2'] Exploring Operation: 6-2=4, Resulting Numbers: [4] 4,27 unequal: No Solution Exploring Operation: 6+2=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 6/2=3, Resulting Numbers: [3] 3,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 27:[38, 30], Operations: ['57-51=6', '36-6=30'] Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 38*30=1140, Resulting Numbers: [1140] 1140,27 unequal: No Solution Exploring Operation: 38+30=68, Resulting Numbers: [68] 68,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 27:[38, 6], Operations: ['57-51=6', '36/6=6'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,27 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,27 unequal: No Solution Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,27 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[36, 51, 19], Operations: ['57-38=19'] Exploring Operation: 36-19=17, Resulting Numbers: [51, 17] Generated Node #0,1,0: 27:[51, 17] Operation: 36-19=17 Exploring Operation: 51-19=32, Resulting Numbers: [36, 32] Generated Node #0,1,1: 27:[36, 32] Operation: 51-19=32 Exploring Operation: 51-36=15, Resulting Numbers: [19, 15] Generated Node #0,1,2: 27:[19, 15] Operation: 51-36=15 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[36, 32], Operations: ['57-38=19', '51-19=32'] Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,27 unequal: No Solution Exploring Operation: 36*32=1152, Resulting Numbers: [1152] 1152,27 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 27:[19, 15], Operations: ['57-38=19', '51-36=15'] Exploring Operation: 19*15=285, Resulting Numbers: [285] 285,27 unequal: No Solution Exploring Operation: 19+15=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[51, 17], Operations: ['57-38=19', '36-19=17'] Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 51+17=68, Resulting Numbers: [68] 68,27 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,27 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 Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[51, 38, 21], Operations: ['57-36=21'] Exploring Operation: 51-38=13, Resulting Numbers: [21, 13] Generated Node #0,2,0: 27:[21, 13] Operation: 51-38=13 Exploring Operation: 51-21=30, Resulting Numbers: [38, 30] Generated Node #0,2,1: 27:[38, 30] Operation: 51-21=30 Exploring Operation: 38-21=17, Resulting Numbers: [51, 17] Generated Node #0,2,2: 27:[51, 17] Operation: 38-21=17 Moving to Node #0,2,0 Current State: 27:[21, 13], Operations: ['57-36=21', '51-38=13'] Exploring Operation: 21-13=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 21*13=273, Resulting Numbers: [273] 273,27 unequal: No Solution Exploring Operation: 21+13=34, Resulting Numbers: [34] 34,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[38, 30], Operations: ['57-36=21', '51-21=30'] Exploring Operation: 38-30=8, Resulting Numbers: [8] 8,27 unequal: No Solution Exploring Operation: 38*30=1140, Resulting Numbers: [1140] 1140,27 unequal: No Solution Exploring Operation: 38+30=68, Resulting Numbers: [68] 68,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[51, 17], Operations: ['57-36=21', '38-21=17'] Exploring Operation: 51-17=34, Resulting Numbers: [34] 34,27 unequal: No Solution Exploring Operation: 51+17=68, Resulting Numbers: [68] 68,27 unequal: No Solution Exploring Operation: 51/17=3, Resulting Numbers: [3] 3,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 50, 72, 12, 50 ]
40
[ "72-50=22", "12+50=62", "62-22=40" ]
Current State: 40:[50, 72, 12, 50], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [12, 22] Generated Node #2: [12, 22] from Operation: 72-50=22 Current State: 40:[12, 22], Operations: ['72-50=22'] Exploring Operation: 12+50=62, Resulting Numbers: [22, 62] Generated Node #3: [22, 62] from Operation: 12+50=62 Current State: 40:[22, 62], Operations: ['72-50=22', '12+50=62'] Exploring Operation: 62-22=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[50, 72, 12, 50], Operations: [] Exploring Operation: 72-50=22, Resulting Numbers: [12, 50, 22] Generated Node #0,0: 40:[12, 50, 22] Operation: 72-50=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[12, 50, 22], Operations: ['72-50=22'] Exploring Operation: 50-12=38, Resulting Numbers: [22, 38] Generated Node #0,0,0: 40:[22, 38] Operation: 50-12=38 Moving to Node #0,0,0 Current State: 40:[22, 38], Operations: ['72-50=22', '50-12=38'] Exploring Operation: 38-22=16, Resulting Numbers: [16] 16,40 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
[ 10, 85, 81, 58 ]
98
[ "85-10=75", "81-58=23", "75+23=98" ]
Current State: 98:[10, 85, 81, 58], Operations: [] Exploring Operation: 85-10=75, Resulting Numbers: [81, 58, 75] Generated Node #2: [81, 58, 75] from Operation: 85-10=75 Current State: 98:[81, 58, 75], Operations: ['85-10=75'] Exploring Operation: 81-58=23, Resulting Numbers: [75, 23] Generated Node #3: [75, 23] from Operation: 81-58=23 Current State: 98:[75, 23], Operations: ['85-10=75', '81-58=23'] Exploring Operation: 75+23=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[10, 85, 81, 58], Operations: [] Exploring Operation: 85-81=4, Resulting Numbers: [10, 58, 4] Generated Node #0,0: 98:[10, 58, 4] Operation: 85-81=4 Moving to Node #0,0 Current State: 98:[10, 58, 4], Operations: ['85-81=4'] Exploring Operation: 58-10=48, Resulting Numbers: [4, 48] Generated Node #0,0,0: 98:[4, 48] Operation: 58-10=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[4, 48], Operations: ['85-81=4', '58-10=48'] Exploring Operation: 48/4=12, Resulting Numbers: [12] 12,98 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
[ 43, 12, 52, 54 ]
19
[ "54-52=2", "12*2=24", "43-24=19" ]
Current State: 19:[43, 12, 52, 54], Operations: [] Exploring Operation: 54-52=2, Resulting Numbers: [43, 12, 2] Generated Node #2: [43, 12, 2] from Operation: 54-52=2 Current State: 19:[43, 12, 2], Operations: ['54-52=2'] Exploring Operation: 12*2=24, Resulting Numbers: [43, 24] Generated Node #3: [43, 24] from Operation: 12*2=24 Current State: 19:[43, 24], Operations: ['54-52=2', '12*2=24'] Exploring Operation: 43-24=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[43, 12, 52, 54], Operations: [] Exploring Operation: 54-43=11, Resulting Numbers: [12, 52, 11] Generated Node #0,0: 19:[12, 52, 11] Operation: 54-43=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[12, 52, 11], Operations: ['54-43=11'] Exploring Operation: 52-12=40, Resulting Numbers: [11, 40] Generated Node #0,0,0: 19:[11, 40] Operation: 52-12=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[11, 40], Operations: ['54-43=11', '52-12=40'] Exploring Operation: 40-11=29, Resulting Numbers: [29] 29,19 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
[ 74, 37, 43, 64 ]
42
[ "74/37=2", "64-43=21", "2*21=42" ]
Current State: 42:[74, 37, 43, 64], Operations: [] Exploring Operation: 74/37=2, Resulting Numbers: [43, 64, 2] Generated Node #2: [43, 64, 2] from Operation: 74/37=2 Current State: 42:[43, 64, 2], Operations: ['74/37=2'] Exploring Operation: 64-43=21, Resulting Numbers: [2, 21] Generated Node #3: [2, 21] from Operation: 64-43=21 Current State: 42:[2, 21], Operations: ['74/37=2', '64-43=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[74, 37, 43, 64], Operations: [] Exploring Operation: 74-64=10, Resulting Numbers: [37, 43, 10] Generated Node #0,0: 42:[37, 43, 10] Operation: 74-64=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 42:[37, 43, 10], Operations: ['74-64=10'] Exploring Operation: 43-37=6, Resulting Numbers: [10, 6] Generated Node #0,0,0: 42:[10, 6] Operation: 43-37=6 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 42:[10, 6], Operations: ['74-64=10', '43-37=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,42 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 77, 62, 55, 63 ]
17
[ "55*63=3465", "3465/77=45", "62-45=17" ]
Current State: 17:[77, 62, 55, 63], Operations: [] Exploring Operation: 55*63=3465, Resulting Numbers: [77, 62, 3465] Generated Node #2: [77, 62, 3465] from Operation: 55*63=3465 Current State: 17:[77, 62, 3465], Operations: ['55*63=3465'] Exploring Operation: 3465/77=45, Resulting Numbers: [62, 45] Generated Node #3: [62, 45] from Operation: 3465/77=45 Current State: 17:[62, 45], Operations: ['55*63=3465', '3465/77=45'] Exploring Operation: 62-45=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[77, 62, 55, 63], Operations: [] Exploring Operation: 77-63=14, Resulting Numbers: [62, 55, 14] Generated Node #0,0: 17:[62, 55, 14] Operation: 77-63=14 Exploring Operation: 77-62=15, Resulting Numbers: [55, 63, 15] Generated Node #0,1: 17:[55, 63, 15] Operation: 77-62=15 Exploring Operation: 77-55=22, Resulting Numbers: [62, 63, 22] Generated Node #0,2: 17:[62, 63, 22] Operation: 77-55=22 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[62, 55, 14], Operations: ['77-63=14'] Exploring Operation: 62-55=7, Resulting Numbers: [14, 7] Generated Node #0,0,0: 17:[14, 7] Operation: 62-55=7 Exploring Operation: 55-14=41, Resulting Numbers: [62, 41] Generated Node #0,0,1: 17:[62, 41] Operation: 55-14=41 Exploring Operation: 62-14=48, Resulting Numbers: [55, 48] Generated Node #0,0,2: 17:[55, 48] Operation: 62-14=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[14, 7], Operations: ['77-63=14', '62-55=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 14/7=2, Resulting Numbers: [2] 2,17 unequal: No Solution Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,17 unequal: No Solution No 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: 17:[62, 41], Operations: ['77-63=14', '55-14=41'] Exploring Operation: 62*41=2542, Resulting Numbers: [2542] 2542,17 unequal: No Solution Exploring Operation: 62+41=103, Resulting Numbers: [103] 103,17 unequal: No Solution Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,17 unequal: No Solution No 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: 17:[55, 48], Operations: ['77-63=14', '62-14=48'] Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,17 unequal: No Solution Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[55, 63, 15], Operations: ['77-62=15'] Exploring Operation: 63-15=48, Resulting Numbers: [55, 48] Generated Node #0,1,0: 17:[55, 48] Operation: 63-15=48 Exploring Operation: 63-55=8, Resulting Numbers: [15, 8] Generated Node #0,1,1: 17:[15, 8] Operation: 63-55=8 Exploring Operation: 55-15=40, Resulting Numbers: [63, 40] Generated Node #0,1,2: 17:[63, 40] Operation: 55-15=40 Moving to Node #0,1,1 Current State: 17:[15, 8], Operations: ['77-62=15', '63-55=8'] Exploring Operation: 15*8=120, Resulting Numbers: [120] 120,17 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 15+8=23, Resulting Numbers: [23] 23,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[55, 48], Operations: ['77-62=15', '63-15=48'] Exploring Operation: 55-48=7, Resulting Numbers: [7] 7,17 unequal: No Solution Exploring Operation: 55*48=2640, Resulting Numbers: [2640] 2640,17 unequal: No Solution Exploring Operation: 55+48=103, Resulting Numbers: [103] 103,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[63, 40], Operations: ['77-62=15', '55-15=40'] Exploring Operation: 63+40=103, Resulting Numbers: [103] 103,17 unequal: No Solution Exploring Operation: 63*40=2520, Resulting Numbers: [2520] 2520,17 unequal: No Solution Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 17:[62, 63, 22], Operations: ['77-55=22'] Exploring Operation: 63-62=1, Resulting Numbers: [22, 1] Generated Node #0,2,0: 17:[22, 1] Operation: 63-62=1 Exploring Operation: 63-22=41, Resulting Numbers: [62, 41] Generated Node #0,2,1: 17:[62, 41] Operation: 63-22=41 Exploring Operation: 62-22=40, Resulting Numbers: [63, 40] Generated Node #0,2,2: 17:[63, 40] Operation: 62-22=40 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 17:[22, 1], Operations: ['77-55=22', '63-62=1'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,17 unequal: No Solution Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,17 unequal: No Solution No 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: 17:[62, 41], Operations: ['77-55=22', '63-22=41'] Exploring Operation: 62-41=21, Resulting Numbers: [21] 21,17 unequal: No Solution Exploring Operation: 62*41=2542, Resulting Numbers: [2542] 2542,17 unequal: No Solution Exploring Operation: 62+41=103, Resulting Numbers: [103] 103,17 unequal: No Solution No 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: 17:[63, 40], Operations: ['77-55=22', '62-22=40'] Exploring Operation: 63-40=23, Resulting Numbers: [23] 23,17 unequal: No Solution Exploring Operation: 63*40=2520, Resulting Numbers: [2520] 2520,17 unequal: No Solution Exploring Operation: 63+40=103, Resulting Numbers: [103] 103,17 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 31, 95, 61, 58 ]
67
[ "95-31=64", "61-58=3", "64+3=67" ]
Current State: 67:[31, 95, 61, 58], Operations: [] Exploring Operation: 95-31=64, Resulting Numbers: [61, 58, 64] Generated Node #2: [61, 58, 64] from Operation: 95-31=64 Current State: 67:[61, 58, 64], Operations: ['95-31=64'] Exploring Operation: 61-58=3, Resulting Numbers: [64, 3] Generated Node #3: [64, 3] from Operation: 61-58=3 Current State: 67:[64, 3], Operations: ['95-31=64', '61-58=3'] Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[31, 95, 61, 58], Operations: [] Exploring Operation: 95-31=64, Resulting Numbers: [61, 58, 64] Generated Node #0,0: 67:[61, 58, 64] Operation: 95-31=64 Start Sub Search at level 1: Moving to Node #0,0 Current State: 67:[61, 58, 64], Operations: ['95-31=64'] Exploring Operation: 61+58=119, Resulting Numbers: [64, 119] Generated Node #0,0,0: 67:[64, 119] Operation: 61+58=119 Moving to Node #0,0,0 Current State: 67:[64, 119], Operations: ['95-31=64', '61+58=119'] Exploring Operation: 119-64=55, Resulting Numbers: [55] 55,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 53, 20, 12, 9 ]
53
[ "20-12=8", "9-8=1", "53*1=53" ]
Current State: 53:[53, 20, 12, 9], Operations: [] Exploring Operation: 20-12=8, Resulting Numbers: [53, 9, 8] Generated Node #2: [53, 9, 8] from Operation: 20-12=8 Current State: 53:[53, 9, 8], Operations: ['20-12=8'] Exploring Operation: 9-8=1, Resulting Numbers: [53, 1] Generated Node #3: [53, 1] from Operation: 9-8=1 Current State: 53:[53, 1], Operations: ['20-12=8', '9-8=1'] Exploring Operation: 53*1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[53, 20, 12, 9], Operations: [] Exploring Operation: 20+9=29, Resulting Numbers: [53, 12, 29] Generated Node #0,0: 53:[53, 12, 29] Operation: 20+9=29 Exploring Operation: 12+9=21, Resulting Numbers: [53, 20, 21] Generated Node #0,1: 53:[53, 20, 21] Operation: 12+9=21 Exploring Operation: 20+12=32, Resulting Numbers: [53, 9, 32] Generated Node #0,2: 53:[53, 9, 32] Operation: 20+12=32 Exploring Operation: 53+9=62, Resulting Numbers: [20, 12, 62] Generated Node #0,3: 53:[20, 12, 62] Operation: 53+9=62 Moving to Node #0,0 Current State: 53:[53, 12, 29], Operations: ['20+9=29'] Exploring Operation: 12+29=41, Resulting Numbers: [53, 41] Generated Node #0,0,0: 53:[53, 41] Operation: 12+29=41 Exploring Operation: 29-12=17, Resulting Numbers: [53, 17] Generated Node #0,0,1: 53:[53, 17] Operation: 29-12=17 Exploring Operation: 53+12=65, Resulting Numbers: [29, 65] Generated Node #0,0,2: 53:[29, 65] Operation: 53+12=65 Exploring Operation: 53-12=41, Resulting Numbers: [29, 41] Generated Node #0,0,3: 53:[29, 41] Operation: 53-12=41 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[53, 41], Operations: ['20+9=29', '12+29=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,53 unequal: No Solution Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,53 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,53 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 #0,0,1 Current State: 53:[53, 17], Operations: ['20+9=29', '29-12=17'] Exploring Operation: 53-17=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 53*17=901, Resulting Numbers: [901] 901,53 unequal: No Solution Exploring Operation: 53+17=70, Resulting Numbers: [70] 70,53 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 #0,0,2 Current State: 53:[29, 65], Operations: ['20+9=29', '53+12=65'] Exploring Operation: 65-29=36, Resulting Numbers: [36] 36,53 unequal: No Solution Exploring Operation: 29*65=1885, Resulting Numbers: [1885] 1885,53 unequal: No Solution Exploring Operation: 29+65=94, Resulting Numbers: [94] 94,53 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 #0,0,3 Current State: 53:[29, 41], Operations: ['20+9=29', '53-12=41'] Exploring Operation: 41-29=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 29+41=70, Resulting Numbers: [70] 70,53 unequal: No Solution Exploring Operation: 29*41=1189, Resulting Numbers: [1189] 1189,53 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: 53:[53, 9, 32], Operations: ['20+12=32'] Exploring Operation: 9+32=41, Resulting Numbers: [53, 41] Generated Node #0,2,0: 53:[53, 41] Operation: 9+32=41 Exploring Operation: 53-9=44, Resulting Numbers: [32, 44] Generated Node #0,2,1: 53:[32, 44] Operation: 53-9=44 Exploring Operation: 32-9=23, Resulting Numbers: [53, 23] Generated Node #0,2,2: 53:[53, 23] Operation: 32-9=23 Exploring Operation: 53+9=62, Resulting Numbers: [32, 62] Generated Node #0,2,3: 53:[32, 62] Operation: 53+9=62 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 53:[53, 41], Operations: ['20+12=32', '9+32=41'] Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,53 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,53 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 #0,2,1 Current State: 53:[32, 44], Operations: ['20+12=32', '53-9=44'] Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,53 unequal: No Solution Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,53 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,53 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 #0,2,2 Current State: 53:[53, 23], Operations: ['20+12=32', '32-9=23'] Exploring Operation: 53-23=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 53*23=1219, Resulting Numbers: [1219] 1219,53 unequal: No Solution Exploring Operation: 53+23=76, Resulting Numbers: [76] 76,53 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 #0,2,3 Current State: 53:[32, 62], Operations: ['20+12=32', '53+9=62'] Exploring Operation: 32*62=1984, Resulting Numbers: [1984] 1984,53 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,53 unequal: No Solution Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,53 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: 53:[53, 20, 21], Operations: ['12+9=21'] Exploring Operation: 20+21=41, Resulting Numbers: [53, 41] Generated Node #0,1,0: 53:[53, 41] Operation: 20+21=41 Exploring Operation: 53-20=33, Resulting Numbers: [21, 33] Generated Node #0,1,1: 53:[21, 33] Operation: 53-20=33 Exploring Operation: 53+20=73, Resulting Numbers: [21, 73] Generated Node #0,1,2: 53:[21, 73] Operation: 53+20=73 Exploring Operation: 21-20=1, Resulting Numbers: [53, 1] Generated Node #0,1,3: 53:[53, 1] Operation: 21-20=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 53:[53, 41], Operations: ['12+9=21', '20+21=41'] Exploring Operation: 53*41=2173, Resulting Numbers: [2173] 2173,53 unequal: No Solution Exploring Operation: 53-41=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 53+41=94, Resulting Numbers: [94] 94,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 53:[21, 33], Operations: ['12+9=21', '53-20=33'] Exploring Operation: 21*33=693, Resulting Numbers: [693] 693,53 unequal: No Solution Exploring Operation: 33-21=12, Resulting Numbers: [12] 12,53 unequal: No Solution Exploring Operation: 21+33=54, Resulting Numbers: [54] 54,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 53:[21, 73], Operations: ['12+9=21', '53+20=73'] Exploring Operation: 21*73=1533, Resulting Numbers: [1533] 1533,53 unequal: No Solution Exploring Operation: 73-21=52, Resulting Numbers: [52] 52,53 unequal: No Solution Exploring Operation: 21+73=94, Resulting Numbers: [94] 94,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 53:[53, 1], Operations: ['12+9=21', '21-20=1'] Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[53, 20, 12, 9], Operations: [] Exploring Operation: 12+9=21, Resulting Numbers: [53, 20, 21] Generated Node #0,1: 53:[53, 20, 21] Operation: 12+9=21 Moving to Node #0,1 Current State: 53:[53, 20, 21], Operations: ['12+9=21'] Exploring Operation: 21-20=1, Resulting Numbers: [53, 1] Generated Node #0,1,3: 53:[53, 1] Operation: 21-20=1 Moving to Node #0,1,3 Current State: 53:[53, 1], Operations: ['12+9=21', '21-20=1'] Exploring Operation: 53/1=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Exit Sub Search at level 1
0.953125
hs_4
mult_heuristic
[ 23, 23, 73, 43 ]
70
[ "23+23=46", "73+43=116", "116-46=70" ]
Current State: 70:[23, 23, 73, 43], Operations: [] Exploring Operation: 23+23=46, Resulting Numbers: [73, 43, 46] Generated Node #2: [73, 43, 46] from Operation: 23+23=46 Current State: 70:[73, 43, 46], Operations: ['23+23=46'] Exploring Operation: 73+43=116, Resulting Numbers: [46, 116] Generated Node #3: [46, 116] from Operation: 73+43=116 Current State: 70:[46, 116], Operations: ['23+23=46', '73+43=116'] Exploring Operation: 116-46=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[23, 23, 73, 43], Operations: [] Exploring Operation: 23+43=66, Resulting Numbers: [23, 73, 66] Generated Node #0,0: 70:[23, 73, 66] Operation: 23+43=66 Exploring Operation: 23-23=0, Resulting Numbers: [73, 43, 0] Generated Node #0,1: 70:[73, 43, 0] Operation: 23-23=0 Exploring Operation: 43-23=20, Resulting Numbers: [23, 73, 20] Generated Node #0,2: 70:[23, 73, 20] Operation: 43-23=20 Exploring Operation: 23/23=1, Resulting Numbers: [73, 43, 1] Generated Node #0,3: 70:[73, 43, 1] Operation: 23/23=1 Exploring Operation: 23+43=66, Resulting Numbers: [23, 73, 66] Generated Node #0,4: 70:[23, 73, 66] Operation: 23+43=66 Moving to Node #0,3 Current State: 70:[73, 43, 1], Operations: ['23/23=1'] Exploring Operation: 73/1=73, Resulting Numbers: [43, 73] Generated Node #0,3,0: 70:[43, 73] Operation: 73/1=73 Exploring Operation: 73-43=30, Resulting Numbers: [1, 30] Generated Node #0,3,1: 70:[1, 30] Operation: 73-43=30 Exploring Operation: 73*1=73, Resulting Numbers: [43, 73] Generated Node #0,3,2: 70:[43, 73] Operation: 73*1=73 Exploring Operation: 73-1=72, Resulting Numbers: [43, 72] Generated Node #0,3,3: 70:[43, 72] Operation: 73-1=72 Exploring Operation: 43-1=42, Resulting Numbers: [73, 42] Generated Node #0,3,4: 70:[73, 42] Operation: 43-1=42 Moving to Node #0,1 Current State: 70:[73, 43, 0], Operations: ['23-23=0'] Exploring Operation: 73-0=73, Resulting Numbers: [43, 73] Generated Node #0,1,0: 70:[43, 73] Operation: 73-0=73 Exploring Operation: 73-43=30, Resulting Numbers: [0, 30] Generated Node #0,1,1: 70:[0, 30] Operation: 73-43=30 Exploring Operation: 43*0=0, Resulting Numbers: [73, 0] Generated Node #0,1,2: 70:[73, 0] Operation: 43*0=0 Exploring Operation: 73*0=0, Resulting Numbers: [43, 0] Generated Node #0,1,3: 70:[43, 0] Operation: 73*0=0 Exploring Operation: 73+0=73, Resulting Numbers: [43, 73] Generated Node #0,1,4: 70:[43, 73] Operation: 73+0=73 Moving to Node #0,0 Current State: 70:[23, 73, 66], Operations: ['23+43=66'] Exploring Operation: 73-66=7, Resulting Numbers: [23, 7] Generated Node #0,0,0: 70:[23, 7] Operation: 73-66=7 Exploring Operation: 73-23=50, Resulting Numbers: [66, 50] Generated Node #0,0,1: 70:[66, 50] Operation: 73-23=50 Exploring Operation: 23+73=96, Resulting Numbers: [66, 96] Generated Node #0,0,2: 70:[66, 96] Operation: 23+73=96 Exploring Operation: 23+66=89, Resulting Numbers: [73, 89] Generated Node #0,0,3: 70:[73, 89] Operation: 23+66=89 Exploring Operation: 66-23=43, Resulting Numbers: [73, 43] Generated Node #0,0,4: 70:[73, 43] Operation: 66-23=43 Moving to Node #0,4 Current State: 70:[23, 73, 66], Operations: ['23+43=66'] Exploring Operation: 23+73=96, Resulting Numbers: [66, 96] Generated Node #0,4,0: 70:[66, 96] Operation: 23+73=96 Exploring Operation: 66-23=43, Resulting Numbers: [73, 43] Generated Node #0,4,1: 70:[73, 43] Operation: 66-23=43 Exploring Operation: 73-66=7, Resulting Numbers: [23, 7] Generated Node #0,4,2: 70:[23, 7] Operation: 73-66=7 Exploring Operation: 23+66=89, Resulting Numbers: [73, 89] Generated Node #0,4,3: 70:[73, 89] Operation: 23+66=89 Exploring Operation: 73-23=50, Resulting Numbers: [66, 50] Generated Node #0,4,4: 70:[66, 50] Operation: 73-23=50 Moving to Node #0,2 Current State: 70:[23, 73, 20], Operations: ['43-23=20'] Exploring Operation: 23+73=96, Resulting Numbers: [20, 96] Generated Node #0,2,0: 70:[20, 96] Operation: 23+73=96 Exploring Operation: 73-23=50, Resulting Numbers: [20, 50] Generated Node #0,2,1: 70:[20, 50] Operation: 73-23=50 Exploring Operation: 73-20=53, Resulting Numbers: [23, 53] Generated Node #0,2,2: 70:[23, 53] Operation: 73-20=53 Exploring Operation: 23+20=43, Resulting Numbers: [73, 43] Generated Node #0,2,3: 70:[73, 43] Operation: 23+20=43 Exploring Operation: 23-20=3, Resulting Numbers: [73, 3] Generated Node #0,2,4: 70:[73, 3] Operation: 23-20=3 Moving to Node #0,2,4 Current State: 70:[73, 3], Operations: ['43-23=20', '23-20=3'] Exploring Operation: 73+3=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 73*3=219, Resulting Numbers: [219] 219,70 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[23, 23, 73, 43], Operations: [] Exploring Operation: 43-23=20, Resulting Numbers: [23, 73, 20] Generated Node #0,2: 70:[23, 73, 20] Operation: 43-23=20 Moving to Node #0,2 Current State: 70:[23, 73, 20], Operations: ['43-23=20'] Exploring Operation: 23-20=3, Resulting Numbers: [73, 3] Generated Node #0,2,4: 70:[73, 3] Operation: 23-20=3 Moving to Node #0,2,4 Current State: 70:[73, 3], Operations: ['43-23=20', '23-20=3'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
0.967882
hs_5
sum_heuristic
[ 56, 6, 65, 17 ]
10
[ "56-17=39", "6*65=390", "390/39=10" ]
Current State: 10:[56, 6, 65, 17], Operations: [] Exploring Operation: 56-17=39, Resulting Numbers: [6, 65, 39] Generated Node #2: [6, 65, 39] from Operation: 56-17=39 Current State: 10:[6, 65, 39], Operations: ['56-17=39'] Exploring Operation: 6*65=390, Resulting Numbers: [39, 390] Generated Node #3: [39, 390] from Operation: 6*65=390 Current State: 10:[39, 390], Operations: ['56-17=39', '6*65=390'] Exploring Operation: 390/39=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[56, 6, 65, 17], Operations: [] Exploring Operation: 56-17=39, Resulting Numbers: [6, 65, 39] Generated Node #0,0: 10:[6, 65, 39] Operation: 56-17=39 Exploring Operation: 65-56=9, Resulting Numbers: [6, 17, 9] Generated Node #0,1: 10:[6, 17, 9] Operation: 65-56=9 Exploring Operation: 65-17=48, Resulting Numbers: [56, 6, 48] Generated Node #0,2: 10:[56, 6, 48] Operation: 65-17=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[6, 17, 9], Operations: ['65-56=9'] Exploring Operation: 17-9=8, Resulting Numbers: [6, 8] Generated Node #0,1,0: 10:[6, 8] Operation: 17-9=8 Exploring Operation: 17-6=11, Resulting Numbers: [9, 11] Generated Node #0,1,1: 10:[9, 11] Operation: 17-6=11 Exploring Operation: 9-6=3, Resulting Numbers: [17, 3] Generated Node #0,1,2: 10:[17, 3] Operation: 9-6=3 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 10:[9, 11], Operations: ['65-56=9', '17-6=11'] Exploring Operation: 11-9=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 9*11=99, Resulting Numbers: [99] 99,10 unequal: No Solution Exploring Operation: 9+11=20, Resulting Numbers: [20] 20,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 10:[6, 8], Operations: ['65-56=9', '17-9=8'] Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 10:[17, 3], Operations: ['65-56=9', '9-6=3'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,10 unequal: No Solution Exploring Operation: 17+3=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 17*3=51, Resulting Numbers: [51] 51,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 10:[6, 65, 39], Operations: ['56-17=39'] Exploring Operation: 65-6=59, Resulting Numbers: [39, 59] Generated Node #0,0,0: 10:[39, 59] Operation: 65-6=59 Exploring Operation: 65-39=26, Resulting Numbers: [6, 26] Generated Node #0,0,1: 10:[6, 26] Operation: 65-39=26 Exploring Operation: 39-6=33, Resulting Numbers: [65, 33] Generated Node #0,0,2: 10:[65, 33] Operation: 39-6=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 10:[6, 26], Operations: ['56-17=39', '65-39=26'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,10 unequal: No Solution Exploring Operation: 6+26=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 6*26=156, Resulting Numbers: [156] 156,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 10:[39, 59], Operations: ['56-17=39', '65-6=59'] Exploring Operation: 39*59=2301, Resulting Numbers: [2301] 2301,10 unequal: No Solution Exploring Operation: 39+59=98, Resulting Numbers: [98] 98,10 unequal: No Solution Exploring Operation: 59-39=20, Resulting Numbers: [20] 20,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 10:[65, 33], Operations: ['56-17=39', '39-6=33'] Exploring Operation: 65-33=32, Resulting Numbers: [32] 32,10 unequal: No Solution Exploring Operation: 65*33=2145, Resulting Numbers: [2145] 2145,10 unequal: No Solution Exploring Operation: 65+33=98, Resulting Numbers: [98] 98,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 10:[56, 6, 48], Operations: ['65-17=48'] Exploring Operation: 56-48=8, Resulting Numbers: [6, 8] Generated Node #0,2,0: 10:[6, 8] Operation: 56-48=8 Exploring Operation: 56-6=50, Resulting Numbers: [48, 50] Generated Node #0,2,1: 10:[48, 50] Operation: 56-6=50 Exploring Operation: 48/6=8, Resulting Numbers: [56, 8] Generated Node #0,2,2: 10:[56, 8] Operation: 48/6=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 10:[6, 8], Operations: ['65-17=48', '56-48=8'] Exploring Operation: 6*8=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 8-6=2, Resulting Numbers: [2] 2,10 unequal: No Solution Exploring Operation: 6+8=14, Resulting Numbers: [14] 14,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 10:[56, 8], Operations: ['65-17=48', '48/6=8'] Exploring Operation: 56-8=48, Resulting Numbers: [48] 48,10 unequal: No Solution Exploring Operation: 56+8=64, Resulting Numbers: [64] 64,10 unequal: No Solution Exploring Operation: 56/8=7, Resulting Numbers: [7] 7,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 10:[48, 50], Operations: ['65-17=48', '56-6=50'] Exploring Operation: 48*50=2400, Resulting Numbers: [2400] 2400,10 unequal: No Solution Exploring Operation: 48+50=98, Resulting Numbers: [98] 98,10 unequal: No Solution Exploring Operation: 50-48=2, Resulting Numbers: [2] 2,10 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 56, 47, 6, 59 ]
54
[ "59-47=12", "12/6=2", "56-2=54" ]
Current State: 54:[56, 47, 6, 59], Operations: [] Exploring Operation: 59-47=12, Resulting Numbers: [56, 6, 12] Generated Node #2: [56, 6, 12] from Operation: 59-47=12 Current State: 54:[56, 6, 12], Operations: ['59-47=12'] Exploring Operation: 12/6=2, Resulting Numbers: [56, 2] Generated Node #3: [56, 2] from Operation: 12/6=2 Current State: 54:[56, 2], Operations: ['59-47=12', '12/6=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[56, 47, 6, 59], Operations: [] Exploring Operation: 56-47=9, Resulting Numbers: [6, 59, 9] Generated Node #0,0: 54:[6, 59, 9] Operation: 56-47=9 Exploring Operation: 59-56=3, Resulting Numbers: [47, 6, 3] Generated Node #0,1: 54:[47, 6, 3] Operation: 59-56=3 Exploring Operation: 59-47=12, Resulting Numbers: [56, 6, 12] Generated Node #0,2: 54:[56, 6, 12] Operation: 59-47=12 Exploring Operation: 47+6=53, Resulting Numbers: [56, 59, 53] Generated Node #0,3: 54:[56, 59, 53] Operation: 47+6=53 Moving to Node #0,0 Current State: 54:[6, 59, 9], Operations: ['56-47=9'] Exploring Operation: 59-9=50, Resulting Numbers: [6, 50] Generated Node #0,0,0: 54:[6, 50] Operation: 59-9=50 Exploring Operation: 9-6=3, Resulting Numbers: [59, 3] Generated Node #0,0,1: 54:[59, 3] Operation: 9-6=3 Exploring Operation: 6*9=54, Resulting Numbers: [59, 54] Generated Node #0,0,2: 54:[59, 54] Operation: 6*9=54 Exploring Operation: 59-6=53, Resulting Numbers: [9, 53] Generated Node #0,0,3: 54:[9, 53] Operation: 59-6=53 Moving to Node #0,2 Current State: 54:[56, 6, 12], Operations: ['59-47=12'] Exploring Operation: 12/6=2, Resulting Numbers: [56, 2] Generated Node #0,2,0: 54:[56, 2] Operation: 12/6=2 Exploring Operation: 56-6=50, Resulting Numbers: [12, 50] Generated Node #0,2,1: 54:[12, 50] Operation: 56-6=50 Exploring Operation: 12-6=6, Resulting Numbers: [56, 6] Generated Node #0,2,2: 54:[56, 6] Operation: 12-6=6 Exploring Operation: 6+12=18, Resulting Numbers: [56, 18] Generated Node #0,2,3: 54:[56, 18] Operation: 6+12=18 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 54:[56, 2], Operations: ['59-47=12', '12/6=2'] Exploring Operation: 56/2=28, Resulting Numbers: [28] 28,54 unequal: No Solution Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[56, 47, 6, 59], Operations: [] Exploring Operation: 59-47=12, Resulting Numbers: [56, 6, 12] Generated Node #0,2: 54:[56, 6, 12] Operation: 59-47=12 Moving to Node #0,2 Current State: 54:[56, 6, 12], Operations: ['59-47=12'] Exploring Operation: 12/6=2, Resulting Numbers: [56, 2] Generated Node #0,2,0: 54:[56, 2] Operation: 12/6=2 Moving to Node #0,2,0 Current State: 54:[56, 2], Operations: ['59-47=12', '12/6=2'] Exploring Operation: 56-2=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 56, 49, 42, 74 ]
37
[ "56+42=98", "49*74=3626", "3626/98=37" ]
Current State: 37:[56, 49, 42, 74], Operations: [] Exploring Operation: 56+42=98, Resulting Numbers: [49, 74, 98] Generated Node #2: [49, 74, 98] from Operation: 56+42=98 Current State: 37:[49, 74, 98], Operations: ['56+42=98'] Exploring Operation: 49*74=3626, Resulting Numbers: [98, 3626] Generated Node #3: [98, 3626] from Operation: 49*74=3626 Current State: 37:[98, 3626], Operations: ['56+42=98', '49*74=3626'] Exploring Operation: 3626/98=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[56, 49, 42, 74], Operations: [] Exploring Operation: 74-56=18, Resulting Numbers: [49, 42, 18] Generated Node #0,0: 37:[49, 42, 18] Operation: 74-56=18 Exploring Operation: 56-42=14, Resulting Numbers: [49, 74, 14] Generated Node #0,1: 37:[49, 74, 14] Operation: 56-42=14 Exploring Operation: 56-49=7, Resulting Numbers: [42, 74, 7] Generated Node #0,2: 37:[42, 74, 7] Operation: 56-49=7 Exploring Operation: 74-49=25, Resulting Numbers: [56, 42, 25] Generated Node #0,3: 37:[56, 42, 25] Operation: 74-49=25 Exploring Operation: 74-42=32, Resulting Numbers: [56, 49, 32] Generated Node #0,4: 37:[56, 49, 32] Operation: 74-42=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 37:[49, 42, 18], Operations: ['74-56=18'] Exploring Operation: 42-18=24, Resulting Numbers: [49, 24] Generated Node #0,0,0: 37:[49, 24] Operation: 42-18=24 Exploring Operation: 49-18=31, Resulting Numbers: [42, 31] Generated Node #0,0,1: 37:[42, 31] Operation: 49-18=31 Exploring Operation: 42+18=60, Resulting Numbers: [49, 60] Generated Node #0,0,2: 37:[49, 60] Operation: 42+18=60 Exploring Operation: 49-42=7, Resulting Numbers: [18, 7] Generated Node #0,0,3: 37:[18, 7] Operation: 49-42=7 Exploring Operation: 49+18=67, Resulting Numbers: [42, 67] Generated Node #0,0,4: 37:[42, 67] Operation: 49+18=67 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 37:[42, 31], Operations: ['74-56=18', '49-18=31'] Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,37 unequal: No Solution Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 37:[49, 24], Operations: ['74-56=18', '42-18=24'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,37 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 37:[49, 60], Operations: ['74-56=18', '42+18=60'] Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 37:[42, 67], Operations: ['74-56=18', '49+18=67'] Exploring Operation: 67-42=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 42+67=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 42*67=2814, Resulting Numbers: [2814] 2814,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 37:[18, 7], Operations: ['74-56=18', '49-42=7'] Exploring Operation: 18*7=126, Resulting Numbers: [126] 126,37 unequal: No Solution Exploring Operation: 18-7=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 18+7=25, Resulting Numbers: [25] 25,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[56, 42, 25], Operations: ['74-49=25'] Exploring Operation: 56-42=14, Resulting Numbers: [25, 14] Generated Node #0,3,0: 37:[25, 14] Operation: 56-42=14 Exploring Operation: 56-25=31, Resulting Numbers: [42, 31] Generated Node #0,3,1: 37:[42, 31] Operation: 56-25=31 Exploring Operation: 42-25=17, Resulting Numbers: [56, 17] Generated Node #0,3,2: 37:[56, 17] Operation: 42-25=17 Exploring Operation: 42+25=67, Resulting Numbers: [56, 67] Generated Node #0,3,3: 37:[56, 67] Operation: 42+25=67 Exploring Operation: 56+25=81, Resulting Numbers: [42, 81] Generated Node #0,3,4: 37:[42, 81] Operation: 56+25=81 Moving to Node #0,3,1 Current State: 37:[42, 31], Operations: ['74-49=25', '56-25=31'] Exploring Operation: 42-31=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 42+31=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 42*31=1302, Resulting Numbers: [1302] 1302,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[25, 14], Operations: ['74-49=25', '56-42=14'] Exploring Operation: 25+14=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 25*14=350, Resulting Numbers: [350] 350,37 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,3,2 Current State: 37:[56, 17], Operations: ['74-49=25', '42-25=17'] Exploring Operation: 56*17=952, Resulting Numbers: [952] 952,37 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 56+17=73, Resulting Numbers: [73] 73,37 unequal: No Solution Moving to Node #0,3,3 Current State: 37:[56, 67], Operations: ['74-49=25', '42+25=67'] Exploring Operation: 56+67=123, Resulting Numbers: [123] 123,37 unequal: No Solution Exploring Operation: 67-56=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 56*67=3752, Resulting Numbers: [3752] 3752,37 unequal: No Solution Moving to Node #0,3,4 Current State: 37:[42, 81], Operations: ['74-49=25', '56+25=81'] Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 42+81=123, Resulting Numbers: [123] 123,37 unequal: No Solution Exploring Operation: 42*81=3402, Resulting Numbers: [3402] 3402,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 37:[56, 49, 32], Operations: ['74-42=32'] Exploring Operation: 56+32=88, Resulting Numbers: [49, 88] Generated Node #0,4,0: 37:[49, 88] Operation: 56+32=88 Exploring Operation: 49-32=17, Resulting Numbers: [56, 17] Generated Node #0,4,1: 37:[56, 17] Operation: 49-32=17 Exploring Operation: 56-32=24, Resulting Numbers: [49, 24] Generated Node #0,4,2: 37:[49, 24] Operation: 56-32=24 Exploring Operation: 56-49=7, Resulting Numbers: [32, 7] Generated Node #0,4,3: 37:[32, 7] Operation: 56-49=7 Exploring Operation: 49+32=81, Resulting Numbers: [56, 81] Generated Node #0,4,4: 37:[56, 81] Operation: 49+32=81 Moving to Node #0,4,2 Current State: 37:[49, 24], Operations: ['74-42=32', '56-32=24'] Exploring Operation: 49-24=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 49+24=73, Resulting Numbers: [73] 73,37 unequal: No Solution Exploring Operation: 49*24=1176, Resulting Numbers: [1176] 1176,37 unequal: No Solution Moving to Node #0,4,3 Current State: 37:[32, 7], Operations: ['74-42=32', '56-49=7'] Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,37 unequal: No Solution Moving to Node #0,4,1 Current State: 37:[56, 17], Operations: ['74-42=32', '49-32=17'] Exploring Operation: 56*17=952, Resulting Numbers: [952] 952,37 unequal: No Solution Exploring Operation: 56-17=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 56+17=73, Resulting Numbers: [73] 73,37 unequal: No Solution Moving to Node #0,4,0 Current State: 37:[49, 88], Operations: ['74-42=32', '56+32=88'] Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 49*88=4312, Resulting Numbers: [4312] 4312,37 unequal: No Solution Exploring Operation: 49+88=137, Resulting Numbers: [137] 137,37 unequal: No Solution Moving to Node #0,4,4 Current State: 37:[56, 81], Operations: ['74-42=32', '49+32=81'] Exploring Operation: 81-56=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 56*81=4536, Resulting Numbers: [4536] 4536,37 unequal: No Solution Exploring Operation: 56+81=137, Resulting Numbers: [137] 137,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 37:[49, 74, 14], Operations: ['56-42=14'] Exploring Operation: 74+14=88, Resulting Numbers: [49, 88] Generated Node #0,1,0: 37:[49, 88] Operation: 74+14=88 Exploring Operation: 74-49=25, Resulting Numbers: [14, 25] Generated Node #0,1,1: 37:[14, 25] Operation: 74-49=25 Exploring Operation: 49+14=63, Resulting Numbers: [74, 63] Generated Node #0,1,2: 37:[74, 63] Operation: 49+14=63 Exploring Operation: 49-14=35, Resulting Numbers: [74, 35] Generated Node #0,1,3: 37:[74, 35] Operation: 49-14=35 Exploring Operation: 74-14=60, Resulting Numbers: [49, 60] Generated Node #0,1,4: 37:[49, 60] Operation: 74-14=60 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 37:[14, 25], Operations: ['56-42=14', '74-49=25'] Exploring Operation: 14+25=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 14*25=350, Resulting Numbers: [350] 350,37 unequal: No Solution Exploring Operation: 25-14=11, Resulting Numbers: [11] 11,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 37:[49, 60], Operations: ['56-42=14', '74-14=60'] Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 37:[74, 35], Operations: ['56-42=14', '49-14=35'] Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,37 unequal: No Solution Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 37:[49, 88], Operations: ['56-42=14', '74+14=88'] Exploring Operation: 49*88=4312, Resulting Numbers: [4312] 4312,37 unequal: No Solution Exploring Operation: 88-49=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 49+88=137, Resulting Numbers: [137] 137,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 37:[74, 63], Operations: ['56-42=14', '49+14=63'] Exploring Operation: 74*63=4662, Resulting Numbers: [4662] 4662,37 unequal: No Solution Exploring Operation: 74+63=137, Resulting Numbers: [137] 137,37 unequal: No Solution Exploring Operation: 74-63=11, Resulting Numbers: [11] 11,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 37:[42, 74, 7], Operations: ['56-49=7'] Exploring Operation: 74+7=81, Resulting Numbers: [42, 81] Generated Node #0,2,0: 37:[42, 81] Operation: 74+7=81 Exploring Operation: 74-42=32, Resulting Numbers: [7, 32] Generated Node #0,2,1: 37:[7, 32] Operation: 74-42=32 Exploring Operation: 42+7=49, Resulting Numbers: [74, 49] Generated Node #0,2,2: 37:[74, 49] Operation: 42+7=49 Exploring Operation: 42-7=35, Resulting Numbers: [74, 35] Generated Node #0,2,3: 37:[74, 35] Operation: 42-7=35 Exploring Operation: 74-7=67, Resulting Numbers: [42, 67] Generated Node #0,2,4: 37:[42, 67] Operation: 74-7=67 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 37:[7, 32], Operations: ['56-49=7', '74-42=32'] Exploring Operation: 7*32=224, Resulting Numbers: [224] 224,37 unequal: No Solution Exploring Operation: 7+32=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 37:[42, 67], Operations: ['56-49=7', '74-7=67'] Exploring Operation: 42+67=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 42*67=2814, Resulting Numbers: [2814] 2814,37 unequal: No Solution Exploring Operation: 67-42=25, Resulting Numbers: [25] 25,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 37:[74, 35], Operations: ['56-49=7', '42-7=35'] Exploring Operation: 74-35=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 74+35=109, Resulting Numbers: [109] 109,37 unequal: No Solution Exploring Operation: 74*35=2590, Resulting Numbers: [2590] 2590,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 37:[42, 81], Operations: ['56-49=7', '74+7=81'] Exploring Operation: 42*81=3402, Resulting Numbers: [3402] 3402,37 unequal: No Solution Exploring Operation: 42+81=123, Resulting Numbers: [123] 123,37 unequal: No Solution Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 37:[74, 49], Operations: ['56-49=7', '42+7=49'] Exploring Operation: 74*49=3626, Resulting Numbers: [3626] 3626,37 unequal: No Solution Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,37 unequal: No Solution Exploring Operation: 74+49=123, Resulting Numbers: [123] 123,37 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 63, 16, 59, 34 ]
22
[ "63-16=47", "59-34=25", "47-25=22" ]
Current State: 22:[63, 16, 59, 34], Operations: [] Exploring Operation: 63-16=47, Resulting Numbers: [59, 34, 47] Generated Node #2: [59, 34, 47] from Operation: 63-16=47 Current State: 22:[59, 34, 47], Operations: ['63-16=47'] Exploring Operation: 59-34=25, Resulting Numbers: [47, 25] Generated Node #3: [47, 25] from Operation: 59-34=25 Current State: 22:[47, 25], Operations: ['63-16=47', '59-34=25'] Exploring Operation: 47-25=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[63, 16, 59, 34], Operations: [] Exploring Operation: 63-34=29, Resulting Numbers: [16, 59, 29] Generated Node #0,0: 22:[16, 59, 29] Operation: 63-34=29 Exploring Operation: 63-16=47, Resulting Numbers: [59, 34, 47] Generated Node #0,1: 22:[59, 34, 47] Operation: 63-16=47 Exploring Operation: 63-59=4, Resulting Numbers: [16, 34, 4] Generated Node #0,2: 22:[16, 34, 4] Operation: 63-59=4 Exploring Operation: 59-34=25, Resulting Numbers: [63, 16, 25] Generated Node #0,3: 22:[63, 16, 25] Operation: 59-34=25 Moving to Node #0,2 Current State: 22:[16, 34, 4], Operations: ['63-59=4'] Exploring Operation: 16+4=20, Resulting Numbers: [34, 20] Generated Node #0,2,0: 22:[34, 20] Operation: 16+4=20 Exploring Operation: 16-4=12, Resulting Numbers: [34, 12] Generated Node #0,2,1: 22:[34, 12] Operation: 16-4=12 Exploring Operation: 34-16=18, Resulting Numbers: [4, 18] Generated Node #0,2,2: 22:[4, 18] Operation: 34-16=18 Exploring Operation: 34-4=30, Resulting Numbers: [16, 30] Generated Node #0,2,3: 22:[16, 30] Operation: 34-4=30 Moving to Node #0,3 Current State: 22:[63, 16, 25], Operations: ['59-34=25'] Exploring Operation: 25-16=9, Resulting Numbers: [63, 9] Generated Node #0,3,0: 22:[63, 9] Operation: 25-16=9 Exploring Operation: 63+16=79, Resulting Numbers: [25, 79] Generated Node #0,3,1: 22:[25, 79] Operation: 63+16=79 Exploring Operation: 63-16=47, Resulting Numbers: [25, 47] Generated Node #0,3,2: 22:[25, 47] Operation: 63-16=47 Exploring Operation: 63-25=38, Resulting Numbers: [16, 38] Generated Node #0,3,3: 22:[16, 38] Operation: 63-25=38 Moving to Node #0,0 Current State: 22:[16, 59, 29], Operations: ['63-34=29'] Exploring Operation: 29-16=13, Resulting Numbers: [59, 13] Generated Node #0,0,0: 22:[59, 13] Operation: 29-16=13 Exploring Operation: 59-16=43, Resulting Numbers: [29, 43] Generated Node #0,0,1: 22:[29, 43] Operation: 59-16=43 Exploring Operation: 16+59=75, Resulting Numbers: [29, 75] Generated Node #0,0,2: 22:[29, 75] Operation: 16+59=75 Exploring Operation: 59-29=30, Resulting Numbers: [16, 30] Generated Node #0,0,3: 22:[16, 30] Operation: 59-29=30 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 22:[16, 30], Operations: ['63-34=29', '59-29=30'] Exploring Operation: 30-16=14, Resulting Numbers: [14] 14,22 unequal: No Solution Exploring Operation: 16*30=480, Resulting Numbers: [480] 480,22 unequal: No Solution Exploring Operation: 16+30=46, Resulting Numbers: [46] 46,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 22:[29, 43], Operations: ['63-34=29', '59-16=43'] Exploring Operation: 29*43=1247, Resulting Numbers: [1247] 1247,22 unequal: No Solution Exploring Operation: 29+43=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 43-29=14, Resulting Numbers: [14] 14,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[59, 13], Operations: ['63-34=29', '29-16=13'] Exploring Operation: 59-13=46, Resulting Numbers: [46] 46,22 unequal: No Solution Exploring Operation: 59+13=72, Resulting Numbers: [72] 72,22 unequal: No Solution Exploring Operation: 59*13=767, Resulting Numbers: [767] 767,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 22:[29, 75], Operations: ['63-34=29', '16+59=75'] Exploring Operation: 29*75=2175, Resulting Numbers: [2175] 2175,22 unequal: No Solution Exploring Operation: 29+75=104, Resulting Numbers: [104] 104,22 unequal: No Solution Exploring Operation: 75-29=46, Resulting Numbers: [46] 46,22 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: 22:[59, 34, 47], Operations: ['63-16=47'] Exploring Operation: 59-47=12, Resulting Numbers: [34, 12] Generated Node #0,1,0: 22:[34, 12] Operation: 59-47=12 Exploring Operation: 59-34=25, Resulting Numbers: [47, 25] Generated Node #0,1,1: 22:[47, 25] Operation: 59-34=25 Exploring Operation: 47-34=13, Resulting Numbers: [59, 13] Generated Node #0,1,2: 22:[59, 13] Operation: 47-34=13 Exploring Operation: 59+34=93, Resulting Numbers: [47, 93] Generated Node #0,1,3: 22:[47, 93] Operation: 59+34=93 Moving to Node #0,2,2 Current State: 22:[4, 18], Operations: ['63-59=4', '34-16=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[63, 16, 59, 34], Operations: [] Exploring Operation: 63-59=4, Resulting Numbers: [16, 34, 4] Generated Node #0,2: 22:[16, 34, 4] Operation: 63-59=4 Moving to Node #0,2 Current State: 22:[16, 34, 4], Operations: ['63-59=4'] Exploring Operation: 34-16=18, Resulting Numbers: [4, 18] Generated Node #0,2,2: 22:[4, 18] Operation: 34-16=18 Moving to Node #0,2,2 Current State: 22:[4, 18], Operations: ['63-59=4', '34-16=18'] Exploring Operation: 4+18=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.967882
hs_4
sum_heuristic
[ 6, 16, 76, 3 ]
54
[ "6/3=2", "76/2=38", "16+38=54" ]
Current State: 54:[6, 16, 76, 3], Operations: [] Exploring Operation: 6/3=2, Resulting Numbers: [16, 76, 2] Generated Node #2: [16, 76, 2] from Operation: 6/3=2 Current State: 54:[16, 76, 2], Operations: ['6/3=2'] Exploring Operation: 76/2=38, Resulting Numbers: [16, 38] Generated Node #3: [16, 38] from Operation: 76/2=38 Current State: 54:[16, 38], Operations: ['6/3=2', '76/2=38'] Exploring Operation: 16+38=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[6, 16, 76, 3], Operations: [] Exploring Operation: 76-16=60, Resulting Numbers: [6, 3, 60] Generated Node #0,0: 54:[6, 3, 60] Operation: 76-16=60 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[6, 3, 60], Operations: ['76-16=60'] Exploring Operation: 60-6=54, Resulting Numbers: [3, 54] Generated Node #0,0,0: 54:[3, 54] Operation: 60-6=54 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 54:[3, 54], Operations: ['76-16=60', '60-6=54'] Exploring Operation: 54/3=18, Resulting Numbers: [18] 18,54 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
[ 24, 19, 19, 14 ]
76
[ "24+19=43", "19+14=33", "43+33=76" ]
Current State: 76:[24, 19, 19, 14], Operations: [] Exploring Operation: 24+19=43, Resulting Numbers: [14, 43] Generated Node #2: [14, 43] from Operation: 24+19=43 Current State: 76:[14, 43], Operations: ['24+19=43'] Exploring Operation: 19+14=33, Resulting Numbers: [43, 33] Generated Node #3: [43, 33] from Operation: 19+14=33 Current State: 76:[43, 33], Operations: ['24+19=43', '19+14=33'] Exploring Operation: 43+33=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[24, 19, 19, 14], Operations: [] Exploring Operation: 24-19=5, Resulting Numbers: [19, 14, 5] Generated Node #0,0: 76:[19, 14, 5] Operation: 24-19=5 Exploring Operation: 24+14=38, Resulting Numbers: [19, 19, 38] Generated Node #0,1: 76:[19, 19, 38] Operation: 24+14=38 Exploring Operation: 24-19=5, Resulting Numbers: [19, 14, 5] Generated Node #0,2: 76:[19, 14, 5] Operation: 24-19=5 Exploring Operation: 24-14=10, Resulting Numbers: [19, 19, 10] Generated Node #0,3: 76:[19, 19, 10] Operation: 24-14=10 Start Sub Search at level 1: Moving to Node #0,1 Current State: 76:[19, 19, 38], Operations: ['24+14=38'] Exploring Operation: 38/19=2, Resulting Numbers: [19, 2] Generated Node #0,1,0: 76:[19, 2] Operation: 38/19=2 Exploring Operation: 38-19=19, Resulting Numbers: [19, 19] Generated Node #0,1,1: 76:[19, 19] Operation: 38-19=19 Exploring Operation: 19+19=38, Resulting Numbers: [38, 38] Generated Node #0,1,2: 76:[38, 38] Operation: 19+19=38 Exploring Operation: 38-19=19, Resulting Numbers: [19, 19] Generated Node #0,1,3: 76:[19, 19] Operation: 38-19=19 Moving to Node #0,1,0 Current State: 76:[19, 2], Operations: ['24+14=38', '38/19=2'] Exploring Operation: 19+2=21, Resulting Numbers: [21] 21,76 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,76 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,76 unequal: No Solution Moving to Node #0,1,2 Current State: 76:[38, 38], Operations: ['24+14=38', '19+19=38'] Exploring Operation: 38/38=1, Resulting Numbers: [1] 1,76 unequal: No Solution Exploring Operation: 38-38=0, Resulting Numbers: [0] 0,76 unequal: No Solution Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[24, 19, 19, 14], Operations: [] Exploring Operation: 24+14=38, Resulting Numbers: [19, 19, 38] Generated Node #0,1: 76:[19, 19, 38] Operation: 24+14=38 Moving to Node #0,1 Current State: 76:[19, 19, 38], Operations: ['24+14=38'] Exploring Operation: 19+19=38, Resulting Numbers: [38, 38] Generated Node #0,1,2: 76:[38, 38] Operation: 19+19=38 Moving to Node #0,1,2 Current State: 76:[38, 38], Operations: ['24+14=38', '19+19=38'] Exploring Operation: 38+38=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 27, 13, 96, 93 ]
22
[ "96-93=3", "27/3=9", "13+9=22" ]
Current State: 22:[27, 13, 96, 93], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [27, 13, 3] Generated Node #2: [27, 13, 3] from Operation: 96-93=3 Current State: 22:[27, 13, 3], Operations: ['96-93=3'] Exploring Operation: 27/3=9, Resulting Numbers: [13, 9] Generated Node #3: [13, 9] from Operation: 27/3=9 Current State: 22:[13, 9], Operations: ['96-93=3', '27/3=9'] Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[27, 13, 96, 93], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [27, 13, 3] Generated Node #0,0: 22:[27, 13, 3] Operation: 96-93=3 Exploring Operation: 93-27=66, Resulting Numbers: [13, 96, 66] Generated Node #0,1: 22:[13, 96, 66] Operation: 93-27=66 Exploring Operation: 96-27=69, Resulting Numbers: [13, 93, 69] Generated Node #0,2: 22:[13, 93, 69] Operation: 96-27=69 Moving to Node #0,0 Current State: 22:[27, 13, 3], Operations: ['96-93=3'] Exploring Operation: 27/3=9, Resulting Numbers: [13, 9] Generated Node #0,0,0: 22:[13, 9] Operation: 27/3=9 Exploring Operation: 27-3=24, Resulting Numbers: [13, 24] Generated Node #0,0,1: 22:[13, 24] Operation: 27-3=24 Exploring Operation: 27-13=14, Resulting Numbers: [3, 14] Generated Node #0,0,2: 22:[3, 14] Operation: 27-13=14 Moving to Node #0,1 Current State: 22:[13, 96, 66], Operations: ['93-27=66'] Exploring Operation: 66-13=53, Resulting Numbers: [96, 53] Generated Node #0,1,0: 22:[96, 53] Operation: 66-13=53 Exploring Operation: 96-13=83, Resulting Numbers: [66, 83] Generated Node #0,1,1: 22:[66, 83] Operation: 96-13=83 Exploring Operation: 96-66=30, Resulting Numbers: [13, 30] Generated Node #0,1,2: 22:[13, 30] Operation: 96-66=30 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 22:[13, 30], Operations: ['93-27=66', '96-66=30'] Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,22 unequal: No Solution Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[96, 53], Operations: ['93-27=66', '66-13=53'] Exploring Operation: 96-53=43, Resulting Numbers: [43] 43,22 unequal: No Solution Exploring Operation: 96*53=5088, Resulting Numbers: [5088] 5088,22 unequal: No Solution Exploring Operation: 96+53=149, Resulting Numbers: [149] 149,22 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 22:[66, 83], Operations: ['93-27=66', '96-13=83'] Exploring Operation: 66*83=5478, Resulting Numbers: [5478] 5478,22 unequal: No Solution Exploring Operation: 66+83=149, Resulting Numbers: [149] 149,22 unequal: No Solution Exploring Operation: 83-66=17, Resulting Numbers: [17] 17,22 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: 22:[13, 93, 69], Operations: ['96-27=69'] Exploring Operation: 93-69=24, Resulting Numbers: [13, 24] Generated Node #0,2,0: 22:[13, 24] Operation: 93-69=24 Exploring Operation: 69-13=56, Resulting Numbers: [93, 56] Generated Node #0,2,1: 22:[93, 56] Operation: 69-13=56 Exploring Operation: 93-13=80, Resulting Numbers: [69, 80] Generated Node #0,2,2: 22:[69, 80] Operation: 93-13=80 Moving to Node #0,0,0 Current State: 22:[13, 9], Operations: ['96-93=3', '27/3=9'] Exploring Operation: 13-9=4, Resulting Numbers: [4] 4,22 unequal: No Solution Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached Moving to Node #0 Current State: 22:[27, 13, 96, 93], Operations: [] Exploring Operation: 96-93=3, Resulting Numbers: [27, 13, 3] Generated Node #0,0: 22:[27, 13, 3] Operation: 96-93=3 Moving to Node #0,0 Current State: 22:[27, 13, 3], Operations: ['96-93=3'] Exploring Operation: 27/3=9, Resulting Numbers: [13, 9] Generated Node #0,0,0: 22:[13, 9] Operation: 27/3=9 Moving to Node #0,0,0 Current State: 22:[13, 9], Operations: ['96-93=3', '27/3=9'] Exploring Operation: 13+9=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 86, 48, 47, 78 ]
53
[ "86-78=8", "48/8=6", "47+6=53" ]
Current State: 53:[86, 48, 47, 78], Operations: [] Exploring Operation: 86-78=8, Resulting Numbers: [48, 47, 8] Generated Node #2: [48, 47, 8] from Operation: 86-78=8 Current State: 53:[48, 47, 8], Operations: ['86-78=8'] Exploring Operation: 48/8=6, Resulting Numbers: [47, 6] Generated Node #3: [47, 6] from Operation: 48/8=6 Current State: 53:[47, 6], Operations: ['86-78=8', '48/8=6'] Exploring Operation: 47+6=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[86, 48, 47, 78], Operations: [] Exploring Operation: 86-47=39, Resulting Numbers: [48, 78, 39] Generated Node #0,0: 53:[48, 78, 39] Operation: 86-47=39 Moving to Node #0,0 Current State: 53:[48, 78, 39], Operations: ['86-47=39'] Exploring Operation: 78-39=39, Resulting Numbers: [48, 39] Generated Node #0,0,0: 53:[48, 39] Operation: 78-39=39 Moving to Node #0,0,0 Current State: 53:[48, 39], Operations: ['86-47=39', '78-39=39'] Exploring Operation: 48+39=87, Resulting Numbers: [87] 87,53 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 12, 72, 6, 43 ]
53
[ "72-12=60", "60/6=10", "43+10=53" ]
Current State: 53:[12, 72, 6, 43], Operations: [] Exploring Operation: 72-12=60, Resulting Numbers: [6, 43, 60] Generated Node #2: [6, 43, 60] from Operation: 72-12=60 Current State: 53:[6, 43, 60], Operations: ['72-12=60'] Exploring Operation: 60/6=10, Resulting Numbers: [43, 10] Generated Node #3: [43, 10] from Operation: 60/6=10 Current State: 53:[43, 10], Operations: ['72-12=60', '60/6=10'] Exploring Operation: 43+10=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[12, 72, 6, 43], Operations: [] Exploring Operation: 12*6=72, Resulting Numbers: [72, 43, 72] Generated Node #0,0: 53:[72, 43, 72] Operation: 12*6=72 Exploring Operation: 72-12=60, Resulting Numbers: [6, 43, 60] Generated Node #0,1: 53:[6, 43, 60] Operation: 72-12=60 Exploring Operation: 12+6=18, Resulting Numbers: [72, 43, 18] Generated Node #0,2: 53:[72, 43, 18] Operation: 12+6=18 Exploring Operation: 72-6=66, Resulting Numbers: [12, 43, 66] Generated Node #0,3: 53:[12, 43, 66] Operation: 72-6=66 Start Sub Search at level 1: Moving to Node #0,0 Current State: 53:[72, 43, 72], Operations: ['12*6=72'] Exploring Operation: 72-43=29, Resulting Numbers: [72, 29] Generated Node #0,0,0: 53:[72, 29] Operation: 72-43=29 Exploring Operation: 72-43=29, Resulting Numbers: [72, 29] Generated Node #0,0,1: 53:[72, 29] Operation: 72-43=29 Exploring Operation: 72-72=0, Resulting Numbers: [43, 0] Generated Node #0,0,2: 53:[43, 0] Operation: 72-72=0 Exploring Operation: 72/72=1, Resulting Numbers: [43, 1] Generated Node #0,0,3: 53:[43, 1] Operation: 72/72=1 Moving to Node #0,0,0 Current State: 53:[72, 29], Operations: ['12*6=72', '72-43=29'] Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 72+29=101, Resulting Numbers: [101] 101,53 unequal: No Solution Exploring Operation: 72*29=2088, Resulting Numbers: [2088] 2088,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[72, 29], Operations: ['12*6=72', '72-43=29'] Exploring Operation: 72-29=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 72*29=2088, Resulting Numbers: [2088] 2088,53 unequal: No Solution Exploring Operation: 72+29=101, Resulting Numbers: [101] 101,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[43, 1], Operations: ['12*6=72', '72/72=1'] Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,53 unequal: No Solution Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[43, 0], Operations: ['12*6=72', '72-72=0'] Exploring Operation: 43*0=0, Resulting Numbers: [0] 0,53 unequal: No Solution Exploring Operation: 43+0=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 43-0=43, Resulting Numbers: [43] 43,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 53:[6, 43, 60], Operations: ['72-12=60'] Exploring Operation: 60-6=54, Resulting Numbers: [43, 54] Generated Node #0,1,0: 53:[43, 54] Operation: 60-6=54 Exploring Operation: 6+43=49, Resulting Numbers: [60, 49] Generated Node #0,1,1: 53:[60, 49] Operation: 6+43=49 Exploring Operation: 43-6=37, Resulting Numbers: [60, 37] Generated Node #0,1,2: 53:[60, 37] Operation: 43-6=37 Exploring Operation: 6+60=66, Resulting Numbers: [43, 66] Generated Node #0,1,3: 53:[43, 66] Operation: 6+60=66 Moving to Node #0,1,0 Current State: 53:[43, 54], Operations: ['72-12=60', '60-6=54'] Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,53 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[60, 49], Operations: ['72-12=60', '6+43=49'] Exploring Operation: 60+49=109, Resulting Numbers: [109] 109,53 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 60*49=2940, Resulting Numbers: [2940] 2940,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[43, 66], Operations: ['72-12=60', '6+60=66'] Exploring Operation: 43*66=2838, Resulting Numbers: [2838] 2838,53 unequal: No Solution Exploring Operation: 43+66=109, Resulting Numbers: [109] 109,53 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[60, 37], Operations: ['72-12=60', '43-6=37'] Exploring Operation: 60+37=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 60-37=23, Resulting Numbers: [23] 23,53 unequal: No Solution Exploring Operation: 60*37=2220, Resulting Numbers: [2220] 2220,53 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 #0,2 Current State: 53:[72, 43, 18], Operations: ['12+6=18'] Exploring Operation: 72+18=90, Resulting Numbers: [43, 90] Generated Node #0,2,0: 53:[43, 90] Operation: 72+18=90 Exploring Operation: 43-18=25, Resulting Numbers: [72, 25] Generated Node #0,2,1: 53:[72, 25] Operation: 43-18=25 Exploring Operation: 43+18=61, Resulting Numbers: [72, 61] Generated Node #0,2,2: 53:[72, 61] Operation: 43+18=61 Exploring Operation: 72-18=54, Resulting Numbers: [43, 54] Generated Node #0,2,3: 53:[43, 54] Operation: 72-18=54 Moving to Node #0,2,3 Current State: 53:[43, 54], Operations: ['12+6=18', '72-18=54'] Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,53 unequal: No Solution Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[72, 61], Operations: ['12+6=18', '43+18=61'] Exploring Operation: 72+61=133, Resulting Numbers: [133] 133,53 unequal: No Solution Exploring Operation: 72-61=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 72*61=4392, Resulting Numbers: [4392] 4392,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[72, 25], Operations: ['12+6=18', '43-18=25'] Exploring Operation: 72+25=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 72*25=1800, Resulting Numbers: [1800] 1800,53 unequal: No Solution Exploring Operation: 72-25=47, Resulting Numbers: [47] 47,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[43, 90], Operations: ['12+6=18', '72+18=90'] Exploring Operation: 90-43=47, Resulting Numbers: [47] 47,53 unequal: No Solution Exploring Operation: 43*90=3870, Resulting Numbers: [3870] 3870,53 unequal: No Solution Exploring Operation: 43+90=133, Resulting Numbers: [133] 133,53 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 #0,3 Current State: 53:[12, 43, 66], Operations: ['72-6=66'] Exploring Operation: 12+43=55, Resulting Numbers: [66, 55] Generated Node #0,3,0: 53:[66, 55] Operation: 12+43=55 Exploring Operation: 43-12=31, Resulting Numbers: [66, 31] Generated Node #0,3,1: 53:[66, 31] Operation: 43-12=31 Exploring Operation: 66-12=54, Resulting Numbers: [43, 54] Generated Node #0,3,2: 53:[43, 54] Operation: 66-12=54 Exploring Operation: 12+66=78, Resulting Numbers: [43, 78] Generated Node #0,3,3: 53:[43, 78] Operation: 12+66=78 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 53:[43, 54], Operations: ['72-6=66', '66-12=54'] Exploring Operation: 54-43=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 43*54=2322, Resulting Numbers: [2322] 2322,53 unequal: No Solution Exploring Operation: 43+54=97, Resulting Numbers: [97] 97,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 53:[66, 55], Operations: ['72-6=66', '12+43=55'] Exploring Operation: 66*55=3630, Resulting Numbers: [3630] 3630,53 unequal: No Solution Exploring Operation: 66-55=11, Resulting Numbers: [11] 11,53 unequal: No Solution Exploring Operation: 66+55=121, Resulting Numbers: [121] 121,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 53:[66, 31], Operations: ['72-6=66', '43-12=31'] Exploring Operation: 66+31=97, Resulting Numbers: [97] 97,53 unequal: No Solution Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 66*31=2046, Resulting Numbers: [2046] 2046,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 53:[43, 78], Operations: ['72-6=66', '12+66=78'] Exploring Operation: 78-43=35, Resulting Numbers: [35] 35,53 unequal: No Solution Exploring Operation: 43*78=3354, Resulting Numbers: [3354] 3354,53 unequal: No Solution Exploring Operation: 43+78=121, Resulting Numbers: [121] 121,53 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 63, 36, 34, 37 ]
52
[ "63-37=26", "36-34=2", "26*2=52" ]
Current State: 52:[63, 36, 34, 37], Operations: [] Exploring Operation: 63-37=26, Resulting Numbers: [36, 34, 26] Generated Node #2: [36, 34, 26] from Operation: 63-37=26 Current State: 52:[36, 34, 26], Operations: ['63-37=26'] Exploring Operation: 36-34=2, Resulting Numbers: [26, 2] Generated Node #3: [26, 2] from Operation: 36-34=2 Current State: 52:[26, 2], Operations: ['63-37=26', '36-34=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[63, 36, 34, 37], Operations: [] Exploring Operation: 63-37=26, Resulting Numbers: [36, 34, 26] Generated Node #0,0: 52:[36, 34, 26] Operation: 63-37=26 Exploring Operation: 63-36=27, Resulting Numbers: [34, 37, 27] Generated Node #0,1: 52:[34, 37, 27] Operation: 63-36=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[36, 34, 26], Operations: ['63-37=26'] Exploring Operation: 36-26=10, Resulting Numbers: [34, 10] Generated Node #0,0,0: 52:[34, 10] Operation: 36-26=10 Exploring Operation: 36-34=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 52:[26, 2] Operation: 36-34=2 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 52:[26, 2], Operations: ['63-37=26', '36-34=2'] Exploring Operation: 26/2=13, Resulting Numbers: [13] 13,52 unequal: No Solution Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Moving to Node #0 Current State: 52:[63, 36, 34, 37], Operations: [] Exploring Operation: 63-37=26, Resulting Numbers: [36, 34, 26] Generated Node #0,0: 52:[36, 34, 26] Operation: 63-37=26 Moving to Node #0,0 Current State: 52:[36, 34, 26], Operations: ['63-37=26'] Exploring Operation: 36-34=2, Resulting Numbers: [26, 2] Generated Node #0,0,1: 52:[26, 2] Operation: 36-34=2 Moving to Node #0,0,1 Current State: 52:[26, 2], Operations: ['63-37=26', '36-34=2'] Exploring Operation: 26*2=52, Resulting Numbers: [52] 52,52 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
sum_heuristic
[ 86, 4, 72, 34 ]
16
[ "86+4=90", "72+34=106", "106-90=16" ]
Current State: 16:[86, 4, 72, 34], Operations: [] Exploring Operation: 86+4=90, Resulting Numbers: [72, 34, 90] Generated Node #2: [72, 34, 90] from Operation: 86+4=90 Current State: 16:[72, 34, 90], Operations: ['86+4=90'] Exploring Operation: 72+34=106, Resulting Numbers: [90, 106] Generated Node #3: [90, 106] from Operation: 72+34=106 Current State: 16:[90, 106], Operations: ['86+4=90', '72+34=106'] Exploring Operation: 106-90=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[86, 4, 72, 34], Operations: [] Exploring Operation: 86-34=52, Resulting Numbers: [4, 72, 52] Generated Node #0,0: 16:[4, 72, 52] Operation: 86-34=52 Exploring Operation: 72/4=18, Resulting Numbers: [86, 34, 18] Generated Node #0,1: 16:[86, 34, 18] Operation: 72/4=18 Exploring Operation: 86-72=14, Resulting Numbers: [4, 34, 14] Generated Node #0,2: 16:[4, 34, 14] Operation: 86-72=14 Start Sub Search at level 1: Moving to Node #0,2 Current State: 16:[4, 34, 14], Operations: ['86-72=14'] Exploring Operation: 34-14=20, Resulting Numbers: [4, 20] Generated Node #0,2,0: 16:[4, 20] Operation: 34-14=20 Exploring Operation: 34-4=30, Resulting Numbers: [14, 30] Generated Node #0,2,1: 16:[14, 30] Operation: 34-4=30 Exploring Operation: 4+14=18, Resulting Numbers: [34, 18] Generated Node #0,2,2: 16:[34, 18] Operation: 4+14=18 Moving to Node #0,2,0 Current State: 16:[4, 20], Operations: ['86-72=14', '34-14=20'] Exploring Operation: 20/4=5, Resulting Numbers: [5] 5,16 unequal: No Solution Exploring Operation: 4+20=24, Resulting Numbers: [24] 24,16 unequal: No Solution Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[86, 4, 72, 34], Operations: [] Exploring Operation: 86-72=14, Resulting Numbers: [4, 34, 14] Generated Node #0,2: 16:[4, 34, 14] Operation: 86-72=14 Moving to Node #0,2 Current State: 16:[4, 34, 14], Operations: ['86-72=14'] Exploring Operation: 34-14=20, Resulting Numbers: [4, 20] Generated Node #0,2,0: 16:[4, 20] Operation: 34-14=20 Moving to Node #0,2,0 Current State: 16:[4, 20], Operations: ['86-72=14', '34-14=20'] Exploring Operation: 20-4=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 78, 42, 41, 36 ]
42
[ "78-42=36", "36/36=1", "41+1=42" ]
Current State: 42:[78, 42, 41, 36], Operations: [] Exploring Operation: 78-42=36, Resulting Numbers: [41, 36, 36] Generated Node #2: [41, 36, 36] from Operation: 78-42=36 Current State: 42:[41, 36, 36], Operations: ['78-42=36'] Exploring Operation: 36/36=1, Resulting Numbers: [41, 1] Generated Node #3: [41, 1] from Operation: 36/36=1 Current State: 42:[41, 1], Operations: ['78-42=36', '36/36=1'] Exploring Operation: 41+1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[78, 42, 41, 36], Operations: [] Exploring Operation: 78-41=37, Resulting Numbers: [42, 36, 37] Generated Node #0,0: 42:[42, 36, 37] Operation: 78-41=37 Exploring Operation: 78-42=36, Resulting Numbers: [41, 36, 36] Generated Node #0,1: 42:[41, 36, 36] Operation: 78-42=36 Exploring Operation: 78-36=42, Resulting Numbers: [42, 41, 42] Generated Node #0,2: 42:[42, 41, 42] Operation: 78-36=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 42:[42, 41, 42], Operations: ['78-36=42'] Exploring Operation: 42-41=1, Resulting Numbers: [42, 1] Generated Node #0,2,0: 42:[42, 1] Operation: 42-41=1 Exploring Operation: 42/42=1, Resulting Numbers: [41, 1] Generated Node #0,2,1: 42:[41, 1] Operation: 42/42=1 Exploring Operation: 42-41=1, Resulting Numbers: [42, 1] Generated Node #0,2,2: 42:[42, 1] Operation: 42-41=1 Moving to Node #0,2,0 Current State: 42:[42, 1], Operations: ['78-36=42', '42-41=1'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[78, 42, 41, 36], Operations: [] Exploring Operation: 78-36=42, Resulting Numbers: [42, 41, 42] Generated Node #0,2: 42:[42, 41, 42] Operation: 78-36=42 Moving to Node #0,2 Current State: 42:[42, 41, 42], Operations: ['78-36=42'] Exploring Operation: 42-41=1, Resulting Numbers: [42, 1] Generated Node #0,2,0: 42:[42, 1] Operation: 42-41=1 Moving to Node #0,2,0 Current State: 42:[42, 1], Operations: ['78-36=42', '42-41=1'] Exploring Operation: 42/1=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_3
mult_heuristic
[ 47, 5, 20, 97 ]
38
[ "47-20=27", "5*27=135", "135-97=38" ]
Current State: 38:[47, 5, 20, 97], Operations: [] Exploring Operation: 47-20=27, Resulting Numbers: [5, 97, 27] Generated Node #2: [5, 97, 27] from Operation: 47-20=27 Current State: 38:[5, 97, 27], Operations: ['47-20=27'] Exploring Operation: 5*27=135, Resulting Numbers: [97, 135] Generated Node #3: [97, 135] from Operation: 5*27=135 Current State: 38:[97, 135], Operations: ['47-20=27', '5*27=135'] Exploring Operation: 135-97=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[47, 5, 20, 97], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [47, 5, 77] Generated Node #0,0: 38:[47, 5, 77] Operation: 97-20=77 Exploring Operation: 97-5=92, Resulting Numbers: [47, 20, 92] Generated Node #0,1: 38:[47, 20, 92] Operation: 97-5=92 Exploring Operation: 47-5=42, Resulting Numbers: [20, 97, 42] Generated Node #0,2: 38:[20, 97, 42] Operation: 47-5=42 Exploring Operation: 47-20=27, Resulting Numbers: [5, 97, 27] Generated Node #0,3: 38:[5, 97, 27] Operation: 47-20=27 Exploring Operation: 97-47=50, Resulting Numbers: [5, 20, 50] Generated Node #0,4: 38:[5, 20, 50] Operation: 97-47=50 Start Sub Search at level 1: Moving to Node #0,4 Current State: 38:[5, 20, 50], Operations: ['97-47=50'] Exploring Operation: 50-5=45, Resulting Numbers: [20, 45] Generated Node #0,4,0: 38:[20, 45] Operation: 50-5=45 Exploring Operation: 20-5=15, Resulting Numbers: [50, 15] Generated Node #0,4,1: 38:[50, 15] Operation: 20-5=15 Exploring Operation: 50/5=10, Resulting Numbers: [20, 10] Generated Node #0,4,2: 38:[20, 10] Operation: 50/5=10 Exploring Operation: 20/5=4, Resulting Numbers: [50, 4] Generated Node #0,4,3: 38:[50, 4] Operation: 20/5=4 Exploring Operation: 50-20=30, Resulting Numbers: [5, 30] Generated Node #0,4,4: 38:[5, 30] Operation: 50-20=30 Moving to Node #0,4,0 Current State: 38:[20, 45], Operations: ['97-47=50', '50-5=45'] Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,38 unequal: No Solution Moving to Node #0,4,2 Current State: 38:[20, 10], Operations: ['97-47=50', '50/5=10'] Exploring Operation: 20*10=200, Resulting Numbers: [200] 200,38 unequal: No Solution Exploring Operation: 20/10=2, Resulting Numbers: [2] 2,38 unequal: No Solution Exploring Operation: 20+10=30, Resulting Numbers: [30] 30,38 unequal: No Solution Exploring Operation: 20-10=10, Resulting Numbers: [10] 10,38 unequal: No Solution Moving to Node #0,4,4 Current State: 38:[5, 30], Operations: ['97-47=50', '50-20=30'] Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 5*30=150, Resulting Numbers: [150] 150,38 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,38 unequal: No Solution Moving to Node #0,4,3 Current State: 38:[50, 4], Operations: ['97-47=50', '20/5=4'] Exploring Operation: 50+4=54, Resulting Numbers: [54] 54,38 unequal: No Solution Exploring Operation: 50*4=200, Resulting Numbers: [200] 200,38 unequal: No Solution Exploring Operation: 50-4=46, Resulting Numbers: [46] 46,38 unequal: No Solution Moving to Node #0,4,1 Current State: 38:[50, 15], Operations: ['97-47=50', '20-5=15'] Exploring Operation: 50*15=750, Resulting Numbers: [750] 750,38 unequal: No Solution Exploring Operation: 50-15=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 50+15=65, Resulting Numbers: [65] 65,38 unequal: No Solution No 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: 38:[47, 5, 77], Operations: ['97-20=77'] Exploring Operation: 77-5=72, Resulting Numbers: [47, 72] Generated Node #0,0,0: 38:[47, 72] Operation: 77-5=72 Exploring Operation: 77-47=30, Resulting Numbers: [5, 30] Generated Node #0,0,1: 38:[5, 30] Operation: 77-47=30 Exploring Operation: 5+77=82, Resulting Numbers: [47, 82] Generated Node #0,0,2: 38:[47, 82] Operation: 5+77=82 Exploring Operation: 47+5=52, Resulting Numbers: [77, 52] Generated Node #0,0,3: 38:[77, 52] Operation: 47+5=52 Exploring Operation: 47-5=42, Resulting Numbers: [77, 42] Generated Node #0,0,4: 38:[77, 42] Operation: 47-5=42 Moving to Node #0,0,1 Current State: 38:[5, 30], Operations: ['97-20=77', '77-47=30'] Exploring Operation: 5+30=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 30/5=6, Resulting Numbers: [6] 6,38 unequal: No Solution Exploring Operation: 30-5=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 5*30=150, Resulting Numbers: [150] 150,38 unequal: No Solution Moving to Node #0,0,4 Current State: 38:[77, 42], Operations: ['97-20=77', '47-5=42'] Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 77*42=3234, Resulting Numbers: [3234] 3234,38 unequal: No Solution Exploring Operation: 77+42=119, Resulting Numbers: [119] 119,38 unequal: No Solution Moving to Node #0,0,0 Current State: 38:[47, 72], Operations: ['97-20=77', '77-5=72'] Exploring Operation: 47*72=3384, Resulting Numbers: [3384] 3384,38 unequal: No Solution Exploring Operation: 47+72=119, Resulting Numbers: [119] 119,38 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,38 unequal: No Solution Moving to Node #0,0,2 Current State: 38:[47, 82], Operations: ['97-20=77', '5+77=82'] Exploring Operation: 82-47=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 47*82=3854, Resulting Numbers: [3854] 3854,38 unequal: No Solution Exploring Operation: 47+82=129, Resulting Numbers: [129] 129,38 unequal: No Solution Moving to Node #0,0,3 Current State: 38:[77, 52], Operations: ['97-20=77', '47+5=52'] Exploring Operation: 77+52=129, Resulting Numbers: [129] 129,38 unequal: No Solution Exploring Operation: 77-52=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 77*52=4004, Resulting Numbers: [4004] 4004,38 unequal: No Solution No 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: 38:[47, 20, 92], Operations: ['97-5=92'] Exploring Operation: 92-20=72, Resulting Numbers: [47, 72] Generated Node #0,1,0: 38:[47, 72] Operation: 92-20=72 Exploring Operation: 47-20=27, Resulting Numbers: [92, 27] Generated Node #0,1,1: 38:[92, 27] Operation: 47-20=27 Exploring Operation: 47+20=67, Resulting Numbers: [92, 67] Generated Node #0,1,2: 38:[92, 67] Operation: 47+20=67 Exploring Operation: 20+92=112, Resulting Numbers: [47, 112] Generated Node #0,1,3: 38:[47, 112] Operation: 20+92=112 Exploring Operation: 92-47=45, Resulting Numbers: [20, 45] Generated Node #0,1,4: 38:[20, 45] Operation: 92-47=45 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 38:[20, 45], Operations: ['97-5=92', '92-47=45'] Exploring Operation: 20+45=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 20*45=900, Resulting Numbers: [900] 900,38 unequal: No Solution Exploring Operation: 45-20=25, Resulting Numbers: [25] 25,38 unequal: No Solution No 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: 38:[47, 72], Operations: ['97-5=92', '92-20=72'] Exploring Operation: 47*72=3384, Resulting Numbers: [3384] 3384,38 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,38 unequal: No Solution Exploring Operation: 47+72=119, Resulting Numbers: [119] 119,38 unequal: No Solution No 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: 38:[92, 27], Operations: ['97-5=92', '47-20=27'] Exploring Operation: 92+27=119, Resulting Numbers: [119] 119,38 unequal: No Solution Exploring Operation: 92*27=2484, Resulting Numbers: [2484] 2484,38 unequal: No Solution Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,38 unequal: No Solution No 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: 38:[92, 67], Operations: ['97-5=92', '47+20=67'] Exploring Operation: 92*67=6164, Resulting Numbers: [6164] 6164,38 unequal: No Solution Exploring Operation: 92+67=159, Resulting Numbers: [159] 159,38 unequal: No Solution Exploring Operation: 92-67=25, Resulting Numbers: [25] 25,38 unequal: No Solution No 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: 38:[47, 112], Operations: ['97-5=92', '20+92=112'] Exploring Operation: 47*112=5264, Resulting Numbers: [5264] 5264,38 unequal: No Solution Exploring Operation: 112-47=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 47+112=159, Resulting Numbers: [159] 159,38 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: 38:[20, 97, 42], Operations: ['47-5=42'] Exploring Operation: 97-20=77, Resulting Numbers: [42, 77] Generated Node #0,2,0: 38:[42, 77] Operation: 97-20=77 Exploring Operation: 97-42=55, Resulting Numbers: [20, 55] Generated Node #0,2,1: 38:[20, 55] Operation: 97-42=55 Exploring Operation: 20+97=117, Resulting Numbers: [42, 117] Generated Node #0,2,2: 38:[42, 117] Operation: 20+97=117 Exploring Operation: 20+42=62, Resulting Numbers: [97, 62] Generated Node #0,2,3: 38:[97, 62] Operation: 20+42=62 Exploring Operation: 42-20=22, Resulting Numbers: [97, 22] Generated Node #0,2,4: 38:[97, 22] Operation: 42-20=22 Moving to Node #0,2,1 Current State: 38:[20, 55], Operations: ['47-5=42', '97-42=55'] Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,38 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,38 unequal: No Solution Moving to Node #0,2,0 Current State: 38:[42, 77], Operations: ['47-5=42', '97-20=77'] Exploring Operation: 42+77=119, Resulting Numbers: [119] 119,38 unequal: No Solution Exploring Operation: 77-42=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 42*77=3234, Resulting Numbers: [3234] 3234,38 unequal: No Solution Moving to Node #0,2,4 Current State: 38:[97, 22], Operations: ['47-5=42', '42-20=22'] Exploring Operation: 97*22=2134, Resulting Numbers: [2134] 2134,38 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,38 unequal: No Solution Exploring Operation: 97+22=119, Resulting Numbers: [119] 119,38 unequal: No Solution Moving to Node #0,2,2 Current State: 38:[42, 117], Operations: ['47-5=42', '20+97=117'] Exploring Operation: 42+117=159, Resulting Numbers: [159] 159,38 unequal: No Solution Exploring Operation: 117-42=75, Resulting Numbers: [75] 75,38 unequal: No Solution Exploring Operation: 42*117=4914, Resulting Numbers: [4914] 4914,38 unequal: No Solution Moving to Node #0,2,3 Current State: 38:[97, 62], Operations: ['47-5=42', '20+42=62'] Exploring Operation: 97-62=35, Resulting Numbers: [35] 35,38 unequal: No Solution Exploring Operation: 97*62=6014, Resulting Numbers: [6014] 6014,38 unequal: No Solution Exploring Operation: 97+62=159, Resulting Numbers: [159] 159,38 unequal: No Solution No 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: 38:[5, 97, 27], Operations: ['47-20=27'] Exploring Operation: 5+97=102, Resulting Numbers: [27, 102] Generated Node #0,3,0: 38:[27, 102] Operation: 5+97=102 Exploring Operation: 97-27=70, Resulting Numbers: [5, 70] Generated Node #0,3,1: 38:[5, 70] Operation: 97-27=70 Exploring Operation: 97-5=92, Resulting Numbers: [27, 92] Generated Node #0,3,2: 38:[27, 92] Operation: 97-5=92 Exploring Operation: 27-5=22, Resulting Numbers: [97, 22] Generated Node #0,3,3: 38:[97, 22] Operation: 27-5=22 Exploring Operation: 5+27=32, Resulting Numbers: [97, 32] Generated Node #0,3,4: 38:[97, 32] Operation: 5+27=32 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 38:[5, 70], Operations: ['47-20=27', '97-27=70'] Exploring Operation: 70/5=14, Resulting Numbers: [14] 14,38 unequal: No Solution Exploring Operation: 70-5=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 5+70=75, Resulting Numbers: [75] 75,38 unequal: No Solution Exploring Operation: 5*70=350, Resulting Numbers: [350] 350,38 unequal: No Solution No 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: 38:[27, 92], Operations: ['47-20=27', '97-5=92'] Exploring Operation: 27*92=2484, Resulting Numbers: [2484] 2484,38 unequal: No Solution Exploring Operation: 92-27=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 27+92=119, Resulting Numbers: [119] 119,38 unequal: No Solution No 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: 38:[97, 22], Operations: ['47-20=27', '27-5=22'] Exploring Operation: 97+22=119, Resulting Numbers: [119] 119,38 unequal: No Solution Exploring Operation: 97*22=2134, Resulting Numbers: [2134] 2134,38 unequal: No Solution Exploring Operation: 97-22=75, Resulting Numbers: [75] 75,38 unequal: No Solution No 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: 38:[97, 32], Operations: ['47-20=27', '5+27=32'] Exploring Operation: 97*32=3104, Resulting Numbers: [3104] 3104,38 unequal: No Solution Exploring Operation: 97-32=65, Resulting Numbers: [65] 65,38 unequal: No Solution Exploring Operation: 97+32=129, Resulting Numbers: [129] 129,38 unequal: No Solution No 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: 38:[27, 102], Operations: ['47-20=27', '5+97=102'] Exploring Operation: 27+102=129, Resulting Numbers: [129] 129,38 unequal: No Solution Exploring Operation: 27*102=2754, Resulting Numbers: [2754] 2754,38 unequal: No Solution Exploring Operation: 102-27=75, Resulting Numbers: [75] 75,38 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
[ 32, 6, 12, 65 ]
51
[ "32-6=26", "12+65=77", "77-26=51" ]
Current State: 51:[32, 6, 12, 65], Operations: [] Exploring Operation: 32-6=26, Resulting Numbers: [12, 65, 26] Generated Node #2: [12, 65, 26] from Operation: 32-6=26 Current State: 51:[12, 65, 26], Operations: ['32-6=26'] Exploring Operation: 12+65=77, Resulting Numbers: [26, 77] Generated Node #3: [26, 77] from Operation: 12+65=77 Current State: 51:[26, 77], Operations: ['32-6=26', '12+65=77'] Exploring Operation: 77-26=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[32, 6, 12, 65], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [6, 65, 20] Generated Node #0,0: 51:[6, 65, 20] Operation: 32-12=20 Exploring Operation: 65-32=33, Resulting Numbers: [6, 12, 33] Generated Node #0,1: 51:[6, 12, 33] Operation: 65-32=33 Exploring Operation: 65-12=53, Resulting Numbers: [32, 6, 53] Generated Node #0,2: 51:[32, 6, 53] Operation: 65-12=53 Exploring Operation: 32-6=26, Resulting Numbers: [12, 65, 26] Generated Node #0,3: 51:[12, 65, 26] Operation: 32-6=26 Exploring Operation: 32+12=44, Resulting Numbers: [6, 65, 44] Generated Node #0,4: 51:[6, 65, 44] Operation: 32+12=44 Moving to Node #0,0 Current State: 51:[6, 65, 20], Operations: ['32-12=20'] Exploring Operation: 65-6=59, Resulting Numbers: [20, 59] Generated Node #0,0,0: 51:[20, 59] Operation: 65-6=59 Exploring Operation: 65-20=45, Resulting Numbers: [6, 45] Generated Node #0,0,1: 51:[6, 45] Operation: 65-20=45 Exploring Operation: 6+20=26, Resulting Numbers: [65, 26] Generated Node #0,0,2: 51:[65, 26] Operation: 6+20=26 Exploring Operation: 6+65=71, Resulting Numbers: [20, 71] Generated Node #0,0,3: 51:[20, 71] Operation: 6+65=71 Exploring Operation: 20-6=14, Resulting Numbers: [65, 14] Generated Node #0,0,4: 51:[65, 14] Operation: 20-6=14 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 51:[6, 45], Operations: ['32-12=20', '65-20=45'] Exploring Operation: 6*45=270, Resulting Numbers: [270] 270,51 unequal: No Solution Exploring Operation: 45-6=39, Resulting Numbers: [39] 39,51 unequal: No Solution Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[32, 6, 12, 65], Operations: [] Exploring Operation: 32-12=20, Resulting Numbers: [6, 65, 20] Generated Node #0,0: 51:[6, 65, 20] Operation: 32-12=20 Moving to Node #0,0 Current State: 51:[6, 65, 20], Operations: ['32-12=20'] Exploring Operation: 65-20=45, Resulting Numbers: [6, 45] Generated Node #0,0,1: 51:[6, 45] Operation: 65-20=45 Moving to Node #0,0,1 Current State: 51:[6, 45], Operations: ['32-12=20', '65-20=45'] Exploring Operation: 6+45=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
sum_heuristic
[ 6, 89, 55, 43 ]
95
[ "89-6=83", "55-43=12", "83+12=95" ]
Current State: 95:[6, 89, 55, 43], Operations: [] Exploring Operation: 89-6=83, Resulting Numbers: [55, 43, 83] Generated Node #2: [55, 43, 83] from Operation: 89-6=83 Current State: 95:[55, 43, 83], Operations: ['89-6=83'] Exploring Operation: 55-43=12, Resulting Numbers: [83, 12] Generated Node #3: [83, 12] from Operation: 55-43=12 Current State: 95:[83, 12], Operations: ['89-6=83', '55-43=12'] Exploring Operation: 83+12=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[6, 89, 55, 43], Operations: [] Exploring Operation: 55-43=12, Resulting Numbers: [6, 89, 12] Generated Node #0,0: 95:[6, 89, 12] Operation: 55-43=12 Exploring Operation: 55+43=98, Resulting Numbers: [6, 89, 98] Generated Node #0,1: 95:[6, 89, 98] Operation: 55+43=98 Moving to Node #0,1 Current State: 95:[6, 89, 98], Operations: ['55+43=98'] Exploring Operation: 98-89=9, Resulting Numbers: [6, 9] Generated Node #0,1,0: 95:[6, 9] Operation: 98-89=9 Exploring Operation: 6+89=95, Resulting Numbers: [98, 95] Generated Node #0,1,1: 95:[98, 95] Operation: 6+89=95 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 95:[98, 95], Operations: ['55+43=98', '6+89=95'] Exploring Operation: 98-95=3, Resulting Numbers: [3] 3,95 unequal: No Solution Exploring Operation: 98+95=193, Resulting Numbers: [193] 193,95 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 95:[6, 9], Operations: ['55+43=98', '98-89=9'] Exploring Operation: 6+9=15, Resulting Numbers: [15] 15,95 unequal: No Solution Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,95 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: 95:[6, 89, 12], Operations: ['55-43=12'] Exploring Operation: 6+12=18, Resulting Numbers: [89, 18] Generated Node #0,0,0: 95:[89, 18] Operation: 6+12=18 Exploring Operation: 6+89=95, Resulting Numbers: [12, 95] Generated Node #0,0,1: 95:[12, 95] Operation: 6+89=95 Moving to Node #0,0,0 Current State: 95:[89, 18], Operations: ['55-43=12', '6+12=18'] Exploring Operation: 89+18=107, Resulting Numbers: [107] 107,95 unequal: No Solution Exploring Operation: 89-18=71, Resulting Numbers: [71] 71,95 unequal: No Solution Moving to Node #0,0,1 Current State: 95:[12, 95], Operations: ['55-43=12', '6+89=95'] Exploring Operation: 95-12=83, Resulting Numbers: [83] 83,95 unequal: No Solution Exploring Operation: 12+95=107, Resulting Numbers: [107] 107,95 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 4, 60, 34, 10 ]
57
[ "34-4=30", "30/10=3", "60-3=57" ]
Current State: 57:[4, 60, 34, 10], Operations: [] Exploring Operation: 34-4=30, Resulting Numbers: [60, 10, 30] Generated Node #2: [60, 10, 30] from Operation: 34-4=30 Current State: 57:[60, 10, 30], Operations: ['34-4=30'] Exploring Operation: 30/10=3, Resulting Numbers: [60, 3] Generated Node #3: [60, 3] from Operation: 30/10=3 Current State: 57:[60, 3], Operations: ['34-4=30', '30/10=3'] Exploring Operation: 60-3=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[4, 60, 34, 10], Operations: [] Exploring Operation: 60-34=26, Resulting Numbers: [4, 10, 26] Generated Node #0,0: 57:[4, 10, 26] Operation: 60-34=26 Exploring Operation: 34-10=24, Resulting Numbers: [4, 60, 24] Generated Node #0,1: 57:[4, 60, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,1 Current State: 57:[4, 60, 24], Operations: ['34-10=24'] Exploring Operation: 60-4=56, Resulting Numbers: [24, 56] Generated Node #0,1,0: 57:[24, 56] Operation: 60-4=56 Exploring Operation: 24-4=20, Resulting Numbers: [60, 20] Generated Node #0,1,1: 57:[60, 20] Operation: 24-4=20 Moving to Node #0,1,1 Current State: 57:[60, 20], Operations: ['34-10=24', '24-4=20'] Exploring Operation: 60-20=40, Resulting Numbers: [40] 40,57 unequal: No Solution Exploring Operation: 60/20=3, Resulting Numbers: [3] 3,57 unequal: No Solution Moving to Node #0,1,0 Current State: 57:[24, 56], Operations: ['34-10=24', '60-4=56'] Exploring Operation: 24+56=80, Resulting Numbers: [80] 80,57 unequal: No Solution Exploring Operation: 56-24=32, Resulting Numbers: [32] 32,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[4, 10, 26], Operations: ['60-34=26'] Exploring Operation: 10-4=6, Resulting Numbers: [26, 6] Generated Node #0,0,0: 57:[26, 6] Operation: 10-4=6 Exploring Operation: 26-10=16, Resulting Numbers: [4, 16] Generated Node #0,0,1: 57:[4, 16] Operation: 26-10=16 Moving to Node #0,0,1 Current State: 57:[4, 16], Operations: ['60-34=26', '26-10=16'] Exploring Operation: 16/4=4, Resulting Numbers: [4] 4,57 unequal: No Solution Exploring Operation: 4+16=20, Resulting Numbers: [20] 20,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[26, 6], Operations: ['60-34=26', '10-4=6'] Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,57 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
[ 16, 63, 52, 80 ]
16
[ "63-16=47", "52-47=5", "80/5=16" ]
Current State: 16:[16, 63, 52, 80], Operations: [] Exploring Operation: 63-16=47, Resulting Numbers: [52, 80, 47] Generated Node #2: [52, 80, 47] from Operation: 63-16=47 Current State: 16:[52, 80, 47], Operations: ['63-16=47'] Exploring Operation: 52-47=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 52-47=5 Current State: 16:[80, 5], Operations: ['63-16=47', '52-47=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[16, 63, 52, 80], Operations: [] Exploring Operation: 80-63=17, Resulting Numbers: [16, 52, 17] Generated Node #0,0: 16:[16, 52, 17] Operation: 80-63=17 Exploring Operation: 80-52=28, Resulting Numbers: [16, 63, 28] Generated Node #0,1: 16:[16, 63, 28] Operation: 80-52=28 Exploring Operation: 80/16=5, Resulting Numbers: [63, 52, 5] Generated Node #0,2: 16:[63, 52, 5] Operation: 80/16=5 Exploring Operation: 63-52=11, Resulting Numbers: [16, 80, 11] Generated Node #0,3: 16:[16, 80, 11] Operation: 63-52=11 Start Sub Search at level 1: Moving to Node #0,0 Current State: 16:[16, 52, 17], Operations: ['80-63=17'] Exploring Operation: 17-16=1, Resulting Numbers: [52, 1] Generated Node #0,0,0: 16:[52, 1] Operation: 17-16=1 Exploring Operation: 16+52=68, Resulting Numbers: [17, 68] Generated Node #0,0,1: 16:[17, 68] Operation: 16+52=68 Exploring Operation: 52-17=35, Resulting Numbers: [16, 35] Generated Node #0,0,2: 16:[16, 35] Operation: 52-17=35 Exploring Operation: 52-16=36, Resulting Numbers: [17, 36] Generated Node #0,0,3: 16:[17, 36] Operation: 52-16=36 Moving to Node #0,0,2 Current State: 16:[16, 35], Operations: ['80-63=17', '52-17=35'] Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,16 unequal: No Solution Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,0,3 Current State: 16:[17, 36], Operations: ['80-63=17', '52-16=36'] Exploring Operation: 17*36=612, Resulting Numbers: [612] 612,16 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,16 unequal: No Solution Exploring Operation: 17+36=53, Resulting Numbers: [53] 53,16 unequal: No Solution Moving to Node #0,0,0 Current State: 16:[52, 1], Operations: ['80-63=17', '17-16=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 52*1=52, Resulting Numbers: [52] 52,16 unequal: No Solution Exploring Operation: 52+1=53, Resulting Numbers: [53] 53,16 unequal: No Solution Exploring Operation: 52/1=52, Resulting Numbers: [52] 52,16 unequal: No Solution Moving to Node #0,0,1 Current State: 16:[17, 68], Operations: ['80-63=17', '16+52=68'] Exploring Operation: 17*68=1156, Resulting Numbers: [1156] 1156,16 unequal: No Solution Exploring Operation: 68-17=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 17+68=85, Resulting Numbers: [85] 85,16 unequal: No Solution Exploring Operation: 68/17=4, Resulting Numbers: [4] 4,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 16:[16, 63, 28], Operations: ['80-52=28'] Exploring Operation: 28-16=12, Resulting Numbers: [63, 12] Generated Node #0,1,0: 16:[63, 12] Operation: 28-16=12 Exploring Operation: 63-16=47, Resulting Numbers: [28, 47] Generated Node #0,1,1: 16:[28, 47] Operation: 63-16=47 Exploring Operation: 63-28=35, Resulting Numbers: [16, 35] Generated Node #0,1,2: 16:[16, 35] Operation: 63-28=35 Exploring Operation: 16+63=79, Resulting Numbers: [28, 79] Generated Node #0,1,3: 16:[28, 79] Operation: 16+63=79 Moving to Node #0,1,2 Current State: 16:[16, 35], Operations: ['80-52=28', '63-28=35'] Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,16 unequal: No Solution Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[28, 47], Operations: ['80-52=28', '63-16=47'] Exploring Operation: 28*47=1316, Resulting Numbers: [1316] 1316,16 unequal: No Solution Exploring Operation: 28+47=75, Resulting Numbers: [75] 75,16 unequal: No Solution Exploring Operation: 47-28=19, Resulting Numbers: [19] 19,16 unequal: No Solution Moving to Node #0,1,0 Current State: 16:[63, 12], Operations: ['80-52=28', '28-16=12'] Exploring Operation: 63-12=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 63*12=756, Resulting Numbers: [756] 756,16 unequal: No Solution Exploring Operation: 63+12=75, Resulting Numbers: [75] 75,16 unequal: No Solution Moving to Node #0,1,3 Current State: 16:[28, 79], Operations: ['80-52=28', '16+63=79'] Exploring Operation: 28+79=107, Resulting Numbers: [107] 107,16 unequal: No Solution Exploring Operation: 28*79=2212, Resulting Numbers: [2212] 2212,16 unequal: No Solution Exploring Operation: 79-28=51, Resulting Numbers: [51] 51,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 16:[16, 80, 11], Operations: ['63-52=11'] Exploring Operation: 80/16=5, Resulting Numbers: [11, 5] Generated Node #0,3,0: 16:[11, 5] Operation: 80/16=5 Exploring Operation: 16-11=5, Resulting Numbers: [80, 5] Generated Node #0,3,1: 16:[80, 5] Operation: 16-11=5 Exploring Operation: 80-11=69, Resulting Numbers: [16, 69] Generated Node #0,3,2: 16:[16, 69] Operation: 80-11=69 Exploring Operation: 80-16=64, Resulting Numbers: [11, 64] Generated Node #0,3,3: 16:[11, 64] Operation: 80-16=64 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 16:[11, 5], Operations: ['63-52=11', '80/16=5'] Exploring Operation: 11*5=55, Resulting Numbers: [55] 55,16 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,16 unequal: No Solution Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[16, 63, 52, 80], Operations: [] Exploring Operation: 63-52=11, Resulting Numbers: [16, 80, 11] Generated Node #0,3: 16:[16, 80, 11] Operation: 63-52=11 Moving to Node #0,3 Current State: 16:[16, 80, 11], Operations: ['63-52=11'] Exploring Operation: 80/16=5, Resulting Numbers: [11, 5] Generated Node #0,3,0: 16:[11, 5] Operation: 80/16=5 Moving to Node #0,3,0 Current State: 16:[11, 5], Operations: ['63-52=11', '80/16=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.957465
hs_4
sum_heuristic
[ 74, 25, 20, 50 ]
84
[ "25*20=500", "500/50=10", "74+10=84" ]
Current State: 84:[74, 25, 20, 50], Operations: [] Exploring Operation: 25*20=500, Resulting Numbers: [74, 50, 500] Generated Node #2: [74, 50, 500] from Operation: 25*20=500 Current State: 84:[74, 50, 500], Operations: ['25*20=500'] Exploring Operation: 500/50=10, Resulting Numbers: [74, 10] Generated Node #3: [74, 10] from Operation: 500/50=10 Current State: 84:[74, 10], Operations: ['25*20=500', '500/50=10'] Exploring Operation: 74+10=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[74, 25, 20, 50], Operations: [] Exploring Operation: 50-25=25, Resulting Numbers: [74, 20, 25] Generated Node #0,0: 84:[74, 20, 25] Operation: 50-25=25 Exploring Operation: 74-50=24, Resulting Numbers: [25, 20, 24] Generated Node #0,1: 84:[25, 20, 24] Operation: 74-50=24 Exploring Operation: 50/25=2, Resulting Numbers: [74, 20, 2] Generated Node #0,2: 84:[74, 20, 2] Operation: 50/25=2 Exploring Operation: 50-20=30, Resulting Numbers: [74, 25, 30] Generated Node #0,3: 84:[74, 25, 30] Operation: 50-20=30 Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[25, 20, 24], Operations: ['74-50=24'] Exploring Operation: 20+24=44, Resulting Numbers: [25, 44] Generated Node #0,1,0: 84:[25, 44] Operation: 20+24=44 Exploring Operation: 25-24=1, Resulting Numbers: [20, 1] Generated Node #0,1,1: 84:[20, 1] Operation: 25-24=1 Exploring Operation: 25-20=5, Resulting Numbers: [24, 5] Generated Node #0,1,2: 84:[24, 5] Operation: 25-20=5 Exploring Operation: 24-20=4, Resulting Numbers: [25, 4] Generated Node #0,1,3: 84:[25, 4] Operation: 24-20=4 Moving to Node #0,1,1 Current State: 84:[20, 1], Operations: ['74-50=24', '25-24=1'] Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 20*1=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 20+1=21, Resulting Numbers: [21] 21,84 unequal: No Solution Moving to Node #0,1,3 Current State: 84:[25, 4], Operations: ['74-50=24', '24-20=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,84 unequal: No Solution Exploring Operation: 25-4=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 25+4=29, Resulting Numbers: [29] 29,84 unequal: No Solution Moving to Node #0,1,2 Current State: 84:[24, 5], Operations: ['74-50=24', '25-20=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,84 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,84 unequal: No Solution Moving to Node #0,1,0 Current State: 84:[25, 44], Operations: ['74-50=24', '20+24=44'] Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 25*44=1100, Resulting Numbers: [1100] 1100,84 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 84:[74, 20, 2], Operations: ['50/25=2'] Exploring Operation: 74+20=94, Resulting Numbers: [2, 94] Generated Node #0,2,0: 84:[2, 94] Operation: 74+20=94 Exploring Operation: 74/2=37, Resulting Numbers: [20, 37] Generated Node #0,2,1: 84:[20, 37] Operation: 74/2=37 Exploring Operation: 74+2=76, Resulting Numbers: [20, 76] Generated Node #0,2,2: 84:[20, 76] Operation: 74+2=76 Exploring Operation: 20+2=22, Resulting Numbers: [74, 22] Generated Node #0,2,3: 84:[74, 22] Operation: 20+2=22 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 84:[20, 37], Operations: ['50/25=2', '74/2=37'] Exploring Operation: 20*37=740, Resulting Numbers: [740] 740,84 unequal: No Solution Exploring Operation: 37-20=17, Resulting Numbers: [17] 17,84 unequal: No Solution Exploring Operation: 20+37=57, Resulting Numbers: [57] 57,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 84:[20, 76], Operations: ['50/25=2', '74+2=76'] Exploring Operation: 20+76=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 76-20=56, Resulting Numbers: [56] 56,84 unequal: No Solution Exploring Operation: 20*76=1520, Resulting Numbers: [1520] 1520,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 84:[2, 94], Operations: ['50/25=2', '74+20=94'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 2*94=188, Resulting Numbers: [188] 188,84 unequal: No Solution Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 84:[74, 22], Operations: ['50/25=2', '20+2=22'] Exploring Operation: 74*22=1628, Resulting Numbers: [1628] 1628,84 unequal: No Solution Exploring Operation: 74+22=96, Resulting Numbers: [96] 96,84 unequal: No Solution Exploring Operation: 74-22=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[74, 20, 25], Operations: ['50-25=25'] Exploring Operation: 25-20=5, Resulting Numbers: [74, 5] Generated Node #0,0,0: 84:[74, 5] Operation: 25-20=5 Exploring Operation: 74+20=94, Resulting Numbers: [25, 94] Generated Node #0,0,1: 84:[25, 94] Operation: 74+20=94 Exploring Operation: 74-25=49, Resulting Numbers: [20, 49] Generated Node #0,0,2: 84:[20, 49] Operation: 74-25=49 Exploring Operation: 20+25=45, Resulting Numbers: [74, 45] Generated Node #0,0,3: 84:[74, 45] Operation: 20+25=45 Moving to Node #0,0,2 Current State: 84:[20, 49], Operations: ['50-25=25', '74-25=49'] Exploring Operation: 49-20=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 20*49=980, Resulting Numbers: [980] 980,84 unequal: No Solution Exploring Operation: 20+49=69, Resulting Numbers: [69] 69,84 unequal: No Solution Moving to Node #0,0,0 Current State: 84:[74, 5], Operations: ['50-25=25', '25-20=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 74*5=370, Resulting Numbers: [370] 370,84 unequal: No Solution Moving to Node #0,0,3 Current State: 84:[74, 45], Operations: ['50-25=25', '20+25=45'] Exploring Operation: 74-45=29, Resulting Numbers: [29] 29,84 unequal: No Solution Exploring Operation: 74+45=119, Resulting Numbers: [119] 119,84 unequal: No Solution Exploring Operation: 74*45=3330, Resulting Numbers: [3330] 3330,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[25, 94], Operations: ['50-25=25', '74+20=94'] Exploring Operation: 94-25=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 25+94=119, Resulting Numbers: [119] 119,84 unequal: No Solution Exploring Operation: 25*94=2350, Resulting Numbers: [2350] 2350,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 84:[74, 25, 30], Operations: ['50-20=30'] Exploring Operation: 74-25=49, Resulting Numbers: [30, 49] Generated Node #0,3,0: 84:[30, 49] Operation: 74-25=49 Exploring Operation: 74-30=44, Resulting Numbers: [25, 44] Generated Node #0,3,1: 84:[25, 44] Operation: 74-30=44 Exploring Operation: 30-25=5, Resulting Numbers: [74, 5] Generated Node #0,3,2: 84:[74, 5] Operation: 30-25=5 Exploring Operation: 74+25=99, Resulting Numbers: [30, 99] Generated Node #0,3,3: 84:[30, 99] Operation: 74+25=99 Moving to Node #0,3,1 Current State: 84:[25, 44], Operations: ['50-20=30', '74-30=44'] Exploring Operation: 25*44=1100, Resulting Numbers: [1100] 1100,84 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,84 unequal: No Solution Exploring Operation: 25+44=69, Resulting Numbers: [69] 69,84 unequal: No Solution Moving to Node #0,3,0 Current State: 84:[30, 49], Operations: ['50-20=30', '74-25=49'] Exploring Operation: 30*49=1470, Resulting Numbers: [1470] 1470,84 unequal: No Solution Exploring Operation: 30+49=79, Resulting Numbers: [79] 79,84 unequal: No Solution Exploring Operation: 49-30=19, Resulting Numbers: [19] 19,84 unequal: No Solution Moving to Node #0,3,2 Current State: 84:[74, 5], Operations: ['50-20=30', '30-25=5'] Exploring Operation: 74-5=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 74*5=370, Resulting Numbers: [370] 370,84 unequal: No Solution Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,84 unequal: No Solution Moving to Node #0,3,3 Current State: 84:[30, 99], Operations: ['50-20=30', '74+25=99'] Exploring Operation: 99-30=69, Resulting Numbers: [69] 69,84 unequal: No Solution Exploring Operation: 30*99=2970, Resulting Numbers: [2970] 2970,84 unequal: No Solution Exploring Operation: 30+99=129, Resulting Numbers: [129] 129,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 22, 52, 89, 71 ]
13
[ "89-22=67", "71-67=4", "52/4=13" ]
Current State: 13:[22, 52, 89, 71], Operations: [] Exploring Operation: 89-22=67, Resulting Numbers: [52, 71, 67] Generated Node #2: [52, 71, 67] from Operation: 89-22=67 Current State: 13:[52, 71, 67], Operations: ['89-22=67'] Exploring Operation: 71-67=4, Resulting Numbers: [52, 4] Generated Node #3: [52, 4] from Operation: 71-67=4 Current State: 13:[52, 4], Operations: ['89-22=67', '71-67=4'] Exploring Operation: 52/4=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[22, 52, 89, 71], Operations: [] Exploring Operation: 89-71=18, Resulting Numbers: [22, 52, 18] Generated Node #0,0: 13:[22, 52, 18] Operation: 89-71=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[22, 52, 18], Operations: ['89-71=18'] Exploring Operation: 52-22=30, Resulting Numbers: [18, 30] Generated Node #0,0,0: 13:[18, 30] Operation: 52-22=30 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 13:[18, 30], Operations: ['89-71=18', '52-22=30'] Exploring Operation: 30-18=12, Resulting Numbers: [12] 12,13 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
[ 2, 69, 41, 13 ]
27
[ "69-41=28", "28/2=14", "13+14=27" ]
Current State: 27:[2, 69, 41, 13], Operations: [] Exploring Operation: 69-41=28, Resulting Numbers: [2, 13, 28] Generated Node #2: [2, 13, 28] from Operation: 69-41=28 Current State: 27:[2, 13, 28], Operations: ['69-41=28'] Exploring Operation: 28/2=14, Resulting Numbers: [13, 14] Generated Node #3: [13, 14] from Operation: 28/2=14 Current State: 27:[13, 14], Operations: ['69-41=28', '28/2=14'] Exploring Operation: 13+14=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[2, 69, 41, 13], Operations: [] Exploring Operation: 41-13=28, Resulting Numbers: [2, 69, 28] Generated Node #0,0: 27:[2, 69, 28] Operation: 41-13=28 Exploring Operation: 69-2=67, Resulting Numbers: [41, 13, 67] Generated Node #0,1: 27:[41, 13, 67] Operation: 69-2=67 Exploring Operation: 69-13=56, Resulting Numbers: [2, 41, 56] Generated Node #0,2: 27:[2, 41, 56] Operation: 69-13=56 Exploring Operation: 2*13=26, Resulting Numbers: [69, 41, 26] Generated Node #0,3: 27:[69, 41, 26] Operation: 2*13=26 Exploring Operation: 69-41=28, Resulting Numbers: [2, 13, 28] Generated Node #0,4: 27:[2, 13, 28] Operation: 69-41=28 Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[2, 13, 28], Operations: ['69-41=28'] Exploring Operation: 2*13=26, Resulting Numbers: [28, 26] Generated Node #0,4,0: 27:[28, 26] Operation: 2*13=26 Exploring Operation: 2+28=30, Resulting Numbers: [13, 30] Generated Node #0,4,1: 27:[13, 30] Operation: 2+28=30 Exploring Operation: 2+13=15, Resulting Numbers: [28, 15] Generated Node #0,4,2: 27:[28, 15] Operation: 2+13=15 Exploring Operation: 13-2=11, Resulting Numbers: [28, 11] Generated Node #0,4,3: 27:[28, 11] Operation: 13-2=11 Exploring Operation: 28-2=26, Resulting Numbers: [13, 26] Generated Node #0,4,4: 27:[13, 26] Operation: 28-2=26 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 27:[28, 26], Operations: ['69-41=28', '2*13=26'] Exploring Operation: 28+26=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 28*26=728, Resulting Numbers: [728] 728,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 27:[28, 11], Operations: ['69-41=28', '13-2=11'] Exploring Operation: 28+11=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 28-11=17, Resulting Numbers: [17] 17,27 unequal: No Solution Exploring Operation: 28*11=308, Resulting Numbers: [308] 308,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 27:[13, 26], Operations: ['69-41=28', '28-2=26'] Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,27 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 27:[13, 30], Operations: ['69-41=28', '2+28=30'] Exploring Operation: 13+30=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 13*30=390, Resulting Numbers: [390] 390,27 unequal: No Solution Exploring Operation: 30-13=17, Resulting Numbers: [17] 17,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 27:[28, 15], Operations: ['69-41=28', '2+13=15'] Exploring Operation: 28+15=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 28-15=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 28*15=420, Resulting Numbers: [420] 420,27 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 Start Sub Search at level 1: Moving to Node #0,0 Current State: 27:[2, 69, 28], Operations: ['41-13=28'] Exploring Operation: 69-2=67, Resulting Numbers: [28, 67] Generated Node #0,0,0: 27:[28, 67] Operation: 69-2=67 Exploring Operation: 28-2=26, Resulting Numbers: [69, 26] Generated Node #0,0,1: 27:[69, 26] Operation: 28-2=26 Exploring Operation: 2+28=30, Resulting Numbers: [69, 30] Generated Node #0,0,2: 27:[69, 30] Operation: 2+28=30 Exploring Operation: 69-28=41, Resulting Numbers: [2, 41] Generated Node #0,0,3: 27:[2, 41] Operation: 69-28=41 Exploring Operation: 2+69=71, Resulting Numbers: [28, 71] Generated Node #0,0,4: 27:[28, 71] Operation: 2+69=71 Moving to Node #0,0,3 Current State: 27:[2, 41], Operations: ['41-13=28', '69-28=41'] Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,27 unequal: No Solution Moving to Node #0,0,0 Current State: 27:[28, 67], Operations: ['41-13=28', '69-2=67'] Exploring Operation: 28*67=1876, Resulting Numbers: [1876] 1876,27 unequal: No Solution Exploring Operation: 28+67=95, Resulting Numbers: [95] 95,27 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,27 unequal: No Solution Moving to Node #0,0,1 Current State: 27:[69, 26], Operations: ['41-13=28', '28-2=26'] Exploring Operation: 69+26=95, Resulting Numbers: [95] 95,27 unequal: No Solution Exploring Operation: 69*26=1794, Resulting Numbers: [1794] 1794,27 unequal: No Solution Exploring Operation: 69-26=43, Resulting Numbers: [43] 43,27 unequal: No Solution Moving to Node #0,0,2 Current State: 27:[69, 30], Operations: ['41-13=28', '2+28=30'] Exploring Operation: 69+30=99, Resulting Numbers: [99] 99,27 unequal: No Solution Exploring Operation: 69*30=2070, Resulting Numbers: [2070] 2070,27 unequal: No Solution Exploring Operation: 69-30=39, Resulting Numbers: [39] 39,27 unequal: No Solution Moving to Node #0,0,4 Current State: 27:[28, 71], Operations: ['41-13=28', '2+69=71'] Exploring Operation: 71-28=43, Resulting Numbers: [43] 43,27 unequal: No Solution Exploring Operation: 28*71=1988, Resulting Numbers: [1988] 1988,27 unequal: No Solution Exploring Operation: 28+71=99, Resulting Numbers: [99] 99,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 27:[2, 41, 56], Operations: ['69-13=56'] Exploring Operation: 56-2=54, Resulting Numbers: [41, 54] Generated Node #0,2,0: 27:[41, 54] Operation: 56-2=54 Exploring Operation: 41-2=39, Resulting Numbers: [56, 39] Generated Node #0,2,1: 27:[56, 39] Operation: 41-2=39 Exploring Operation: 56/2=28, Resulting Numbers: [41, 28] Generated Node #0,2,2: 27:[41, 28] Operation: 56/2=28 Exploring Operation: 2+41=43, Resulting Numbers: [56, 43] Generated Node #0,2,3: 27:[56, 43] Operation: 2+41=43 Exploring Operation: 56-41=15, Resulting Numbers: [2, 15] Generated Node #0,2,4: 27:[2, 15] Operation: 56-41=15 Moving to Node #0,2,4 Current State: 27:[2, 15], Operations: ['69-13=56', '56-41=15'] Exploring Operation: 2*15=30, Resulting Numbers: [30] 30,27 unequal: No Solution Exploring Operation: 2+15=17, Resulting Numbers: [17] 17,27 unequal: No Solution Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,27 unequal: No Solution Moving to Node #0,2,2 Current State: 27:[41, 28], Operations: ['69-13=56', '56/2=28'] Exploring Operation: 41+28=69, Resulting Numbers: [69] 69,27 unequal: No Solution Exploring Operation: 41-28=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 41*28=1148, Resulting Numbers: [1148] 1148,27 unequal: No Solution Moving to Node #0,2,0 Current State: 27:[41, 54], Operations: ['69-13=56', '56-2=54'] Exploring Operation: 41*54=2214, Resulting Numbers: [2214] 2214,27 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 41+54=95, Resulting Numbers: [95] 95,27 unequal: No Solution Moving to Node #0,2,1 Current State: 27:[56, 39], Operations: ['69-13=56', '41-2=39'] Exploring Operation: 56*39=2184, Resulting Numbers: [2184] 2184,27 unequal: No Solution Exploring Operation: 56-39=17, Resulting Numbers: [17] 17,27 unequal: No Solution Exploring Operation: 56+39=95, Resulting Numbers: [95] 95,27 unequal: No Solution Moving to Node #0,2,3 Current State: 27:[56, 43], Operations: ['69-13=56', '2+41=43'] Exploring Operation: 56*43=2408, Resulting Numbers: [2408] 2408,27 unequal: No Solution Exploring Operation: 56-43=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 56+43=99, Resulting Numbers: [99] 99,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 27:[69, 41, 26], Operations: ['2*13=26'] Exploring Operation: 69-26=43, Resulting Numbers: [41, 43] Generated Node #0,3,0: 27:[41, 43] Operation: 69-26=43 Exploring Operation: 41-26=15, Resulting Numbers: [69, 15] Generated Node #0,3,1: 27:[69, 15] Operation: 41-26=15 Exploring Operation: 69+26=95, Resulting Numbers: [41, 95] Generated Node #0,3,2: 27:[41, 95] Operation: 69+26=95 Exploring Operation: 41+26=67, Resulting Numbers: [69, 67] Generated Node #0,3,3: 27:[69, 67] Operation: 41+26=67 Exploring Operation: 69-41=28, Resulting Numbers: [26, 28] Generated Node #0,3,4: 27:[26, 28] Operation: 69-41=28 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 27:[26, 28], Operations: ['2*13=26', '69-41=28'] Exploring Operation: 26*28=728, Resulting Numbers: [728] 728,27 unequal: No Solution Exploring Operation: 28-26=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 26+28=54, Resulting Numbers: [54] 54,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 27:[41, 43], Operations: ['2*13=26', '69-26=43'] Exploring Operation: 41*43=1763, Resulting Numbers: [1763] 1763,27 unequal: No Solution Exploring Operation: 41+43=84, Resulting Numbers: [84] 84,27 unequal: No Solution Exploring Operation: 43-41=2, Resulting Numbers: [2] 2,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 27:[69, 15], Operations: ['2*13=26', '41-26=15'] Exploring Operation: 69-15=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 69*15=1035, Resulting Numbers: [1035] 1035,27 unequal: No Solution Exploring Operation: 69+15=84, Resulting Numbers: [84] 84,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 27:[41, 95], Operations: ['2*13=26', '69+26=95'] Exploring Operation: 95-41=54, Resulting Numbers: [54] 54,27 unequal: No Solution Exploring Operation: 41+95=136, Resulting Numbers: [136] 136,27 unequal: No Solution Exploring Operation: 41*95=3895, Resulting Numbers: [3895] 3895,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 27:[69, 67], Operations: ['2*13=26', '41+26=67'] Exploring Operation: 69-67=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 69+67=136, Resulting Numbers: [136] 136,27 unequal: No Solution Exploring Operation: 69*67=4623, Resulting Numbers: [4623] 4623,27 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 Start Sub Search at level 1: Moving to Node #0,1 Current State: 27:[41, 13, 67], Operations: ['69-2=67'] Exploring Operation: 41+13=54, Resulting Numbers: [67, 54] Generated Node #0,1,0: 27:[67, 54] Operation: 41+13=54 Exploring Operation: 67-13=54, Resulting Numbers: [41, 54] Generated Node #0,1,1: 27:[41, 54] Operation: 67-13=54 Exploring Operation: 13+67=80, Resulting Numbers: [41, 80] Generated Node #0,1,2: 27:[41, 80] Operation: 13+67=80 Exploring Operation: 67-41=26, Resulting Numbers: [13, 26] Generated Node #0,1,3: 27:[13, 26] Operation: 67-41=26 Exploring Operation: 41-13=28, Resulting Numbers: [67, 28] Generated Node #0,1,4: 27:[67, 28] Operation: 41-13=28 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 27:[13, 26], Operations: ['69-2=67', '67-41=26'] Exploring Operation: 13+26=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 26-13=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 26/13=2, Resulting Numbers: [2] 2,27 unequal: No Solution Exploring Operation: 13*26=338, Resulting Numbers: [338] 338,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 27:[41, 54], Operations: ['69-2=67', '67-13=54'] Exploring Operation: 41+54=95, Resulting Numbers: [95] 95,27 unequal: No Solution Exploring Operation: 54-41=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 41*54=2214, Resulting Numbers: [2214] 2214,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 27:[67, 28], Operations: ['69-2=67', '41-13=28'] Exploring Operation: 67+28=95, Resulting Numbers: [95] 95,27 unequal: No Solution Exploring Operation: 67*28=1876, Resulting Numbers: [1876] 1876,27 unequal: No Solution Exploring Operation: 67-28=39, Resulting Numbers: [39] 39,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 27:[67, 54], Operations: ['69-2=67', '41+13=54'] Exploring Operation: 67-54=13, Resulting Numbers: [13] 13,27 unequal: No Solution Exploring Operation: 67+54=121, Resulting Numbers: [121] 121,27 unequal: No Solution Exploring Operation: 67*54=3618, Resulting Numbers: [3618] 3618,27 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 27:[41, 80], Operations: ['69-2=67', '13+67=80'] Exploring Operation: 80-41=39, Resulting Numbers: [39] 39,27 unequal: No Solution Exploring Operation: 41+80=121, Resulting Numbers: [121] 121,27 unequal: No Solution Exploring Operation: 41*80=3280, Resulting Numbers: [3280] 3280,27 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_5
mult_heuristic
[ 56, 44, 4, 79 ]
12
[ "79-56=23", "44/4=11", "23-11=12" ]
Current State: 12:[56, 44, 4, 79], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [44, 4, 23] Generated Node #2: [44, 4, 23] from Operation: 79-56=23 Current State: 12:[44, 4, 23], Operations: ['79-56=23'] Exploring Operation: 44/4=11, Resulting Numbers: [23, 11] Generated Node #3: [23, 11] from Operation: 44/4=11 Current State: 12:[23, 11], Operations: ['79-56=23', '44/4=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[56, 44, 4, 79], Operations: [] Exploring Operation: 56/4=14, Resulting Numbers: [44, 79, 14] Generated Node #0,0: 12:[44, 79, 14] Operation: 56/4=14 Exploring Operation: 79-56=23, Resulting Numbers: [44, 4, 23] Generated Node #0,1: 12:[44, 4, 23] Operation: 79-56=23 Exploring Operation: 56-44=12, Resulting Numbers: [4, 79, 12] Generated Node #0,2: 12:[4, 79, 12] Operation: 56-44=12 Exploring Operation: 79-44=35, Resulting Numbers: [56, 4, 35] Generated Node #0,3: 12:[56, 4, 35] Operation: 79-44=35 Start Sub Search at level 1: Moving to Node #0,1 Current State: 12:[44, 4, 23], Operations: ['79-56=23'] Exploring Operation: 23-4=19, Resulting Numbers: [44, 19] Generated Node #0,1,0: 12:[44, 19] Operation: 23-4=19 Exploring Operation: 44-4=40, Resulting Numbers: [23, 40] Generated Node #0,1,1: 12:[23, 40] Operation: 44-4=40 Exploring Operation: 44-23=21, Resulting Numbers: [4, 21] Generated Node #0,1,2: 12:[4, 21] Operation: 44-23=21 Exploring Operation: 44/4=11, Resulting Numbers: [23, 11] Generated Node #0,1,3: 12:[23, 11] Operation: 44/4=11 Moving to Node #0,1,2 Current State: 12:[4, 21], Operations: ['79-56=23', '44-23=21'] Exploring Operation: 4*21=84, Resulting Numbers: [84] 84,12 unequal: No Solution Exploring Operation: 4+21=25, Resulting Numbers: [25] 25,12 unequal: No Solution Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,12 unequal: No Solution Moving to Node #0,1,3 Current State: 12:[23, 11], Operations: ['79-56=23', '44/4=11'] Exploring Operation: 23*11=253, Resulting Numbers: [253] 253,12 unequal: No Solution Exploring Operation: 23+11=34, Resulting Numbers: [34] 34,12 unequal: No Solution Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[56, 44, 4, 79], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [44, 4, 23] Generated Node #0,1: 12:[44, 4, 23] Operation: 79-56=23 Moving to Node #0,1 Current State: 12:[44, 4, 23], Operations: ['79-56=23'] Exploring Operation: 44/4=11, Resulting Numbers: [23, 11] Generated Node #0,1,3: 12:[23, 11] Operation: 44/4=11 Moving to Node #0,1,3 Current State: 12:[23, 11], Operations: ['79-56=23', '44/4=11'] Exploring Operation: 23-11=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
mult_heuristic
[ 55, 26, 77, 22 ]
27
[ "77-55=22", "22/22=1", "26+1=27" ]
Current State: 27:[55, 26, 77, 22], Operations: [] Exploring Operation: 77-55=22, Resulting Numbers: [26, 22, 22] Generated Node #2: [26, 22, 22] from Operation: 77-55=22 Current State: 27:[26, 22, 22], Operations: ['77-55=22'] Exploring Operation: 22/22=1, Resulting Numbers: [26, 1] Generated Node #3: [26, 1] from Operation: 22/22=1 Current State: 27:[26, 1], Operations: ['77-55=22', '22/22=1'] Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[55, 26, 77, 22], Operations: [] Exploring Operation: 55-26=29, Resulting Numbers: [77, 22, 29] Generated Node #0,0: 27:[77, 22, 29] Operation: 55-26=29 Exploring Operation: 77-22=55, Resulting Numbers: [55, 26, 55] Generated Node #0,1: 27:[55, 26, 55] Operation: 77-22=55 Exploring Operation: 77-26=51, Resulting Numbers: [55, 22, 51] Generated Node #0,2: 27:[55, 22, 51] Operation: 77-26=51 Exploring Operation: 55-22=33, Resulting Numbers: [26, 77, 33] Generated Node #0,3: 27:[26, 77, 33] Operation: 55-22=33 Exploring Operation: 77-55=22, Resulting Numbers: [26, 22, 22] Generated Node #0,4: 27:[26, 22, 22] Operation: 77-55=22 Start Sub Search at level 1: Moving to Node #0,4 Current State: 27:[26, 22, 22], Operations: ['77-55=22'] Exploring Operation: 26-22=4, Resulting Numbers: [22, 4] Generated Node #0,4,0: 27:[22, 4] Operation: 26-22=4 Exploring Operation: 22+22=44, Resulting Numbers: [26, 44] Generated Node #0,4,1: 27:[26, 44] Operation: 22+22=44 Exploring Operation: 26-22=4, Resulting Numbers: [22, 4] Generated Node #0,4,2: 27:[22, 4] Operation: 26-22=4 Exploring Operation: 22/22=1, Resulting Numbers: [26, 1] Generated Node #0,4,3: 27:[26, 1] Operation: 22/22=1 Exploring Operation: 22-22=0, Resulting Numbers: [26, 0] Generated Node #0,4,4: 27:[26, 0] Operation: 22-22=0 Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 27:[26, 1], Operations: ['77-55=22', '22/22=1'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,27 unequal: No Solution Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[55, 26, 77, 22], Operations: [] Exploring Operation: 77-55=22, Resulting Numbers: [26, 22, 22] Generated Node #0,4: 27:[26, 22, 22] Operation: 77-55=22 Moving to Node #0,4 Current State: 27:[26, 22, 22], Operations: ['77-55=22'] Exploring Operation: 22/22=1, Resulting Numbers: [26, 1] Generated Node #0,4,3: 27:[26, 1] Operation: 22/22=1 Moving to Node #0,4,3 Current State: 27:[26, 1], Operations: ['77-55=22', '22/22=1'] Exploring Operation: 26+1=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
sum_heuristic
[ 63, 18, 60, 3 ]
87
[ "63+18=81", "81/3=27", "60+27=87" ]
Current State: 87:[63, 18, 60, 3], Operations: [] Exploring Operation: 63+18=81, Resulting Numbers: [60, 3, 81] Generated Node #2: [60, 3, 81] from Operation: 63+18=81 Current State: 87:[60, 3, 81], Operations: ['63+18=81'] Exploring Operation: 81/3=27, Resulting Numbers: [60, 27] Generated Node #3: [60, 27] from Operation: 81/3=27 Current State: 87:[60, 27], Operations: ['63+18=81', '81/3=27'] Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[63, 18, 60, 3], Operations: [] Exploring Operation: 63-18=45, Resulting Numbers: [60, 3, 45] Generated Node #0,0: 87:[60, 3, 45] Operation: 63-18=45 Exploring Operation: 60-18=42, Resulting Numbers: [63, 3, 42] Generated Node #0,1: 87:[63, 3, 42] Operation: 60-18=42 Exploring Operation: 63-60=3, Resulting Numbers: [18, 3, 3] Generated Node #0,2: 87:[18, 3, 3] Operation: 63-60=3 Exploring Operation: 18+60=78, Resulting Numbers: [63, 3, 78] Generated Node #0,3: 87:[63, 3, 78] Operation: 18+60=78 Exploring Operation: 63+18=81, Resulting Numbers: [60, 3, 81] Generated Node #0,4: 87:[60, 3, 81] Operation: 63+18=81 Moving to Node #0,2 Current State: 87:[18, 3, 3], Operations: ['63-60=3'] Exploring Operation: 18+3=21, Resulting Numbers: [3, 21] Generated Node #0,2,0: 87:[3, 21] Operation: 18+3=21 Exploring Operation: 18-3=15, Resulting Numbers: [3, 15] Generated Node #0,2,1: 87:[3, 15] Operation: 18-3=15 Exploring Operation: 18/3=6, Resulting Numbers: [3, 6] Generated Node #0,2,2: 87:[3, 6] Operation: 18/3=6 Exploring Operation: 18/3=6, Resulting Numbers: [3, 6] Generated Node #0,2,3: 87:[3, 6] Operation: 18/3=6 Exploring Operation: 18+3=21, Resulting Numbers: [3, 21] Generated Node #0,2,4: 87:[3, 21] Operation: 18+3=21 Moving to Node #0,4 Current State: 87:[60, 3, 81], Operations: ['63+18=81'] Exploring Operation: 81-60=21, Resulting Numbers: [3, 21] Generated Node #0,4,0: 87:[3, 21] Operation: 81-60=21 Exploring Operation: 60/3=20, Resulting Numbers: [81, 20] Generated Node #0,4,1: 87:[81, 20] Operation: 60/3=20 Exploring Operation: 81/3=27, Resulting Numbers: [60, 27] Generated Node #0,4,2: 87:[60, 27] Operation: 81/3=27 Exploring Operation: 3+81=84, Resulting Numbers: [60, 84] Generated Node #0,4,3: 87:[60, 84] Operation: 3+81=84 Exploring Operation: 60+3=63, Resulting Numbers: [81, 63] Generated Node #0,4,4: 87:[81, 63] Operation: 60+3=63 Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 87:[3, 21], Operations: ['63+18=81', '81-60=21'] Exploring Operation: 3+21=24, Resulting Numbers: [24] 24,87 unequal: No Solution Exploring Operation: 21-3=18, Resulting Numbers: [18] 18,87 unequal: No Solution Exploring Operation: 21/3=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 3*21=63, Resulting Numbers: [63] 63,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 87:[81, 20], Operations: ['63+18=81', '60/3=20'] Exploring Operation: 81-20=61, Resulting Numbers: [61] 61,87 unequal: No Solution Exploring Operation: 81*20=1620, Resulting Numbers: [1620] 1620,87 unequal: No Solution Exploring Operation: 81+20=101, Resulting Numbers: [101] 101,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 87:[60, 27], Operations: ['63+18=81', '81/3=27'] Exploring Operation: 60*27=1620, Resulting Numbers: [1620] 1620,87 unequal: No Solution Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[63, 18, 60, 3], Operations: [] Exploring Operation: 63+18=81, Resulting Numbers: [60, 3, 81] Generated Node #0,4: 87:[60, 3, 81] Operation: 63+18=81 Moving to Node #0,4 Current State: 87:[60, 3, 81], Operations: ['63+18=81'] Exploring Operation: 81/3=27, Resulting Numbers: [60, 27] Generated Node #0,4,2: 87:[60, 27] Operation: 81/3=27 Moving to Node #0,4,2 Current State: 87:[60, 27], Operations: ['63+18=81', '81/3=27'] Exploring Operation: 60+27=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.975694
hs_5
sum_heuristic
[ 26, 82, 66, 78 ]
88
[ "82-26=56", "66+78=144", "144-56=88" ]
Current State: 88:[26, 82, 66, 78], Operations: [] Exploring Operation: 82-26=56, Resulting Numbers: [66, 78, 56] Generated Node #2: [66, 78, 56] from Operation: 82-26=56 Current State: 88:[66, 78, 56], Operations: ['82-26=56'] Exploring Operation: 66+78=144, Resulting Numbers: [56, 144] Generated Node #3: [56, 144] from Operation: 66+78=144 Current State: 88:[56, 144], Operations: ['82-26=56', '66+78=144'] Exploring Operation: 144-56=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[26, 82, 66, 78], Operations: [] Exploring Operation: 82-66=16, Resulting Numbers: [26, 78, 16] Generated Node #0,0: 88:[26, 78, 16] Operation: 82-66=16 Exploring Operation: 78-66=12, Resulting Numbers: [26, 82, 12] Generated Node #0,1: 88:[26, 82, 12] Operation: 78-66=12 Moving to Node #0,1 Current State: 88:[26, 82, 12], Operations: ['78-66=12'] Exploring Operation: 82+12=94, Resulting Numbers: [26, 94] Generated Node #0,1,0: 88:[26, 94] Operation: 82+12=94 Exploring Operation: 26-12=14, Resulting Numbers: [82, 14] Generated Node #0,1,1: 88:[82, 14] Operation: 26-12=14 Moving to Node #0,0 Current State: 88:[26, 78, 16], Operations: ['82-66=16'] Exploring Operation: 78/26=3, Resulting Numbers: [16, 3] Generated Node #0,0,0: 88:[16, 3] Operation: 78/26=3 Exploring Operation: 78+16=94, Resulting Numbers: [26, 94] Generated Node #0,0,1: 88:[26, 94] Operation: 78+16=94 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 88:[16, 3], Operations: ['82-66=16', '78/26=3'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,88 unequal: No Solution Exploring Operation: 16+3=19, Resulting Numbers: [19] 19,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 88:[26, 94], Operations: ['82-66=16', '78+16=94'] Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,88 unequal: No Solution Exploring Operation: 26+94=120, Resulting Numbers: [120] 120,88 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: 88:[82, 14], Operations: ['78-66=12', '26-12=14'] Exploring Operation: 82+14=96, Resulting Numbers: [96] 96,88 unequal: No Solution Exploring Operation: 82-14=68, Resulting Numbers: [68] 68,88 unequal: No Solution Moving to Node #0,1,0 Current State: 88:[26, 94], Operations: ['78-66=12', '82+12=94'] Exploring Operation: 26+94=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 94-26=68, Resulting Numbers: [68] 68,88 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 78, 47, 25, 49 ]
51
[ "78+47=125", "25+49=74", "125-74=51" ]
Current State: 51:[78, 47, 25, 49], Operations: [] Exploring Operation: 78+47=125, Resulting Numbers: [25, 49, 125] Generated Node #2: [25, 49, 125] from Operation: 78+47=125 Current State: 51:[25, 49, 125], Operations: ['78+47=125'] Exploring Operation: 25+49=74, Resulting Numbers: [125, 74] Generated Node #3: [125, 74] from Operation: 25+49=74 Current State: 51:[125, 74], Operations: ['78+47=125', '25+49=74'] Exploring Operation: 125-74=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[78, 47, 25, 49], Operations: [] Exploring Operation: 78-25=53, Resulting Numbers: [47, 49, 53] Generated Node #0,0: 51:[47, 49, 53] Operation: 78-25=53 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[47, 49, 53], Operations: ['78-25=53'] Exploring Operation: 49-47=2, Resulting Numbers: [53, 2] Generated Node #0,0,0: 51:[53, 2] Operation: 49-47=2 Moving to Node #0,0,0 Current State: 51:[53, 2], Operations: ['78-25=53', '49-47=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[78, 47, 25, 49], Operations: [] Exploring Operation: 78-25=53, Resulting Numbers: [47, 49, 53] Generated Node #0,0: 51:[47, 49, 53] Operation: 78-25=53 Moving to Node #0,0 Current State: 51:[47, 49, 53], Operations: ['78-25=53'] Exploring Operation: 49-47=2, Resulting Numbers: [53, 2] Generated Node #0,0,0: 51:[53, 2] Operation: 49-47=2 Moving to Node #0,0,0 Current State: 51:[53, 2], Operations: ['78-25=53', '49-47=2'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 64, 31, 1, 6 ]
40
[ "64-31=33", "1+6=7", "33+7=40" ]
Current State: 40:[64, 31, 1, 6], Operations: [] Exploring Operation: 64-31=33, Resulting Numbers: [1, 6, 33] Generated Node #2: [1, 6, 33] from Operation: 64-31=33 Current State: 40:[1, 6, 33], Operations: ['64-31=33'] Exploring Operation: 1+6=7, Resulting Numbers: [33, 7] Generated Node #3: [33, 7] from Operation: 1+6=7 Current State: 40:[33, 7], Operations: ['64-31=33', '1+6=7'] Exploring Operation: 33+7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[64, 31, 1, 6], Operations: [] Exploring Operation: 64-31=33, Resulting Numbers: [1, 6, 33] Generated Node #0,0: 40:[1, 6, 33] Operation: 64-31=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[1, 6, 33], Operations: ['64-31=33'] Exploring Operation: 6+33=39, Resulting Numbers: [1, 39] Generated Node #0,0,0: 40:[1, 39] Operation: 6+33=39 Moving to Node #0,0,0 Current State: 40:[1, 39], Operations: ['64-31=33', '6+33=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[64, 31, 1, 6], Operations: [] Exploring Operation: 64-31=33, Resulting Numbers: [1, 6, 33] Generated Node #0,0: 40:[1, 6, 33] Operation: 64-31=33 Moving to Node #0,0 Current State: 40:[1, 6, 33], Operations: ['64-31=33'] Exploring Operation: 6+33=39, Resulting Numbers: [1, 39] Generated Node #0,0,0: 40:[1, 39] Operation: 6+33=39 Moving to Node #0,0,0 Current State: 40:[1, 39], Operations: ['64-31=33', '6+33=39'] Exploring Operation: 1+39=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 82, 75, 14, 27 ]
77
[ "14+27=41", "82/41=2", "75+2=77" ]
Current State: 77:[82, 75, 14, 27], Operations: [] Exploring Operation: 14+27=41, Resulting Numbers: [82, 75, 41] Generated Node #2: [82, 75, 41] from Operation: 14+27=41 Current State: 77:[82, 75, 41], Operations: ['14+27=41'] Exploring Operation: 82/41=2, Resulting Numbers: [75, 2] Generated Node #3: [75, 2] from Operation: 82/41=2 Current State: 77:[75, 2], Operations: ['14+27=41', '82/41=2'] Exploring Operation: 75+2=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[82, 75, 14, 27], Operations: [] Exploring Operation: 27-14=13, Resulting Numbers: [82, 75, 13] Generated Node #0,0: 77:[82, 75, 13] Operation: 27-14=13 Exploring Operation: 82-75=7, Resulting Numbers: [14, 27, 7] Generated Node #0,1: 77:[14, 27, 7] Operation: 82-75=7 Moving to Node #0,0 Current State: 77:[82, 75, 13], Operations: ['27-14=13'] Exploring Operation: 82-13=69, Resulting Numbers: [75, 69] Generated Node #0,0,0: 77:[75, 69] Operation: 82-13=69 Exploring Operation: 82-75=7, Resulting Numbers: [13, 7] Generated Node #0,0,1: 77:[13, 7] Operation: 82-75=7 Moving to Node #0,1 Current State: 77:[14, 27, 7], Operations: ['82-75=7'] Exploring Operation: 27-7=20, Resulting Numbers: [14, 20] Generated Node #0,1,0: 77:[14, 20] Operation: 27-7=20 Exploring Operation: 27-14=13, Resulting Numbers: [7, 13] Generated Node #0,1,1: 77:[7, 13] Operation: 27-14=13 Moving to Node #0,0,1 Current State: 77:[13, 7], Operations: ['27-14=13', '82-75=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,77 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,77 unequal: No Solution Moving to Node #0,1,1 Current State: 77:[7, 13], Operations: ['82-75=7', '27-14=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,77 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,77 unequal: No Solution Moving to Node #0,0,0 Current State: 77:[75, 69], Operations: ['27-14=13', '82-13=69'] Exploring Operation: 75+69=144, Resulting Numbers: [144] 144,77 unequal: No Solution Exploring Operation: 75-69=6, Resulting Numbers: [6] 6,77 unequal: No Solution Moving to Node #0,1,0 Current State: 77:[14, 20], Operations: ['82-75=7', '27-7=20'] Exploring Operation: 14+20=34, Resulting Numbers: [34] 34,77 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,77 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 30, 46, 9, 23 ]
23
[ "30-9=21", "46/23=2", "21+2=23" ]
Current State: 23:[30, 46, 9, 23], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [46, 23, 21] Generated Node #2: [46, 23, 21] from Operation: 30-9=21 Current State: 23:[46, 23, 21], Operations: ['30-9=21'] Exploring Operation: 46/23=2, Resulting Numbers: [21, 2] Generated Node #3: [21, 2] from Operation: 46/23=2 Current State: 23:[21, 2], Operations: ['30-9=21', '46/23=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[30, 46, 9, 23], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [46, 23, 21] Generated Node #0,0: 23:[46, 23, 21] Operation: 30-9=21 Exploring Operation: 46-30=16, Resulting Numbers: [9, 23, 16] Generated Node #0,1: 23:[9, 23, 16] Operation: 46-30=16 Exploring Operation: 46-23=23, Resulting Numbers: [30, 9, 23] Generated Node #0,2: 23:[30, 9, 23] Operation: 46-23=23 Exploring Operation: 46-9=37, Resulting Numbers: [30, 23, 37] Generated Node #0,3: 23:[30, 23, 37] Operation: 46-9=37 Start Sub Search at level 1: Moving to Node #0,1 Current State: 23:[9, 23, 16], Operations: ['46-30=16'] Exploring Operation: 9+16=25, Resulting Numbers: [23, 25] Generated Node #0,1,0: 23:[23, 25] Operation: 9+16=25 Exploring Operation: 9+23=32, Resulting Numbers: [16, 32] Generated Node #0,1,1: 23:[16, 32] Operation: 9+23=32 Exploring Operation: 23-9=14, Resulting Numbers: [16, 14] Generated Node #0,1,2: 23:[16, 14] Operation: 23-9=14 Exploring Operation: 16-9=7, Resulting Numbers: [23, 7] Generated Node #0,1,3: 23:[23, 7] Operation: 16-9=7 Moving to Node #0,1,0 Current State: 23:[23, 25], Operations: ['46-30=16', '9+16=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,23 unequal: No Solution Moving to Node #0,1,2 Current State: 23:[16, 14], Operations: ['46-30=16', '23-9=14'] Exploring Operation: 16*14=224, Resulting Numbers: [224] 224,23 unequal: No Solution Exploring Operation: 16-14=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 16+14=30, Resulting Numbers: [30] 30,23 unequal: No Solution Moving to Node #0,1,1 Current State: 23:[16, 32], Operations: ['46-30=16', '9+23=32'] Exploring Operation: 16+32=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 32-16=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 16*32=512, Resulting Numbers: [512] 512,23 unequal: No Solution Exploring Operation: 32/16=2, Resulting Numbers: [2] 2,23 unequal: No Solution Moving to Node #0,1,3 Current State: 23:[23, 7], Operations: ['46-30=16', '16-9=7'] Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 23:[30, 9, 23], Operations: ['46-23=23'] Exploring Operation: 23-9=14, Resulting Numbers: [30, 14] Generated Node #0,2,0: 23:[30, 14] Operation: 23-9=14 Exploring Operation: 30-9=21, Resulting Numbers: [23, 21] Generated Node #0,2,1: 23:[23, 21] Operation: 30-9=21 Exploring Operation: 9+23=32, Resulting Numbers: [30, 32] Generated Node #0,2,2: 23:[30, 32] Operation: 9+23=32 Exploring Operation: 30+9=39, Resulting Numbers: [23, 39] Generated Node #0,2,3: 23:[23, 39] Operation: 30+9=39 Moving to Node #0,2,1 Current State: 23:[23, 21], Operations: ['46-23=23', '30-9=21'] Exploring Operation: 23*21=483, Resulting Numbers: [483] 483,23 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 23+21=44, Resulting Numbers: [44] 44,23 unequal: No Solution Moving to Node #0,2,2 Current State: 23:[30, 32], Operations: ['46-23=23', '9+23=32'] Exploring Operation: 30*32=960, Resulting Numbers: [960] 960,23 unequal: No Solution Exploring Operation: 32-30=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 30+32=62, Resulting Numbers: [62] 62,23 unequal: No Solution Moving to Node #0,2,0 Current State: 23:[30, 14], Operations: ['46-23=23', '23-9=14'] Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,23 unequal: No Solution Moving to Node #0,2,3 Current State: 23:[23, 39], Operations: ['46-23=23', '30+9=39'] Exploring Operation: 23+39=62, Resulting Numbers: [62] 62,23 unequal: No Solution Exploring Operation: 23*39=897, Resulting Numbers: [897] 897,23 unequal: No Solution Exploring Operation: 39-23=16, Resulting Numbers: [16] 16,23 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 Current State: 23:[30, 23, 37], Operations: ['46-9=37'] Exploring Operation: 30+23=53, Resulting Numbers: [37, 53] Generated Node #0,3,0: 23:[37, 53] Operation: 30+23=53 Exploring Operation: 37-23=14, Resulting Numbers: [30, 14] Generated Node #0,3,1: 23:[30, 14] Operation: 37-23=14 Exploring Operation: 30-23=7, Resulting Numbers: [37, 7] Generated Node #0,3,2: 23:[37, 7] Operation: 30-23=7 Exploring Operation: 37-30=7, Resulting Numbers: [23, 7] Generated Node #0,3,3: 23:[23, 7] Operation: 37-30=7 Moving to Node #0,3,1 Current State: 23:[30, 14], Operations: ['46-9=37', '37-23=14'] Exploring Operation: 30+14=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 30*14=420, Resulting Numbers: [420] 420,23 unequal: No Solution Exploring Operation: 30-14=16, Resulting Numbers: [16] 16,23 unequal: No Solution Moving to Node #0,3,3 Current State: 23:[23, 7], Operations: ['46-9=37', '37-30=7'] Exploring Operation: 23*7=161, Resulting Numbers: [161] 161,23 unequal: No Solution Exploring Operation: 23+7=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 23-7=16, Resulting Numbers: [16] 16,23 unequal: No Solution Moving to Node #0,3,2 Current State: 23:[37, 7], Operations: ['46-9=37', '30-23=7'] Exploring Operation: 37*7=259, Resulting Numbers: [259] 259,23 unequal: No Solution Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,23 unequal: No Solution Exploring Operation: 37+7=44, Resulting Numbers: [44] 44,23 unequal: No Solution Moving to Node #0,3,0 Current State: 23:[37, 53], Operations: ['46-9=37', '30+23=53'] Exploring Operation: 37*53=1961, Resulting Numbers: [1961] 1961,23 unequal: No Solution Exploring Operation: 53-37=16, Resulting Numbers: [16] 16,23 unequal: No Solution Exploring Operation: 37+53=90, Resulting Numbers: [90] 90,23 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 Current State: 23:[46, 23, 21], Operations: ['30-9=21'] Exploring Operation: 46+21=67, Resulting Numbers: [23, 67] Generated Node #0,0,0: 23:[23, 67] Operation: 46+21=67 Exploring Operation: 46/23=2, Resulting Numbers: [21, 2] Generated Node #0,0,1: 23:[21, 2] Operation: 46/23=2 Exploring Operation: 46-23=23, Resulting Numbers: [21, 23] Generated Node #0,0,2: 23:[21, 23] Operation: 46-23=23 Exploring Operation: 46-21=25, Resulting Numbers: [23, 25] Generated Node #0,0,3: 23:[23, 25] Operation: 46-21=25 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 23:[21, 23], Operations: ['30-9=21', '46-23=23'] Exploring Operation: 21*23=483, Resulting Numbers: [483] 483,23 unequal: No Solution Exploring Operation: 21+23=44, Resulting Numbers: [44] 44,23 unequal: No Solution Exploring Operation: 23-21=2, Resulting Numbers: [2] 2,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 23:[23, 25], Operations: ['30-9=21', '46-21=25'] Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,23 unequal: No Solution Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,23 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,23 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 23:[21, 2], Operations: ['30-9=21', '46/23=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Moving to Node #0 Current State: 23:[30, 46, 9, 23], Operations: [] Exploring Operation: 30-9=21, Resulting Numbers: [46, 23, 21] Generated Node #0,0: 23:[46, 23, 21] Operation: 30-9=21 Moving to Node #0,0 Current State: 23:[46, 23, 21], Operations: ['30-9=21'] Exploring Operation: 46/23=2, Resulting Numbers: [21, 2] Generated Node #0,0,1: 23:[21, 2] Operation: 46/23=2 Moving to Node #0,0,1 Current State: 23:[21, 2], Operations: ['30-9=21', '46/23=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,23 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.940972
hs_4
sum_heuristic
[ 79, 94, 1, 63 ]
79
[ "94-79=15", "1+63=64", "15+64=79" ]
Current State: 79:[79, 94, 1, 63], Operations: [] Exploring Operation: 94-79=15, Resulting Numbers: [1, 63, 15] Generated Node #2: [1, 63, 15] from Operation: 94-79=15 Current State: 79:[1, 63, 15], Operations: ['94-79=15'] Exploring Operation: 1+63=64, Resulting Numbers: [15, 64] Generated Node #3: [15, 64] from Operation: 1+63=64 Current State: 79:[15, 64], Operations: ['94-79=15', '1+63=64'] Exploring Operation: 15+64=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[79, 94, 1, 63], Operations: [] Exploring Operation: 1+63=64, Resulting Numbers: [79, 94, 64] Generated Node #0,0: 79:[79, 94, 64] Operation: 1+63=64 Exploring Operation: 94-1=93, Resulting Numbers: [79, 63, 93] Generated Node #0,1: 79:[79, 63, 93] Operation: 94-1=93 Start Sub Search at level 1: Moving to Node #0,0 Current State: 79:[79, 94, 64], Operations: ['1+63=64'] Exploring Operation: 94-79=15, Resulting Numbers: [64, 15] Generated Node #0,0,0: 79:[64, 15] Operation: 94-79=15 Exploring Operation: 94-64=30, Resulting Numbers: [79, 30] Generated Node #0,0,1: 79:[79, 30] Operation: 94-64=30 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 79:[79, 30], Operations: ['1+63=64', '94-64=30'] Exploring Operation: 79+30=109, Resulting Numbers: [109] 109,79 unequal: No Solution Exploring Operation: 79-30=49, Resulting Numbers: [49] 49,79 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 79:[64, 15], Operations: ['1+63=64', '94-79=15'] Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Moving to Node #0 Current State: 79:[79, 94, 1, 63], Operations: [] Exploring Operation: 1+63=64, Resulting Numbers: [79, 94, 64] Generated Node #0,0: 79:[79, 94, 64] Operation: 1+63=64 Moving to Node #0,0 Current State: 79:[79, 94, 64], Operations: ['1+63=64'] Exploring Operation: 94-79=15, Resulting Numbers: [64, 15] Generated Node #0,0,0: 79:[64, 15] Operation: 94-79=15 Moving to Node #0,0,0 Current State: 79:[64, 15], Operations: ['1+63=64', '94-79=15'] Exploring Operation: 64+15=79, Resulting Numbers: [79] 79,79 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 28, 56, 48, 1 ]
49
[ "56/28=2", "48-1=47", "2+47=49" ]
Current State: 49:[28, 56, 48, 1], Operations: [] Exploring Operation: 56/28=2, Resulting Numbers: [48, 1, 2] Generated Node #2: [48, 1, 2] from Operation: 56/28=2 Current State: 49:[48, 1, 2], Operations: ['56/28=2'] Exploring Operation: 48-1=47, Resulting Numbers: [2, 47] Generated Node #3: [2, 47] from Operation: 48-1=47 Current State: 49:[2, 47], Operations: ['56/28=2', '48-1=47'] Exploring Operation: 2+47=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[28, 56, 48, 1], Operations: [] Exploring Operation: 48-28=20, Resulting Numbers: [56, 1, 20] Generated Node #0,0: 49:[56, 1, 20] Operation: 48-28=20 Exploring Operation: 28+1=29, Resulting Numbers: [56, 48, 29] Generated Node #0,1: 49:[56, 48, 29] Operation: 28+1=29 Exploring Operation: 56/28=2, Resulting Numbers: [48, 1, 2] Generated Node #0,2: 49:[48, 1, 2] Operation: 56/28=2 Exploring Operation: 56-28=28, Resulting Numbers: [48, 1, 28] Generated Node #0,3: 49:[48, 1, 28] Operation: 56-28=28 Start Sub Search at level 1: Moving to Node #0,2 Current State: 49:[48, 1, 2], Operations: ['56/28=2'] Exploring Operation: 48/1=48, Resulting Numbers: [2, 48] Generated Node #0,2,0: 49:[2, 48] Operation: 48/1=48 Exploring Operation: 1+2=3, Resulting Numbers: [48, 3] Generated Node #0,2,1: 49:[48, 3] Operation: 1+2=3 Exploring Operation: 48*1=48, Resulting Numbers: [2, 48] Generated Node #0,2,2: 49:[2, 48] Operation: 48*1=48 Exploring Operation: 48+1=49, Resulting Numbers: [2, 49] Generated Node #0,2,3: 49:[2, 49] Operation: 48+1=49 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 49:[48, 3], Operations: ['56/28=2', '1+2=3'] Exploring Operation: 48*3=144, Resulting Numbers: [144] 144,49 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,49 unequal: No Solution Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,49 unequal: No Solution Exploring Operation: 48+3=51, Resulting Numbers: [51] 51,49 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 #0,2,3 Current State: 49:[2, 49], Operations: ['56/28=2', '48+1=49'] Exploring Operation: 2+49=51, Resulting Numbers: [51] 51,49 unequal: No Solution Exploring Operation: 49-2=47, Resulting Numbers: [47] 47,49 unequal: No Solution Exploring Operation: 2*49=98, Resulting Numbers: [98] 98,49 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 #0,2,0 Current State: 49:[2, 48], Operations: ['56/28=2', '48/1=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,49 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,49 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 #0,2,2 Current State: 49:[2, 48], Operations: ['56/28=2', '48*1=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,49 unequal: No Solution Exploring Operation: 2*48=96, Resulting Numbers: [96] 96,49 unequal: No Solution Exploring Operation: 48-2=46, Resulting Numbers: [46] 46,49 unequal: No Solution Exploring Operation: 48/2=24, Resulting Numbers: [24] 24,49 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 #0,0 Current State: 49:[56, 1, 20], Operations: ['48-28=20'] Exploring Operation: 56-1=55, Resulting Numbers: [20, 55] Generated Node #0,0,0: 49:[20, 55] Operation: 56-1=55 Exploring Operation: 20-1=19, Resulting Numbers: [56, 19] Generated Node #0,0,1: 49:[56, 19] Operation: 20-1=19 Exploring Operation: 56-20=36, Resulting Numbers: [1, 36] Generated Node #0,0,2: 49:[1, 36] Operation: 56-20=36 Exploring Operation: 56*1=56, Resulting Numbers: [20, 56] Generated Node #0,0,3: 49:[20, 56] Operation: 56*1=56 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[20, 55], Operations: ['48-28=20', '56-1=55'] Exploring Operation: 20+55=75, Resulting Numbers: [75] 75,49 unequal: No Solution Exploring Operation: 55-20=35, Resulting Numbers: [35] 35,49 unequal: No Solution Exploring Operation: 20*55=1100, Resulting Numbers: [1100] 1100,49 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:[56, 19], Operations: ['48-28=20', '20-1=19'] Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,49 unequal: No Solution Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 56*19=1064, Resulting Numbers: [1064] 1064,49 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 #0,0,2 Current State: 49:[1, 36], Operations: ['48-28=20', '56-20=36'] Exploring Operation: 36-1=35, Resulting Numbers: [35] 35,49 unequal: No Solution Exploring Operation: 36/1=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 1+36=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 1*36=36, Resulting Numbers: [36] 36,49 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:[20, 56], Operations: ['48-28=20', '56*1=56'] Exploring Operation: 20+56=76, Resulting Numbers: [76] 76,49 unequal: No Solution Exploring Operation: 56-20=36, Resulting Numbers: [36] 36,49 unequal: No Solution Exploring Operation: 20*56=1120, Resulting Numbers: [1120] 1120,49 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 #0,1 Current State: 49:[56, 48, 29], Operations: ['28+1=29'] Exploring Operation: 56-29=27, Resulting Numbers: [48, 27] Generated Node #0,1,0: 49:[48, 27] Operation: 56-29=27 Exploring Operation: 48-29=19, Resulting Numbers: [56, 19] Generated Node #0,1,1: 49:[56, 19] Operation: 48-29=19 Exploring Operation: 48+29=77, Resulting Numbers: [56, 77] Generated Node #0,1,2: 49:[56, 77] Operation: 48+29=77 Exploring Operation: 56-48=8, Resulting Numbers: [29, 8] Generated Node #0,1,3: 49:[29, 8] Operation: 56-48=8 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 49:[56, 19], Operations: ['28+1=29', '48-29=19'] Exploring Operation: 56+19=75, Resulting Numbers: [75] 75,49 unequal: No Solution Exploring Operation: 56*19=1064, Resulting Numbers: [1064] 1064,49 unequal: No Solution Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,49 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:[48, 27], Operations: ['28+1=29', '56-29=27'] Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,49 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,49 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:[29, 8], Operations: ['28+1=29', '56-48=8'] Exploring Operation: 29+8=37, Resulting Numbers: [37] 37,49 unequal: No Solution Exploring Operation: 29-8=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 29*8=232, Resulting Numbers: [232] 232,49 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 #0,1,2 Current State: 49:[56, 77], Operations: ['28+1=29', '48+29=77'] Exploring Operation: 56*77=4312, Resulting Numbers: [4312] 4312,49 unequal: No Solution Exploring Operation: 56+77=133, Resulting Numbers: [133] 133,49 unequal: No Solution Exploring Operation: 77-56=21, Resulting Numbers: [21] 21,49 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:[48, 1, 28], Operations: ['56-28=28'] Exploring Operation: 28-1=27, Resulting Numbers: [48, 27] Generated Node #0,3,0: 49:[48, 27] Operation: 28-1=27 Exploring Operation: 1+28=29, Resulting Numbers: [48, 29] Generated Node #0,3,1: 49:[48, 29] Operation: 1+28=29 Exploring Operation: 48-28=20, Resulting Numbers: [1, 20] Generated Node #0,3,2: 49:[1, 20] Operation: 48-28=20 Exploring Operation: 48+1=49, Resulting Numbers: [28, 49] Generated Node #0,3,3: 49:[28, 49] Operation: 48+1=49 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 49:[1, 20], Operations: ['56-28=28', '48-28=20'] Exploring Operation: 1+20=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 1*20=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 20/1=20, Resulting Numbers: [20] 20,49 unequal: No Solution Exploring Operation: 20-1=19, Resulting Numbers: [19] 19,49 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 #0,3,0 Current State: 49:[48, 27], Operations: ['56-28=28', '28-1=27'] Exploring Operation: 48*27=1296, Resulting Numbers: [1296] 1296,49 unequal: No Solution Exploring Operation: 48-27=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 48+27=75, Resulting Numbers: [75] 75,49 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 #0,3,1 Current State: 49:[48, 29], Operations: ['56-28=28', '1+28=29'] Exploring Operation: 48*29=1392, Resulting Numbers: [1392] 1392,49 unequal: No Solution Exploring Operation: 48-29=19, Resulting Numbers: [19] 19,49 unequal: No Solution Exploring Operation: 48+29=77, Resulting Numbers: [77] 77,49 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 #0,3,3 Current State: 49:[28, 49], Operations: ['56-28=28', '48+1=49'] Exploring Operation: 28+49=77, Resulting Numbers: [77] 77,49 unequal: No Solution Exploring Operation: 49-28=21, Resulting Numbers: [21] 21,49 unequal: No Solution Exploring Operation: 28*49=1372, Resulting Numbers: [1372] 1372,49 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_4
sum_heuristic