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
[ 68, 49, 41, 1 ]
77
[ "68+49=117", "41-1=40", "117-40=77" ]
Current State: 77:[68, 49, 41, 1], Operations: [] Exploring Operation: 68+49=117, Resulting Numbers: [41, 1, 117] Generated Node #2: [41, 1, 117] from Operation: 68+49=117 Current State: 77:[41, 1, 117], Operations: ['68+49=117'] Exploring Operation: 41-1=40, Resulting Numbers: [117, 40] Generated Node #3: [117, 40] from Operation: 41-1=40 Current State: 77:[117, 40], Operations: ['68+49=117', '41-1=40'] Exploring Operation: 117-40=77, Resulting Numbers: [77] 77,77 equal: Goal Reached
4
Current State: 77:[68, 49, 41, 1], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [68, 1, 8] Generated Node #0,0: 77:[68, 1, 8] Operation: 49-41=8 Moving to Node #0,0 Current State: 77:[68, 1, 8], Operations: ['49-41=8'] Exploring Operation: 68+8=76, Resulting Numbers: [1, 76] Generated Node #0,0,0: 77:[1, 76] Operation: 68+8=76 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 77:[1, 76], Operations: ['49-41=8', '68+8=76'] Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Moving to Node #0 Current State: 77:[68, 49, 41, 1], Operations: [] Exploring Operation: 49-41=8, Resulting Numbers: [68, 1, 8] Generated Node #0,0: 77:[68, 1, 8] Operation: 49-41=8 Moving to Node #0,0 Current State: 77:[68, 1, 8], Operations: ['49-41=8'] Exploring Operation: 68+8=76, Resulting Numbers: [1, 76] Generated Node #0,0,0: 77:[1, 76] Operation: 68+8=76 Moving to Node #0,0,0 Current State: 77:[1, 76], Operations: ['49-41=8', '68+8=76'] Exploring Operation: 1+76=77, Resulting Numbers: [77] 77,77 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 39, 24, 36, 80 ]
54
[ "39*24=936", "936/36=26", "80-26=54" ]
Current State: 54:[39, 24, 36, 80], Operations: [] Exploring Operation: 39*24=936, Resulting Numbers: [36, 80, 936] Generated Node #2: [36, 80, 936] from Operation: 39*24=936 Current State: 54:[36, 80, 936], Operations: ['39*24=936'] Exploring Operation: 936/36=26, Resulting Numbers: [80, 26] Generated Node #3: [80, 26] from Operation: 936/36=26 Current State: 54:[80, 26], Operations: ['39*24=936', '936/36=26'] Exploring Operation: 80-26=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[39, 24, 36, 80], Operations: [] Exploring Operation: 80-39=41, Resulting Numbers: [24, 36, 41] Generated Node #0,0: 54:[24, 36, 41] Operation: 80-39=41 Exploring Operation: 80-24=56, Resulting Numbers: [39, 36, 56] Generated Node #0,1: 54:[39, 36, 56] Operation: 80-24=56 Exploring Operation: 39-36=3, Resulting Numbers: [24, 80, 3] Generated Node #0,2: 54:[24, 80, 3] Operation: 39-36=3 Exploring Operation: 80-36=44, Resulting Numbers: [39, 24, 44] Generated Node #0,3: 54:[39, 24, 44] Operation: 80-36=44 Moving to Node #0,1 Current State: 54:[39, 36, 56], Operations: ['80-24=56'] Exploring Operation: 39+36=75, Resulting Numbers: [56, 75] Generated Node #0,1,0: 54:[56, 75] Operation: 39+36=75 Exploring Operation: 56-39=17, Resulting Numbers: [36, 17] Generated Node #0,1,1: 54:[36, 17] Operation: 56-39=17 Exploring Operation: 56-36=20, Resulting Numbers: [39, 20] Generated Node #0,1,2: 54:[39, 20] Operation: 56-36=20 Exploring Operation: 39-36=3, Resulting Numbers: [56, 3] Generated Node #0,1,3: 54:[56, 3] Operation: 39-36=3 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 54:[56, 3], Operations: ['80-24=56', '39-36=3'] Exploring Operation: 56+3=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 56*3=168, Resulting Numbers: [168] 168,54 unequal: No Solution Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,54 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:[36, 17], Operations: ['80-24=56', '56-39=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,54 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,54 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:[39, 20], Operations: ['80-24=56', '56-36=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,54 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 54:[56, 75], Operations: ['80-24=56', '39+36=75'] Exploring Operation: 56+75=131, Resulting Numbers: [131] 131,54 unequal: No Solution Exploring Operation: 56*75=4200, Resulting Numbers: [4200] 4200,54 unequal: No Solution Exploring Operation: 75-56=19, Resulting Numbers: [19] 19,54 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:[39, 24, 44], Operations: ['80-36=44'] Exploring Operation: 39+24=63, Resulting Numbers: [44, 63] Generated Node #0,3,0: 54:[44, 63] Operation: 39+24=63 Exploring Operation: 44-24=20, Resulting Numbers: [39, 20] Generated Node #0,3,1: 54:[39, 20] Operation: 44-24=20 Exploring Operation: 39-24=15, Resulting Numbers: [44, 15] Generated Node #0,3,2: 54:[44, 15] Operation: 39-24=15 Exploring Operation: 44-39=5, Resulting Numbers: [24, 5] Generated Node #0,3,3: 54:[24, 5] Operation: 44-39=5 Moving to Node #0,0 Current State: 54:[24, 36, 41], Operations: ['80-39=41'] Exploring Operation: 41-36=5, Resulting Numbers: [24, 5] Generated Node #0,0,0: 54:[24, 5] Operation: 41-36=5 Exploring Operation: 36-24=12, Resulting Numbers: [41, 12] Generated Node #0,0,1: 54:[41, 12] Operation: 36-24=12 Exploring Operation: 41-24=17, Resulting Numbers: [36, 17] Generated Node #0,0,2: 54:[36, 17] Operation: 41-24=17 Exploring Operation: 24+36=60, Resulting Numbers: [41, 60] Generated Node #0,0,3: 54:[41, 60] Operation: 24+36=60 Moving to Node #0,2 Current State: 54:[24, 80, 3], Operations: ['39-36=3'] Exploring Operation: 24/3=8, Resulting Numbers: [80, 8] Generated Node #0,2,0: 54:[80, 8] Operation: 24/3=8 Exploring Operation: 80-3=77, Resulting Numbers: [24, 77] Generated Node #0,2,1: 54:[24, 77] Operation: 80-3=77 Exploring Operation: 24+3=27, Resulting Numbers: [80, 27] Generated Node #0,2,2: 54:[80, 27] Operation: 24+3=27 Exploring Operation: 80-24=56, Resulting Numbers: [3, 56] Generated Node #0,2,3: 54:[3, 56] Operation: 80-24=56 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 54:[3, 56], Operations: ['39-36=3', '80-24=56'] Exploring Operation: 56-3=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 3*56=168, Resulting Numbers: [168] 168,54 unequal: No Solution Exploring Operation: 3+56=59, Resulting Numbers: [59] 59,54 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:[24, 77], Operations: ['39-36=3', '80-3=77'] Exploring Operation: 24+77=101, Resulting Numbers: [101] 101,54 unequal: No Solution Exploring Operation: 24*77=1848, Resulting Numbers: [1848] 1848,54 unequal: No Solution Exploring Operation: 77-24=53, Resulting Numbers: [53] 53,54 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:[80, 27], Operations: ['39-36=3', '24+3=27'] Exploring Operation: 80-27=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 80*27=2160, Resulting Numbers: [2160] 2160,54 unequal: No Solution Exploring Operation: 80+27=107, Resulting Numbers: [107] 107,54 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 #0,2,0 Current State: 54:[80, 8], Operations: ['39-36=3', '24/3=8'] Exploring Operation: 80-8=72, Resulting Numbers: [72] 72,54 unequal: No Solution Exploring Operation: 80/8=10, Resulting Numbers: [10] 10,54 unequal: No Solution Exploring Operation: 80*8=640, Resulting Numbers: [640] 640,54 unequal: No Solution Exploring Operation: 80+8=88, Resulting Numbers: [88] 88,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,3 Current State: 54:[24, 5], Operations: ['80-36=44', '44-39=5'] Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,54 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[24, 5], Operations: ['80-39=41', '41-36=5'] Exploring Operation: 24*5=120, Resulting Numbers: [120] 120,54 unequal: No Solution Exploring Operation: 24+5=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 24-5=19, Resulting Numbers: [19] 19,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[36, 17], Operations: ['80-39=41', '41-24=17'] Exploring Operation: 36+17=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 36-17=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 36*17=612, Resulting Numbers: [612] 612,54 unequal: No Solution Moving to Node #0,3,2 Current State: 54:[44, 15], Operations: ['80-36=44', '39-24=15'] Exploring Operation: 44-15=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 44*15=660, Resulting Numbers: [660] 660,54 unequal: No Solution Exploring Operation: 44+15=59, Resulting Numbers: [59] 59,54 unequal: No Solution Moving to Node #0,3,1 Current State: 54:[39, 20], Operations: ['80-36=44', '44-24=20'] Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,54 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,54 unequal: No Solution Moving to Node #0,0,1 Current State: 54:[41, 12], Operations: ['80-39=41', '36-24=12'] Exploring Operation: 41+12=53, Resulting Numbers: [53] 53,54 unequal: No Solution Exploring Operation: 41-12=29, Resulting Numbers: [29] 29,54 unequal: No Solution Exploring Operation: 41*12=492, Resulting Numbers: [492] 492,54 unequal: No Solution Moving to Node #0,3,0 Current State: 54:[44, 63], Operations: ['80-36=44', '39+24=63'] Exploring Operation: 44+63=107, Resulting Numbers: [107] 107,54 unequal: No Solution Exploring Operation: 44*63=2772, Resulting Numbers: [2772] 2772,54 unequal: No Solution Exploring Operation: 63-44=19, Resulting Numbers: [19] 19,54 unequal: No Solution Moving to Node #0,0,3 Current State: 54:[41, 60], Operations: ['80-39=41', '24+36=60'] Exploring Operation: 41+60=101, Resulting Numbers: [101] 101,54 unequal: No Solution Exploring Operation: 60-41=19, Resulting Numbers: [19] 19,54 unequal: No Solution Exploring Operation: 41*60=2460, Resulting Numbers: [2460] 2460,54 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 66, 6, 42, 74 ]
28
[ "66-6=60", "74-42=32", "60-32=28" ]
Current State: 28:[66, 6, 42, 74], Operations: [] Exploring Operation: 66-6=60, Resulting Numbers: [42, 74, 60] Generated Node #2: [42, 74, 60] from Operation: 66-6=60 Current State: 28:[42, 74, 60], Operations: ['66-6=60'] Exploring Operation: 74-42=32, Resulting Numbers: [60, 32] Generated Node #3: [60, 32] from Operation: 74-42=32 Current State: 28:[60, 32], Operations: ['66-6=60', '74-42=32'] Exploring Operation: 60-32=28, Resulting Numbers: [28] 28,28 equal: Goal Reached
4
Current State: 28:[66, 6, 42, 74], Operations: [] Exploring Operation: 74-66=8, Resulting Numbers: [6, 42, 8] Generated Node #0,0: 28:[6, 42, 8] Operation: 74-66=8 Start Sub Search at level 1: Moving to Node #0,0 Current State: 28:[6, 42, 8], Operations: ['74-66=8'] Exploring Operation: 42/6=7, Resulting Numbers: [8, 7] Generated Node #0,0,0: 28:[8, 7] Operation: 42/6=7 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 28:[8, 7], Operations: ['74-66=8', '42/6=7'] Exploring Operation: 8+7=15, Resulting Numbers: [15] 15,28 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 63, 31, 30, 62 ]
62
[ "63+31=94", "62-30=32", "94-32=62" ]
Current State: 62:[63, 31, 30, 62], Operations: [] Exploring Operation: 63+31=94, Resulting Numbers: [30, 62, 94] Generated Node #2: [30, 62, 94] from Operation: 63+31=94 Current State: 62:[30, 62, 94], Operations: ['63+31=94'] Exploring Operation: 62-30=32, Resulting Numbers: [94, 32] Generated Node #3: [94, 32] from Operation: 62-30=32 Current State: 62:[94, 32], Operations: ['63+31=94', '62-30=32'] Exploring Operation: 94-32=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[63, 31, 30, 62], Operations: [] Exploring Operation: 63-31=32, Resulting Numbers: [30, 62, 32] Generated Node #0,0: 62:[30, 62, 32] Operation: 63-31=32 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[30, 62, 32], Operations: ['63-31=32'] Exploring Operation: 30+32=62, Resulting Numbers: [62, 62] Generated Node #0,0,0: 62:[62, 62] Operation: 30+32=62 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 62:[62, 62], Operations: ['63-31=32', '30+32=62'] Exploring Operation: 62/62=1, Resulting Numbers: [1] 1,62 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 8, 67, 8, 64 ]
16
[ "67-64=3", "8*3=24", "24-8=16" ]
Current State: 16:[8, 67, 8, 64], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [8, 8, 3] Generated Node #2: [8, 8, 3] from Operation: 67-64=3 Current State: 16:[8, 8, 3], Operations: ['67-64=3'] Exploring Operation: 8*3=24, Resulting Numbers: [24] 24,16 equal: Goal Reached Exploring Operation: 24-8=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[8, 67, 8, 64], Operations: [] Exploring Operation: 67-64=3, Resulting Numbers: [8, 8, 3] Generated Node #0,0: 16:[8, 8, 3] Operation: 67-64=3 Exploring Operation: 64/8=8, Resulting Numbers: [67, 8, 8] Generated Node #0,1: 16:[67, 8, 8] Operation: 64/8=8 Moving to Node #0,0 Current State: 16:[8, 8, 3], Operations: ['67-64=3'] Exploring Operation: 8-3=5, Resulting Numbers: [8, 5] Generated Node #0,0,0: 16:[8, 5] Operation: 8-3=5 Exploring Operation: 8+8=16, Resulting Numbers: [3, 16] Generated Node #0,0,1: 16:[3, 16] Operation: 8+8=16 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 16:[8, 5], Operations: ['67-64=3', '8-3=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,16 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,16 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 16:[3, 16], Operations: ['67-64=3', '8+8=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,16 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,16 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: 16:[67, 8, 8], Operations: ['64/8=8'] Exploring Operation: 67-8=59, Resulting Numbers: [8, 59] Generated Node #0,1,0: 16:[8, 59] Operation: 67-8=59 Exploring Operation: 67-8=59, Resulting Numbers: [8, 59] Generated Node #0,1,1: 16:[8, 59] Operation: 67-8=59 Moving to Node #0,1,0 Current State: 16:[8, 59], Operations: ['64/8=8', '67-8=59'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 8+59=67, Resulting Numbers: [67] 67,16 unequal: No Solution Moving to Node #0,1,1 Current State: 16:[8, 59], Operations: ['64/8=8', '67-8=59'] Exploring Operation: 59-8=51, Resulting Numbers: [51] 51,16 unequal: No Solution Exploring Operation: 8+59=67, Resulting Numbers: [67] 67,16 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 46, 48, 91, 34 ]
31
[ "46+48=94", "91+34=125", "125-94=31" ]
Current State: 31:[46, 48, 91, 34], Operations: [] Exploring Operation: 46+48=94, Resulting Numbers: [91, 34, 94] Generated Node #2: [91, 34, 94] from Operation: 46+48=94 Current State: 31:[91, 34, 94], Operations: ['46+48=94'] Exploring Operation: 91+34=125, Resulting Numbers: [94, 125] Generated Node #3: [94, 125] from Operation: 91+34=125 Current State: 31:[94, 125], Operations: ['46+48=94', '91+34=125'] Exploring Operation: 125-94=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[46, 48, 91, 34], Operations: [] Exploring Operation: 91-34=57, Resulting Numbers: [46, 48, 57] Generated Node #0,0: 31:[46, 48, 57] Operation: 91-34=57 Exploring Operation: 48-46=2, Resulting Numbers: [91, 34, 2] Generated Node #0,1: 31:[91, 34, 2] Operation: 48-46=2 Exploring Operation: 91-48=43, Resulting Numbers: [46, 34, 43] Generated Node #0,2: 31:[46, 34, 43] Operation: 91-48=43 Exploring Operation: 91-46=45, Resulting Numbers: [48, 34, 45] Generated Node #0,3: 31:[48, 34, 45] Operation: 91-46=45 Start Sub Search at level 1: Moving to Node #0,2 Current State: 31:[46, 34, 43], Operations: ['91-48=43'] Exploring Operation: 43-34=9, Resulting Numbers: [46, 9] Generated Node #0,2,0: 31:[46, 9] Operation: 43-34=9 Exploring Operation: 46-43=3, Resulting Numbers: [34, 3] Generated Node #0,2,1: 31:[34, 3] Operation: 46-43=3 Exploring Operation: 46-34=12, Resulting Numbers: [43, 12] Generated Node #0,2,2: 31:[43, 12] Operation: 46-34=12 Exploring Operation: 46+34=80, Resulting Numbers: [43, 80] Generated Node #0,2,3: 31:[43, 80] Operation: 46+34=80 Moving to Node #0,2,1 Current State: 31:[34, 3], Operations: ['91-48=43', '46-43=3'] Exploring Operation: 34+3=37, Resulting Numbers: [37] 37,31 unequal: No Solution Exploring Operation: 34*3=102, Resulting Numbers: [102] 102,31 unequal: No Solution Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[46, 48, 91, 34], Operations: [] Exploring Operation: 91-48=43, Resulting Numbers: [46, 34, 43] Generated Node #0,2: 31:[46, 34, 43] Operation: 91-48=43 Moving to Node #0,2 Current State: 31:[46, 34, 43], Operations: ['91-48=43'] Exploring Operation: 46-43=3, Resulting Numbers: [34, 3] Generated Node #0,2,1: 31:[34, 3] Operation: 46-43=3 Moving to Node #0,2,1 Current State: 31:[34, 3], Operations: ['91-48=43', '46-43=3'] Exploring Operation: 34-3=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 9, 13, 97, 2 ]
18
[ "9*13=117", "97+2=99", "117-99=18" ]
Current State: 18:[9, 13, 97, 2], Operations: [] Exploring Operation: 9*13=117, Resulting Numbers: [97, 2, 117] Generated Node #2: [97, 2, 117] from Operation: 9*13=117 Current State: 18:[97, 2, 117], Operations: ['9*13=117'] Exploring Operation: 97+2=99, Resulting Numbers: [117, 99] Generated Node #3: [117, 99] from Operation: 97+2=99 Current State: 18:[117, 99], Operations: ['9*13=117', '97+2=99'] Exploring Operation: 117-99=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[9, 13, 97, 2], Operations: [] Exploring Operation: 97-13=84, Resulting Numbers: [9, 2, 84] Generated Node #0,0: 18:[9, 2, 84] Operation: 97-13=84 Exploring Operation: 97-9=88, Resulting Numbers: [13, 2, 88] Generated Node #0,1: 18:[13, 2, 88] Operation: 97-9=88 Exploring Operation: 13-9=4, Resulting Numbers: [97, 2, 4] Generated Node #0,2: 18:[97, 2, 4] Operation: 13-9=4 Moving to Node #0,0 Current State: 18:[9, 2, 84], Operations: ['97-13=84'] Exploring Operation: 84-2=82, Resulting Numbers: [9, 82] Generated Node #0,0,0: 18:[9, 82] Operation: 84-2=82 Exploring Operation: 84/2=42, Resulting Numbers: [9, 42] Generated Node #0,0,1: 18:[9, 42] Operation: 84/2=42 Exploring Operation: 84-9=75, Resulting Numbers: [2, 75] Generated Node #0,0,2: 18:[2, 75] Operation: 84-9=75 Moving to Node #0,1 Current State: 18:[13, 2, 88], Operations: ['97-9=88'] Exploring Operation: 88-13=75, Resulting Numbers: [2, 75] Generated Node #0,1,0: 18:[2, 75] Operation: 88-13=75 Exploring Operation: 88/2=44, Resulting Numbers: [13, 44] Generated Node #0,1,1: 18:[13, 44] Operation: 88/2=44 Exploring Operation: 13-2=11, Resulting Numbers: [88, 11] Generated Node #0,1,2: 18:[88, 11] Operation: 13-2=11 Moving to Node #0,2 Current State: 18:[97, 2, 4], Operations: ['13-9=4'] Exploring Operation: 2+4=6, Resulting Numbers: [97, 6] Generated Node #0,2,0: 18:[97, 6] Operation: 2+4=6 Exploring Operation: 97-4=93, Resulting Numbers: [2, 93] Generated Node #0,2,1: 18:[2, 93] Operation: 97-4=93 Exploring Operation: 97-2=95, Resulting Numbers: [4, 95] Generated Node #0,2,2: 18:[4, 95] Operation: 97-2=95 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[2, 93], Operations: ['13-9=4', '97-4=93'] Exploring Operation: 2+93=95, Resulting Numbers: [95] 95,18 unequal: No Solution Exploring Operation: 93-2=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 2*93=186, Resulting Numbers: [186] 186,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 18:[4, 95], Operations: ['13-9=4', '97-2=95'] Exploring Operation: 4*95=380, Resulting Numbers: [380] 380,18 unequal: No Solution Exploring Operation: 4+95=99, Resulting Numbers: [99] 99,18 unequal: No Solution Exploring Operation: 95-4=91, Resulting Numbers: [91] 91,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[97, 6], Operations: ['13-9=4', '2+4=6'] Exploring Operation: 97*6=582, Resulting Numbers: [582] 582,18 unequal: No Solution Exploring Operation: 97-6=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 97+6=103, Resulting Numbers: [103] 103,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,1 Current State: 18:[9, 42], Operations: ['97-13=84', '84/2=42'] Exploring Operation: 9+42=51, Resulting Numbers: [51] 51,18 unequal: No Solution Exploring Operation: 9*42=378, Resulting Numbers: [378] 378,18 unequal: No Solution Exploring Operation: 42-9=33, Resulting Numbers: [33] 33,18 unequal: No Solution Moving to Node #0,1,1 Current State: 18:[13, 44], Operations: ['97-9=88', '88/2=44'] Exploring Operation: 13*44=572, Resulting Numbers: [572] 572,18 unequal: No Solution Exploring Operation: 13+44=57, Resulting Numbers: [57] 57,18 unequal: No Solution Exploring Operation: 44-13=31, Resulting Numbers: [31] 31,18 unequal: No Solution Moving to Node #0,1,0 Current State: 18:[2, 75], Operations: ['97-9=88', '88-13=75'] Exploring Operation: 2*75=150, Resulting Numbers: [150] 150,18 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,18 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,18 unequal: No Solution Moving to Node #0,0,2 Current State: 18:[2, 75], Operations: ['97-13=84', '84-9=75'] Exploring Operation: 2*75=150, Resulting Numbers: [150] 150,18 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,18 unequal: No Solution Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,18 unequal: No Solution Moving to Node #0,0,0 Current State: 18:[9, 82], Operations: ['97-13=84', '84-2=82'] Exploring Operation: 9+82=91, Resulting Numbers: [91] 91,18 unequal: No Solution Exploring Operation: 9*82=738, Resulting Numbers: [738] 738,18 unequal: No Solution Exploring Operation: 82-9=73, Resulting Numbers: [73] 73,18 unequal: No Solution Moving to Node #0,1,2 Current State: 18:[88, 11], Operations: ['97-9=88', '13-2=11'] Exploring Operation: 88+11=99, Resulting Numbers: [99] 99,18 unequal: No Solution Exploring Operation: 88-11=77, Resulting Numbers: [77] 77,18 unequal: No Solution Exploring Operation: 88/11=8, Resulting Numbers: [8] 8,18 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 30, 74, 25, 28 ]
62
[ "30-28=2", "74/2=37", "25+37=62" ]
Current State: 62:[30, 74, 25, 28], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [74, 25, 2] Generated Node #2: [74, 25, 2] from Operation: 30-28=2 Current State: 62:[74, 25, 2], Operations: ['30-28=2'] Exploring Operation: 74/2=37, Resulting Numbers: [25, 37] Generated Node #3: [25, 37] from Operation: 74/2=37 Current State: 62:[25, 37], Operations: ['30-28=2', '74/2=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[30, 74, 25, 28], Operations: [] Exploring Operation: 30-25=5, Resulting Numbers: [74, 28, 5] Generated Node #0,0: 62:[74, 28, 5] Operation: 30-25=5 Exploring Operation: 28-25=3, Resulting Numbers: [30, 74, 3] Generated Node #0,1: 62:[30, 74, 3] Operation: 28-25=3 Exploring Operation: 30-28=2, Resulting Numbers: [74, 25, 2] Generated Node #0,2: 62:[74, 25, 2] Operation: 30-28=2 Exploring Operation: 74-25=49, Resulting Numbers: [30, 28, 49] Generated Node #0,3: 62:[30, 28, 49] Operation: 74-25=49 Moving to Node #0,1 Current State: 62:[30, 74, 3], Operations: ['28-25=3'] Exploring Operation: 74-3=71, Resulting Numbers: [30, 71] Generated Node #0,1,0: 62:[30, 71] Operation: 74-3=71 Exploring Operation: 30-3=27, Resulting Numbers: [74, 27] Generated Node #0,1,1: 62:[74, 27] Operation: 30-3=27 Exploring Operation: 74-30=44, Resulting Numbers: [3, 44] Generated Node #0,1,2: 62:[3, 44] Operation: 74-30=44 Exploring Operation: 30+3=33, Resulting Numbers: [74, 33] Generated Node #0,1,3: 62:[74, 33] Operation: 30+3=33 Moving to Node #0,3 Current State: 62:[30, 28, 49], Operations: ['74-25=49'] Exploring Operation: 49-30=19, Resulting Numbers: [28, 19] Generated Node #0,3,0: 62:[28, 19] Operation: 49-30=19 Exploring Operation: 30-28=2, Resulting Numbers: [49, 2] Generated Node #0,3,1: 62:[49, 2] Operation: 30-28=2 Exploring Operation: 28+49=77, Resulting Numbers: [30, 77] Generated Node #0,3,2: 62:[30, 77] Operation: 28+49=77 Exploring Operation: 49-28=21, Resulting Numbers: [30, 21] Generated Node #0,3,3: 62:[30, 21] Operation: 49-28=21 Moving to Node #0,2 Current State: 62:[74, 25, 2], Operations: ['30-28=2'] Exploring Operation: 74/2=37, Resulting Numbers: [25, 37] Generated Node #0,2,0: 62:[25, 37] Operation: 74/2=37 Exploring Operation: 25+2=27, Resulting Numbers: [74, 27] Generated Node #0,2,1: 62:[74, 27] Operation: 25+2=27 Exploring Operation: 74-2=72, Resulting Numbers: [25, 72] Generated Node #0,2,2: 62:[25, 72] Operation: 74-2=72 Exploring Operation: 74-25=49, Resulting Numbers: [2, 49] Generated Node #0,2,3: 62:[2, 49] Operation: 74-25=49 Moving to Node #0,0 Current State: 62:[74, 28, 5], Operations: ['30-25=5'] Exploring Operation: 74-28=46, Resulting Numbers: [5, 46] Generated Node #0,0,0: 62:[5, 46] Operation: 74-28=46 Exploring Operation: 74+5=79, Resulting Numbers: [28, 79] Generated Node #0,0,1: 62:[28, 79] Operation: 74+5=79 Exploring Operation: 74-5=69, Resulting Numbers: [28, 69] Generated Node #0,0,2: 62:[28, 69] Operation: 74-5=69 Exploring Operation: 28+5=33, Resulting Numbers: [74, 33] Generated Node #0,0,3: 62:[74, 33] Operation: 28+5=33 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 62:[28, 69], Operations: ['30-25=5', '74-5=69'] Exploring Operation: 28*69=1932, Resulting Numbers: [1932] 1932,62 unequal: No Solution Exploring Operation: 69-28=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 28+69=97, Resulting Numbers: [97] 97,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 62:[74, 33], Operations: ['30-25=5', '28+5=33'] Exploring Operation: 74*33=2442, Resulting Numbers: [2442] 2442,62 unequal: No Solution Exploring Operation: 74-33=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 74+33=107, Resulting Numbers: [107] 107,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 62:[5, 46], Operations: ['30-25=5', '74-28=46'] Exploring Operation: 5+46=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 46-5=41, Resulting Numbers: [41] 41,62 unequal: No Solution Exploring Operation: 5*46=230, Resulting Numbers: [230] 230,62 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 62:[28, 79], Operations: ['30-25=5', '74+5=79'] Exploring Operation: 79-28=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 28+79=107, Resulting Numbers: [107] 107,62 unequal: No Solution Exploring Operation: 28*79=2212, Resulting Numbers: [2212] 2212,62 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: 62:[30, 71], Operations: ['28-25=3', '74-3=71'] Exploring Operation: 30*71=2130, Resulting Numbers: [2130] 2130,62 unequal: No Solution Exploring Operation: 30+71=101, Resulting Numbers: [101] 101,62 unequal: No Solution Exploring Operation: 71-30=41, Resulting Numbers: [41] 41,62 unequal: No Solution Moving to Node #0,3,3 Current State: 62:[30, 21], Operations: ['74-25=49', '49-28=21'] Exploring Operation: 30+21=51, Resulting Numbers: [51] 51,62 unequal: No Solution Exploring Operation: 30-21=9, Resulting Numbers: [9] 9,62 unequal: No Solution Exploring Operation: 30*21=630, Resulting Numbers: [630] 630,62 unequal: No Solution Moving to Node #0,2,0 Current State: 62:[25, 37], Operations: ['30-28=2', '74/2=37'] Exploring Operation: 37-25=12, Resulting Numbers: [12] 12,62 unequal: No Solution Exploring Operation: 25*37=925, Resulting Numbers: [925] 925,62 unequal: No Solution Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[30, 74, 25, 28], Operations: [] Exploring Operation: 30-28=2, Resulting Numbers: [74, 25, 2] Generated Node #0,2: 62:[74, 25, 2] Operation: 30-28=2 Moving to Node #0,2 Current State: 62:[74, 25, 2], Operations: ['30-28=2'] Exploring Operation: 74/2=37, Resulting Numbers: [25, 37] Generated Node #0,2,0: 62:[25, 37] Operation: 74/2=37 Moving to Node #0,2,0 Current State: 62:[25, 37], Operations: ['30-28=2', '74/2=37'] Exploring Operation: 25+37=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
0.960938
hs_4
sum_heuristic
[ 69, 30, 35, 14 ]
10
[ "69-30=39", "35+14=49", "49-39=10" ]
Current State: 10:[69, 30, 35, 14], Operations: [] Exploring Operation: 69-30=39, Resulting Numbers: [35, 14, 39] Generated Node #2: [35, 14, 39] from Operation: 69-30=39 Current State: 10:[35, 14, 39], Operations: ['69-30=39'] Exploring Operation: 35+14=49, Resulting Numbers: [39, 49] Generated Node #3: [39, 49] from Operation: 35+14=49 Current State: 10:[39, 49], Operations: ['69-30=39', '35+14=49'] Exploring Operation: 49-39=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[69, 30, 35, 14], Operations: [] Exploring Operation: 69-30=39, Resulting Numbers: [35, 14, 39] Generated Node #0,0: 10:[35, 14, 39] Operation: 69-30=39 Exploring Operation: 69-35=34, Resulting Numbers: [30, 14, 34] Generated Node #0,1: 10:[30, 14, 34] Operation: 69-35=34 Exploring Operation: 35-30=5, Resulting Numbers: [69, 14, 5] Generated Node #0,2: 10:[69, 14, 5] Operation: 35-30=5 Start Sub Search at level 1: Moving to Node #0,1 Current State: 10:[30, 14, 34], Operations: ['69-35=34'] Exploring Operation: 34-30=4, Resulting Numbers: [14, 4] Generated Node #0,1,0: 10:[14, 4] Operation: 34-30=4 Exploring Operation: 30-14=16, Resulting Numbers: [34, 16] Generated Node #0,1,1: 10:[34, 16] Operation: 30-14=16 Exploring Operation: 34-14=20, Resulting Numbers: [30, 20] Generated Node #0,1,2: 10:[30, 20] Operation: 34-14=20 Moving to Node #0,1,0 Current State: 10:[14, 4], Operations: ['69-35=34', '34-30=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,10 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,10 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Moving to Node #0 Current State: 10:[69, 30, 35, 14], Operations: [] Exploring Operation: 69-35=34, Resulting Numbers: [30, 14, 34] Generated Node #0,1: 10:[30, 14, 34] Operation: 69-35=34 Moving to Node #0,1 Current State: 10:[30, 14, 34], Operations: ['69-35=34'] Exploring Operation: 34-30=4, Resulting Numbers: [14, 4] Generated Node #0,1,0: 10:[14, 4] Operation: 34-30=4 Moving to Node #0,1,0 Current State: 10:[14, 4], Operations: ['69-35=34', '34-30=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,10 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
mult_heuristic
[ 61, 48, 3, 86 ]
70
[ "61-48=13", "86-3=83", "83-13=70" ]
Current State: 70:[61, 48, 3, 86], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [3, 86, 13] Generated Node #2: [3, 86, 13] from Operation: 61-48=13 Current State: 70:[3, 86, 13], Operations: ['61-48=13'] Exploring Operation: 86-3=83, Resulting Numbers: [13, 83] Generated Node #3: [13, 83] from Operation: 86-3=83 Current State: 70:[13, 83], Operations: ['61-48=13', '86-3=83'] Exploring Operation: 83-13=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[61, 48, 3, 86], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [3, 86, 13] Generated Node #0,0: 70:[3, 86, 13] Operation: 61-48=13 Exploring Operation: 48/3=16, Resulting Numbers: [61, 86, 16] Generated Node #0,1: 70:[61, 86, 16] Operation: 48/3=16 Exploring Operation: 86-48=38, Resulting Numbers: [61, 3, 38] Generated Node #0,2: 70:[61, 3, 38] Operation: 86-48=38 Exploring Operation: 86-61=25, Resulting Numbers: [48, 3, 25] Generated Node #0,3: 70:[48, 3, 25] Operation: 86-61=25 Moving to Node #0,2 Current State: 70:[61, 3, 38], Operations: ['86-48=38'] Exploring Operation: 38-3=35, Resulting Numbers: [61, 35] Generated Node #0,2,0: 70:[61, 35] Operation: 38-3=35 Exploring Operation: 61-3=58, Resulting Numbers: [38, 58] Generated Node #0,2,1: 70:[38, 58] Operation: 61-3=58 Exploring Operation: 61-38=23, Resulting Numbers: [3, 23] Generated Node #0,2,2: 70:[3, 23] Operation: 61-38=23 Exploring Operation: 61+3=64, Resulting Numbers: [38, 64] Generated Node #0,2,3: 70:[38, 64] Operation: 61+3=64 Moving to Node #0,0 Current State: 70:[3, 86, 13], Operations: ['61-48=13'] Exploring Operation: 86-3=83, Resulting Numbers: [13, 83] Generated Node #0,0,0: 70:[13, 83] Operation: 86-3=83 Exploring Operation: 13-3=10, Resulting Numbers: [86, 10] Generated Node #0,0,1: 70:[86, 10] Operation: 13-3=10 Exploring Operation: 3+13=16, Resulting Numbers: [86, 16] Generated Node #0,0,2: 70:[86, 16] Operation: 3+13=16 Exploring Operation: 86-13=73, Resulting Numbers: [3, 73] Generated Node #0,0,3: 70:[3, 73] Operation: 86-13=73 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 70:[3, 73], Operations: ['61-48=13', '86-13=73'] Exploring Operation: 3+73=76, Resulting Numbers: [76] 76,70 unequal: No Solution Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[61, 48, 3, 86], Operations: [] Exploring Operation: 61-48=13, Resulting Numbers: [3, 86, 13] Generated Node #0,0: 70:[3, 86, 13] Operation: 61-48=13 Moving to Node #0,0 Current State: 70:[3, 86, 13], Operations: ['61-48=13'] Exploring Operation: 86-13=73, Resulting Numbers: [3, 73] Generated Node #0,0,3: 70:[3, 73] Operation: 86-13=73 Moving to Node #0,0,3 Current State: 70:[3, 73], Operations: ['61-48=13', '86-13=73'] Exploring Operation: 73-3=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 11, 70, 2, 75 ]
53
[ "75-70=5", "11*5=55", "55-2=53" ]
Current State: 53:[11, 70, 2, 75], Operations: [] Exploring Operation: 75-70=5, Resulting Numbers: [11, 2, 5] Generated Node #2: [11, 2, 5] from Operation: 75-70=5 Current State: 53:[11, 2, 5], Operations: ['75-70=5'] Exploring Operation: 11*5=55, Resulting Numbers: [2, 55] Generated Node #3: [2, 55] from Operation: 11*5=55 Current State: 53:[2, 55], Operations: ['75-70=5', '11*5=55'] Exploring Operation: 55-2=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[11, 70, 2, 75], Operations: [] Exploring Operation: 70-2=68, Resulting Numbers: [11, 75, 68] Generated Node #0,0: 53:[11, 75, 68] Operation: 70-2=68 Exploring Operation: 11*2=22, Resulting Numbers: [70, 75, 22] Generated Node #0,1: 53:[70, 75, 22] Operation: 11*2=22 Exploring Operation: 75-11=64, Resulting Numbers: [70, 2, 64] Generated Node #0,2: 53:[70, 2, 64] Operation: 75-11=64 Exploring Operation: 70-11=59, Resulting Numbers: [2, 75, 59] Generated Node #0,3: 53:[2, 75, 59] Operation: 70-11=59 Exploring Operation: 11+2=13, Resulting Numbers: [70, 75, 13] Generated Node #0,4: 53:[70, 75, 13] Operation: 11+2=13 Moving to Node #0,1 Current State: 53:[70, 75, 22], Operations: ['11*2=22'] Exploring Operation: 75-22=53, Resulting Numbers: [70, 53] Generated Node #0,1,0: 53:[70, 53] Operation: 75-22=53 Exploring Operation: 75-70=5, Resulting Numbers: [22, 5] Generated Node #0,1,1: 53:[22, 5] Operation: 75-70=5 Exploring Operation: 70-22=48, Resulting Numbers: [75, 48] Generated Node #0,1,2: 53:[75, 48] Operation: 70-22=48 Exploring Operation: 75+22=97, Resulting Numbers: [70, 97] Generated Node #0,1,3: 53:[70, 97] Operation: 75+22=97 Exploring Operation: 70+22=92, Resulting Numbers: [75, 92] Generated Node #0,1,4: 53:[75, 92] Operation: 70+22=92 Moving to Node #0,2 Current State: 53:[70, 2, 64], Operations: ['75-11=64'] Exploring Operation: 70/2=35, Resulting Numbers: [64, 35] Generated Node #0,2,0: 53:[64, 35] Operation: 70/2=35 Exploring Operation: 2+64=66, Resulting Numbers: [70, 66] Generated Node #0,2,1: 53:[70, 66] Operation: 2+64=66 Exploring Operation: 64-2=62, Resulting Numbers: [70, 62] Generated Node #0,2,2: 53:[70, 62] Operation: 64-2=62 Exploring Operation: 70-2=68, Resulting Numbers: [64, 68] Generated Node #0,2,3: 53:[64, 68] Operation: 70-2=68 Exploring Operation: 70+2=72, Resulting Numbers: [64, 72] Generated Node #0,2,4: 53:[64, 72] Operation: 70+2=72 Moving to Node #0,4 Current State: 53:[70, 75, 13], Operations: ['11+2=13'] Exploring Operation: 70-13=57, Resulting Numbers: [75, 57] Generated Node #0,4,0: 53:[75, 57] Operation: 70-13=57 Exploring Operation: 75-70=5, Resulting Numbers: [13, 5] Generated Node #0,4,1: 53:[13, 5] Operation: 75-70=5 Exploring Operation: 75-13=62, Resulting Numbers: [70, 62] Generated Node #0,4,2: 53:[70, 62] Operation: 75-13=62 Exploring Operation: 70+13=83, Resulting Numbers: [75, 83] Generated Node #0,4,3: 53:[75, 83] Operation: 70+13=83 Exploring Operation: 75+13=88, Resulting Numbers: [70, 88] Generated Node #0,4,4: 53:[70, 88] Operation: 75+13=88 Moving to Node #0,0 Current State: 53:[11, 75, 68], Operations: ['70-2=68'] Exploring Operation: 75-11=64, Resulting Numbers: [68, 64] Generated Node #0,0,0: 53:[68, 64] Operation: 75-11=64 Exploring Operation: 75-68=7, Resulting Numbers: [11, 7] Generated Node #0,0,1: 53:[11, 7] Operation: 75-68=7 Exploring Operation: 68-11=57, Resulting Numbers: [75, 57] Generated Node #0,0,2: 53:[75, 57] Operation: 68-11=57 Exploring Operation: 11+68=79, Resulting Numbers: [75, 79] Generated Node #0,0,3: 53:[75, 79] Operation: 11+68=79 Exploring Operation: 11+75=86, Resulting Numbers: [68, 86] Generated Node #0,0,4: 53:[68, 86] Operation: 11+75=86 Moving to Node #0,3 Current State: 53:[2, 75, 59], Operations: ['70-11=59'] Exploring Operation: 2+59=61, Resulting Numbers: [75, 61] Generated Node #0,3,0: 53:[75, 61] Operation: 2+59=61 Exploring Operation: 75-2=73, Resulting Numbers: [59, 73] Generated Node #0,3,1: 53:[59, 73] Operation: 75-2=73 Exploring Operation: 59-2=57, Resulting Numbers: [75, 57] Generated Node #0,3,2: 53:[75, 57] Operation: 59-2=57 Exploring Operation: 2+75=77, Resulting Numbers: [59, 77] Generated Node #0,3,3: 53:[59, 77] Operation: 2+75=77 Exploring Operation: 2*59=118, Resulting Numbers: [75, 118] Generated Node #0,3,4: 53:[75, 118] Operation: 2*59=118 Moving to Node #0,1,0 Current State: 53:[70, 53], Operations: ['11*2=22', '75-22=53'] Exploring Operation: 70-53=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 70*53=3710, Resulting Numbers: [3710] 3710,53 unequal: No Solution Exploring Operation: 70+53=123, Resulting Numbers: [123] 123,53 unequal: No Solution Moving to Node #0,2,2 Current State: 53:[70, 62], Operations: ['75-11=64', '64-2=62'] Exploring Operation: 70*62=4340, Resulting Numbers: [4340] 4340,53 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 70+62=132, Resulting Numbers: [132] 132,53 unequal: No Solution Moving to Node #0,2,3 Current State: 53:[64, 68], Operations: ['75-11=64', '70-2=68'] Exploring Operation: 68-64=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 64+68=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 64*68=4352, Resulting Numbers: [4352] 4352,53 unequal: No Solution Moving to Node #0,4,2 Current State: 53:[70, 62], Operations: ['11+2=13', '75-13=62'] Exploring Operation: 70+62=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 70*62=4340, Resulting Numbers: [4340] 4340,53 unequal: No Solution Exploring Operation: 70-62=8, Resulting Numbers: [8] 8,53 unequal: No Solution Moving to Node #0,4,0 Current State: 53:[75, 57], Operations: ['11+2=13', '70-13=57'] Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,53 unequal: No Solution Moving to Node #0,3,1 Current State: 53:[59, 73], Operations: ['70-11=59', '75-2=73'] Exploring Operation: 59*73=4307, Resulting Numbers: [4307] 4307,53 unequal: No Solution Exploring Operation: 73-59=14, Resulting Numbers: [14] 14,53 unequal: No Solution Exploring Operation: 59+73=132, Resulting Numbers: [132] 132,53 unequal: No Solution Moving to Node #0,3,2 Current State: 53:[75, 57], Operations: ['70-11=59', '59-2=57'] Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,53 unequal: No Solution Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,53 unequal: No Solution Moving to Node #0,0,0 Current State: 53:[68, 64], Operations: ['70-2=68', '75-11=64'] Exploring Operation: 68+64=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 68-64=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 68*64=4352, Resulting Numbers: [4352] 4352,53 unequal: No Solution Moving to Node #0,0,2 Current State: 53:[75, 57], Operations: ['70-2=68', '68-11=57'] Exploring Operation: 75*57=4275, Resulting Numbers: [4275] 4275,53 unequal: No Solution Exploring Operation: 75+57=132, Resulting Numbers: [132] 132,53 unequal: No Solution Exploring Operation: 75-57=18, Resulting Numbers: [18] 18,53 unequal: No Solution Moving to Node #0,1,2 Current State: 53:[75, 48], Operations: ['11*2=22', '70-22=48'] Exploring Operation: 75*48=3600, Resulting Numbers: [3600] 3600,53 unequal: No Solution Exploring Operation: 75-48=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 75+48=123, Resulting Numbers: [123] 123,53 unequal: No Solution Moving to Node #0,2,0 Current State: 53:[64, 35], Operations: ['75-11=64', '70/2=35'] Exploring Operation: 64+35=99, Resulting Numbers: [99] 99,53 unequal: No Solution Exploring Operation: 64-35=29, Resulting Numbers: [29] 29,53 unequal: No Solution Exploring Operation: 64*35=2240, Resulting Numbers: [2240] 2240,53 unequal: No Solution Moving to Node #0,3,3 Current State: 53:[59, 77], Operations: ['70-11=59', '2+75=77'] Exploring Operation: 59*77=4543, Resulting Numbers: [4543] 4543,53 unequal: No Solution Exploring Operation: 77-59=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 59+77=136, Resulting Numbers: [136] 136,53 unequal: No Solution Moving to Node #0,3,0 Current State: 53:[75, 61], Operations: ['70-11=59', '2+59=61'] Exploring Operation: 75+61=136, Resulting Numbers: [136] 136,53 unequal: No Solution Exploring Operation: 75*61=4575, Resulting Numbers: [4575] 4575,53 unequal: No Solution Exploring Operation: 75-61=14, Resulting Numbers: [14] 14,53 unequal: No Solution Moving to Node #0,2,4 Current State: 53:[64, 72], Operations: ['75-11=64', '70+2=72'] Exploring Operation: 72-64=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 64*72=4608, Resulting Numbers: [4608] 4608,53 unequal: No Solution Exploring Operation: 64+72=136, Resulting Numbers: [136] 136,53 unequal: No Solution Moving to Node #0,2,1 Current State: 53:[70, 66], Operations: ['75-11=64', '2+64=66'] Exploring Operation: 70*66=4620, Resulting Numbers: [4620] 4620,53 unequal: No Solution Exploring Operation: 70+66=136, Resulting Numbers: [136] 136,53 unequal: No Solution Exploring Operation: 70-66=4, Resulting Numbers: [4] 4,53 unequal: No Solution Moving to Node #0,0,3 Current State: 53:[75, 79], Operations: ['70-2=68', '11+68=79'] Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 75*79=5925, Resulting Numbers: [5925] 5925,53 unequal: No Solution Exploring Operation: 75+79=154, Resulting Numbers: [154] 154,53 unequal: No Solution Moving to Node #0,0,4 Current State: 53:[68, 86], Operations: ['70-2=68', '11+75=86'] Exploring Operation: 86-68=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 68+86=154, Resulting Numbers: [154] 154,53 unequal: No Solution Exploring Operation: 68*86=5848, Resulting Numbers: [5848] 5848,53 unequal: No Solution Moving to Node #0,4,4 Current State: 53:[70, 88], Operations: ['11+2=13', '75+13=88'] Exploring Operation: 70*88=6160, Resulting Numbers: [6160] 6160,53 unequal: No Solution Exploring Operation: 70+88=158, Resulting Numbers: [158] 158,53 unequal: No Solution Exploring Operation: 88-70=18, Resulting Numbers: [18] 18,53 unequal: No Solution Moving to Node #0,4,3 Current State: 53:[75, 83], Operations: ['11+2=13', '70+13=83'] Exploring Operation: 83-75=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 75*83=6225, Resulting Numbers: [6225] 6225,53 unequal: No Solution Exploring Operation: 75+83=158, Resulting Numbers: [158] 158,53 unequal: No Solution Moving to Node #0,1,4 Current State: 53:[75, 92], Operations: ['11*2=22', '70+22=92'] Exploring Operation: 75*92=6900, Resulting Numbers: [6900] 6900,53 unequal: No Solution Exploring Operation: 92-75=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 75+92=167, Resulting Numbers: [167] 167,53 unequal: No Solution Moving to Node #0,1,3 Current State: 53:[70, 97], Operations: ['11*2=22', '75+22=97'] Exploring Operation: 97-70=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 70+97=167, Resulting Numbers: [167] 167,53 unequal: No Solution Exploring Operation: 70*97=6790, Resulting Numbers: [6790] 6790,53 unequal: No Solution Moving to Node #0,1,1 Current State: 53:[22, 5], Operations: ['11*2=22', '75-70=5'] Exploring Operation: 22+5=27, Resulting Numbers: [27] 27,53 unequal: No Solution Exploring Operation: 22-5=17, Resulting Numbers: [17] 17,53 unequal: No Solution Exploring Operation: 22*5=110, Resulting Numbers: [110] 110,53 unequal: No Solution Moving to Node #0,3,4 Current State: 53:[75, 118], Operations: ['70-11=59', '2*59=118'] Exploring Operation: 118-75=43, Resulting Numbers: [43] 43,53 unequal: No Solution Exploring Operation: 75*118=8850, Resulting Numbers: [8850] 8850,53 unequal: No Solution Exploring Operation: 75+118=193, Resulting Numbers: [193] 193,53 unequal: No Solution Moving to Node #0,4,1 Current State: 53:[13, 5], Operations: ['11+2=13', '75-70=5'] Exploring Operation: 13+5=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 13-5=8, Resulting Numbers: [8] 8,53 unequal: No Solution Exploring Operation: 13*5=65, Resulting Numbers: [65] 65,53 unequal: No Solution Moving to Node #0,0,1 Current State: 53:[11, 7], Operations: ['70-2=68', '75-68=7'] Exploring Operation: 11-7=4, Resulting Numbers: [4] 4,53 unequal: No Solution Exploring Operation: 11+7=18, Resulting Numbers: [18] 18,53 unequal: No Solution Exploring Operation: 11*7=77, Resulting Numbers: [77] 77,53 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 49, 63, 75, 70 ]
70
[ "63-49=14", "75-70=5", "14*5=70" ]
Current State: 70:[49, 63, 75, 70], Operations: [] Exploring Operation: 63-49=14, Resulting Numbers: [75, 70, 14] Generated Node #2: [75, 70, 14] from Operation: 63-49=14 Current State: 70:[75, 70, 14], Operations: ['63-49=14'] Exploring Operation: 75-70=5, Resulting Numbers: [14, 5] Generated Node #3: [14, 5] from Operation: 75-70=5 Current State: 70:[14, 5], Operations: ['63-49=14', '75-70=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[49, 63, 75, 70], Operations: [] Exploring Operation: 63-49=14, Resulting Numbers: [75, 70, 14] Generated Node #0,0: 70:[75, 70, 14] Operation: 63-49=14 Exploring Operation: 75-49=26, Resulting Numbers: [63, 70, 26] Generated Node #0,1: 70:[63, 70, 26] Operation: 75-49=26 Exploring Operation: 75-63=12, Resulting Numbers: [49, 70, 12] Generated Node #0,2: 70:[49, 70, 12] Operation: 75-63=12 Moving to Node #0,0 Current State: 70:[75, 70, 14], Operations: ['63-49=14'] Exploring Operation: 70/14=5, Resulting Numbers: [75, 5] Generated Node #0,0,0: 70:[75, 5] Operation: 70/14=5 Exploring Operation: 75-14=61, Resulting Numbers: [70, 61] Generated Node #0,0,1: 70:[70, 61] Operation: 75-14=61 Exploring Operation: 75-70=5, Resulting Numbers: [14, 5] Generated Node #0,0,2: 70:[14, 5] Operation: 75-70=5 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 70:[14, 5], Operations: ['63-49=14', '75-70=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[49, 63, 75, 70], Operations: [] Exploring Operation: 63-49=14, Resulting Numbers: [75, 70, 14] Generated Node #0,0: 70:[75, 70, 14] Operation: 63-49=14 Moving to Node #0,0 Current State: 70:[75, 70, 14], Operations: ['63-49=14'] Exploring Operation: 75-70=5, Resulting Numbers: [14, 5] Generated Node #0,0,2: 70:[14, 5] Operation: 75-70=5 Moving to Node #0,0,2 Current State: 70:[14, 5], Operations: ['63-49=14', '75-70=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 34, 55, 43, 59 ]
58
[ "43+59=102", "102/34=3", "55+3=58" ]
Current State: 58:[34, 55, 43, 59], Operations: [] Exploring Operation: 43+59=102, Resulting Numbers: [34, 55, 102] Generated Node #2: [34, 55, 102] from Operation: 43+59=102 Current State: 58:[34, 55, 102], Operations: ['43+59=102'] Exploring Operation: 102/34=3, Resulting Numbers: [55, 3] Generated Node #3: [55, 3] from Operation: 102/34=3 Current State: 58:[55, 3], Operations: ['43+59=102', '102/34=3'] Exploring Operation: 55+3=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[34, 55, 43, 59], Operations: [] Exploring Operation: 59-34=25, Resulting Numbers: [55, 43, 25] Generated Node #0,0: 58:[55, 43, 25] Operation: 59-34=25 Exploring Operation: 55-43=12, Resulting Numbers: [34, 59, 12] Generated Node #0,1: 58:[34, 59, 12] Operation: 55-43=12 Exploring Operation: 43-34=9, Resulting Numbers: [55, 59, 9] Generated Node #0,2: 58:[55, 59, 9] Operation: 43-34=9 Exploring Operation: 59-55=4, Resulting Numbers: [34, 43, 4] Generated Node #0,3: 58:[34, 43, 4] Operation: 59-55=4 Moving to Node #0,2 Current State: 58:[55, 59, 9], Operations: ['43-34=9'] Exploring Operation: 59-55=4, Resulting Numbers: [9, 4] Generated Node #0,2,0: 58:[9, 4] Operation: 59-55=4 Exploring Operation: 55+9=64, Resulting Numbers: [59, 64] Generated Node #0,2,1: 58:[59, 64] Operation: 55+9=64 Exploring Operation: 55-9=46, Resulting Numbers: [59, 46] Generated Node #0,2,2: 58:[59, 46] Operation: 55-9=46 Exploring Operation: 59-9=50, Resulting Numbers: [55, 50] Generated Node #0,2,3: 58:[55, 50] Operation: 59-9=50 Moving to Node #0,1 Current State: 58:[34, 59, 12], Operations: ['55-43=12'] Exploring Operation: 59-34=25, Resulting Numbers: [12, 25] Generated Node #0,1,0: 58:[12, 25] Operation: 59-34=25 Exploring Operation: 59-12=47, Resulting Numbers: [34, 47] Generated Node #0,1,1: 58:[34, 47] Operation: 59-12=47 Exploring Operation: 34+12=46, Resulting Numbers: [59, 46] Generated Node #0,1,2: 58:[59, 46] Operation: 34+12=46 Exploring Operation: 34-12=22, Resulting Numbers: [59, 22] Generated Node #0,1,3: 58:[59, 22] Operation: 34-12=22 Moving to Node #0,3 Current State: 58:[34, 43, 4], Operations: ['59-55=4'] Exploring Operation: 43-4=39, Resulting Numbers: [34, 39] Generated Node #0,3,0: 58:[34, 39] Operation: 43-4=39 Exploring Operation: 43-34=9, Resulting Numbers: [4, 9] Generated Node #0,3,1: 58:[4, 9] Operation: 43-34=9 Exploring Operation: 34-4=30, Resulting Numbers: [43, 30] Generated Node #0,3,2: 58:[43, 30] Operation: 34-4=30 Exploring Operation: 43+4=47, Resulting Numbers: [34, 47] Generated Node #0,3,3: 58:[34, 47] Operation: 43+4=47 Moving to Node #0,0 Current State: 58:[55, 43, 25], Operations: ['59-34=25'] Exploring Operation: 55-43=12, Resulting Numbers: [25, 12] Generated Node #0,0,0: 58:[25, 12] Operation: 55-43=12 Exploring Operation: 43-25=18, Resulting Numbers: [55, 18] Generated Node #0,0,1: 58:[55, 18] Operation: 43-25=18 Exploring Operation: 55-25=30, Resulting Numbers: [43, 30] Generated Node #0,0,2: 58:[43, 30] Operation: 55-25=30 Exploring Operation: 43+25=68, Resulting Numbers: [55, 68] Generated Node #0,0,3: 58:[55, 68] Operation: 43+25=68 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 58:[55, 68], Operations: ['59-34=25', '43+25=68'] Exploring Operation: 55*68=3740, Resulting Numbers: [3740] 3740,58 unequal: No Solution Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 55+68=123, Resulting Numbers: [123] 123,58 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 #0,0,0 Current State: 58:[25, 12], Operations: ['59-34=25', '55-43=12'] Exploring Operation: 25*12=300, Resulting Numbers: [300] 300,58 unequal: No Solution Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 25+12=37, Resulting Numbers: [37] 37,58 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:[55, 18], Operations: ['59-34=25', '43-25=18'] Exploring Operation: 55+18=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 55-18=37, Resulting Numbers: [37] 37,58 unequal: No Solution Exploring Operation: 55*18=990, Resulting Numbers: [990] 990,58 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 #0,0,2 Current State: 58:[43, 30], Operations: ['59-34=25', '55-25=30'] Exploring Operation: 43+30=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 43*30=1290, Resulting Numbers: [1290] 1290,58 unequal: No Solution Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,1 Current State: 58:[59, 64], Operations: ['43-34=9', '55+9=64'] Exploring Operation: 59*64=3776, Resulting Numbers: [3776] 3776,58 unequal: No Solution Exploring Operation: 59+64=123, Resulting Numbers: [123] 123,58 unequal: No Solution Exploring Operation: 64-59=5, Resulting Numbers: [5] 5,58 unequal: No Solution Moving to Node #0,1,3 Current State: 58:[59, 22], Operations: ['55-43=12', '34-12=22'] Exploring Operation: 59*22=1298, Resulting Numbers: [1298] 1298,58 unequal: No Solution Exploring Operation: 59+22=81, Resulting Numbers: [81] 81,58 unequal: No Solution Exploring Operation: 59-22=37, Resulting Numbers: [37] 37,58 unequal: No Solution Moving to Node #0,2,0 Current State: 58:[9, 4], Operations: ['43-34=9', '59-55=4'] Exploring Operation: 9*4=36, Resulting Numbers: [36] 36,58 unequal: No Solution Exploring Operation: 9+4=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,58 unequal: No Solution Moving to Node #0,3,1 Current State: 58:[4, 9], Operations: ['59-55=4', '43-34=9'] Exploring Operation: 4+9=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 9-4=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 4*9=36, Resulting Numbers: [36] 36,58 unequal: No Solution Moving to Node #0,2,3 Current State: 58:[55, 50], Operations: ['43-34=9', '59-9=50'] Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 55*50=2750, Resulting Numbers: [2750] 2750,58 unequal: No Solution Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[59, 46], Operations: ['55-43=12', '34+12=46'] Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,58 unequal: No Solution Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,58 unequal: No Solution Moving to Node #0,2,2 Current State: 58:[59, 46], Operations: ['43-34=9', '55-9=46'] Exploring Operation: 59+46=105, Resulting Numbers: [105] 105,58 unequal: No Solution Exploring Operation: 59-46=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 59*46=2714, Resulting Numbers: [2714] 2714,58 unequal: No Solution Moving to Node #0,1,0 Current State: 58:[12, 25], Operations: ['55-43=12', '59-34=25'] Exploring Operation: 25-12=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 12+25=37, Resulting Numbers: [37] 37,58 unequal: No Solution Exploring Operation: 12*25=300, Resulting Numbers: [300] 300,58 unequal: No Solution Moving to Node #0,3,2 Current State: 58:[43, 30], Operations: ['59-55=4', '34-4=30'] Exploring Operation: 43-30=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 43+30=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 43*30=1290, Resulting Numbers: [1290] 1290,58 unequal: No Solution Moving to Node #0,3,0 Current State: 58:[34, 39], Operations: ['59-55=4', '43-4=39'] Exploring Operation: 39-34=5, Resulting Numbers: [5] 5,58 unequal: No Solution Exploring Operation: 34+39=73, Resulting Numbers: [73] 73,58 unequal: No Solution Exploring Operation: 34*39=1326, Resulting Numbers: [1326] 1326,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[34, 47], Operations: ['55-43=12', '59-12=47'] Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,58 unequal: No Solution Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[34, 47], Operations: ['59-55=4', '43+4=47'] Exploring Operation: 34*47=1598, Resulting Numbers: [1598] 1598,58 unequal: No Solution Exploring Operation: 47-34=13, Resulting Numbers: [13] 13,58 unequal: No Solution Exploring Operation: 34+47=81, Resulting Numbers: [81] 81,58 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 7, 5, 38, 84 ]
80
[ "7-5=2", "84/2=42", "38+42=80" ]
Current State: 80:[7, 5, 38, 84], Operations: [] Exploring Operation: 7-5=2, Resulting Numbers: [38, 84, 2] Generated Node #2: [38, 84, 2] from Operation: 7-5=2 Current State: 80:[38, 84, 2], Operations: ['7-5=2'] Exploring Operation: 84/2=42, Resulting Numbers: [38, 42] Generated Node #3: [38, 42] from Operation: 84/2=42 Current State: 80:[38, 42], Operations: ['7-5=2', '84/2=42'] Exploring Operation: 38+42=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[7, 5, 38, 84], Operations: [] Exploring Operation: 84/7=12, Resulting Numbers: [5, 38, 12] Generated Node #0,0: 80:[5, 38, 12] Operation: 84/7=12 Start Sub Search at level 1: Moving to Node #0,0 Current State: 80:[5, 38, 12], Operations: ['84/7=12'] Exploring Operation: 5+12=17, Resulting Numbers: [38, 17] Generated Node #0,0,0: 80:[38, 17] Operation: 5+12=17 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 80:[38, 17], Operations: ['84/7=12', '5+12=17'] Exploring Operation: 38-17=21, Resulting Numbers: [21] 21,80 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 No solution found.
0
hs_1
sum_heuristic
[ 20, 2, 40, 27 ]
26
[ "20*2=40", "40/40=1", "27-1=26" ]
Current State: 26:[20, 2, 40, 27], Operations: [] Exploring Operation: 20*2=40, Resulting Numbers: [40, 27, 40] Generated Node #2: [40, 27, 40] from Operation: 20*2=40 Current State: 26:[40, 27, 40], Operations: ['20*2=40'] Exploring Operation: 40/40=1, Resulting Numbers: [27, 1] Generated Node #3: [27, 1] from Operation: 40/40=1 Current State: 26:[27, 1], Operations: ['20*2=40', '40/40=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[20, 2, 40, 27], Operations: [] Exploring Operation: 40-27=13, Resulting Numbers: [20, 2, 13] Generated Node #0,0: 26:[20, 2, 13] Operation: 40-27=13 Exploring Operation: 40/20=2, Resulting Numbers: [2, 27, 2] Generated Node #0,1: 26:[2, 27, 2] Operation: 40/20=2 Exploring Operation: 40-20=20, Resulting Numbers: [2, 27, 20] Generated Node #0,2: 26:[2, 27, 20] Operation: 40-20=20 Moving to Node #0,1 Current State: 26:[2, 27, 2], Operations: ['40/20=2'] Exploring Operation: 27-2=25, Resulting Numbers: [2, 25] Generated Node #0,1,0: 26:[2, 25] Operation: 27-2=25 Exploring Operation: 27-2=25, Resulting Numbers: [2, 25] Generated Node #0,1,1: 26:[2, 25] Operation: 27-2=25 Exploring Operation: 2/2=1, Resulting Numbers: [27, 1] Generated Node #0,1,2: 26:[27, 1] Operation: 2/2=1 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 26:[2, 25], Operations: ['40/20=2', '27-2=25'] Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,26 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[2, 25], Operations: ['40/20=2', '27-2=25'] Exploring Operation: 2+25=27, Resulting Numbers: [27] 27,26 unequal: No Solution Exploring Operation: 2*25=50, Resulting Numbers: [50] 50,26 unequal: No Solution Exploring Operation: 25-2=23, Resulting Numbers: [23] 23,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 26:[27, 1], Operations: ['40/20=2', '2/2=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[20, 2, 40, 27], Operations: [] Exploring Operation: 40/20=2, Resulting Numbers: [2, 27, 2] Generated Node #0,1: 26:[2, 27, 2] Operation: 40/20=2 Moving to Node #0,1 Current State: 26:[2, 27, 2], Operations: ['40/20=2'] Exploring Operation: 2/2=1, Resulting Numbers: [27, 1] Generated Node #0,1,2: 26:[27, 1] Operation: 2/2=1 Moving to Node #0,1,2 Current State: 26:[27, 1], Operations: ['40/20=2', '2/2=1'] Exploring Operation: 27-1=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 10, 92, 30, 38 ]
43
[ "92+38=130", "130/10=13", "30+13=43" ]
Current State: 43:[10, 92, 30, 38], Operations: [] Exploring Operation: 92+38=130, Resulting Numbers: [10, 30, 130] Generated Node #2: [10, 30, 130] from Operation: 92+38=130 Current State: 43:[10, 30, 130], Operations: ['92+38=130'] Exploring Operation: 130/10=13, Resulting Numbers: [30, 13] Generated Node #3: [30, 13] from Operation: 130/10=13 Current State: 43:[30, 13], Operations: ['92+38=130', '130/10=13'] Exploring Operation: 30+13=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[10, 92, 30, 38], Operations: [] Exploring Operation: 92-10=82, Resulting Numbers: [30, 38, 82] Generated Node #0,0: 43:[30, 38, 82] Operation: 92-10=82 Exploring Operation: 10+30=40, Resulting Numbers: [92, 38, 40] Generated Node #0,1: 43:[92, 38, 40] Operation: 10+30=40 Exploring Operation: 92-30=62, Resulting Numbers: [10, 38, 62] Generated Node #0,2: 43:[10, 38, 62] Operation: 92-30=62 Exploring Operation: 92-38=54, Resulting Numbers: [10, 30, 54] Generated Node #0,3: 43:[10, 30, 54] Operation: 92-38=54 Moving to Node #0,0 Current State: 43:[30, 38, 82], Operations: ['92-10=82'] Exploring Operation: 82-30=52, Resulting Numbers: [38, 52] Generated Node #0,0,0: 43:[38, 52] Operation: 82-30=52 Exploring Operation: 30+38=68, Resulting Numbers: [82, 68] Generated Node #0,0,1: 43:[82, 68] Operation: 30+38=68 Exploring Operation: 38-30=8, Resulting Numbers: [82, 8] Generated Node #0,0,2: 43:[82, 8] Operation: 38-30=8 Exploring Operation: 82-38=44, Resulting Numbers: [30, 44] Generated Node #0,0,3: 43:[30, 44] Operation: 82-38=44 Moving to Node #0,2 Current State: 43:[10, 38, 62], Operations: ['92-30=62'] Exploring Operation: 10+38=48, Resulting Numbers: [62, 48] Generated Node #0,2,0: 43:[62, 48] Operation: 10+38=48 Exploring Operation: 62-10=52, Resulting Numbers: [38, 52] Generated Node #0,2,1: 43:[38, 52] Operation: 62-10=52 Exploring Operation: 10+62=72, Resulting Numbers: [38, 72] Generated Node #0,2,2: 43:[38, 72] Operation: 10+62=72 Exploring Operation: 38-10=28, Resulting Numbers: [62, 28] Generated Node #0,2,3: 43:[62, 28] Operation: 38-10=28 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 43:[38, 52], Operations: ['92-30=62', '62-10=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 43:[62, 48], Operations: ['92-30=62', '10+38=48'] Exploring Operation: 62*48=2976, Resulting Numbers: [2976] 2976,43 unequal: No Solution Exploring Operation: 62-48=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 62+48=110, Resulting Numbers: [110] 110,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 43:[38, 72], Operations: ['92-30=62', '10+62=72'] Exploring Operation: 38*72=2736, Resulting Numbers: [2736] 2736,43 unequal: No Solution Exploring Operation: 72-38=34, Resulting Numbers: [34] 34,43 unequal: No Solution Exploring Operation: 38+72=110, Resulting Numbers: [110] 110,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 43:[62, 28], Operations: ['92-30=62', '38-10=28'] Exploring Operation: 62*28=1736, Resulting Numbers: [1736] 1736,43 unequal: No Solution Exploring Operation: 62+28=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 62-28=34, Resulting Numbers: [34] 34,43 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: 43:[92, 38, 40], Operations: ['10+30=40'] Exploring Operation: 38+40=78, Resulting Numbers: [92, 78] Generated Node #0,1,0: 43:[92, 78] Operation: 38+40=78 Exploring Operation: 92-38=54, Resulting Numbers: [40, 54] Generated Node #0,1,1: 43:[40, 54] Operation: 92-38=54 Exploring Operation: 92-40=52, Resulting Numbers: [38, 52] Generated Node #0,1,2: 43:[38, 52] Operation: 92-40=52 Exploring Operation: 92+38=130, Resulting Numbers: [40, 130] Generated Node #0,1,3: 43:[40, 130] Operation: 92+38=130 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 43:[40, 54], Operations: ['10+30=40', '92-38=54'] Exploring Operation: 40*54=2160, Resulting Numbers: [2160] 2160,43 unequal: No Solution Exploring Operation: 40+54=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 43:[38, 52], Operations: ['10+30=40', '92-40=52'] Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,43 unequal: No Solution Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 43:[92, 78], Operations: ['10+30=40', '38+40=78'] Exploring Operation: 92+78=170, Resulting Numbers: [170] 170,43 unequal: No Solution Exploring Operation: 92-78=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 92*78=7176, Resulting Numbers: [7176] 7176,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 43:[40, 130], Operations: ['10+30=40', '92+38=130'] Exploring Operation: 130-40=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 40+130=170, Resulting Numbers: [170] 170,43 unequal: No Solution Exploring Operation: 40*130=5200, Resulting Numbers: [5200] 5200,43 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: 43:[10, 30, 54], Operations: ['92-38=54'] Exploring Operation: 30-10=20, Resulting Numbers: [54, 20] Generated Node #0,3,0: 43:[54, 20] Operation: 30-10=20 Exploring Operation: 54-10=44, Resulting Numbers: [30, 44] Generated Node #0,3,1: 43:[30, 44] Operation: 54-10=44 Exploring Operation: 10+54=64, Resulting Numbers: [30, 64] Generated Node #0,3,2: 43:[30, 64] Operation: 10+54=64 Exploring Operation: 10+30=40, Resulting Numbers: [54, 40] Generated Node #0,3,3: 43:[54, 40] Operation: 10+30=40 Moving to Node #0,0,0 Current State: 43:[38, 52], Operations: ['92-10=82', '82-30=52'] Exploring Operation: 52-38=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 38+52=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 38*52=1976, Resulting Numbers: [1976] 1976,43 unequal: No Solution Moving to Node #0,3,3 Current State: 43:[54, 40], Operations: ['92-38=54', '10+30=40'] Exploring Operation: 54+40=94, Resulting Numbers: [94] 94,43 unequal: No Solution Exploring Operation: 54-40=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 54*40=2160, Resulting Numbers: [2160] 2160,43 unequal: No Solution Moving to Node #0,0,3 Current State: 43:[30, 44], Operations: ['92-10=82', '82-38=44'] Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,43 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,43 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,43 unequal: No Solution Moving to Node #0,3,1 Current State: 43:[30, 44], Operations: ['92-38=54', '54-10=44'] Exploring Operation: 30*44=1320, Resulting Numbers: [1320] 1320,43 unequal: No Solution Exploring Operation: 44-30=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 30+44=74, Resulting Numbers: [74] 74,43 unequal: No Solution Moving to Node #0,3,0 Current State: 43:[54, 20], Operations: ['92-38=54', '30-10=20'] Exploring Operation: 54-20=34, Resulting Numbers: [34] 34,43 unequal: No Solution Exploring Operation: 54+20=74, Resulting Numbers: [74] 74,43 unequal: No Solution Exploring Operation: 54*20=1080, Resulting Numbers: [1080] 1080,43 unequal: No Solution Moving to Node #0,3,2 Current State: 43:[30, 64], Operations: ['92-38=54', '10+54=64'] Exploring Operation: 64-30=34, Resulting Numbers: [34] 34,43 unequal: No Solution Exploring Operation: 30*64=1920, Resulting Numbers: [1920] 1920,43 unequal: No Solution Exploring Operation: 30+64=94, Resulting Numbers: [94] 94,43 unequal: No Solution Moving to Node #0,0,1 Current State: 43:[82, 68], Operations: ['92-10=82', '30+38=68'] Exploring Operation: 82-68=14, Resulting Numbers: [14] 14,43 unequal: No Solution Exploring Operation: 82+68=150, Resulting Numbers: [150] 150,43 unequal: No Solution Exploring Operation: 82*68=5576, Resulting Numbers: [5576] 5576,43 unequal: No Solution Moving to Node #0,0,2 Current State: 43:[82, 8], Operations: ['92-10=82', '38-30=8'] Exploring Operation: 82*8=656, Resulting Numbers: [656] 656,43 unequal: No Solution Exploring Operation: 82+8=90, Resulting Numbers: [90] 90,43 unequal: No Solution Exploring Operation: 82-8=74, Resulting Numbers: [74] 74,43 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 33, 64, 67, 98 ]
67
[ "33+64=97", "98-97=1", "67*1=67" ]
Current State: 67:[33, 64, 67, 98], Operations: [] Exploring Operation: 33+64=97, Resulting Numbers: [67, 98, 97] Generated Node #2: [67, 98, 97] from Operation: 33+64=97 Current State: 67:[67, 98, 97], Operations: ['33+64=97'] Exploring Operation: 98-97=1, Resulting Numbers: [67, 1] Generated Node #3: [67, 1] from Operation: 98-97=1 Current State: 67:[67, 1], Operations: ['33+64=97', '98-97=1'] Exploring Operation: 67*1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[33, 64, 67, 98], Operations: [] Exploring Operation: 64-33=31, Resulting Numbers: [67, 98, 31] Generated Node #0,0: 67:[67, 98, 31] Operation: 64-33=31 Exploring Operation: 33+64=97, Resulting Numbers: [67, 98, 97] Generated Node #0,1: 67:[67, 98, 97] Operation: 33+64=97 Exploring Operation: 98-33=65, Resulting Numbers: [64, 67, 65] Generated Node #0,2: 67:[64, 67, 65] Operation: 98-33=65 Exploring Operation: 33+67=100, Resulting Numbers: [64, 98, 100] Generated Node #0,3: 67:[64, 98, 100] Operation: 33+67=100 Moving to Node #0,2 Current State: 67:[64, 67, 65], Operations: ['98-33=65'] Exploring Operation: 64+65=129, Resulting Numbers: [67, 129] Generated Node #0,2,0: 67:[67, 129] Operation: 64+65=129 Exploring Operation: 64+67=131, Resulting Numbers: [65, 131] Generated Node #0,2,1: 67:[65, 131] Operation: 64+67=131 Exploring Operation: 67-64=3, Resulting Numbers: [65, 3] Generated Node #0,2,2: 67:[65, 3] Operation: 67-64=3 Exploring Operation: 65-64=1, Resulting Numbers: [67, 1] Generated Node #0,2,3: 67:[67, 1] Operation: 65-64=1 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 67:[67, 129], Operations: ['98-33=65', '64+65=129'] Exploring Operation: 129-67=62, Resulting Numbers: [62] 62,67 unequal: No Solution Exploring Operation: 67*129=8643, Resulting Numbers: [8643] 8643,67 unequal: No Solution Exploring Operation: 67+129=196, Resulting Numbers: [196] 196,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 67:[65, 131], Operations: ['98-33=65', '64+67=131'] Exploring Operation: 65+131=196, Resulting Numbers: [196] 196,67 unequal: No Solution Exploring Operation: 65*131=8515, Resulting Numbers: [8515] 8515,67 unequal: No Solution Exploring Operation: 131-65=66, Resulting Numbers: [66] 66,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 67:[65, 3], Operations: ['98-33=65', '67-64=3'] Exploring Operation: 65*3=195, Resulting Numbers: [195] 195,67 unequal: No Solution Exploring Operation: 65+3=68, Resulting Numbers: [68] 68,67 unequal: No Solution Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,67 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 67:[67, 1], Operations: ['98-33=65', '65-64=1'] Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[33, 64, 67, 98], Operations: [] Exploring Operation: 98-33=65, Resulting Numbers: [64, 67, 65] Generated Node #0,2: 67:[64, 67, 65] Operation: 98-33=65 Moving to Node #0,2 Current State: 67:[64, 67, 65], Operations: ['98-33=65'] Exploring Operation: 65-64=1, Resulting Numbers: [67, 1] Generated Node #0,2,3: 67:[67, 1] Operation: 65-64=1 Moving to Node #0,2,3 Current State: 67:[67, 1], Operations: ['98-33=65', '65-64=1'] Exploring Operation: 67/1=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.980903
hs_4
sum_heuristic
[ 9, 92, 96, 91 ]
96
[ "9+92=101", "96-91=5", "101-5=96" ]
Current State: 96:[9, 92, 96, 91], Operations: [] Exploring Operation: 9+92=101, Resulting Numbers: [96, 91, 101] Generated Node #2: [96, 91, 101] from Operation: 9+92=101 Current State: 96:[96, 91, 101], Operations: ['9+92=101'] Exploring Operation: 96-91=5, Resulting Numbers: [101, 5] Generated Node #3: [101, 5] from Operation: 96-91=5 Current State: 96:[101, 5], Operations: ['9+92=101', '96-91=5'] Exploring Operation: 101-5=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[9, 92, 96, 91], Operations: [] Exploring Operation: 92-91=1, Resulting Numbers: [9, 96, 1] Generated Node #0,0: 96:[9, 96, 1] Operation: 92-91=1 Exploring Operation: 96-91=5, Resulting Numbers: [9, 92, 5] Generated Node #0,1: 96:[9, 92, 5] Operation: 96-91=5 Exploring Operation: 96-92=4, Resulting Numbers: [9, 91, 4] Generated Node #0,2: 96:[9, 91, 4] Operation: 96-92=4 Moving to Node #0,0 Current State: 96:[9, 96, 1], Operations: ['92-91=1'] Exploring Operation: 9/1=9, Resulting Numbers: [96, 9] Generated Node #0,0,0: 96:[96, 9] Operation: 9/1=9 Exploring Operation: 9*1=9, Resulting Numbers: [96, 9] Generated Node #0,0,1: 96:[96, 9] Operation: 9*1=9 Exploring Operation: 9-1=8, Resulting Numbers: [96, 8] Generated Node #0,0,2: 96:[96, 8] Operation: 9-1=8 Moving to Node #0,1 Current State: 96:[9, 92, 5], Operations: ['96-91=5'] Exploring Operation: 92+5=97, Resulting Numbers: [9, 97] Generated Node #0,1,0: 96:[9, 97] Operation: 92+5=97 Exploring Operation: 9-5=4, Resulting Numbers: [92, 4] Generated Node #0,1,1: 96:[92, 4] Operation: 9-5=4 Exploring Operation: 9+92=101, Resulting Numbers: [5, 101] Generated Node #0,1,2: 96:[5, 101] Operation: 9+92=101 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 96:[9, 97], Operations: ['96-91=5', '92+5=97'] Exploring Operation: 9*97=873, Resulting Numbers: [873] 873,96 unequal: No Solution Exploring Operation: 9+97=106, Resulting Numbers: [106] 106,96 unequal: No Solution Exploring Operation: 97-9=88, Resulting Numbers: [88] 88,96 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 96:[92, 4], Operations: ['96-91=5', '9-5=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[9, 92, 96, 91], Operations: [] Exploring Operation: 96-91=5, Resulting Numbers: [9, 92, 5] Generated Node #0,1: 96:[9, 92, 5] Operation: 96-91=5 Moving to Node #0,1 Current State: 96:[9, 92, 5], Operations: ['96-91=5'] Exploring Operation: 9-5=4, Resulting Numbers: [92, 4] Generated Node #0,1,1: 96:[92, 4] Operation: 9-5=4 Moving to Node #0,1,1 Current State: 96:[92, 4], Operations: ['96-91=5', '9-5=4'] Exploring Operation: 92+4=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_3
mult_heuristic
[ 36, 74, 42, 84 ]
55
[ "36+74=110", "84/42=2", "110/2=55" ]
Current State: 55:[36, 74, 42, 84], Operations: [] Exploring Operation: 36+74=110, Resulting Numbers: [42, 84, 110] Generated Node #2: [42, 84, 110] from Operation: 36+74=110 Current State: 55:[42, 84, 110], Operations: ['36+74=110'] Exploring Operation: 84/42=2, Resulting Numbers: [110, 2] Generated Node #3: [110, 2] from Operation: 84/42=2 Current State: 55:[110, 2], Operations: ['36+74=110', '84/42=2'] Exploring Operation: 110/2=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[36, 74, 42, 84], Operations: [] Exploring Operation: 84-36=48, Resulting Numbers: [74, 42, 48] Generated Node #0,0: 55:[74, 42, 48] Operation: 84-36=48 Exploring Operation: 42-36=6, Resulting Numbers: [74, 84, 6] Generated Node #0,1: 55:[74, 84, 6] Operation: 42-36=6 Exploring Operation: 84-74=10, Resulting Numbers: [36, 42, 10] Generated Node #0,2: 55:[36, 42, 10] Operation: 84-74=10 Exploring Operation: 84/42=2, Resulting Numbers: [36, 74, 2] Generated Node #0,3: 55:[36, 74, 2] Operation: 84/42=2 Exploring Operation: 84-42=42, Resulting Numbers: [36, 74, 42] Generated Node #0,4: 55:[36, 74, 42] Operation: 84-42=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[36, 42, 10], Operations: ['84-74=10'] Exploring Operation: 36-10=26, Resulting Numbers: [42, 26] Generated Node #0,2,0: 55:[42, 26] Operation: 36-10=26 Exploring Operation: 42+10=52, Resulting Numbers: [36, 52] Generated Node #0,2,1: 55:[36, 52] Operation: 42+10=52 Exploring Operation: 36+10=46, Resulting Numbers: [42, 46] Generated Node #0,2,2: 55:[42, 46] Operation: 36+10=46 Exploring Operation: 42-36=6, Resulting Numbers: [10, 6] Generated Node #0,2,3: 55:[10, 6] Operation: 42-36=6 Exploring Operation: 36+42=78, Resulting Numbers: [10, 78] Generated Node #0,2,4: 55:[10, 78] Operation: 36+42=78 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[10, 6], Operations: ['84-74=10', '42-36=6'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 10*6=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 10+6=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[36, 52], Operations: ['84-74=10', '42+10=52'] Exploring Operation: 36*52=1872, Resulting Numbers: [1872] 1872,55 unequal: No Solution Exploring Operation: 52-36=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 36+52=88, Resulting Numbers: [88] 88,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[42, 46], Operations: ['84-74=10', '36+10=46'] Exploring Operation: 46-42=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 42+46=88, Resulting Numbers: [88] 88,55 unequal: No Solution Exploring Operation: 42*46=1932, Resulting Numbers: [1932] 1932,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 55:[10, 78], Operations: ['84-74=10', '36+42=78'] Exploring Operation: 10+78=88, Resulting Numbers: [88] 88,55 unequal: No Solution Exploring Operation: 10*78=780, Resulting Numbers: [780] 780,55 unequal: No Solution Exploring Operation: 78-10=68, Resulting Numbers: [68] 68,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[42, 26], Operations: ['84-74=10', '36-10=26'] Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[74, 42, 48], Operations: ['84-36=48'] Exploring Operation: 74-48=26, Resulting Numbers: [42, 26] Generated Node #0,0,0: 55:[42, 26] Operation: 74-48=26 Exploring Operation: 74+42=116, Resulting Numbers: [48, 116] Generated Node #0,0,1: 55:[48, 116] Operation: 74+42=116 Exploring Operation: 48-42=6, Resulting Numbers: [74, 6] Generated Node #0,0,2: 55:[74, 6] Operation: 48-42=6 Exploring Operation: 74-42=32, Resulting Numbers: [48, 32] Generated Node #0,0,3: 55:[48, 32] Operation: 74-42=32 Exploring Operation: 42+48=90, Resulting Numbers: [74, 90] Generated Node #0,0,4: 55:[74, 90] Operation: 42+48=90 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[74, 6], Operations: ['84-36=48', '48-42=6'] Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,55 unequal: No Solution Exploring Operation: 74*6=444, Resulting Numbers: [444] 444,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[42, 26], Operations: ['84-36=48', '74-48=26'] Exploring Operation: 42-26=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 42+26=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 42*26=1092, Resulting Numbers: [1092] 1092,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 55:[48, 32], Operations: ['84-36=48', '74-42=32'] Exploring Operation: 48-32=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 48+32=80, Resulting Numbers: [80] 80,55 unequal: No Solution Exploring Operation: 48*32=1536, Resulting Numbers: [1536] 1536,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 55:[74, 90], Operations: ['84-36=48', '42+48=90'] Exploring Operation: 74*90=6660, Resulting Numbers: [6660] 6660,55 unequal: No Solution Exploring Operation: 74+90=164, Resulting Numbers: [164] 164,55 unequal: No Solution Exploring Operation: 90-74=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[48, 116], Operations: ['84-36=48', '74+42=116'] Exploring Operation: 116-48=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 48+116=164, Resulting Numbers: [164] 164,55 unequal: No Solution Exploring Operation: 48*116=5568, Resulting Numbers: [5568] 5568,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[36, 74, 2], Operations: ['84/42=2'] Exploring Operation: 74-36=38, Resulting Numbers: [2, 38] Generated Node #0,3,0: 55:[2, 38] Operation: 74-36=38 Exploring Operation: 36+2=38, Resulting Numbers: [74, 38] Generated Node #0,3,1: 55:[74, 38] Operation: 36+2=38 Exploring Operation: 36*2=72, Resulting Numbers: [74, 72] Generated Node #0,3,2: 55:[74, 72] Operation: 36*2=72 Exploring Operation: 74-2=72, Resulting Numbers: [36, 72] Generated Node #0,3,3: 55:[36, 72] Operation: 74-2=72 Exploring Operation: 36/2=18, Resulting Numbers: [74, 18] Generated Node #0,3,4: 55:[74, 18] Operation: 36/2=18 Moving to Node #0,3,0 Current State: 55:[2, 38], Operations: ['84/42=2', '74-36=38'] Exploring Operation: 2+38=40, Resulting Numbers: [40] 40,55 unequal: No Solution Exploring Operation: 2*38=76, Resulting Numbers: [76] 76,55 unequal: No Solution Exploring Operation: 38-2=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 38/2=19, Resulting Numbers: [19] 19,55 unequal: No Solution Moving to Node #0,3,4 Current State: 55:[74, 18], Operations: ['84/42=2', '36/2=18'] Exploring Operation: 74*18=1332, Resulting Numbers: [1332] 1332,55 unequal: No Solution Exploring Operation: 74+18=92, Resulting Numbers: [92] 92,55 unequal: No Solution Exploring Operation: 74-18=56, Resulting Numbers: [56] 56,55 unequal: No Solution Moving to Node #0,3,1 Current State: 55:[74, 38], Operations: ['84/42=2', '36+2=38'] Exploring Operation: 74*38=2812, Resulting Numbers: [2812] 2812,55 unequal: No Solution Exploring Operation: 74-38=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 74+38=112, Resulting Numbers: [112] 112,55 unequal: No Solution Moving to Node #0,3,2 Current State: 55:[74, 72], Operations: ['84/42=2', '36*2=72'] Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 74+72=146, Resulting Numbers: [146] 146,55 unequal: No Solution Exploring Operation: 74*72=5328, Resulting Numbers: [5328] 5328,55 unequal: No Solution Moving to Node #0,3,3 Current State: 55:[36, 72], Operations: ['84/42=2', '74-2=72'] Exploring Operation: 36*72=2592, Resulting Numbers: [2592] 2592,55 unequal: No Solution Exploring Operation: 72-36=36, Resulting Numbers: [36] 36,55 unequal: No Solution Exploring Operation: 72/36=2, Resulting Numbers: [2] 2,55 unequal: No Solution Exploring Operation: 36+72=108, Resulting Numbers: [108] 108,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[74, 84, 6], Operations: ['42-36=6'] Exploring Operation: 74+6=80, Resulting Numbers: [84, 80] Generated Node #0,1,0: 55:[84, 80] Operation: 74+6=80 Exploring Operation: 84-6=78, Resulting Numbers: [74, 78] Generated Node #0,1,1: 55:[74, 78] Operation: 84-6=78 Exploring Operation: 84-74=10, Resulting Numbers: [6, 10] Generated Node #0,1,2: 55:[6, 10] Operation: 84-74=10 Exploring Operation: 84/6=14, Resulting Numbers: [74, 14] Generated Node #0,1,3: 55:[74, 14] Operation: 84/6=14 Exploring Operation: 74-6=68, Resulting Numbers: [84, 68] Generated Node #0,1,4: 55:[84, 68] Operation: 74-6=68 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 55:[6, 10], Operations: ['42-36=6', '84-74=10'] Exploring Operation: 10-6=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 6*10=60, Resulting Numbers: [60] 60,55 unequal: No Solution Exploring Operation: 6+10=16, Resulting Numbers: [16] 16,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 55:[74, 14], Operations: ['42-36=6', '84/6=14'] Exploring Operation: 74*14=1036, Resulting Numbers: [1036] 1036,55 unequal: No Solution Exploring Operation: 74+14=88, Resulting Numbers: [88] 88,55 unequal: No Solution Exploring Operation: 74-14=60, Resulting Numbers: [60] 60,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 55:[74, 78], Operations: ['42-36=6', '84-6=78'] Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,55 unequal: No Solution Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 55:[84, 68], Operations: ['42-36=6', '74-6=68'] Exploring Operation: 84-68=16, Resulting Numbers: [16] 16,55 unequal: No Solution Exploring Operation: 84+68=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 84*68=5712, Resulting Numbers: [5712] 5712,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 55:[84, 80], Operations: ['42-36=6', '74+6=80'] Exploring Operation: 84+80=164, Resulting Numbers: [164] 164,55 unequal: No Solution Exploring Operation: 84-80=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 84*80=6720, Resulting Numbers: [6720] 6720,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 55:[36, 74, 42], Operations: ['84-42=42'] Exploring Operation: 36+74=110, Resulting Numbers: [42, 110] Generated Node #0,4,0: 55:[42, 110] Operation: 36+74=110 Exploring Operation: 42-36=6, Resulting Numbers: [74, 6] Generated Node #0,4,1: 55:[74, 6] Operation: 42-36=6 Exploring Operation: 74-36=38, Resulting Numbers: [42, 38] Generated Node #0,4,2: 55:[42, 38] Operation: 74-36=38 Exploring Operation: 74-42=32, Resulting Numbers: [36, 32] Generated Node #0,4,3: 55:[36, 32] Operation: 74-42=32 Exploring Operation: 36+42=78, Resulting Numbers: [74, 78] Generated Node #0,4,4: 55:[74, 78] Operation: 36+42=78 Moving to Node #0,4,1 Current State: 55:[74, 6], Operations: ['84-42=42', '42-36=6'] Exploring Operation: 74+6=80, Resulting Numbers: [80] 80,55 unequal: No Solution Exploring Operation: 74*6=444, Resulting Numbers: [444] 444,55 unequal: No Solution Exploring Operation: 74-6=68, Resulting Numbers: [68] 68,55 unequal: No Solution Moving to Node #0,4,2 Current State: 55:[42, 38], Operations: ['84-42=42', '74-36=38'] Exploring Operation: 42+38=80, Resulting Numbers: [80] 80,55 unequal: No Solution Exploring Operation: 42-38=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 42*38=1596, Resulting Numbers: [1596] 1596,55 unequal: No Solution Moving to Node #0,4,3 Current State: 55:[36, 32], Operations: ['84-42=42', '74-42=32'] Exploring Operation: 36+32=68, Resulting Numbers: [68] 68,55 unequal: No Solution Exploring Operation: 36*32=1152, Resulting Numbers: [1152] 1152,55 unequal: No Solution Exploring Operation: 36-32=4, Resulting Numbers: [4] 4,55 unequal: No Solution Moving to Node #0,4,4 Current State: 55:[74, 78], Operations: ['84-42=42', '36+42=78'] Exploring Operation: 74+78=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 78-74=4, Resulting Numbers: [4] 4,55 unequal: No Solution Exploring Operation: 74*78=5772, Resulting Numbers: [5772] 5772,55 unequal: No Solution Moving to Node #0,4,0 Current State: 55:[42, 110], Operations: ['84-42=42', '36+74=110'] Exploring Operation: 42*110=4620, Resulting Numbers: [4620] 4620,55 unequal: No Solution Exploring Operation: 42+110=152, Resulting Numbers: [152] 152,55 unequal: No Solution Exploring Operation: 110-42=68, Resulting Numbers: [68] 68,55 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
[ 6, 26, 2, 21 ]
35
[ "6*2=12", "26+21=47", "47-12=35" ]
Current State: 35:[6, 26, 2, 21], Operations: [] Exploring Operation: 6*2=12, Resulting Numbers: [26, 21, 12] Generated Node #2: [26, 21, 12] from Operation: 6*2=12 Current State: 35:[26, 21, 12], Operations: ['6*2=12'] Exploring Operation: 26+21=47, Resulting Numbers: [12, 47] Generated Node #3: [12, 47] from Operation: 26+21=47 Current State: 35:[12, 47], Operations: ['6*2=12', '26+21=47'] Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[6, 26, 2, 21], Operations: [] Exploring Operation: 26-21=5, Resulting Numbers: [6, 2, 5] Generated Node #0,0: 35:[6, 2, 5] Operation: 26-21=5 Moving to Node #0,0 Current State: 35:[6, 2, 5], Operations: ['26-21=5'] Exploring Operation: 6+2=8, Resulting Numbers: [5, 8] Generated Node #0,0,0: 35:[5, 8] Operation: 6+2=8 Moving to Node #0,0,0 Current State: 35:[5, 8], Operations: ['26-21=5', '6+2=8'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,35 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 82, 44, 34, 21 ]
40
[ "82+44=126", "126/21=6", "34+6=40" ]
Current State: 40:[82, 44, 34, 21], Operations: [] Exploring Operation: 82+44=126, Resulting Numbers: [34, 21, 126] Generated Node #2: [34, 21, 126] from Operation: 82+44=126 Current State: 40:[34, 21, 126], Operations: ['82+44=126'] Exploring Operation: 126/21=6, Resulting Numbers: [34, 6] Generated Node #3: [34, 6] from Operation: 126/21=6 Current State: 40:[34, 6], Operations: ['82+44=126', '126/21=6'] Exploring Operation: 34+6=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[82, 44, 34, 21], Operations: [] Exploring Operation: 82-44=38, Resulting Numbers: [34, 21, 38] Generated Node #0,0: 40:[34, 21, 38] Operation: 82-44=38 Moving to Node #0,0 Current State: 40:[34, 21, 38], Operations: ['82-44=38'] Exploring Operation: 38-34=4, Resulting Numbers: [21, 4] Generated Node #0,0,0: 40:[21, 4] Operation: 38-34=4 Moving to Node #0,0,0 Current State: 40:[21, 4], Operations: ['82-44=38', '38-34=4'] Exploring Operation: 21-4=17, Resulting Numbers: [17] 17,40 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 85, 90, 3, 43 ]
98
[ "85+43=128", "90/3=30", "128-30=98" ]
Current State: 98:[85, 90, 3, 43], Operations: [] Exploring Operation: 85+43=128, Resulting Numbers: [90, 3, 128] Generated Node #2: [90, 3, 128] from Operation: 85+43=128 Current State: 98:[90, 3, 128], Operations: ['85+43=128'] Exploring Operation: 90/3=30, Resulting Numbers: [128, 30] Generated Node #3: [128, 30] from Operation: 90/3=30 Current State: 98:[128, 30], Operations: ['85+43=128', '90/3=30'] Exploring Operation: 128-30=98, Resulting Numbers: [98] 98,98 equal: Goal Reached
4
Current State: 98:[85, 90, 3, 43], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [3, 43, 5] Generated Node #0,0: 98:[3, 43, 5] Operation: 90-85=5 Moving to Node #0,0 Current State: 98:[3, 43, 5], Operations: ['90-85=5'] Exploring Operation: 43+5=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 98:[3, 48] Operation: 43+5=48 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 98:[3, 48], Operations: ['90-85=5', '43+5=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,98 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
[ 12, 18, 96, 71 ]
61
[ "96/12=8", "71-18=53", "8+53=61" ]
Current State: 61:[12, 18, 96, 71], Operations: [] Exploring Operation: 96/12=8, Resulting Numbers: [18, 71, 8] Generated Node #2: [18, 71, 8] from Operation: 96/12=8 Current State: 61:[18, 71, 8], Operations: ['96/12=8'] Exploring Operation: 71-18=53, Resulting Numbers: [8, 53] Generated Node #3: [8, 53] from Operation: 71-18=53 Current State: 61:[8, 53], Operations: ['96/12=8', '71-18=53'] Exploring Operation: 8+53=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[12, 18, 96, 71], Operations: [] Exploring Operation: 96-12=84, Resulting Numbers: [18, 71, 84] Generated Node #0,0: 61:[18, 71, 84] Operation: 96-12=84 Exploring Operation: 12+18=30, Resulting Numbers: [96, 71, 30] Generated Node #0,1: 61:[96, 71, 30] Operation: 12+18=30 Start Sub Search at level 1: Moving to Node #0,0 Current State: 61:[18, 71, 84], Operations: ['96-12=84'] Exploring Operation: 71-18=53, Resulting Numbers: [84, 53] Generated Node #0,0,0: 61:[84, 53] Operation: 71-18=53 Exploring Operation: 84-18=66, Resulting Numbers: [71, 66] Generated Node #0,0,1: 61:[71, 66] Operation: 84-18=66 Moving to Node #0,0,1 Current State: 61:[71, 66], Operations: ['96-12=84', '84-18=66'] Exploring Operation: 71+66=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 71-66=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,0,0 Current State: 61:[84, 53], Operations: ['96-12=84', '71-18=53'] Exploring Operation: 84-53=31, Resulting Numbers: [31] 31,61 unequal: No Solution Exploring Operation: 84+53=137, Resulting Numbers: [137] 137,61 unequal: No Solution No 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: 61:[96, 71, 30], Operations: ['12+18=30'] Exploring Operation: 96-30=66, Resulting Numbers: [71, 66] Generated Node #0,1,0: 61:[71, 66] Operation: 96-30=66 Exploring Operation: 71-30=41, Resulting Numbers: [96, 41] Generated Node #0,1,1: 61:[96, 41] Operation: 71-30=41 Moving to Node #0,1,0 Current State: 61:[71, 66], Operations: ['12+18=30', '96-30=66'] Exploring Operation: 71+66=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 71-66=5, Resulting Numbers: [5] 5,61 unequal: No Solution Moving to Node #0,1,1 Current State: 61:[96, 41], Operations: ['12+18=30', '71-30=41'] Exploring Operation: 96+41=137, Resulting Numbers: [137] 137,61 unequal: No Solution Exploring Operation: 96-41=55, Resulting Numbers: [55] 55,61 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 38, 91, 99, 96 ]
23
[ "99-96=3", "38*3=114", "114-91=23" ]
Current State: 23:[38, 91, 99, 96], Operations: [] Exploring Operation: 99-96=3, Resulting Numbers: [38, 91, 3] Generated Node #2: [38, 91, 3] from Operation: 99-96=3 Current State: 23:[38, 91, 3], Operations: ['99-96=3'] Exploring Operation: 38*3=114, Resulting Numbers: [91, 114] Generated Node #3: [91, 114] from Operation: 38*3=114 Current State: 23:[91, 114], Operations: ['99-96=3', '38*3=114'] Exploring Operation: 114-91=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[38, 91, 99, 96], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [38, 96, 8] Generated Node #0,0: 23:[38, 96, 8] Operation: 99-91=8 Exploring Operation: 99-96=3, Resulting Numbers: [38, 91, 3] Generated Node #0,1: 23:[38, 91, 3] Operation: 99-96=3 Moving to Node #0,0 Current State: 23:[38, 96, 8], Operations: ['99-91=8'] Exploring Operation: 96/8=12, Resulting Numbers: [38, 12] Generated Node #0,0,0: 23:[38, 12] Operation: 96/8=12 Exploring Operation: 96-38=58, Resulting Numbers: [8, 58] Generated Node #0,0,1: 23:[8, 58] Operation: 96-38=58 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[38, 12], Operations: ['99-91=8', '96/8=12'] Exploring Operation: 38+12=50, Resulting Numbers: [50] 50,23 unequal: No Solution Exploring Operation: 38-12=26, Resulting Numbers: [26] 26,23 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 #0,0,1 Current State: 23:[8, 58], Operations: ['99-91=8', '96-38=58'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,23 unequal: No Solution Exploring Operation: 8+58=66, Resulting Numbers: [66] 66,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 23:[38, 91, 3], Operations: ['99-96=3'] Exploring Operation: 38-3=35, Resulting Numbers: [91, 35] Generated Node #0,1,0: 23:[91, 35] Operation: 38-3=35 Exploring Operation: 91-38=53, Resulting Numbers: [3, 53] Generated Node #0,1,1: 23:[3, 53] Operation: 91-38=53 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 23:[3, 53], Operations: ['99-96=3', '91-38=53'] Exploring Operation: 3+53=56, Resulting Numbers: [56] 56,23 unequal: No Solution Exploring Operation: 53-3=50, Resulting Numbers: [50] 50,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 23:[91, 35], Operations: ['99-96=3', '38-3=35'] Exploring Operation: 91+35=126, Resulting Numbers: [126] 126,23 unequal: No Solution Exploring Operation: 91-35=56, Resulting Numbers: [56] 56,23 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
[ 4, 18, 37, 41 ]
100
[ "4+18=22", "37+41=78", "22+78=100" ]
Current State: 100:[4, 18, 37, 41], Operations: [] Exploring Operation: 4+18=22, Resulting Numbers: [37, 41, 22] Generated Node #2: [37, 41, 22] from Operation: 4+18=22 Current State: 100:[37, 41, 22], Operations: ['4+18=22'] Exploring Operation: 37+41=78, Resulting Numbers: [22, 78] Generated Node #3: [22, 78] from Operation: 37+41=78 Current State: 100:[22, 78], Operations: ['4+18=22', '37+41=78'] Exploring Operation: 22+78=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[4, 18, 37, 41], Operations: [] Exploring Operation: 18+37=55, Resulting Numbers: [4, 41, 55] Generated Node #0,0: 100:[4, 41, 55] Operation: 18+37=55 Exploring Operation: 41-37=4, Resulting Numbers: [4, 18, 4] Generated Node #0,1: 100:[4, 18, 4] Operation: 41-37=4 Exploring Operation: 37-18=19, Resulting Numbers: [4, 41, 19] Generated Node #0,2: 100:[4, 41, 19] Operation: 37-18=19 Exploring Operation: 41-18=23, Resulting Numbers: [4, 37, 23] Generated Node #0,3: 100:[4, 37, 23] Operation: 41-18=23 Moving to Node #0,1 Current State: 100:[4, 18, 4], Operations: ['41-37=4'] Exploring Operation: 4+18=22, Resulting Numbers: [4, 22] Generated Node #0,1,0: 100:[4, 22] Operation: 4+18=22 Exploring Operation: 18+4=22, Resulting Numbers: [4, 22] Generated Node #0,1,1: 100:[4, 22] Operation: 18+4=22 Exploring Operation: 18-4=14, Resulting Numbers: [4, 14] Generated Node #0,1,2: 100:[4, 14] Operation: 18-4=14 Exploring Operation: 4/4=1, Resulting Numbers: [18, 1] Generated Node #0,1,3: 100:[18, 1] Operation: 4/4=1 Moving to Node #0,2 Current State: 100:[4, 41, 19], Operations: ['37-18=19'] Exploring Operation: 4+19=23, Resulting Numbers: [41, 23] Generated Node #0,2,0: 100:[41, 23] Operation: 4+19=23 Exploring Operation: 4+41=45, Resulting Numbers: [19, 45] Generated Node #0,2,1: 100:[19, 45] Operation: 4+41=45 Exploring Operation: 41+19=60, Resulting Numbers: [4, 60] Generated Node #0,2,2: 100:[4, 60] Operation: 41+19=60 Exploring Operation: 41-19=22, Resulting Numbers: [4, 22] Generated Node #0,2,3: 100:[4, 22] Operation: 41-19=22 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 100:[4, 22], Operations: ['37-18=19', '41-19=22'] Exploring Operation: 4+22=26, Resulting Numbers: [26] 26,100 unequal: No Solution Exploring Operation: 22-4=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 4*22=88, Resulting Numbers: [88] 88,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 100:[19, 45], Operations: ['37-18=19', '4+41=45'] Exploring Operation: 19*45=855, Resulting Numbers: [855] 855,100 unequal: No Solution Exploring Operation: 45-19=26, Resulting Numbers: [26] 26,100 unequal: No Solution Exploring Operation: 19+45=64, Resulting Numbers: [64] 64,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 100:[4, 60], Operations: ['37-18=19', '41+19=60'] Exploring Operation: 4+60=64, Resulting Numbers: [64] 64,100 unequal: No Solution Exploring Operation: 60/4=15, Resulting Numbers: [15] 15,100 unequal: No Solution Exploring Operation: 60-4=56, Resulting Numbers: [56] 56,100 unequal: No Solution Exploring Operation: 4*60=240, Resulting Numbers: [240] 240,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 100:[41, 23], Operations: ['37-18=19', '4+19=23'] Exploring Operation: 41+23=64, Resulting Numbers: [64] 64,100 unequal: No Solution Exploring Operation: 41-23=18, Resulting Numbers: [18] 18,100 unequal: No Solution Exploring Operation: 41*23=943, Resulting Numbers: [943] 943,100 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 100:[4, 37, 23], Operations: ['41-18=23'] Exploring Operation: 37-4=33, Resulting Numbers: [23, 33] Generated Node #0,3,0: 100:[23, 33] Operation: 37-4=33 Exploring Operation: 37-23=14, Resulting Numbers: [4, 14] Generated Node #0,3,1: 100:[4, 14] Operation: 37-23=14 Exploring Operation: 37+23=60, Resulting Numbers: [4, 60] Generated Node #0,3,2: 100:[4, 60] Operation: 37+23=60 Exploring Operation: 4+37=41, Resulting Numbers: [23, 41] Generated Node #0,3,3: 100:[23, 41] Operation: 4+37=41 Moving to Node #0,0 Current State: 100:[4, 41, 55], Operations: ['18+37=55'] Exploring Operation: 41+55=96, Resulting Numbers: [4, 96] Generated Node #0,0,0: 100:[4, 96] Operation: 41+55=96 Exploring Operation: 4+41=45, Resulting Numbers: [55, 45] Generated Node #0,0,1: 100:[55, 45] Operation: 4+41=45 Exploring Operation: 55-41=14, Resulting Numbers: [4, 14] Generated Node #0,0,2: 100:[4, 14] Operation: 55-41=14 Exploring Operation: 55-4=51, Resulting Numbers: [41, 51] Generated Node #0,0,3: 100:[41, 51] Operation: 55-4=51 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 100:[4, 96], Operations: ['18+37=55', '41+55=96'] Exploring Operation: 4+96=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Moving to Node #0 Current State: 100:[4, 18, 37, 41], Operations: [] Exploring Operation: 18+37=55, Resulting Numbers: [4, 41, 55] Generated Node #0,0: 100:[4, 41, 55] Operation: 18+37=55 Moving to Node #0,0 Current State: 100:[4, 41, 55], Operations: ['18+37=55'] Exploring Operation: 41+55=96, Resulting Numbers: [4, 96] Generated Node #0,0,0: 100:[4, 96] Operation: 41+55=96 Moving to Node #0,0,0 Current State: 100:[4, 96], Operations: ['18+37=55', '41+55=96'] Exploring Operation: 4+96=100, Resulting Numbers: [100] 100,100 equal: Goal Reached Exit Sub Search at level 1
0.967014
hs_4
sum_heuristic
[ 3, 51, 90, 66 ]
41
[ "51/3=17", "90-66=24", "17+24=41" ]
Current State: 41:[3, 51, 90, 66], Operations: [] Exploring Operation: 51/3=17, Resulting Numbers: [90, 66, 17] Generated Node #2: [90, 66, 17] from Operation: 51/3=17 Current State: 41:[90, 66, 17], Operations: ['51/3=17'] Exploring Operation: 90-66=24, Resulting Numbers: [17, 24] Generated Node #3: [17, 24] from Operation: 90-66=24 Current State: 41:[17, 24], Operations: ['51/3=17', '90-66=24'] Exploring Operation: 17+24=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[3, 51, 90, 66], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [51, 66, 30] Generated Node #0,0: 41:[51, 66, 30] Operation: 90/3=30 Moving to Node #0,0 Current State: 41:[51, 66, 30], Operations: ['90/3=30'] Exploring Operation: 66-30=36, Resulting Numbers: [51, 36] Generated Node #0,0,0: 41:[51, 36] Operation: 66-30=36 Moving to Node #0,0,0 Current State: 41:[51, 36], Operations: ['90/3=30', '66-30=36'] Exploring Operation: 51-36=15, Resulting Numbers: [15] 15,41 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 90, 86, 72, 44 ]
83
[ "90-86=4", "44/4=11", "72+11=83" ]
Current State: 83:[90, 86, 72, 44], Operations: [] Exploring Operation: 90-86=4, Resulting Numbers: [72, 44, 4] Generated Node #2: [72, 44, 4] from Operation: 90-86=4 Current State: 83:[72, 44, 4], Operations: ['90-86=4'] Exploring Operation: 44/4=11, Resulting Numbers: [72, 11] Generated Node #3: [72, 11] from Operation: 44/4=11 Current State: 83:[72, 11], Operations: ['90-86=4', '44/4=11'] Exploring Operation: 72+11=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[90, 86, 72, 44], Operations: [] Exploring Operation: 90-44=46, Resulting Numbers: [86, 72, 46] Generated Node #0,0: 83:[86, 72, 46] Operation: 90-44=46 Exploring Operation: 72+44=116, Resulting Numbers: [90, 86, 116] Generated Node #0,1: 83:[90, 86, 116] Operation: 72+44=116 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[90, 86, 116], Operations: ['72+44=116'] Exploring Operation: 116-90=26, Resulting Numbers: [86, 26] Generated Node #0,1,0: 83:[86, 26] Operation: 116-90=26 Exploring Operation: 116-86=30, Resulting Numbers: [90, 30] Generated Node #0,1,1: 83:[90, 30] Operation: 116-86=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[86, 26], Operations: ['72+44=116', '116-90=26'] Exploring Operation: 86+26=112, Resulting Numbers: [112] 112,83 unequal: No Solution Exploring Operation: 86-26=60, Resulting Numbers: [60] 60,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[90, 30], Operations: ['72+44=116', '116-86=30'] Exploring Operation: 90+30=120, Resulting Numbers: [120] 120,83 unequal: No Solution Exploring Operation: 90-30=60, Resulting Numbers: [60] 60,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[86, 72, 46], Operations: ['90-44=46'] Exploring Operation: 72+46=118, Resulting Numbers: [86, 118] Generated Node #0,0,0: 83:[86, 118] Operation: 72+46=118 Exploring Operation: 86-46=40, Resulting Numbers: [72, 40] Generated Node #0,0,1: 83:[72, 40] Operation: 86-46=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[86, 118], Operations: ['90-44=46', '72+46=118'] Exploring Operation: 118-86=32, Resulting Numbers: [32] 32,83 unequal: No Solution Exploring Operation: 86+118=204, Resulting Numbers: [204] 204,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[72, 40], Operations: ['90-44=46', '86-46=40'] Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,83 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 84, 80, 16, 89 ]
32
[ "89-84=5", "80/5=16", "16+16=32" ]
Current State: 32:[84, 80, 16, 89], Operations: [] Exploring Operation: 89-84=5, Resulting Numbers: [80, 16, 5] Generated Node #2: [80, 16, 5] from Operation: 89-84=5 Current State: 32:[80, 16, 5], Operations: ['89-84=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16, 16] Generated Node #3: [16, 16] from Operation: 80/5=16 Current State: 32:[16, 16], Operations: ['89-84=5', '80/5=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[84, 80, 16, 89], Operations: [] Exploring Operation: 84-16=68, Resulting Numbers: [80, 89, 68] Generated Node #0,0: 32:[80, 89, 68] Operation: 84-16=68 Exploring Operation: 89-84=5, Resulting Numbers: [80, 16, 5] Generated Node #0,1: 32:[80, 16, 5] Operation: 89-84=5 Exploring Operation: 84-80=4, Resulting Numbers: [16, 89, 4] Generated Node #0,2: 32:[16, 89, 4] Operation: 84-80=4 Exploring Operation: 80/16=5, Resulting Numbers: [84, 89, 5] Generated Node #0,3: 32:[84, 89, 5] Operation: 80/16=5 Exploring Operation: 89-80=9, Resulting Numbers: [84, 16, 9] Generated Node #0,4: 32:[84, 16, 9] Operation: 89-80=9 Moving to Node #0,1 Current State: 32:[80, 16, 5], Operations: ['89-84=5'] Exploring Operation: 80/16=5, Resulting Numbers: [5, 5] Generated Node #0,1,0: 32:[5, 5] Operation: 80/16=5 Exploring Operation: 80-5=75, Resulting Numbers: [16, 75] Generated Node #0,1,1: 32:[16, 75] Operation: 80-5=75 Exploring Operation: 80-16=64, Resulting Numbers: [5, 64] Generated Node #0,1,2: 32:[5, 64] Operation: 80-16=64 Exploring Operation: 80/5=16, Resulting Numbers: [16, 16] Generated Node #0,1,3: 32:[16, 16] Operation: 80/5=16 Exploring Operation: 16-5=11, Resulting Numbers: [80, 11] Generated Node #0,1,4: 32:[80, 11] Operation: 16-5=11 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 32:[16, 16], Operations: ['89-84=5', '80/5=16'] Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,32 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,32 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[84, 80, 16, 89], Operations: [] Exploring Operation: 89-84=5, Resulting Numbers: [80, 16, 5] Generated Node #0,1: 32:[80, 16, 5] Operation: 89-84=5 Moving to Node #0,1 Current State: 32:[80, 16, 5], Operations: ['89-84=5'] Exploring Operation: 80/5=16, Resulting Numbers: [16, 16] Generated Node #0,1,3: 32:[16, 16] Operation: 80/5=16 Moving to Node #0,1,3 Current State: 32:[16, 16], Operations: ['89-84=5', '80/5=16'] Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 32, 45, 5, 2 ]
70
[ "32+45=77", "5+2=7", "77-7=70" ]
Current State: 70:[32, 45, 5, 2], Operations: [] Exploring Operation: 32+45=77, Resulting Numbers: [5, 2, 77] Generated Node #2: [5, 2, 77] from Operation: 32+45=77 Current State: 70:[5, 2, 77], Operations: ['32+45=77'] Exploring Operation: 5+2=7, Resulting Numbers: [77, 7] Generated Node #3: [77, 7] from Operation: 5+2=7 Current State: 70:[77, 7], Operations: ['32+45=77', '5+2=7'] Exploring Operation: 77-7=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[32, 45, 5, 2], Operations: [] Exploring Operation: 45-32=13, Resulting Numbers: [5, 2, 13] Generated Node #0,0: 70:[5, 2, 13] Operation: 45-32=13 Exploring Operation: 45/5=9, Resulting Numbers: [32, 2, 9] Generated Node #0,1: 70:[32, 2, 9] Operation: 45/5=9 Exploring Operation: 32+45=77, Resulting Numbers: [5, 2, 77] Generated Node #0,2: 70:[5, 2, 77] Operation: 32+45=77 Exploring Operation: 45-5=40, Resulting Numbers: [32, 2, 40] Generated Node #0,3: 70:[32, 2, 40] Operation: 45-5=40 Exploring Operation: 32+2=34, Resulting Numbers: [45, 5, 34] Generated Node #0,4: 70:[45, 5, 34] Operation: 32+2=34 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[5, 2, 13], Operations: ['45-32=13'] Exploring Operation: 5*2=10, Resulting Numbers: [13, 10] Generated Node #0,0,0: 70:[13, 10] Operation: 5*2=10 Exploring Operation: 5+2=7, Resulting Numbers: [13, 7] Generated Node #0,0,1: 70:[13, 7] Operation: 5+2=7 Exploring Operation: 13-2=11, Resulting Numbers: [5, 11] Generated Node #0,0,2: 70:[5, 11] Operation: 13-2=11 Exploring Operation: 2+13=15, Resulting Numbers: [5, 15] Generated Node #0,0,3: 70:[5, 15] Operation: 2+13=15 Exploring Operation: 13-5=8, Resulting Numbers: [2, 8] Generated Node #0,0,4: 70:[2, 8] Operation: 13-5=8 Moving to Node #0,0,0 Current State: 70:[13, 10], Operations: ['45-32=13', '5*2=10'] Exploring Operation: 13+10=23, Resulting Numbers: [23] 23,70 unequal: No Solution Exploring Operation: 13-10=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 13*10=130, Resulting Numbers: [130] 130,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[5, 11], Operations: ['45-32=13', '13-2=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,70 unequal: No Solution Exploring Operation: 11-5=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 5*11=55, Resulting Numbers: [55] 55,70 unequal: No Solution Moving to Node #0,0,4 Current State: 70:[2, 8], Operations: ['45-32=13', '13-5=8'] Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,70 unequal: No Solution Exploring Operation: 2*8=16, Resulting Numbers: [16] 16,70 unequal: No Solution Moving to Node #0,0,1 Current State: 70:[13, 7], Operations: ['45-32=13', '5+2=7'] Exploring Operation: 13+7=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 13*7=91, Resulting Numbers: [91] 91,70 unequal: No Solution Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,70 unequal: No Solution Moving to Node #0,0,3 Current State: 70:[5, 15], Operations: ['45-32=13', '2+13=15'] Exploring Operation: 5+15=20, Resulting Numbers: [20] 20,70 unequal: No Solution Exploring Operation: 15/5=3, Resulting Numbers: [3] 3,70 unequal: No Solution Exploring Operation: 5*15=75, Resulting Numbers: [75] 75,70 unequal: No Solution Exploring Operation: 15-5=10, Resulting Numbers: [10] 10,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 70:[32, 2, 9], Operations: ['45/5=9'] Exploring Operation: 32/2=16, Resulting Numbers: [9, 16] Generated Node #0,1,0: 70:[9, 16] Operation: 32/2=16 Exploring Operation: 9-2=7, Resulting Numbers: [32, 7] Generated Node #0,1,1: 70:[32, 7] Operation: 9-2=7 Exploring Operation: 32-2=30, Resulting Numbers: [9, 30] Generated Node #0,1,2: 70:[9, 30] Operation: 32-2=30 Exploring Operation: 32+2=34, Resulting Numbers: [9, 34] Generated Node #0,1,3: 70:[9, 34] Operation: 32+2=34 Exploring Operation: 2+9=11, Resulting Numbers: [32, 11] Generated Node #0,1,4: 70:[32, 11] Operation: 2+9=11 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 70:[9, 34], Operations: ['45/5=9', '32+2=34'] Exploring Operation: 9*34=306, Resulting Numbers: [306] 306,70 unequal: No Solution Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,70 unequal: No Solution Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,70 unequal: No Solution No 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: 70:[9, 16], Operations: ['45/5=9', '32/2=16'] Exploring Operation: 9*16=144, Resulting Numbers: [144] 144,70 unequal: No Solution Exploring Operation: 9+16=25, Resulting Numbers: [25] 25,70 unequal: No Solution Exploring Operation: 16-9=7, Resulting Numbers: [7] 7,70 unequal: No Solution No 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: 70:[32, 7], Operations: ['45/5=9', '9-2=7'] Exploring Operation: 32*7=224, Resulting Numbers: [224] 224,70 unequal: No Solution Exploring Operation: 32-7=25, Resulting Numbers: [25] 25,70 unequal: No Solution Exploring Operation: 32+7=39, Resulting Numbers: [39] 39,70 unequal: No Solution No 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: 70:[32, 11], Operations: ['45/5=9', '2+9=11'] Exploring Operation: 32+11=43, Resulting Numbers: [43] 43,70 unequal: No Solution Exploring Operation: 32*11=352, Resulting Numbers: [352] 352,70 unequal: No Solution Exploring Operation: 32-11=21, Resulting Numbers: [21] 21,70 unequal: No Solution No 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: 70:[9, 30], Operations: ['45/5=9', '32-2=30'] Exploring Operation: 9*30=270, Resulting Numbers: [270] 270,70 unequal: No Solution Exploring Operation: 30-9=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 9+30=39, Resulting Numbers: [39] 39,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[5, 2, 77], Operations: ['32+45=77'] Exploring Operation: 77-5=72, Resulting Numbers: [2, 72] Generated Node #0,2,0: 70:[2, 72] Operation: 77-5=72 Exploring Operation: 5-2=3, Resulting Numbers: [77, 3] Generated Node #0,2,1: 70:[77, 3] Operation: 5-2=3 Exploring Operation: 5*2=10, Resulting Numbers: [77, 10] Generated Node #0,2,2: 70:[77, 10] Operation: 5*2=10 Exploring Operation: 5+2=7, Resulting Numbers: [77, 7] Generated Node #0,2,3: 70:[77, 7] Operation: 5+2=7 Exploring Operation: 77-2=75, Resulting Numbers: [5, 75] Generated Node #0,2,4: 70:[5, 75] Operation: 77-2=75 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 70:[2, 72], Operations: ['32+45=77', '77-5=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[32, 45, 5, 2], Operations: [] Exploring Operation: 32+45=77, Resulting Numbers: [5, 2, 77] Generated Node #0,2: 70:[5, 2, 77] Operation: 32+45=77 Moving to Node #0,2 Current State: 70:[5, 2, 77], Operations: ['32+45=77'] Exploring Operation: 77-5=72, Resulting Numbers: [2, 72] Generated Node #0,2,0: 70:[2, 72] Operation: 77-5=72 Moving to Node #0,2,0 Current State: 70:[2, 72], Operations: ['32+45=77', '77-5=72'] Exploring Operation: 72-2=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.950521
hs_5
sum_heuristic
[ 6, 91, 6, 80 ]
60
[ "91-80=11", "6*11=66", "66-6=60" ]
Current State: 60:[6, 91, 6, 80], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [6, 6, 11] Generated Node #2: [6, 6, 11] from Operation: 91-80=11 Current State: 60:[6, 6, 11], Operations: ['91-80=11'] Exploring Operation: 6*11=66, Resulting Numbers: [66] 66,60 equal: Goal Reached Exploring Operation: 66-6=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[6, 91, 6, 80], Operations: [] Exploring Operation: 91-80=11, Resulting Numbers: [6, 6, 11] Generated Node #0,0: 60:[6, 6, 11] Operation: 91-80=11 Moving to Node #0,0 Current State: 60:[6, 6, 11], Operations: ['91-80=11'] Exploring Operation: 11-6=5, Resulting Numbers: [6, 5] Generated Node #0,0,0: 60:[6, 5] Operation: 11-6=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 60:[6, 5], Operations: ['91-80=11', '11-6=5'] Exploring Operation: 6*5=30, Resulting Numbers: [30] 30,60 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 5, 85, 61, 54 ]
83
[ "5+85=90", "61-54=7", "90-7=83" ]
Current State: 83:[5, 85, 61, 54], Operations: [] Exploring Operation: 5+85=90, Resulting Numbers: [61, 54, 90] Generated Node #2: [61, 54, 90] from Operation: 5+85=90 Current State: 83:[61, 54, 90], Operations: ['5+85=90'] Exploring Operation: 61-54=7, Resulting Numbers: [90, 7] Generated Node #3: [90, 7] from Operation: 61-54=7 Current State: 83:[90, 7], Operations: ['5+85=90', '61-54=7'] Exploring Operation: 90-7=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[5, 85, 61, 54], Operations: [] Exploring Operation: 85-5=80, Resulting Numbers: [61, 54, 80] Generated Node #0,0: 83:[61, 54, 80] Operation: 85-5=80 Exploring Operation: 5+61=66, Resulting Numbers: [85, 54, 66] Generated Node #0,1: 83:[85, 54, 66] Operation: 5+61=66 Exploring Operation: 5+54=59, Resulting Numbers: [85, 61, 59] Generated Node #0,2: 83:[85, 61, 59] Operation: 5+54=59 Exploring Operation: 5+85=90, Resulting Numbers: [61, 54, 90] Generated Node #0,3: 83:[61, 54, 90] Operation: 5+85=90 Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[85, 54, 66], Operations: ['5+61=66'] Exploring Operation: 85-54=31, Resulting Numbers: [66, 31] Generated Node #0,1,0: 83:[66, 31] Operation: 85-54=31 Exploring Operation: 66-54=12, Resulting Numbers: [85, 12] Generated Node #0,1,1: 83:[85, 12] Operation: 66-54=12 Exploring Operation: 54+66=120, Resulting Numbers: [85, 120] Generated Node #0,1,2: 83:[85, 120] Operation: 54+66=120 Exploring Operation: 85+54=139, Resulting Numbers: [66, 139] Generated Node #0,1,3: 83:[66, 139] Operation: 85+54=139 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 83:[85, 120], Operations: ['5+61=66', '54+66=120'] Exploring Operation: 85*120=10200, Resulting Numbers: [10200] 10200,83 unequal: No Solution Exploring Operation: 85+120=205, Resulting Numbers: [205] 205,83 unequal: No Solution Exploring Operation: 120-85=35, Resulting Numbers: [35] 35,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[66, 31], Operations: ['5+61=66', '85-54=31'] Exploring Operation: 66-31=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 66*31=2046, Resulting Numbers: [2046] 2046,83 unequal: No Solution Exploring Operation: 66+31=97, Resulting Numbers: [97] 97,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[85, 12], Operations: ['5+61=66', '66-54=12'] Exploring Operation: 85*12=1020, Resulting Numbers: [1020] 1020,83 unequal: No Solution Exploring Operation: 85+12=97, Resulting Numbers: [97] 97,83 unequal: No Solution Exploring Operation: 85-12=73, Resulting Numbers: [73] 73,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 83:[66, 139], Operations: ['5+61=66', '85+54=139'] Exploring Operation: 66*139=9174, Resulting Numbers: [9174] 9174,83 unequal: No Solution Exploring Operation: 66+139=205, Resulting Numbers: [205] 205,83 unequal: No Solution Exploring Operation: 139-66=73, Resulting Numbers: [73] 73,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 83:[85, 61, 59], Operations: ['5+54=59'] Exploring Operation: 85-61=24, Resulting Numbers: [59, 24] Generated Node #0,2,0: 83:[59, 24] Operation: 85-61=24 Exploring Operation: 85-59=26, Resulting Numbers: [61, 26] Generated Node #0,2,1: 83:[61, 26] Operation: 85-59=26 Exploring Operation: 85+59=144, Resulting Numbers: [61, 144] Generated Node #0,2,2: 83:[61, 144] Operation: 85+59=144 Exploring Operation: 61+59=120, Resulting Numbers: [85, 120] Generated Node #0,2,3: 83:[85, 120] Operation: 61+59=120 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 83:[85, 120], Operations: ['5+54=59', '61+59=120'] Exploring Operation: 120-85=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 85+120=205, Resulting Numbers: [205] 205,83 unequal: No Solution Exploring Operation: 85*120=10200, Resulting Numbers: [10200] 10200,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 83:[61, 26], Operations: ['5+54=59', '85-59=26'] Exploring Operation: 61-26=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 61+26=87, Resulting Numbers: [87] 87,83 unequal: No Solution Exploring Operation: 61*26=1586, Resulting Numbers: [1586] 1586,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 83:[59, 24], Operations: ['5+54=59', '85-61=24'] Exploring Operation: 59*24=1416, Resulting Numbers: [1416] 1416,83 unequal: No Solution Exploring Operation: 59-24=35, Resulting Numbers: [35] 35,83 unequal: No Solution Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Moving to Node #0 Current State: 83:[5, 85, 61, 54], Operations: [] Exploring Operation: 5+54=59, Resulting Numbers: [85, 61, 59] Generated Node #0,2: 83:[85, 61, 59] Operation: 5+54=59 Moving to Node #0,2 Current State: 83:[85, 61, 59], Operations: ['5+54=59'] Exploring Operation: 85-61=24, Resulting Numbers: [59, 24] Generated Node #0,2,0: 83:[59, 24] Operation: 85-61=24 Moving to Node #0,2,0 Current State: 83:[59, 24], Operations: ['5+54=59', '85-61=24'] Exploring Operation: 59+24=83, Resulting Numbers: [83] 83,83 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_4
mult_heuristic
[ 74, 2, 80, 14 ]
20
[ "74-14=60", "80/2=40", "60-40=20" ]
Current State: 20:[74, 2, 80, 14], Operations: [] Exploring Operation: 74-14=60, Resulting Numbers: [2, 80, 60] Generated Node #2: [2, 80, 60] from Operation: 74-14=60 Current State: 20:[2, 80, 60], Operations: ['74-14=60'] Exploring Operation: 80/2=40, Resulting Numbers: [60, 40] Generated Node #3: [60, 40] from Operation: 80/2=40 Current State: 20:[60, 40], Operations: ['74-14=60', '80/2=40'] Exploring Operation: 60-40=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
4
Current State: 20:[74, 2, 80, 14], Operations: [] Exploring Operation: 80/2=40, Resulting Numbers: [74, 14, 40] Generated Node #0,0: 20:[74, 14, 40] Operation: 80/2=40 Exploring Operation: 80-74=6, Resulting Numbers: [2, 14, 6] Generated Node #0,1: 20:[2, 14, 6] Operation: 80-74=6 Exploring Operation: 74/2=37, Resulting Numbers: [80, 14, 37] Generated Node #0,2: 20:[80, 14, 37] Operation: 74/2=37 Moving to Node #0,1 Current State: 20:[2, 14, 6], Operations: ['80-74=6'] Exploring Operation: 14-2=12, Resulting Numbers: [6, 12] Generated Node #0,1,0: 20:[6, 12] Operation: 14-2=12 Exploring Operation: 14-6=8, Resulting Numbers: [2, 8] Generated Node #0,1,1: 20:[2, 8] Operation: 14-6=8 Exploring Operation: 14+6=20, Resulting Numbers: [2, 20] Generated Node #0,1,2: 20:[2, 20] Operation: 14+6=20 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 20:[2, 20], Operations: ['80-74=6', '14+6=20'] Exploring Operation: 2+20=22, Resulting Numbers: [22] 22,20 unequal: No Solution Exploring Operation: 20/2=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 20-2=18, Resulting Numbers: [18] 18,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 20:[2, 8], Operations: ['80-74=6', '14-6=8'] Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 2+8=10, Resulting Numbers: [10] 10,20 unequal: No Solution Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,20 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 20:[6, 12], Operations: ['80-74=6', '14-2=12'] Exploring Operation: 12-6=6, Resulting Numbers: [6] 6,20 unequal: No Solution Exploring Operation: 12/6=2, Resulting Numbers: [2] 2,20 unequal: No Solution Exploring Operation: 6+12=18, Resulting Numbers: [18] 18,20 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: 20:[74, 14, 40], Operations: ['80/2=40'] Exploring Operation: 40-14=26, Resulting Numbers: [74, 26] Generated Node #0,0,0: 20:[74, 26] Operation: 40-14=26 Exploring Operation: 74-14=60, Resulting Numbers: [40, 60] Generated Node #0,0,1: 20:[40, 60] Operation: 74-14=60 Exploring Operation: 74-40=34, Resulting Numbers: [14, 34] Generated Node #0,0,2: 20:[14, 34] Operation: 74-40=34 Moving to Node #0,2 Current State: 20:[80, 14, 37], Operations: ['74/2=37'] Exploring Operation: 80-14=66, Resulting Numbers: [37, 66] Generated Node #0,2,0: 20:[37, 66] Operation: 80-14=66 Exploring Operation: 37-14=23, Resulting Numbers: [80, 23] Generated Node #0,2,1: 20:[80, 23] Operation: 37-14=23 Exploring Operation: 80-37=43, Resulting Numbers: [14, 43] Generated Node #0,2,2: 20:[14, 43] Operation: 80-37=43 Moving to Node #0,0,2 Current State: 20:[14, 34], Operations: ['80/2=40', '74-40=34'] Exploring Operation: 14*34=476, Resulting Numbers: [476] 476,20 unequal: No Solution Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,20 equal: Goal Reached Moving to Node #0 Current State: 20:[74, 2, 80, 14], Operations: [] Exploring Operation: 80/2=40, Resulting Numbers: [74, 14, 40] Generated Node #0,0: 20:[74, 14, 40] Operation: 80/2=40 Moving to Node #0,0 Current State: 20:[74, 14, 40], Operations: ['80/2=40'] Exploring Operation: 74-40=34, Resulting Numbers: [14, 34] Generated Node #0,0,2: 20:[14, 34] Operation: 74-40=34 Moving to Node #0,0,2 Current State: 20:[14, 34], Operations: ['80/2=40', '74-40=34'] Exploring Operation: 34-14=20, Resulting Numbers: [20] 20,20 equal: Goal Reached
0.976563
hs_3
mult_heuristic
[ 90, 15, 1, 70 ]
63
[ "90/15=6", "70-1=69", "69-6=63" ]
Current State: 63:[90, 15, 1, 70], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [1, 70, 6] Generated Node #2: [1, 70, 6] from Operation: 90/15=6 Current State: 63:[1, 70, 6], Operations: ['90/15=6'] Exploring Operation: 70-1=69, Resulting Numbers: [6, 69] Generated Node #3: [6, 69] from Operation: 70-1=69 Current State: 63:[6, 69], Operations: ['90/15=6', '70-1=69'] Exploring Operation: 69-6=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[90, 15, 1, 70], Operations: [] Exploring Operation: 90-70=20, Resulting Numbers: [15, 1, 20] Generated Node #0,0: 63:[15, 1, 20] Operation: 90-70=20 Exploring Operation: 90-15=75, Resulting Numbers: [1, 70, 75] Generated Node #0,1: 63:[1, 70, 75] Operation: 90-15=75 Exploring Operation: 90/15=6, Resulting Numbers: [1, 70, 6] Generated Node #0,2: 63:[1, 70, 6] Operation: 90/15=6 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[15, 1, 20], Operations: ['90-70=20'] Exploring Operation: 15+1=16, Resulting Numbers: [20, 16] Generated Node #0,0,0: 63:[20, 16] Operation: 15+1=16 Exploring Operation: 20-15=5, Resulting Numbers: [1, 5] Generated Node #0,0,1: 63:[1, 5] Operation: 20-15=5 Exploring Operation: 15-1=14, Resulting Numbers: [20, 14] Generated Node #0,0,2: 63:[20, 14] Operation: 15-1=14 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 63:[1, 5], Operations: ['90-70=20', '20-15=5'] Exploring Operation: 1+5=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 1*5=5, Resulting Numbers: [5] 5,63 unequal: No Solution Exploring Operation: 5-1=4, Resulting Numbers: [4] 4,63 unequal: No Solution No 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: 63:[20, 16], Operations: ['90-70=20', '15+1=16'] Exploring Operation: 20*16=320, Resulting Numbers: [320] 320,63 unequal: No Solution Exploring Operation: 20-16=4, Resulting Numbers: [4] 4,63 unequal: No Solution Exploring Operation: 20+16=36, Resulting Numbers: [36] 36,63 unequal: No Solution No 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: 63:[20, 14], Operations: ['90-70=20', '15-1=14'] Exploring Operation: 20*14=280, Resulting Numbers: [280] 280,63 unequal: No Solution Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,63 unequal: No Solution Exploring Operation: 20+14=34, Resulting Numbers: [34] 34,63 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: 63:[1, 70, 6], Operations: ['90/15=6'] Exploring Operation: 1+6=7, Resulting Numbers: [70, 7] Generated Node #0,2,0: 63:[70, 7] Operation: 1+6=7 Exploring Operation: 70-1=69, Resulting Numbers: [6, 69] Generated Node #0,2,1: 63:[6, 69] Operation: 70-1=69 Exploring Operation: 70-6=64, Resulting Numbers: [1, 64] Generated Node #0,2,2: 63:[1, 64] Operation: 70-6=64 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 63:[1, 64], Operations: ['90/15=6', '70-6=64'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Moving to Node #0 Current State: 63:[90, 15, 1, 70], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [1, 70, 6] Generated Node #0,2: 63:[1, 70, 6] Operation: 90/15=6 Moving to Node #0,2 Current State: 63:[1, 70, 6], Operations: ['90/15=6'] Exploring Operation: 70-6=64, Resulting Numbers: [1, 64] Generated Node #0,2,2: 63:[1, 64] Operation: 70-6=64 Moving to Node #0,2,2 Current State: 63:[1, 64], Operations: ['90/15=6', '70-6=64'] Exploring Operation: 64-1=63, Resulting Numbers: [63] 63,63 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.980035
hs_3
sum_heuristic
[ 65, 68, 87, 18 ]
47
[ "68-65=3", "87/3=29", "18+29=47" ]
Current State: 47:[65, 68, 87, 18], Operations: [] Exploring Operation: 68-65=3, Resulting Numbers: [87, 18, 3] Generated Node #2: [87, 18, 3] from Operation: 68-65=3 Current State: 47:[87, 18, 3], Operations: ['68-65=3'] Exploring Operation: 87/3=29, Resulting Numbers: [18, 29] Generated Node #3: [18, 29] from Operation: 87/3=29 Current State: 47:[18, 29], Operations: ['68-65=3', '87/3=29'] Exploring Operation: 18+29=47, Resulting Numbers: [47] 47,47 equal: Goal Reached
4
Current State: 47:[65, 68, 87, 18], Operations: [] Exploring Operation: 87-18=69, Resulting Numbers: [65, 68, 69] Generated Node #0,0: 47:[65, 68, 69] Operation: 87-18=69 Exploring Operation: 65-18=47, Resulting Numbers: [68, 87, 47] Generated Node #0,1: 47:[68, 87, 47] Operation: 65-18=47 Exploring Operation: 68-18=50, Resulting Numbers: [65, 87, 50] Generated Node #0,2: 47:[65, 87, 50] Operation: 68-18=50 Moving to Node #0,0 Current State: 47:[65, 68, 69], Operations: ['87-18=69'] Exploring Operation: 68-65=3, Resulting Numbers: [69, 3] Generated Node #0,0,0: 47:[69, 3] Operation: 68-65=3 Exploring Operation: 69-68=1, Resulting Numbers: [65, 1] Generated Node #0,0,1: 47:[65, 1] Operation: 69-68=1 Exploring Operation: 69-65=4, Resulting Numbers: [68, 4] Generated Node #0,0,2: 47:[68, 4] Operation: 69-65=4 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 47:[65, 1], Operations: ['87-18=69', '69-68=1'] Exploring Operation: 65-1=64, Resulting Numbers: [64] 64,47 unequal: No Solution Exploring Operation: 65/1=65, Resulting Numbers: [65] 65,47 unequal: No Solution Exploring Operation: 65*1=65, Resulting Numbers: [65] 65,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 47:[68, 4], Operations: ['87-18=69', '69-65=4'] Exploring Operation: 68+4=72, Resulting Numbers: [72] 72,47 unequal: No Solution Exploring Operation: 68/4=17, Resulting Numbers: [17] 17,47 unequal: No Solution Exploring Operation: 68-4=64, Resulting Numbers: [64] 64,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 47:[69, 3], Operations: ['87-18=69', '68-65=3'] Exploring Operation: 69+3=72, Resulting Numbers: [72] 72,47 unequal: No Solution Exploring Operation: 69-3=66, Resulting Numbers: [66] 66,47 unequal: No Solution Exploring Operation: 69/3=23, Resulting Numbers: [23] 23,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 47:[68, 87, 47], Operations: ['65-18=47'] Exploring Operation: 87-47=40, Resulting Numbers: [68, 40] Generated Node #0,1,0: 47:[68, 40] Operation: 87-47=40 Exploring Operation: 87-68=19, Resulting Numbers: [47, 19] Generated Node #0,1,1: 47:[47, 19] Operation: 87-68=19 Exploring Operation: 68-47=21, Resulting Numbers: [87, 21] Generated Node #0,1,2: 47:[87, 21] Operation: 68-47=21 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 47:[68, 40], Operations: ['65-18=47', '87-47=40'] Exploring Operation: 68+40=108, Resulting Numbers: [108] 108,47 unequal: No Solution Exploring Operation: 68-40=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 68*40=2720, Resulting Numbers: [2720] 2720,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 47:[47, 19], Operations: ['65-18=47', '87-68=19'] Exploring Operation: 47*19=893, Resulting Numbers: [893] 893,47 unequal: No Solution Exploring Operation: 47-19=28, Resulting Numbers: [28] 28,47 unequal: No Solution Exploring Operation: 47+19=66, Resulting Numbers: [66] 66,47 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 47:[87, 21], Operations: ['65-18=47', '68-47=21'] Exploring Operation: 87-21=66, Resulting Numbers: [66] 66,47 unequal: No Solution Exploring Operation: 87*21=1827, Resulting Numbers: [1827] 1827,47 unequal: No Solution Exploring Operation: 87+21=108, Resulting Numbers: [108] 108,47 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: 47:[65, 87, 50], Operations: ['68-18=50'] Exploring Operation: 87-65=22, Resulting Numbers: [50, 22] Generated Node #0,2,0: 47:[50, 22] Operation: 87-65=22 Exploring Operation: 65-50=15, Resulting Numbers: [87, 15] Generated Node #0,2,1: 47:[87, 15] Operation: 65-50=15 Exploring Operation: 87-50=37, Resulting Numbers: [65, 37] Generated Node #0,2,2: 47:[65, 37] Operation: 87-50=37 Moving to Node #0,2,0 Current State: 47:[50, 22], Operations: ['68-18=50', '87-65=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,47 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,47 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,47 unequal: No Solution Moving to Node #0,2,2 Current State: 47:[65, 37], Operations: ['68-18=50', '87-50=37'] Exploring Operation: 65+37=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 65*37=2405, Resulting Numbers: [2405] 2405,47 unequal: No Solution Exploring Operation: 65-37=28, Resulting Numbers: [28] 28,47 unequal: No Solution Moving to Node #0,2,1 Current State: 47:[87, 15], Operations: ['68-18=50', '65-50=15'] Exploring Operation: 87*15=1305, Resulting Numbers: [1305] 1305,47 unequal: No Solution Exploring Operation: 87+15=102, Resulting Numbers: [102] 102,47 unequal: No Solution Exploring Operation: 87-15=72, Resulting Numbers: [72] 72,47 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 24, 1, 64, 18 ]
59
[ "24-1=23", "64+18=82", "82-23=59" ]
Current State: 59:[24, 1, 64, 18], Operations: [] Exploring Operation: 24-1=23, Resulting Numbers: [64, 18, 23] Generated Node #2: [64, 18, 23] from Operation: 24-1=23 Current State: 59:[64, 18, 23], Operations: ['24-1=23'] Exploring Operation: 64+18=82, Resulting Numbers: [23, 82] Generated Node #3: [23, 82] from Operation: 64+18=82 Current State: 59:[23, 82], Operations: ['24-1=23', '64+18=82'] Exploring Operation: 82-23=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[24, 1, 64, 18], Operations: [] Exploring Operation: 64-1=63, Resulting Numbers: [24, 18, 63] Generated Node #0,0: 59:[24, 18, 63] Operation: 64-1=63 Exploring Operation: 24+1=25, Resulting Numbers: [64, 18, 25] Generated Node #0,1: 59:[64, 18, 25] Operation: 24+1=25 Exploring Operation: 24+18=42, Resulting Numbers: [1, 64, 42] Generated Node #0,2: 59:[1, 64, 42] Operation: 24+18=42 Moving to Node #0,0 Current State: 59:[24, 18, 63], Operations: ['64-1=63'] Exploring Operation: 24-18=6, Resulting Numbers: [63, 6] Generated Node #0,0,0: 59:[63, 6] Operation: 24-18=6 Exploring Operation: 63-18=45, Resulting Numbers: [24, 45] Generated Node #0,0,1: 59:[24, 45] Operation: 63-18=45 Exploring Operation: 24+18=42, Resulting Numbers: [63, 42] Generated Node #0,0,2: 59:[63, 42] Operation: 24+18=42 Moving to Node #0,1 Current State: 59:[64, 18, 25], Operations: ['24+1=25'] Exploring Operation: 18+25=43, Resulting Numbers: [64, 43] Generated Node #0,1,0: 59:[64, 43] Operation: 18+25=43 Exploring Operation: 64+18=82, Resulting Numbers: [25, 82] Generated Node #0,1,1: 59:[25, 82] Operation: 64+18=82 Exploring Operation: 64-18=46, Resulting Numbers: [25, 46] Generated Node #0,1,2: 59:[25, 46] Operation: 64-18=46 Moving to Node #0,2 Current State: 59:[1, 64, 42], Operations: ['24+18=42'] Exploring Operation: 1+42=43, Resulting Numbers: [64, 43] Generated Node #0,2,0: 59:[64, 43] Operation: 1+42=43 Exploring Operation: 1*64=64, Resulting Numbers: [42, 64] Generated Node #0,2,1: 59:[42, 64] Operation: 1*64=64 Exploring Operation: 64-1=63, Resulting Numbers: [42, 63] Generated Node #0,2,2: 59:[42, 63] Operation: 64-1=63 Moving to Node #0,0,2 Current State: 59:[63, 42], Operations: ['64-1=63', '24+18=42'] Exploring Operation: 63*42=2646, Resulting Numbers: [2646] 2646,59 unequal: No Solution Exploring Operation: 63+42=105, Resulting Numbers: [105] 105,59 unequal: No Solution Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,59 unequal: No Solution Moving to Node #0,2,0 Current State: 59:[64, 43], Operations: ['24+18=42', '1+42=43'] Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 64+43=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 64*43=2752, Resulting Numbers: [2752] 2752,59 unequal: No Solution Moving to Node #0,1,0 Current State: 59:[64, 43], Operations: ['24+1=25', '18+25=43'] Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 64+43=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 64*43=2752, Resulting Numbers: [2752] 2752,59 unequal: No Solution Moving to Node #0,2,2 Current State: 59:[42, 63], Operations: ['24+18=42', '64-1=63'] Exploring Operation: 42+63=105, Resulting Numbers: [105] 105,59 unequal: No Solution Exploring Operation: 42*63=2646, Resulting Numbers: [2646] 2646,59 unequal: No Solution Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,59 unequal: No Solution Moving to Node #0,2,1 Current State: 59:[42, 64], Operations: ['24+18=42', '1*64=64'] Exploring Operation: 42*64=2688, Resulting Numbers: [2688] 2688,59 unequal: No Solution Exploring Operation: 42+64=106, Resulting Numbers: [106] 106,59 unequal: No Solution Exploring Operation: 64-42=22, Resulting Numbers: [22] 22,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[25, 46], Operations: ['24+1=25', '64-18=46'] Exploring Operation: 25*46=1150, Resulting Numbers: [1150] 1150,59 unequal: No Solution Exploring Operation: 46-25=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 25+46=71, Resulting Numbers: [71] 71,59 unequal: No Solution Moving to Node #0,0,1 Current State: 59:[24, 45], Operations: ['64-1=63', '63-18=45'] Exploring Operation: 45-24=21, Resulting Numbers: [21] 21,59 unequal: No Solution Exploring Operation: 24*45=1080, Resulting Numbers: [1080] 1080,59 unequal: No Solution Exploring Operation: 24+45=69, Resulting Numbers: [69] 69,59 unequal: No Solution Moving to Node #0,0,0 Current State: 59:[63, 6], Operations: ['64-1=63', '24-18=6'] Exploring Operation: 63-6=57, Resulting Numbers: [57] 57,59 unequal: No Solution Exploring Operation: 63+6=69, Resulting Numbers: [69] 69,59 unequal: No Solution Exploring Operation: 63*6=378, Resulting Numbers: [378] 378,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[25, 82], Operations: ['24+1=25', '64+18=82'] Exploring Operation: 25+82=107, Resulting Numbers: [107] 107,59 unequal: No Solution Exploring Operation: 25*82=2050, Resulting Numbers: [2050] 2050,59 unequal: No Solution Exploring Operation: 82-25=57, Resulting Numbers: [57] 57,59 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 83, 4, 22, 16 ]
80
[ "4*22=88", "88-83=5", "16*5=80" ]
Current State: 80:[83, 4, 22, 16], Operations: [] Exploring Operation: 4*22=88, Resulting Numbers: [83, 16, 88] Generated Node #2: [83, 16, 88] from Operation: 4*22=88 Current State: 80:[83, 16, 88], Operations: ['4*22=88'] Exploring Operation: 88-83=5, Resulting Numbers: [16, 5] Generated Node #3: [16, 5] from Operation: 88-83=5 Current State: 80:[16, 5], Operations: ['4*22=88', '88-83=5'] Exploring Operation: 16*5=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[83, 4, 22, 16], Operations: [] Exploring Operation: 4+16=20, Resulting Numbers: [83, 22, 20] Generated Node #0,0: 80:[83, 22, 20] Operation: 4+16=20 Exploring Operation: 22-16=6, Resulting Numbers: [83, 4, 6] Generated Node #0,1: 80:[83, 4, 6] Operation: 22-16=6 Exploring Operation: 83-4=79, Resulting Numbers: [22, 16, 79] Generated Node #0,2: 80:[22, 16, 79] Operation: 83-4=79 Exploring Operation: 22-4=18, Resulting Numbers: [83, 16, 18] Generated Node #0,3: 80:[83, 16, 18] Operation: 22-4=18 Moving to Node #0,2 Current State: 80:[22, 16, 79], Operations: ['83-4=79'] Exploring Operation: 22+16=38, Resulting Numbers: [79, 38] Generated Node #0,2,0: 80:[79, 38] Operation: 22+16=38 Exploring Operation: 79-22=57, Resulting Numbers: [16, 57] Generated Node #0,2,1: 80:[16, 57] Operation: 79-22=57 Exploring Operation: 16+79=95, Resulting Numbers: [22, 95] Generated Node #0,2,2: 80:[22, 95] Operation: 16+79=95 Exploring Operation: 22-16=6, Resulting Numbers: [79, 6] Generated Node #0,2,3: 80:[79, 6] Operation: 22-16=6 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[79, 6], Operations: ['83-4=79', '22-16=6'] Exploring Operation: 79*6=474, Resulting Numbers: [474] 474,80 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 79+6=85, Resulting Numbers: [85] 85,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[79, 38], Operations: ['83-4=79', '22+16=38'] Exploring Operation: 79+38=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 79*38=3002, Resulting Numbers: [3002] 3002,80 unequal: No Solution Exploring Operation: 79-38=41, Resulting Numbers: [41] 41,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[16, 57], Operations: ['83-4=79', '79-22=57'] Exploring Operation: 16+57=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 16*57=912, Resulting Numbers: [912] 912,80 unequal: No Solution Exploring Operation: 57-16=41, Resulting Numbers: [41] 41,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[22, 95], Operations: ['83-4=79', '16+79=95'] Exploring Operation: 22+95=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 95-22=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 22*95=2090, Resulting Numbers: [2090] 2090,80 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: 80:[83, 4, 6], Operations: ['22-16=6'] Exploring Operation: 6-4=2, Resulting Numbers: [83, 2] Generated Node #0,1,0: 80:[83, 2] Operation: 6-4=2 Exploring Operation: 4+6=10, Resulting Numbers: [83, 10] Generated Node #0,1,1: 80:[83, 10] Operation: 4+6=10 Exploring Operation: 83-4=79, Resulting Numbers: [6, 79] Generated Node #0,1,2: 80:[6, 79] Operation: 83-4=79 Exploring Operation: 83-6=77, Resulting Numbers: [4, 77] Generated Node #0,1,3: 80:[4, 77] Operation: 83-6=77 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[6, 79], Operations: ['22-16=6', '83-4=79'] Exploring Operation: 6+79=85, Resulting Numbers: [85] 85,80 unequal: No Solution Exploring Operation: 6*79=474, Resulting Numbers: [474] 474,80 unequal: No Solution Exploring Operation: 79-6=73, Resulting Numbers: [73] 73,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[83, 2], Operations: ['22-16=6', '6-4=2'] Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,80 unequal: No Solution Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,80 unequal: No Solution Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[83, 10], Operations: ['22-16=6', '4+6=10'] Exploring Operation: 83+10=93, Resulting Numbers: [93] 93,80 unequal: No Solution Exploring Operation: 83*10=830, Resulting Numbers: [830] 830,80 unequal: No Solution Exploring Operation: 83-10=73, Resulting Numbers: [73] 73,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[4, 77], Operations: ['22-16=6', '83-6=77'] Exploring Operation: 4+77=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 4*77=308, Resulting Numbers: [308] 308,80 unequal: No Solution Exploring Operation: 77-4=73, Resulting Numbers: [73] 73,80 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: 80:[83, 16, 18], Operations: ['22-4=18'] Exploring Operation: 83-18=65, Resulting Numbers: [16, 65] Generated Node #0,3,0: 80:[16, 65] Operation: 83-18=65 Exploring Operation: 83-16=67, Resulting Numbers: [18, 67] Generated Node #0,3,1: 80:[18, 67] Operation: 83-16=67 Exploring Operation: 18-16=2, Resulting Numbers: [83, 2] Generated Node #0,3,2: 80:[83, 2] Operation: 18-16=2 Exploring Operation: 16+18=34, Resulting Numbers: [83, 34] Generated Node #0,3,3: 80:[83, 34] Operation: 16+18=34 Moving to Node #0,0 Current State: 80:[83, 22, 20], Operations: ['4+16=20'] Exploring Operation: 83-20=63, Resulting Numbers: [22, 63] Generated Node #0,0,0: 80:[22, 63] Operation: 83-20=63 Exploring Operation: 22+20=42, Resulting Numbers: [83, 42] Generated Node #0,0,1: 80:[83, 42] Operation: 22+20=42 Exploring Operation: 22-20=2, Resulting Numbers: [83, 2] Generated Node #0,0,2: 80:[83, 2] Operation: 22-20=2 Exploring Operation: 83-22=61, Resulting Numbers: [20, 61] Generated Node #0,0,3: 80:[20, 61] Operation: 83-22=61 Moving to Node #0,3,2 Current State: 80:[83, 2], Operations: ['22-4=18', '18-16=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,80 unequal: No Solution Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,80 unequal: No Solution Moving to Node #0,0,2 Current State: 80:[83, 2], Operations: ['4+16=20', '22-20=2'] Exploring Operation: 83-2=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 83+2=85, Resulting Numbers: [85] 85,80 unequal: No Solution Exploring Operation: 83*2=166, Resulting Numbers: [166] 166,80 unequal: No Solution Moving to Node #0,0,1 Current State: 80:[83, 42], Operations: ['4+16=20', '22+20=42'] Exploring Operation: 83*42=3486, Resulting Numbers: [3486] 3486,80 unequal: No Solution Exploring Operation: 83+42=125, Resulting Numbers: [125] 125,80 unequal: No Solution Exploring Operation: 83-42=41, Resulting Numbers: [41] 41,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[83, 34], Operations: ['22-4=18', '16+18=34'] Exploring Operation: 83*34=2822, Resulting Numbers: [2822] 2822,80 unequal: No Solution Exploring Operation: 83+34=117, Resulting Numbers: [117] 117,80 unequal: No Solution Exploring Operation: 83-34=49, Resulting Numbers: [49] 49,80 unequal: No Solution Moving to Node #0,3,0 Current State: 80:[16, 65], Operations: ['22-4=18', '83-18=65'] Exploring Operation: 16*65=1040, Resulting Numbers: [1040] 1040,80 unequal: No Solution Exploring Operation: 65-16=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 16+65=81, Resulting Numbers: [81] 81,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[18, 67], Operations: ['22-4=18', '83-16=67'] Exploring Operation: 67-18=49, Resulting Numbers: [49] 49,80 unequal: No Solution Exploring Operation: 18*67=1206, Resulting Numbers: [1206] 1206,80 unequal: No Solution Exploring Operation: 18+67=85, Resulting Numbers: [85] 85,80 unequal: No Solution Moving to Node #0,0,0 Current State: 80:[22, 63], Operations: ['4+16=20', '83-20=63'] Exploring Operation: 63-22=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 22*63=1386, Resulting Numbers: [1386] 1386,80 unequal: No Solution Exploring Operation: 22+63=85, Resulting Numbers: [85] 85,80 unequal: No Solution Moving to Node #0,0,3 Current State: 80:[20, 61], Operations: ['4+16=20', '83-22=61'] Exploring Operation: 20+61=81, Resulting Numbers: [81] 81,80 unequal: No Solution Exploring Operation: 61-20=41, Resulting Numbers: [41] 41,80 unequal: No Solution Exploring Operation: 20*61=1220, Resulting Numbers: [1220] 1220,80 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 36, 42, 38, 37 ]
81
[ "42-36=6", "38+37=75", "6+75=81" ]
Current State: 81:[36, 42, 38, 37], Operations: [] Exploring Operation: 42-36=6, Resulting Numbers: [38, 37, 6] Generated Node #2: [38, 37, 6] from Operation: 42-36=6 Current State: 81:[38, 37, 6], Operations: ['42-36=6'] Exploring Operation: 38+37=75, Resulting Numbers: [6, 75] Generated Node #3: [6, 75] from Operation: 38+37=75 Current State: 81:[6, 75], Operations: ['42-36=6', '38+37=75'] Exploring Operation: 6+75=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[36, 42, 38, 37], Operations: [] Exploring Operation: 42+38=80, Resulting Numbers: [36, 37, 80] Generated Node #0,0: 81:[36, 37, 80] Operation: 42+38=80 Exploring Operation: 42+37=79, Resulting Numbers: [36, 38, 79] Generated Node #0,1: 81:[36, 38, 79] Operation: 42+37=79 Exploring Operation: 42-38=4, Resulting Numbers: [36, 37, 4] Generated Node #0,2: 81:[36, 37, 4] Operation: 42-38=4 Moving to Node #0,0 Current State: 81:[36, 37, 80], Operations: ['42+38=80'] Exploring Operation: 36+37=73, Resulting Numbers: [80, 73] Generated Node #0,0,0: 81:[80, 73] Operation: 36+37=73 Exploring Operation: 80-37=43, Resulting Numbers: [36, 43] Generated Node #0,0,1: 81:[36, 43] Operation: 80-37=43 Exploring Operation: 37-36=1, Resulting Numbers: [80, 1] Generated Node #0,0,2: 81:[80, 1] Operation: 37-36=1 Moving to Node #0,2 Current State: 81:[36, 37, 4], Operations: ['42-38=4'] Exploring Operation: 36/4=9, Resulting Numbers: [37, 9] Generated Node #0,2,0: 81:[37, 9] Operation: 36/4=9 Exploring Operation: 36+37=73, Resulting Numbers: [4, 73] Generated Node #0,2,1: 81:[4, 73] Operation: 36+37=73 Exploring Operation: 37-36=1, Resulting Numbers: [4, 1] Generated Node #0,2,2: 81:[4, 1] Operation: 37-36=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 81:[4, 1], Operations: ['42-38=4', '37-36=1'] Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,81 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,81 unequal: No Solution Exploring Operation: 4*1=4, Resulting Numbers: [4] 4,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 81:[4, 73], Operations: ['42-38=4', '36+37=73'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,81 unequal: No Solution Exploring Operation: 4+73=77, Resulting Numbers: [77] 77,81 unequal: No Solution Exploring Operation: 4*73=292, Resulting Numbers: [292] 292,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 81:[37, 9], Operations: ['42-38=4', '36/4=9'] Exploring Operation: 37*9=333, Resulting Numbers: [333] 333,81 unequal: No Solution Exploring Operation: 37-9=28, Resulting Numbers: [28] 28,81 unequal: No Solution Exploring Operation: 37+9=46, Resulting Numbers: [46] 46,81 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 81:[36, 38, 79], Operations: ['42+37=79'] Exploring Operation: 36+38=74, Resulting Numbers: [79, 74] Generated Node #0,1,0: 81:[79, 74] Operation: 36+38=74 Exploring Operation: 38-36=2, Resulting Numbers: [79, 2] Generated Node #0,1,1: 81:[79, 2] Operation: 38-36=2 Exploring Operation: 79-38=41, Resulting Numbers: [36, 41] Generated Node #0,1,2: 81:[36, 41] Operation: 79-38=41 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 81:[79, 2], Operations: ['42+37=79', '38-36=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[36, 42, 38, 37], Operations: [] Exploring Operation: 42+37=79, Resulting Numbers: [36, 38, 79] Generated Node #0,1: 81:[36, 38, 79] Operation: 42+37=79 Moving to Node #0,1 Current State: 81:[36, 38, 79], Operations: ['42+37=79'] Exploring Operation: 38-36=2, Resulting Numbers: [79, 2] Generated Node #0,1,1: 81:[79, 2] Operation: 38-36=2 Moving to Node #0,1,1 Current State: 81:[79, 2], Operations: ['42+37=79', '38-36=2'] Exploring Operation: 79+2=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.977431
hs_3
mult_heuristic
[ 7, 51, 14, 66 ]
19
[ "7*14=98", "51+66=117", "117-98=19" ]
Current State: 19:[7, 51, 14, 66], Operations: [] Exploring Operation: 7*14=98, Resulting Numbers: [51, 66, 98] Generated Node #2: [51, 66, 98] from Operation: 7*14=98 Current State: 19:[51, 66, 98], Operations: ['7*14=98'] Exploring Operation: 51+66=117, Resulting Numbers: [98, 117] Generated Node #3: [98, 117] from Operation: 51+66=117 Current State: 19:[98, 117], Operations: ['7*14=98', '51+66=117'] Exploring Operation: 117-98=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[7, 51, 14, 66], Operations: [] Exploring Operation: 66-51=15, Resulting Numbers: [7, 14, 15] Generated Node #0,0: 19:[7, 14, 15] Operation: 66-51=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[7, 14, 15], Operations: ['66-51=15'] Exploring Operation: 7+14=21, Resulting Numbers: [15, 21] Generated Node #0,0,0: 19:[15, 21] Operation: 7+14=21 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 19:[15, 21], Operations: ['66-51=15', '7+14=21'] Exploring Operation: 21-15=6, Resulting Numbers: [6] 6,19 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
mult_heuristic
[ 97, 45, 5, 45 ]
97
[ "45-45=0", "5*0=0", "97+0=97" ]
Current State: 97:[97, 45, 5, 45], Operations: [] Exploring Operation: 45-45=0, Resulting Numbers: [97, 5, 0] Generated Node #2: [97, 5, 0] from Operation: 45-45=0 Current State: 97:[97, 5, 0], Operations: ['45-45=0'] Exploring Operation: 5*0=0, Resulting Numbers: [97, 0] Generated Node #3: [97, 0] from Operation: 5*0=0 Current State: 97:[97, 0], Operations: ['45-45=0', '5*0=0'] Exploring Operation: 97+0=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[97, 45, 5, 45], Operations: [] Exploring Operation: 45+5=50, Resulting Numbers: [97, 45, 50] Generated Node #0,0: 97:[97, 45, 50] Operation: 45+5=50 Moving to Node #0,0 Current State: 97:[97, 45, 50], Operations: ['45+5=50'] Exploring Operation: 45+50=95, Resulting Numbers: [97, 95] Generated Node #0,0,0: 97:[97, 95] Operation: 45+50=95 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 97:[97, 95], Operations: ['45+5=50', '45+50=95'] Exploring Operation: 97+95=192, Resulting Numbers: [192] 192,97 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
[ 90, 96, 80, 30 ]
93
[ "90-80=10", "30/10=3", "96-3=93" ]
Current State: 93:[90, 96, 80, 30], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [96, 30, 10] Generated Node #2: [96, 30, 10] from Operation: 90-80=10 Current State: 93:[96, 30, 10], Operations: ['90-80=10'] Exploring Operation: 30/10=3, Resulting Numbers: [96, 3] Generated Node #3: [96, 3] from Operation: 30/10=3 Current State: 93:[96, 3], Operations: ['90-80=10', '30/10=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[90, 96, 80, 30], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [96, 30, 10] Generated Node #0,0: 93:[96, 30, 10] Operation: 90-80=10 Start Sub Search at level 1: Moving to Node #0,0 Current State: 93:[96, 30, 10], Operations: ['90-80=10'] Exploring Operation: 30/10=3, Resulting Numbers: [96, 3] Generated Node #0,0,0: 93:[96, 3] Operation: 30/10=3 Moving to Node #0,0,0 Current State: 93:[96, 3], Operations: ['90-80=10', '30/10=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[90, 96, 80, 30], Operations: [] Exploring Operation: 90-80=10, Resulting Numbers: [96, 30, 10] Generated Node #0,0: 93:[96, 30, 10] Operation: 90-80=10 Moving to Node #0,0 Current State: 93:[96, 30, 10], Operations: ['90-80=10'] Exploring Operation: 30/10=3, Resulting Numbers: [96, 3] Generated Node #0,0,0: 93:[96, 3] Operation: 30/10=3 Moving to Node #0,0,0 Current State: 93:[96, 3], Operations: ['90-80=10', '30/10=3'] Exploring Operation: 96-3=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 3, 19, 58, 23 ]
70
[ "23-19=4", "3*4=12", "58+12=70" ]
Current State: 70:[3, 19, 58, 23], Operations: [] Exploring Operation: 23-19=4, Resulting Numbers: [3, 58, 4] Generated Node #2: [3, 58, 4] from Operation: 23-19=4 Current State: 70:[3, 58, 4], Operations: ['23-19=4'] Exploring Operation: 3*4=12, Resulting Numbers: [58, 12] Generated Node #3: [58, 12] from Operation: 3*4=12 Current State: 70:[58, 12], Operations: ['23-19=4', '3*4=12'] Exploring Operation: 58+12=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[3, 19, 58, 23], Operations: [] Exploring Operation: 58-23=35, Resulting Numbers: [3, 19, 35] Generated Node #0,0: 70:[3, 19, 35] Operation: 58-23=35 Exploring Operation: 58-19=39, Resulting Numbers: [3, 23, 39] Generated Node #0,1: 70:[3, 23, 39] Operation: 58-19=39 Exploring Operation: 23-19=4, Resulting Numbers: [3, 58, 4] Generated Node #0,2: 70:[3, 58, 4] Operation: 23-19=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[3, 19, 35], Operations: ['58-23=35'] Exploring Operation: 35-19=16, Resulting Numbers: [3, 16] Generated Node #0,0,0: 70:[3, 16] Operation: 35-19=16 Exploring Operation: 19-3=16, Resulting Numbers: [35, 16] Generated Node #0,0,1: 70:[35, 16] Operation: 19-3=16 Exploring Operation: 3+19=22, Resulting Numbers: [35, 22] Generated Node #0,0,2: 70:[35, 22] Operation: 3+19=22 Moving to Node #0,0,1 Current State: 70:[35, 16], Operations: ['58-23=35', '19-3=16'] Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 35+16=51, Resulting Numbers: [51] 51,70 unequal: No Solution Exploring Operation: 35*16=560, Resulting Numbers: [560] 560,70 unequal: No Solution Moving to Node #0,0,0 Current State: 70:[3, 16], Operations: ['58-23=35', '35-19=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,70 unequal: No Solution Moving to Node #0,0,2 Current State: 70:[35, 22], Operations: ['58-23=35', '3+19=22'] Exploring Operation: 35+22=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 35*22=770, Resulting Numbers: [770] 770,70 unequal: No Solution Exploring Operation: 35-22=13, Resulting Numbers: [13] 13,70 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 #0,1 Current State: 70:[3, 23, 39], Operations: ['58-19=39'] Exploring Operation: 23+39=62, Resulting Numbers: [3, 62] Generated Node #0,1,0: 70:[3, 62] Operation: 23+39=62 Exploring Operation: 39-23=16, Resulting Numbers: [3, 16] Generated Node #0,1,1: 70:[3, 16] Operation: 39-23=16 Exploring Operation: 3*23=69, Resulting Numbers: [39, 69] Generated Node #0,1,2: 70:[39, 69] Operation: 3*23=69 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 70:[3, 16], Operations: ['58-19=39', '39-23=16'] Exploring Operation: 16-3=13, Resulting Numbers: [13] 13,70 unequal: No Solution Exploring Operation: 3+16=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 3*16=48, Resulting Numbers: [48] 48,70 unequal: No Solution No 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: 70:[39, 69], Operations: ['58-19=39', '3*23=69'] Exploring Operation: 39*69=2691, Resulting Numbers: [2691] 2691,70 unequal: No Solution Exploring Operation: 39+69=108, Resulting Numbers: [108] 108,70 unequal: No Solution Exploring Operation: 69-39=30, Resulting Numbers: [30] 30,70 unequal: No Solution No 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: 70:[3, 62], Operations: ['58-19=39', '23+39=62'] Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,70 unequal: No Solution Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,70 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,70 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 70:[3, 58, 4], Operations: ['23-19=4'] Exploring Operation: 58+4=62, Resulting Numbers: [3, 62] Generated Node #0,2,0: 70:[3, 62] Operation: 58+4=62 Exploring Operation: 3+58=61, Resulting Numbers: [4, 61] Generated Node #0,2,1: 70:[4, 61] Operation: 3+58=61 Exploring Operation: 3+4=7, Resulting Numbers: [58, 7] Generated Node #0,2,2: 70:[58, 7] Operation: 3+4=7 Moving to Node #0,2,0 Current State: 70:[3, 62], Operations: ['23-19=4', '58+4=62'] Exploring Operation: 3*62=186, Resulting Numbers: [186] 186,70 unequal: No Solution Exploring Operation: 62-3=59, Resulting Numbers: [59] 59,70 unequal: No Solution Exploring Operation: 3+62=65, Resulting Numbers: [65] 65,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[4, 61], Operations: ['23-19=4', '3+58=61'] Exploring Operation: 61-4=57, Resulting Numbers: [57] 57,70 unequal: No Solution Exploring Operation: 4*61=244, Resulting Numbers: [244] 244,70 unequal: No Solution Exploring Operation: 4+61=65, Resulting Numbers: [65] 65,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[58, 7], Operations: ['23-19=4', '3+4=7'] Exploring Operation: 58*7=406, Resulting Numbers: [406] 406,70 unequal: No Solution Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,70 unequal: No Solution Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,70 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
[ 75, 28, 52, 3 ]
96
[ "75-28=47", "52-3=49", "47+49=96" ]
Current State: 96:[75, 28, 52, 3], Operations: [] Exploring Operation: 75-28=47, Resulting Numbers: [52, 3, 47] Generated Node #2: [52, 3, 47] from Operation: 75-28=47 Current State: 96:[52, 3, 47], Operations: ['75-28=47'] Exploring Operation: 52-3=49, Resulting Numbers: [47, 49] Generated Node #3: [47, 49] from Operation: 52-3=49 Current State: 96:[47, 49], Operations: ['75-28=47', '52-3=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[75, 28, 52, 3], Operations: [] Exploring Operation: 75-52=23, Resulting Numbers: [28, 3, 23] Generated Node #0,0: 96:[28, 3, 23] Operation: 75-52=23 Exploring Operation: 75-28=47, Resulting Numbers: [52, 3, 47] Generated Node #0,1: 96:[52, 3, 47] Operation: 75-28=47 Exploring Operation: 75/3=25, Resulting Numbers: [28, 52, 25] Generated Node #0,2: 96:[28, 52, 25] Operation: 75/3=25 Exploring Operation: 75+28=103, Resulting Numbers: [52, 3, 103] Generated Node #0,3: 96:[52, 3, 103] Operation: 75+28=103 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[28, 3, 23], Operations: ['75-52=23'] Exploring Operation: 28+3=31, Resulting Numbers: [23, 31] Generated Node #0,0,0: 96:[23, 31] Operation: 28+3=31 Exploring Operation: 28-3=25, Resulting Numbers: [23, 25] Generated Node #0,0,1: 96:[23, 25] Operation: 28-3=25 Exploring Operation: 28-23=5, Resulting Numbers: [3, 5] Generated Node #0,0,2: 96:[3, 5] Operation: 28-23=5 Exploring Operation: 28+23=51, Resulting Numbers: [3, 51] Generated Node #0,0,3: 96:[3, 51] Operation: 28+23=51 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 96:[3, 5], Operations: ['75-52=23', '28-23=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,96 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 96:[23, 31], Operations: ['75-52=23', '28+3=31'] Exploring Operation: 23+31=54, Resulting Numbers: [54] 54,96 unequal: No Solution Exploring Operation: 23*31=713, Resulting Numbers: [713] 713,96 unequal: No Solution Exploring Operation: 31-23=8, Resulting Numbers: [8] 8,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 96:[23, 25], Operations: ['75-52=23', '28-3=25'] Exploring Operation: 25-23=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 23*25=575, Resulting Numbers: [575] 575,96 unequal: No Solution Exploring Operation: 23+25=48, Resulting Numbers: [48] 48,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 96:[3, 51], Operations: ['75-52=23', '28+23=51'] Exploring Operation: 3+51=54, Resulting Numbers: [54] 54,96 unequal: No Solution Exploring Operation: 3*51=153, Resulting Numbers: [153] 153,96 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,96 unequal: No Solution Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 96:[52, 3, 47], Operations: ['75-28=47'] Exploring Operation: 52+47=99, Resulting Numbers: [3, 99] Generated Node #0,1,0: 96:[3, 99] Operation: 52+47=99 Exploring Operation: 52-3=49, Resulting Numbers: [47, 49] Generated Node #0,1,1: 96:[47, 49] Operation: 52-3=49 Exploring Operation: 52-47=5, Resulting Numbers: [3, 5] Generated Node #0,1,2: 96:[3, 5] Operation: 52-47=5 Exploring Operation: 3+47=50, Resulting Numbers: [52, 50] Generated Node #0,1,3: 96:[52, 50] Operation: 3+47=50 Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 96:[3, 5], Operations: ['75-28=47', '52-47=5'] Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,96 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[47, 49], Operations: ['75-28=47', '52-3=49'] Exploring Operation: 49-47=2, Resulting Numbers: [2] 2,96 unequal: No Solution Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[75, 28, 52, 3], Operations: [] Exploring Operation: 75-28=47, Resulting Numbers: [52, 3, 47] Generated Node #0,1: 96:[52, 3, 47] Operation: 75-28=47 Moving to Node #0,1 Current State: 96:[52, 3, 47], Operations: ['75-28=47'] Exploring Operation: 52-3=49, Resulting Numbers: [47, 49] Generated Node #0,1,1: 96:[47, 49] Operation: 52-3=49 Moving to Node #0,1,1 Current State: 96:[47, 49], Operations: ['75-28=47', '52-3=49'] Exploring Operation: 47+49=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.970486
hs_4
sum_heuristic
[ 22, 18, 34, 35 ]
44
[ "22*34=748", "35-18=17", "748/17=44" ]
Current State: 44:[22, 18, 34, 35], Operations: [] Exploring Operation: 22*34=748, Resulting Numbers: [18, 35, 748] Generated Node #2: [18, 35, 748] from Operation: 22*34=748 Current State: 44:[18, 35, 748], Operations: ['22*34=748'] Exploring Operation: 35-18=17, Resulting Numbers: [748, 17] Generated Node #3: [748, 17] from Operation: 35-18=17 Current State: 44:[748, 17], Operations: ['22*34=748', '35-18=17'] Exploring Operation: 748/17=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[22, 18, 34, 35], Operations: [] Exploring Operation: 34-22=12, Resulting Numbers: [18, 35, 12] Generated Node #0,0: 44:[18, 35, 12] Operation: 34-22=12 Exploring Operation: 35-34=1, Resulting Numbers: [22, 18, 1] Generated Node #0,1: 44:[22, 18, 1] Operation: 35-34=1 Exploring Operation: 34-18=16, Resulting Numbers: [22, 35, 16] Generated Node #0,2: 44:[22, 35, 16] Operation: 34-18=16 Exploring Operation: 35-22=13, Resulting Numbers: [18, 34, 13] Generated Node #0,3: 44:[18, 34, 13] Operation: 35-22=13 Exploring Operation: 35-18=17, Resulting Numbers: [22, 34, 17] Generated Node #0,4: 44:[22, 34, 17] Operation: 35-18=17 Start Sub Search at level 1: Moving to Node #0,1 Current State: 44:[22, 18, 1], Operations: ['35-34=1'] Exploring Operation: 22/1=22, Resulting Numbers: [18, 22] Generated Node #0,1,0: 44:[18, 22] Operation: 22/1=22 Exploring Operation: 22*1=22, Resulting Numbers: [18, 22] Generated Node #0,1,1: 44:[18, 22] Operation: 22*1=22 Exploring Operation: 22-18=4, Resulting Numbers: [1, 4] Generated Node #0,1,2: 44:[1, 4] Operation: 22-18=4 Exploring Operation: 18*1=18, Resulting Numbers: [22, 18] Generated Node #0,1,3: 44:[22, 18] Operation: 18*1=18 Exploring Operation: 18+1=19, Resulting Numbers: [22, 19] Generated Node #0,1,4: 44:[22, 19] Operation: 18+1=19 Moving to Node #0,1,2 Current State: 44:[1, 4], Operations: ['35-34=1', '22-18=4'] Exploring Operation: 1+4=5, Resulting Numbers: [5] 5,44 unequal: No Solution Exploring Operation: 4-1=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 1*4=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 4/1=4, Resulting Numbers: [4] 4,44 unequal: No Solution Moving to Node #0,1,4 Current State: 44:[22, 19], Operations: ['35-34=1', '18+1=19'] Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,44 unequal: No Solution Moving to Node #0,1,0 Current State: 44:[18, 22], Operations: ['35-34=1', '22/1=22'] Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,44 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,44 unequal: No Solution Moving to Node #0,1,1 Current State: 44:[18, 22], Operations: ['35-34=1', '22*1=22'] Exploring Operation: 18+22=40, Resulting Numbers: [40] 40,44 unequal: No Solution Exploring Operation: 18*22=396, Resulting Numbers: [396] 396,44 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,44 unequal: No Solution Moving to Node #0,1,3 Current State: 44:[22, 18], Operations: ['35-34=1', '18*1=18'] Exploring Operation: 22*18=396, Resulting Numbers: [396] 396,44 unequal: No Solution Exploring Operation: 22-18=4, Resulting Numbers: [4] 4,44 unequal: No Solution Exploring Operation: 22+18=40, Resulting Numbers: [40] 40,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 44:[18, 35, 12], Operations: ['34-22=12'] Exploring Operation: 35+12=47, Resulting Numbers: [18, 47] Generated Node #0,0,0: 44:[18, 47] Operation: 35+12=47 Exploring Operation: 35-12=23, Resulting Numbers: [18, 23] Generated Node #0,0,1: 44:[18, 23] Operation: 35-12=23 Exploring Operation: 18+35=53, Resulting Numbers: [12, 53] Generated Node #0,0,2: 44:[12, 53] Operation: 18+35=53 Exploring Operation: 18-12=6, Resulting Numbers: [35, 6] Generated Node #0,0,3: 44:[35, 6] Operation: 18-12=6 Exploring Operation: 35-18=17, Resulting Numbers: [12, 17] Generated Node #0,0,4: 44:[12, 17] Operation: 35-18=17 Moving to Node #0,0,1 Current State: 44:[18, 23], Operations: ['34-22=12', '35-12=23'] Exploring Operation: 18*23=414, Resulting Numbers: [414] 414,44 unequal: No Solution Exploring Operation: 18+23=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 23-18=5, Resulting Numbers: [5] 5,44 unequal: No Solution Moving to Node #0,0,4 Current State: 44:[12, 17], Operations: ['34-22=12', '35-18=17'] Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,44 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,44 unequal: No Solution Moving to Node #0,0,0 Current State: 44:[18, 47], Operations: ['34-22=12', '35+12=47'] Exploring Operation: 18+47=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 47-18=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 18*47=846, Resulting Numbers: [846] 846,44 unequal: No Solution Moving to Node #0,0,2 Current State: 44:[12, 53], Operations: ['34-22=12', '18+35=53'] Exploring Operation: 12*53=636, Resulting Numbers: [636] 636,44 unequal: No Solution Exploring Operation: 12+53=65, Resulting Numbers: [65] 65,44 unequal: No Solution Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,44 unequal: No Solution Moving to Node #0,0,3 Current State: 44:[35, 6], Operations: ['34-22=12', '18-12=6'] Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,44 unequal: No Solution Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,44 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 44:[22, 35, 16], Operations: ['34-18=16'] Exploring Operation: 35-16=19, Resulting Numbers: [22, 19] Generated Node #0,2,0: 44:[22, 19] Operation: 35-16=19 Exploring Operation: 22-16=6, Resulting Numbers: [35, 6] Generated Node #0,2,1: 44:[35, 6] Operation: 22-16=6 Exploring Operation: 35+16=51, Resulting Numbers: [22, 51] Generated Node #0,2,2: 44:[22, 51] Operation: 35+16=51 Exploring Operation: 22+16=38, Resulting Numbers: [35, 38] Generated Node #0,2,3: 44:[35, 38] Operation: 22+16=38 Exploring Operation: 35-22=13, Resulting Numbers: [16, 13] Generated Node #0,2,4: 44:[16, 13] Operation: 35-22=13 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 44:[22, 19], Operations: ['34-18=16', '35-16=19'] Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,44 unequal: No Solution Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,44 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 44:[22, 51], Operations: ['34-18=16', '35+16=51'] Exploring Operation: 51-22=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 22+51=73, Resulting Numbers: [73] 73,44 unequal: No Solution Exploring Operation: 22*51=1122, Resulting Numbers: [1122] 1122,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 44:[16, 13], Operations: ['34-18=16', '35-22=13'] Exploring Operation: 16*13=208, Resulting Numbers: [208] 208,44 unequal: No Solution Exploring Operation: 16+13=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 16-13=3, Resulting Numbers: [3] 3,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 44:[35, 6], Operations: ['34-18=16', '22-16=6'] Exploring Operation: 35-6=29, Resulting Numbers: [29] 29,44 unequal: No Solution Exploring Operation: 35*6=210, Resulting Numbers: [210] 210,44 unequal: No Solution Exploring Operation: 35+6=41, Resulting Numbers: [41] 41,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 44:[35, 38], Operations: ['34-18=16', '22+16=38'] Exploring Operation: 35*38=1330, Resulting Numbers: [1330] 1330,44 unequal: No Solution Exploring Operation: 38-35=3, Resulting Numbers: [3] 3,44 unequal: No Solution Exploring Operation: 35+38=73, Resulting Numbers: [73] 73,44 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 44:[22, 34, 17], Operations: ['35-18=17'] Exploring Operation: 22-17=5, Resulting Numbers: [34, 5] Generated Node #0,4,0: 44:[34, 5] Operation: 22-17=5 Exploring Operation: 34/17=2, Resulting Numbers: [22, 2] Generated Node #0,4,1: 44:[22, 2] Operation: 34/17=2 Exploring Operation: 34+17=51, Resulting Numbers: [22, 51] Generated Node #0,4,2: 44:[22, 51] Operation: 34+17=51 Exploring Operation: 34-17=17, Resulting Numbers: [22, 17] Generated Node #0,4,3: 44:[22, 17] Operation: 34-17=17 Exploring Operation: 34-22=12, Resulting Numbers: [17, 12] Generated Node #0,4,4: 44:[17, 12] Operation: 34-22=12 Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 44:[22, 2], Operations: ['35-18=17', '34/17=2'] Exploring Operation: 22-2=20, Resulting Numbers: [20] 20,44 unequal: No Solution Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[22, 18, 34, 35], Operations: [] Exploring Operation: 35-18=17, Resulting Numbers: [22, 34, 17] Generated Node #0,4: 44:[22, 34, 17] Operation: 35-18=17 Moving to Node #0,4 Current State: 44:[22, 34, 17], Operations: ['35-18=17'] Exploring Operation: 34/17=2, Resulting Numbers: [22, 2] Generated Node #0,4,1: 44:[22, 2] Operation: 34/17=2 Moving to Node #0,4,1 Current State: 44:[22, 2], Operations: ['35-18=17', '34/17=2'] Exploring Operation: 22*2=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.93316
hs_5
mult_heuristic
[ 93, 95, 21, 95 ]
21
[ "95-95=0", "93*0=0", "21+0=21" ]
Current State: 21:[93, 95, 21, 95], Operations: [] Exploring Operation: 95-95=0, Resulting Numbers: [93, 21, 0] Generated Node #2: [93, 21, 0] from Operation: 95-95=0 Current State: 21:[93, 21, 0], Operations: ['95-95=0'] Exploring Operation: 93*0=0, Resulting Numbers: [21, 0] Generated Node #3: [21, 0] from Operation: 93*0=0 Current State: 21:[21, 0], Operations: ['95-95=0', '93*0=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[93, 95, 21, 95], Operations: [] Exploring Operation: 95-93=2, Resulting Numbers: [21, 95, 2] Generated Node #0,0: 21:[21, 95, 2] Operation: 95-93=2 Exploring Operation: 95-93=2, Resulting Numbers: [95, 21, 2] Generated Node #0,1: 21:[95, 21, 2] Operation: 95-93=2 Exploring Operation: 95/95=1, Resulting Numbers: [93, 21, 1] Generated Node #0,2: 21:[93, 21, 1] Operation: 95/95=1 Exploring Operation: 95-95=0, Resulting Numbers: [93, 21, 0] Generated Node #0,3: 21:[93, 21, 0] Operation: 95-95=0 Moving to Node #0,2 Current State: 21:[93, 21, 1], Operations: ['95/95=1'] Exploring Operation: 93*1=93, Resulting Numbers: [21, 93] Generated Node #0,2,0: 21:[21, 93] Operation: 93*1=93 Exploring Operation: 93-1=92, Resulting Numbers: [21, 92] Generated Node #0,2,1: 21:[21, 92] Operation: 93-1=92 Exploring Operation: 93-21=72, Resulting Numbers: [1, 72] Generated Node #0,2,2: 21:[1, 72] Operation: 93-21=72 Exploring Operation: 93/1=93, Resulting Numbers: [21, 93] Generated Node #0,2,3: 21:[21, 93] Operation: 93/1=93 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 21:[1, 72], Operations: ['95/95=1', '93-21=72'] Exploring Operation: 1+72=73, Resulting Numbers: [73] 73,21 unequal: No Solution Exploring Operation: 1*72=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 72/1=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 72-1=71, Resulting Numbers: [71] 71,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 21:[21, 92], Operations: ['95/95=1', '93-1=92'] Exploring Operation: 21+92=113, Resulting Numbers: [113] 113,21 unequal: No Solution Exploring Operation: 21*92=1932, Resulting Numbers: [1932] 1932,21 unequal: No Solution Exploring Operation: 92-21=71, Resulting Numbers: [71] 71,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 21:[21, 93], Operations: ['95/95=1', '93*1=93'] Exploring Operation: 21*93=1953, Resulting Numbers: [1953] 1953,21 unequal: No Solution Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,21 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 21:[21, 93], Operations: ['95/95=1', '93/1=93'] Exploring Operation: 93-21=72, Resulting Numbers: [72] 72,21 unequal: No Solution Exploring Operation: 21*93=1953, Resulting Numbers: [1953] 1953,21 unequal: No Solution Exploring Operation: 21+93=114, Resulting Numbers: [114] 114,21 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: 21:[95, 21, 2], Operations: ['95-93=2'] Exploring Operation: 95+2=97, Resulting Numbers: [21, 97] Generated Node #0,1,0: 21:[21, 97] Operation: 95+2=97 Exploring Operation: 21+2=23, Resulting Numbers: [95, 23] Generated Node #0,1,1: 21:[95, 23] Operation: 21+2=23 Exploring Operation: 95-21=74, Resulting Numbers: [2, 74] Generated Node #0,1,2: 21:[2, 74] Operation: 95-21=74 Exploring Operation: 95-2=93, Resulting Numbers: [21, 93] Generated Node #0,1,3: 21:[21, 93] Operation: 95-2=93 Moving to Node #0,0 Current State: 21:[21, 95, 2], Operations: ['95-93=2'] Exploring Operation: 95-21=74, Resulting Numbers: [2, 74] Generated Node #0,0,0: 21:[2, 74] Operation: 95-21=74 Exploring Operation: 21+2=23, Resulting Numbers: [95, 23] Generated Node #0,0,1: 21:[95, 23] Operation: 21+2=23 Exploring Operation: 21-2=19, Resulting Numbers: [95, 19] Generated Node #0,0,2: 21:[95, 19] Operation: 21-2=19 Exploring Operation: 95-2=93, Resulting Numbers: [21, 93] Generated Node #0,0,3: 21:[21, 93] Operation: 95-2=93 Moving to Node #0,3 Current State: 21:[93, 21, 0], Operations: ['95-95=0'] Exploring Operation: 93*0=0, Resulting Numbers: [21, 0] Generated Node #0,3,0: 21:[21, 0] Operation: 93*0=0 Exploring Operation: 93+0=93, Resulting Numbers: [21, 93] Generated Node #0,3,1: 21:[21, 93] Operation: 93+0=93 Exploring Operation: 93-0=93, Resulting Numbers: [21, 93] Generated Node #0,3,2: 21:[21, 93] Operation: 93-0=93 Exploring Operation: 93-21=72, Resulting Numbers: [0, 72] Generated Node #0,3,3: 21:[0, 72] Operation: 93-21=72 Moving to Node #0,3,0 Current State: 21:[21, 0], Operations: ['95-95=0', '93*0=0'] Exploring Operation: 21*0=0, Resulting Numbers: [0] 0,21 unequal: No Solution Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[93, 95, 21, 95], Operations: [] Exploring Operation: 95-95=0, Resulting Numbers: [93, 21, 0] Generated Node #0,3: 21:[93, 21, 0] Operation: 95-95=0 Moving to Node #0,3 Current State: 21:[93, 21, 0], Operations: ['95-95=0'] Exploring Operation: 93*0=0, Resulting Numbers: [21, 0] Generated Node #0,3,0: 21:[21, 0] Operation: 93*0=0 Moving to Node #0,3,0 Current State: 21:[21, 0], Operations: ['95-95=0', '93*0=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
0.966146
hs_4
mult_heuristic
[ 80, 61, 80, 82 ]
82
[ "80-80=0", "61*0=0", "82+0=82" ]
Current State: 82:[80, 61, 80, 82], Operations: [] Exploring Operation: 80-80=0, Resulting Numbers: [61, 82, 0] Generated Node #2: [61, 82, 0] from Operation: 80-80=0 Current State: 82:[61, 82, 0], Operations: ['80-80=0'] Exploring Operation: 61*0=0, Resulting Numbers: [82, 0] Generated Node #3: [82, 0] from Operation: 61*0=0 Current State: 82:[82, 0], Operations: ['80-80=0', '61*0=0'] Exploring Operation: 82+0=82, Resulting Numbers: [82] 82,82 equal: Goal Reached
4
Current State: 82:[80, 61, 80, 82], Operations: [] Exploring Operation: 80-61=19, Resulting Numbers: [80, 82, 19] Generated Node #0,0: 82:[80, 82, 19] Operation: 80-61=19 Exploring Operation: 80-61=19, Resulting Numbers: [80, 82, 19] Generated Node #0,1: 82:[80, 82, 19] Operation: 80-61=19 Start Sub Search at level 1: Moving to Node #0,0 Current State: 82:[80, 82, 19], Operations: ['80-61=19'] Exploring Operation: 80+19=99, Resulting Numbers: [82, 99] Generated Node #0,0,0: 82:[82, 99] Operation: 80+19=99 Exploring Operation: 82-80=2, Resulting Numbers: [19, 2] Generated Node #0,0,1: 82:[19, 2] Operation: 82-80=2 Moving to Node #0,0,0 Current State: 82:[82, 99], Operations: ['80-61=19', '80+19=99'] Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 82+99=181, Resulting Numbers: [181] 181,82 unequal: No Solution Moving to Node #0,0,1 Current State: 82:[19, 2], Operations: ['80-61=19', '82-80=2'] Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,82 unequal: No Solution Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,82 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 82:[80, 82, 19], Operations: ['80-61=19'] Exploring Operation: 80+19=99, Resulting Numbers: [82, 99] Generated Node #0,1,0: 82:[82, 99] Operation: 80+19=99 Exploring Operation: 82-80=2, Resulting Numbers: [19, 2] Generated Node #0,1,1: 82:[19, 2] Operation: 82-80=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 82:[82, 99], Operations: ['80-61=19', '80+19=99'] Exploring Operation: 99-82=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 82+99=181, Resulting Numbers: [181] 181,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 82:[19, 2], Operations: ['80-61=19', '82-80=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,82 unequal: No Solution Exploring Operation: 19*2=38, Resulting Numbers: [38] 38,82 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 76, 87, 91, 96 ]
16
[ "87-76=11", "96-91=5", "11+5=16" ]
Current State: 16:[76, 87, 91, 96], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [91, 96, 11] Generated Node #2: [91, 96, 11] from Operation: 87-76=11 Current State: 16:[91, 96, 11], Operations: ['87-76=11'] Exploring Operation: 96-91=5, Resulting Numbers: [11, 5] Generated Node #3: [11, 5] from Operation: 96-91=5 Current State: 16:[11, 5], Operations: ['87-76=11', '96-91=5'] Exploring Operation: 11+5=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
4
Current State: 16:[76, 87, 91, 96], Operations: [] Exploring Operation: 96-91=5, Resulting Numbers: [76, 87, 5] Generated Node #0,0: 16:[76, 87, 5] Operation: 96-91=5 Moving to Node #0,0 Current State: 16:[76, 87, 5], Operations: ['96-91=5'] Exploring Operation: 87-76=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 16:[5, 11] Operation: 87-76=11 Moving to Node #0,0,0 Current State: 16:[5, 11], Operations: ['96-91=5', '87-76=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached Moving to Node #0 Current State: 16:[76, 87, 91, 96], Operations: [] Exploring Operation: 96-91=5, Resulting Numbers: [76, 87, 5] Generated Node #0,0: 16:[76, 87, 5] Operation: 96-91=5 Moving to Node #0,0 Current State: 16:[76, 87, 5], Operations: ['96-91=5'] Exploring Operation: 87-76=11, Resulting Numbers: [5, 11] Generated Node #0,0,0: 16:[5, 11] Operation: 87-76=11 Moving to Node #0,0,0 Current State: 16:[5, 11], Operations: ['96-91=5', '87-76=11'] Exploring Operation: 5+11=16, Resulting Numbers: [16] 16,16 equal: Goal Reached
0.993924
hs_1
mult_heuristic
[ 60, 97, 15, 62 ]
80
[ "60+97=157", "15+62=77", "157-77=80" ]
Current State: 80:[60, 97, 15, 62], Operations: [] Exploring Operation: 60+97=157, Resulting Numbers: [15, 62, 157] Generated Node #2: [15, 62, 157] from Operation: 60+97=157 Current State: 80:[15, 62, 157], Operations: ['60+97=157'] Exploring Operation: 15+62=77, Resulting Numbers: [157, 77] Generated Node #3: [157, 77] from Operation: 15+62=77 Current State: 80:[157, 77], Operations: ['60+97=157', '15+62=77'] Exploring Operation: 157-77=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[60, 97, 15, 62], Operations: [] Exploring Operation: 97-60=37, Resulting Numbers: [15, 62, 37] Generated Node #0,0: 80:[15, 62, 37] Operation: 97-60=37 Exploring Operation: 62-60=2, Resulting Numbers: [97, 15, 2] Generated Node #0,1: 80:[97, 15, 2] Operation: 62-60=2 Start Sub Search at level 1: Moving to Node #0,1 Current State: 80:[97, 15, 2], Operations: ['62-60=2'] Exploring Operation: 97-2=95, Resulting Numbers: [15, 95] Generated Node #0,1,0: 80:[15, 95] Operation: 97-2=95 Exploring Operation: 97-15=82, Resulting Numbers: [2, 82] Generated Node #0,1,1: 80:[2, 82] Operation: 97-15=82 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 80:[2, 82], Operations: ['62-60=2', '97-15=82'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Moving to Node #0 Current State: 80:[60, 97, 15, 62], Operations: [] Exploring Operation: 62-60=2, Resulting Numbers: [97, 15, 2] Generated Node #0,1: 80:[97, 15, 2] Operation: 62-60=2 Moving to Node #0,1 Current State: 80:[97, 15, 2], Operations: ['62-60=2'] Exploring Operation: 97-15=82, Resulting Numbers: [2, 82] Generated Node #0,1,1: 80:[2, 82] Operation: 97-15=82 Moving to Node #0,1,1 Current State: 80:[2, 82], Operations: ['62-60=2', '97-15=82'] Exploring Operation: 82-2=80, Resulting Numbers: [80] 80,80 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 59, 6, 80, 12 ]
67
[ "59+80=139", "6*12=72", "139-72=67" ]
Current State: 67:[59, 6, 80, 12], Operations: [] Exploring Operation: 59+80=139, Resulting Numbers: [6, 12, 139] Generated Node #2: [6, 12, 139] from Operation: 59+80=139 Current State: 67:[6, 12, 139], Operations: ['59+80=139'] Exploring Operation: 6*12=72, Resulting Numbers: [139, 72] Generated Node #3: [139, 72] from Operation: 6*12=72 Current State: 67:[139, 72], Operations: ['59+80=139', '6*12=72'] Exploring Operation: 139-72=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[59, 6, 80, 12], Operations: [] Exploring Operation: 80-12=68, Resulting Numbers: [59, 6, 68] Generated Node #0,0: 67:[59, 6, 68] Operation: 80-12=68 Exploring Operation: 80-6=74, Resulting Numbers: [59, 12, 74] Generated Node #0,1: 67:[59, 12, 74] Operation: 80-6=74 Exploring Operation: 59+6=65, Resulting Numbers: [80, 12, 65] Generated Node #0,2: 67:[80, 12, 65] Operation: 59+6=65 Exploring Operation: 6*12=72, Resulting Numbers: [59, 80, 72] Generated Node #0,3: 67:[59, 80, 72] Operation: 6*12=72 Exploring Operation: 6+12=18, Resulting Numbers: [59, 80, 18] Generated Node #0,4: 67:[59, 80, 18] Operation: 6+12=18 Start Sub Search at level 1: Moving to Node #0,3 Current State: 67:[59, 80, 72], Operations: ['6*12=72'] Exploring Operation: 72-59=13, Resulting Numbers: [80, 13] Generated Node #0,3,0: 67:[80, 13] Operation: 72-59=13 Exploring Operation: 59+72=131, Resulting Numbers: [80, 131] Generated Node #0,3,1: 67:[80, 131] Operation: 59+72=131 Exploring Operation: 59+80=139, Resulting Numbers: [72, 139] Generated Node #0,3,2: 67:[72, 139] Operation: 59+80=139 Exploring Operation: 80-72=8, Resulting Numbers: [59, 8] Generated Node #0,3,3: 67:[59, 8] Operation: 80-72=8 Exploring Operation: 80-59=21, Resulting Numbers: [72, 21] Generated Node #0,3,4: 67:[72, 21] Operation: 80-59=21 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 67:[72, 21], Operations: ['6*12=72', '80-59=21'] Exploring Operation: 72*21=1512, Resulting Numbers: [1512] 1512,67 unequal: No Solution Exploring Operation: 72+21=93, Resulting Numbers: [93] 93,67 unequal: No Solution Exploring Operation: 72-21=51, Resulting Numbers: [51] 51,67 unequal: No Solution No 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: 67:[80, 13], Operations: ['6*12=72', '72-59=13'] Exploring Operation: 80*13=1040, Resulting Numbers: [1040] 1040,67 unequal: No Solution Exploring Operation: 80+13=93, Resulting Numbers: [93] 93,67 unequal: No Solution Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[59, 6, 80, 12], Operations: [] Exploring Operation: 6*12=72, Resulting Numbers: [59, 80, 72] Generated Node #0,3: 67:[59, 80, 72] Operation: 6*12=72 Moving to Node #0,3 Current State: 67:[59, 80, 72], Operations: ['6*12=72'] Exploring Operation: 72-59=13, Resulting Numbers: [80, 13] Generated Node #0,3,0: 67:[80, 13] Operation: 72-59=13 Moving to Node #0,3,0 Current State: 67:[80, 13], Operations: ['6*12=72', '72-59=13'] Exploring Operation: 80-13=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 42, 39, 28, 27 ]
58
[ "42-39=3", "28+27=55", "3+55=58" ]
Current State: 58:[42, 39, 28, 27], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [28, 27, 3] Generated Node #2: [28, 27, 3] from Operation: 42-39=3 Current State: 58:[28, 27, 3], Operations: ['42-39=3'] Exploring Operation: 28+27=55, Resulting Numbers: [3, 55] Generated Node #3: [3, 55] from Operation: 28+27=55 Current State: 58:[3, 55], Operations: ['42-39=3', '28+27=55'] Exploring Operation: 3+55=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[42, 39, 28, 27], Operations: [] Exploring Operation: 42+27=69, Resulting Numbers: [39, 28, 69] Generated Node #0,0: 58:[39, 28, 69] Operation: 42+27=69 Exploring Operation: 42-39=3, Resulting Numbers: [28, 27, 3] Generated Node #0,1: 58:[28, 27, 3] Operation: 42-39=3 Start Sub Search at level 1: Moving to Node #0,1 Current State: 58:[28, 27, 3], Operations: ['42-39=3'] Exploring Operation: 28-27=1, Resulting Numbers: [3, 1] Generated Node #0,1,0: 58:[3, 1] Operation: 28-27=1 Exploring Operation: 27+3=30, Resulting Numbers: [28, 30] Generated Node #0,1,1: 58:[28, 30] Operation: 27+3=30 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 58:[3, 1], Operations: ['42-39=3', '28-27=1'] Exploring Operation: 3*1=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 58:[28, 30], Operations: ['42-39=3', '27+3=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,58 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[42, 39, 28, 27], Operations: [] Exploring Operation: 42-39=3, Resulting Numbers: [28, 27, 3] Generated Node #0,1: 58:[28, 27, 3] Operation: 42-39=3 Moving to Node #0,1 Current State: 58:[28, 27, 3], Operations: ['42-39=3'] Exploring Operation: 27+3=30, Resulting Numbers: [28, 30] Generated Node #0,1,1: 58:[28, 30] Operation: 27+3=30 Moving to Node #0,1,1 Current State: 58:[28, 30], Operations: ['42-39=3', '27+3=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 3, 32, 97, 51 ]
48
[ "51/3=17", "97-32=65", "65-17=48" ]
Current State: 48:[3, 32, 97, 51], Operations: [] Exploring Operation: 51/3=17, Resulting Numbers: [32, 97, 17] Generated Node #2: [32, 97, 17] from Operation: 51/3=17 Current State: 48:[32, 97, 17], Operations: ['51/3=17'] Exploring Operation: 97-32=65, Resulting Numbers: [17, 65] Generated Node #3: [17, 65] from Operation: 97-32=65 Current State: 48:[17, 65], Operations: ['51/3=17', '97-32=65'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached
4
Current State: 48:[3, 32, 97, 51], Operations: [] Exploring Operation: 51-32=19, Resulting Numbers: [3, 97, 19] Generated Node #0,0: 48:[3, 97, 19] Operation: 51-32=19 Exploring Operation: 97-32=65, Resulting Numbers: [3, 51, 65] Generated Node #0,1: 48:[3, 51, 65] Operation: 97-32=65 Exploring Operation: 32-3=29, Resulting Numbers: [97, 51, 29] Generated Node #0,2: 48:[97, 51, 29] Operation: 32-3=29 Exploring Operation: 97-3=94, Resulting Numbers: [32, 51, 94] Generated Node #0,3: 48:[32, 51, 94] Operation: 97-3=94 Exploring Operation: 97-51=46, Resulting Numbers: [3, 32, 46] Generated Node #0,4: 48:[3, 32, 46] Operation: 97-51=46 Start Sub Search at level 1: Moving to Node #0,4 Current State: 48:[3, 32, 46], Operations: ['97-51=46'] Exploring Operation: 46-3=43, Resulting Numbers: [32, 43] Generated Node #0,4,0: 48:[32, 43] Operation: 46-3=43 Exploring Operation: 3+32=35, Resulting Numbers: [46, 35] Generated Node #0,4,1: 48:[46, 35] Operation: 3+32=35 Exploring Operation: 3+46=49, Resulting Numbers: [32, 49] Generated Node #0,4,2: 48:[32, 49] Operation: 3+46=49 Exploring Operation: 32-3=29, Resulting Numbers: [46, 29] Generated Node #0,4,3: 48:[46, 29] Operation: 32-3=29 Exploring Operation: 46-32=14, Resulting Numbers: [3, 14] Generated Node #0,4,4: 48:[3, 14] Operation: 46-32=14 Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 48:[3, 14], Operations: ['97-51=46', '46-32=14'] Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,48 unequal: No Solution Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,48 unequal: No Solution No 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: 48:[46, 29], Operations: ['97-51=46', '32-3=29'] Exploring Operation: 46+29=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 46*29=1334, Resulting Numbers: [1334] 1334,48 unequal: No Solution Exploring Operation: 46-29=17, Resulting Numbers: [17] 17,48 unequal: No Solution No 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: 48:[32, 49], Operations: ['97-51=46', '3+46=49'] Exploring Operation: 49-32=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 32*49=1568, Resulting Numbers: [1568] 1568,48 unequal: No Solution Exploring Operation: 32+49=81, Resulting Numbers: [81] 81,48 unequal: No Solution No 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: 48:[32, 43], Operations: ['97-51=46', '46-3=43'] Exploring Operation: 32*43=1376, Resulting Numbers: [1376] 1376,48 unequal: No Solution Exploring Operation: 32+43=75, Resulting Numbers: [75] 75,48 unequal: No Solution Exploring Operation: 43-32=11, Resulting Numbers: [11] 11,48 unequal: No Solution No 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: 48:[46, 35], Operations: ['97-51=46', '3+32=35'] Exploring Operation: 46*35=1610, Resulting Numbers: [1610] 1610,48 unequal: No Solution Exploring Operation: 46+35=81, Resulting Numbers: [81] 81,48 unequal: No Solution Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,48 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: 48:[3, 51, 65], Operations: ['97-32=65'] Exploring Operation: 51-3=48, Resulting Numbers: [65, 48] Generated Node #0,1,0: 48:[65, 48] Operation: 51-3=48 Exploring Operation: 51/3=17, Resulting Numbers: [65, 17] Generated Node #0,1,1: 48:[65, 17] Operation: 51/3=17 Exploring Operation: 3+51=54, Resulting Numbers: [65, 54] Generated Node #0,1,2: 48:[65, 54] Operation: 3+51=54 Exploring Operation: 65-51=14, Resulting Numbers: [3, 14] Generated Node #0,1,3: 48:[3, 14] Operation: 65-51=14 Exploring Operation: 65-3=62, Resulting Numbers: [51, 62] Generated Node #0,1,4: 48:[51, 62] Operation: 65-3=62 Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 48:[3, 14], Operations: ['97-32=65', '65-51=14'] Exploring Operation: 3+14=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 3*14=42, Resulting Numbers: [42] 42,48 unequal: No Solution Exploring Operation: 14-3=11, Resulting Numbers: [11] 11,48 unequal: No Solution No 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: 48:[65, 48], Operations: ['97-32=65', '51-3=48'] Exploring Operation: 65-48=17, Resulting Numbers: [17] 17,48 unequal: No Solution Exploring Operation: 65*48=3120, Resulting Numbers: [3120] 3120,48 unequal: No Solution Exploring Operation: 65+48=113, Resulting Numbers: [113] 113,48 unequal: No Solution No 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: 48:[51, 62], Operations: ['97-32=65', '65-3=62'] Exploring Operation: 51+62=113, Resulting Numbers: [113] 113,48 unequal: No Solution Exploring Operation: 51*62=3162, Resulting Numbers: [3162] 3162,48 unequal: No Solution Exploring Operation: 62-51=11, Resulting Numbers: [11] 11,48 unequal: No Solution No 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: 48:[65, 17], Operations: ['97-32=65', '51/3=17'] Exploring Operation: 65*17=1105, Resulting Numbers: [1105] 1105,48 unequal: No Solution Exploring Operation: 65+17=82, Resulting Numbers: [82] 82,48 unequal: No Solution Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Moving to Node #0 Current State: 48:[3, 32, 97, 51], Operations: [] Exploring Operation: 97-32=65, Resulting Numbers: [3, 51, 65] Generated Node #0,1: 48:[3, 51, 65] Operation: 97-32=65 Moving to Node #0,1 Current State: 48:[3, 51, 65], Operations: ['97-32=65'] Exploring Operation: 51/3=17, Resulting Numbers: [65, 17] Generated Node #0,1,1: 48:[65, 17] Operation: 51/3=17 Moving to Node #0,1,1 Current State: 48:[65, 17], Operations: ['97-32=65', '51/3=17'] Exploring Operation: 65-17=48, Resulting Numbers: [48] 48,48 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.960069
hs_5
mult_heuristic
[ 41, 25, 93, 31 ]
46
[ "41-25=16", "93-31=62", "62-16=46" ]
Current State: 46:[41, 25, 93, 31], Operations: [] Exploring Operation: 41-25=16, Resulting Numbers: [93, 31, 16] Generated Node #2: [93, 31, 16] from Operation: 41-25=16 Current State: 46:[93, 31, 16], Operations: ['41-25=16'] Exploring Operation: 93-31=62, Resulting Numbers: [16, 62] Generated Node #3: [16, 62] from Operation: 93-31=62 Current State: 46:[16, 62], Operations: ['41-25=16', '93-31=62'] Exploring Operation: 62-16=46, Resulting Numbers: [46] 46,46 equal: Goal Reached
4
Current State: 46:[41, 25, 93, 31], Operations: [] Exploring Operation: 93/31=3, Resulting Numbers: [41, 25, 3] Generated Node #0,0: 46:[41, 25, 3] Operation: 93/31=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 46:[41, 25, 3], Operations: ['93/31=3'] Exploring Operation: 41+3=44, Resulting Numbers: [25, 44] Generated Node #0,0,0: 46:[25, 44] Operation: 41+3=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 46:[25, 44], Operations: ['93/31=3', '41+3=44'] Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,46 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 36, 51, 88, 44 ]
85
[ "36+51=87", "88/44=2", "87-2=85" ]
Current State: 85:[36, 51, 88, 44], Operations: [] Exploring Operation: 36+51=87, Resulting Numbers: [88, 44, 87] Generated Node #2: [88, 44, 87] from Operation: 36+51=87 Current State: 85:[88, 44, 87], Operations: ['36+51=87'] Exploring Operation: 88/44=2, Resulting Numbers: [87, 2] Generated Node #3: [87, 2] from Operation: 88/44=2 Current State: 85:[87, 2], Operations: ['36+51=87', '88/44=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[36, 51, 88, 44], Operations: [] Exploring Operation: 36+51=87, Resulting Numbers: [88, 44, 87] Generated Node #0,0: 85:[88, 44, 87] Operation: 36+51=87 Exploring Operation: 44-36=8, Resulting Numbers: [51, 88, 8] Generated Node #0,1: 85:[51, 88, 8] Operation: 44-36=8 Exploring Operation: 51+44=95, Resulting Numbers: [36, 88, 95] Generated Node #0,2: 85:[36, 88, 95] Operation: 51+44=95 Exploring Operation: 51-44=7, Resulting Numbers: [36, 88, 7] Generated Node #0,3: 85:[36, 88, 7] Operation: 51-44=7 Exploring Operation: 51-36=15, Resulting Numbers: [88, 44, 15] Generated Node #0,4: 85:[88, 44, 15] Operation: 51-36=15 Moving to Node #0,3 Current State: 85:[36, 88, 7], Operations: ['51-44=7'] Exploring Operation: 88+7=95, Resulting Numbers: [36, 95] Generated Node #0,3,0: 85:[36, 95] Operation: 88+7=95 Exploring Operation: 88-36=52, Resulting Numbers: [7, 52] Generated Node #0,3,1: 85:[7, 52] Operation: 88-36=52 Exploring Operation: 88-7=81, Resulting Numbers: [36, 81] Generated Node #0,3,2: 85:[36, 81] Operation: 88-7=81 Exploring Operation: 36-7=29, Resulting Numbers: [88, 29] Generated Node #0,3,3: 85:[88, 29] Operation: 36-7=29 Exploring Operation: 36+7=43, Resulting Numbers: [88, 43] Generated Node #0,3,4: 85:[88, 43] Operation: 36+7=43 Moving to Node #0,2 Current State: 85:[36, 88, 95], Operations: ['51+44=95'] Exploring Operation: 36+95=131, Resulting Numbers: [88, 131] Generated Node #0,2,0: 85:[88, 131] Operation: 36+95=131 Exploring Operation: 36+88=124, Resulting Numbers: [95, 124] Generated Node #0,2,1: 85:[95, 124] Operation: 36+88=124 Exploring Operation: 95-88=7, Resulting Numbers: [36, 7] Generated Node #0,2,2: 85:[36, 7] Operation: 95-88=7 Exploring Operation: 88-36=52, Resulting Numbers: [95, 52] Generated Node #0,2,3: 85:[95, 52] Operation: 88-36=52 Exploring Operation: 95-36=59, Resulting Numbers: [88, 59] Generated Node #0,2,4: 85:[88, 59] Operation: 95-36=59 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 85:[36, 7], Operations: ['51+44=95', '95-88=7'] Exploring Operation: 36+7=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 36-7=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 36*7=252, Resulting Numbers: [252] 252,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 85:[88, 59], Operations: ['51+44=95', '95-36=59'] Exploring Operation: 88+59=147, Resulting Numbers: [147] 147,85 unequal: No Solution Exploring Operation: 88*59=5192, Resulting Numbers: [5192] 5192,85 unequal: No Solution Exploring Operation: 88-59=29, Resulting Numbers: [29] 29,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 85:[95, 52], Operations: ['51+44=95', '88-36=52'] Exploring Operation: 95-52=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 95+52=147, Resulting Numbers: [147] 147,85 unequal: No Solution Exploring Operation: 95*52=4940, Resulting Numbers: [4940] 4940,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 85:[88, 131], Operations: ['51+44=95', '36+95=131'] Exploring Operation: 88*131=11528, Resulting Numbers: [11528] 11528,85 unequal: No Solution Exploring Operation: 131-88=43, Resulting Numbers: [43] 43,85 unequal: No Solution Exploring Operation: 88+131=219, Resulting Numbers: [219] 219,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 85:[95, 124], Operations: ['51+44=95', '36+88=124'] Exploring Operation: 124-95=29, Resulting Numbers: [29] 29,85 unequal: No Solution Exploring Operation: 95+124=219, Resulting Numbers: [219] 219,85 unequal: No Solution Exploring Operation: 95*124=11780, Resulting Numbers: [11780] 11780,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 85:[88, 44, 87], Operations: ['36+51=87'] Exploring Operation: 88-87=1, Resulting Numbers: [44, 1] Generated Node #0,0,0: 85:[44, 1] Operation: 88-87=1 Exploring Operation: 88-44=44, Resulting Numbers: [87, 44] Generated Node #0,0,1: 85:[87, 44] Operation: 88-44=44 Exploring Operation: 88+44=132, Resulting Numbers: [87, 132] Generated Node #0,0,2: 85:[87, 132] Operation: 88+44=132 Exploring Operation: 88/44=2, Resulting Numbers: [87, 2] Generated Node #0,0,3: 85:[87, 2] Operation: 88/44=2 Exploring Operation: 87-44=43, Resulting Numbers: [88, 43] Generated Node #0,0,4: 85:[88, 43] Operation: 87-44=43 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 85:[87, 2], Operations: ['36+51=87', '88/44=2'] Exploring Operation: 87+2=89, Resulting Numbers: [89] 89,85 unequal: No Solution Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Moving to Node #0 Current State: 85:[36, 51, 88, 44], Operations: [] Exploring Operation: 36+51=87, Resulting Numbers: [88, 44, 87] Generated Node #0,0: 85:[88, 44, 87] Operation: 36+51=87 Moving to Node #0,0 Current State: 85:[88, 44, 87], Operations: ['36+51=87'] Exploring Operation: 88/44=2, Resulting Numbers: [87, 2] Generated Node #0,0,3: 85:[87, 2] Operation: 88/44=2 Moving to Node #0,0,3 Current State: 85:[87, 2], Operations: ['36+51=87', '88/44=2'] Exploring Operation: 87-2=85, Resulting Numbers: [85] 85,85 equal: Goal Reached Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 81, 60, 60, 22 ]
22
[ "60-60=0", "81*0=0", "22+0=22" ]
Current State: 22:[81, 60, 60, 22], Operations: [] Exploring Operation: 60-60=0, Resulting Numbers: [81, 22, 0] Generated Node #2: [81, 22, 0] from Operation: 60-60=0 Current State: 22:[81, 22, 0], Operations: ['60-60=0'] Exploring Operation: 81*0=0, Resulting Numbers: [22, 0] Generated Node #3: [22, 0] from Operation: 81*0=0 Current State: 22:[22, 0], Operations: ['60-60=0', '81*0=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,22 equal: Goal Reached
4
Current State: 22:[81, 60, 60, 22], Operations: [] Exploring Operation: 81-60=21, Resulting Numbers: [60, 22, 21] Generated Node #0,0: 22:[60, 22, 21] Operation: 81-60=21 Exploring Operation: 81-60=21, Resulting Numbers: [60, 22, 21] Generated Node #0,1: 22:[60, 22, 21] Operation: 81-60=21 Moving to Node #0,0 Current State: 22:[60, 22, 21], Operations: ['81-60=21'] Exploring Operation: 60-21=39, Resulting Numbers: [22, 39] Generated Node #0,0,0: 22:[22, 39] Operation: 60-21=39 Exploring Operation: 60-22=38, Resulting Numbers: [21, 38] Generated Node #0,0,1: 22:[21, 38] Operation: 60-22=38 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 22:[22, 39], Operations: ['81-60=21', '60-21=39'] Exploring Operation: 22+39=61, Resulting Numbers: [61] 61,22 unequal: No Solution Exploring Operation: 39-22=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 #0,0,1 Current State: 22:[21, 38], Operations: ['81-60=21', '60-22=38'] Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 38-21=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 #0,1 Current State: 22:[60, 22, 21], Operations: ['81-60=21'] Exploring Operation: 60-21=39, Resulting Numbers: [22, 39] Generated Node #0,1,0: 22:[22, 39] Operation: 60-21=39 Exploring Operation: 60-22=38, Resulting Numbers: [21, 38] Generated Node #0,1,1: 22:[21, 38] Operation: 60-22=38 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 22:[22, 39], Operations: ['81-60=21', '60-21=39'] Exploring Operation: 22+39=61, Resulting Numbers: [61] 61,22 unequal: No Solution Exploring Operation: 39-22=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 #0,1,1 Current State: 22:[21, 38], Operations: ['81-60=21', '60-22=38'] Exploring Operation: 21+38=59, Resulting Numbers: [59] 59,22 unequal: No Solution Exploring Operation: 38-21=17, Resulting Numbers: [17] 17,22 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
[ 9, 72, 10, 15 ]
56
[ "9+72=81", "10+15=25", "81-25=56" ]
Current State: 56:[9, 72, 10, 15], Operations: [] Exploring Operation: 9+72=81, Resulting Numbers: [10, 15, 81] Generated Node #2: [10, 15, 81] from Operation: 9+72=81 Current State: 56:[10, 15, 81], Operations: ['9+72=81'] Exploring Operation: 10+15=25, Resulting Numbers: [81, 25] Generated Node #3: [81, 25] from Operation: 10+15=25 Current State: 56:[81, 25], Operations: ['9+72=81', '10+15=25'] Exploring Operation: 81-25=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[9, 72, 10, 15], Operations: [] Exploring Operation: 72-10=62, Resulting Numbers: [9, 15, 62] Generated Node #0,0: 56:[9, 15, 62] Operation: 72-10=62 Exploring Operation: 72/9=8, Resulting Numbers: [10, 15, 8] Generated Node #0,1: 56:[10, 15, 8] Operation: 72/9=8 Exploring Operation: 72-15=57, Resulting Numbers: [9, 10, 57] Generated Node #0,2: 56:[9, 10, 57] Operation: 72-15=57 Moving to Node #0,1 Current State: 56:[10, 15, 8], Operations: ['72/9=8'] Exploring Operation: 15-8=7, Resulting Numbers: [10, 7] Generated Node #0,1,0: 56:[10, 7] Operation: 15-8=7 Exploring Operation: 15-10=5, Resulting Numbers: [8, 5] Generated Node #0,1,1: 56:[8, 5] Operation: 15-10=5 Exploring Operation: 10-8=2, Resulting Numbers: [15, 2] Generated Node #0,1,2: 56:[15, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 56:[8, 5], Operations: ['72/9=8', '15-10=5'] Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,56 unequal: No Solution No 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: 56:[15, 2], Operations: ['72/9=8', '10-8=2'] Exploring Operation: 15-2=13, Resulting Numbers: [13] 13,56 unequal: No Solution Exploring Operation: 15*2=30, Resulting Numbers: [30] 30,56 unequal: No Solution Exploring Operation: 15+2=17, Resulting Numbers: [17] 17,56 unequal: No Solution No 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: 56:[10, 7], Operations: ['72/9=8', '15-8=7'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,56 unequal: No Solution Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,56 unequal: No Solution Exploring Operation: 10*7=70, Resulting Numbers: [70] 70,56 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: 56:[9, 10, 57], Operations: ['72-15=57'] Exploring Operation: 9+10=19, Resulting Numbers: [57, 19] Generated Node #0,2,0: 56:[57, 19] Operation: 9+10=19 Exploring Operation: 57-9=48, Resulting Numbers: [10, 48] Generated Node #0,2,1: 56:[10, 48] Operation: 57-9=48 Exploring Operation: 10-9=1, Resulting Numbers: [57, 1] Generated Node #0,2,2: 56:[57, 1] Operation: 10-9=1 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 56:[57, 1], Operations: ['72-15=57', '10-9=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,56 unequal: No Solution Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[9, 72, 10, 15], Operations: [] Exploring Operation: 72-15=57, Resulting Numbers: [9, 10, 57] Generated Node #0,2: 56:[9, 10, 57] Operation: 72-15=57 Moving to Node #0,2 Current State: 56:[9, 10, 57], Operations: ['72-15=57'] Exploring Operation: 10-9=1, Resulting Numbers: [57, 1] Generated Node #0,2,2: 56:[57, 1] Operation: 10-9=1 Moving to Node #0,2,2 Current State: 56:[57, 1], Operations: ['72-15=57', '10-9=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.979167
hs_3
mult_heuristic
[ 84, 91, 80, 8 ]
24
[ "91-84=7", "8*7=56", "80-56=24" ]
Current State: 24:[84, 91, 80, 8], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [80, 8, 7] Generated Node #2: [80, 8, 7] from Operation: 91-84=7 Current State: 24:[80, 8, 7], Operations: ['91-84=7'] Exploring Operation: 8*7=56, Resulting Numbers: [80, 56] Generated Node #3: [80, 56] from Operation: 8*7=56 Current State: 24:[80, 56], Operations: ['91-84=7', '8*7=56'] Exploring Operation: 80-56=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[84, 91, 80, 8], Operations: [] Exploring Operation: 91-84=7, Resulting Numbers: [80, 8, 7] Generated Node #0,0: 24:[80, 8, 7] Operation: 91-84=7 Exploring Operation: 84-80=4, Resulting Numbers: [91, 8, 4] Generated Node #0,1: 24:[91, 8, 4] Operation: 84-80=4 Exploring Operation: 91-80=11, Resulting Numbers: [84, 8, 11] Generated Node #0,2: 24:[84, 8, 11] Operation: 91-80=11 Moving to Node #0,0 Current State: 24:[80, 8, 7], Operations: ['91-84=7'] Exploring Operation: 80-8=72, Resulting Numbers: [7, 72] Generated Node #0,0,0: 24:[7, 72] Operation: 80-8=72 Exploring Operation: 80/8=10, Resulting Numbers: [7, 10] Generated Node #0,0,1: 24:[7, 10] Operation: 80/8=10 Exploring Operation: 80-7=73, Resulting Numbers: [8, 73] Generated Node #0,0,2: 24:[8, 73] Operation: 80-7=73 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 24:[7, 10], Operations: ['91-84=7', '80/8=10'] Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,24 unequal: No Solution Exploring Operation: 7*10=70, Resulting Numbers: [70] 70,24 unequal: No Solution Exploring Operation: 7+10=17, Resulting Numbers: [17] 17,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 24:[7, 72], Operations: ['91-84=7', '80-8=72'] Exploring Operation: 7+72=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 72-7=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 7*72=504, Resulting Numbers: [504] 504,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 24:[8, 73], Operations: ['91-84=7', '80-7=73'] Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,24 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,24 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 24:[84, 8, 11], Operations: ['91-80=11'] Exploring Operation: 84-8=76, Resulting Numbers: [11, 76] Generated Node #0,2,0: 24:[11, 76] Operation: 84-8=76 Exploring Operation: 84-11=73, Resulting Numbers: [8, 73] Generated Node #0,2,1: 24:[8, 73] Operation: 84-11=73 Exploring Operation: 11-8=3, Resulting Numbers: [84, 3] Generated Node #0,2,2: 24:[84, 3] Operation: 11-8=3 Moving to Node #0,1 Current State: 24:[91, 8, 4], Operations: ['84-80=4'] Exploring Operation: 91-4=87, Resulting Numbers: [8, 87] Generated Node #0,1,0: 24:[8, 87] Operation: 91-4=87 Exploring Operation: 8+4=12, Resulting Numbers: [91, 12] Generated Node #0,1,1: 24:[91, 12] Operation: 8+4=12 Exploring Operation: 91-8=83, Resulting Numbers: [4, 83] Generated Node #0,1,2: 24:[4, 83] Operation: 91-8=83 Moving to Node #0,2,1 Current State: 24:[8, 73], Operations: ['91-80=11', '84-11=73'] Exploring Operation: 8+73=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 8*73=584, Resulting Numbers: [584] 584,24 unequal: No Solution Moving to Node #0,2,0 Current State: 24:[11, 76], Operations: ['91-80=11', '84-8=76'] Exploring Operation: 76-11=65, Resulting Numbers: [65] 65,24 unequal: No Solution Exploring Operation: 11+76=87, Resulting Numbers: [87] 87,24 unequal: No Solution Exploring Operation: 11*76=836, Resulting Numbers: [836] 836,24 unequal: No Solution Moving to Node #0,1,2 Current State: 24:[4, 83], Operations: ['84-80=4', '91-8=83'] Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,24 unequal: No Solution Exploring Operation: 4+83=87, Resulting Numbers: [87] 87,24 unequal: No Solution Exploring Operation: 4*83=332, Resulting Numbers: [332] 332,24 unequal: No Solution Moving to Node #0,2,2 Current State: 24:[84, 3], Operations: ['91-80=11', '11-8=3'] Exploring Operation: 84-3=81, Resulting Numbers: [81] 81,24 unequal: No Solution Exploring Operation: 84/3=28, Resulting Numbers: [28] 28,24 unequal: No Solution Exploring Operation: 84+3=87, Resulting Numbers: [87] 87,24 unequal: No Solution Moving to Node #0,1,0 Current State: 24:[8, 87], Operations: ['84-80=4', '91-4=87'] Exploring Operation: 8+87=95, Resulting Numbers: [95] 95,24 unequal: No Solution Exploring Operation: 8*87=696, Resulting Numbers: [696] 696,24 unequal: No Solution Exploring Operation: 87-8=79, Resulting Numbers: [79] 79,24 unequal: No Solution Moving to Node #0,1,1 Current State: 24:[91, 12], Operations: ['84-80=4', '8+4=12'] Exploring Operation: 91*12=1092, Resulting Numbers: [1092] 1092,24 unequal: No Solution Exploring Operation: 91+12=103, Resulting Numbers: [103] 103,24 unequal: No Solution Exploring Operation: 91-12=79, Resulting Numbers: [79] 79,24 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 48, 44, 43, 41 ]
70
[ "43-41=2", "44/2=22", "48+22=70" ]
Current State: 70:[48, 44, 43, 41], Operations: [] Exploring Operation: 43-41=2, Resulting Numbers: [48, 44, 2] Generated Node #2: [48, 44, 2] from Operation: 43-41=2 Current State: 70:[48, 44, 2], Operations: ['43-41=2'] Exploring Operation: 44/2=22, Resulting Numbers: [48, 22] Generated Node #3: [48, 22] from Operation: 44/2=22 Current State: 70:[48, 22], Operations: ['43-41=2', '44/2=22'] Exploring Operation: 48+22=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[48, 44, 43, 41], Operations: [] Exploring Operation: 44-43=1, Resulting Numbers: [48, 41, 1] Generated Node #0,0: 70:[48, 41, 1] Operation: 44-43=1 Exploring Operation: 48-44=4, Resulting Numbers: [43, 41, 4] Generated Node #0,1: 70:[43, 41, 4] Operation: 48-44=4 Exploring Operation: 44-41=3, Resulting Numbers: [48, 43, 3] Generated Node #0,2: 70:[48, 43, 3] Operation: 44-41=3 Exploring Operation: 48-43=5, Resulting Numbers: [44, 41, 5] Generated Node #0,3: 70:[44, 41, 5] Operation: 48-43=5 Exploring Operation: 48-41=7, Resulting Numbers: [44, 43, 7] Generated Node #0,4: 70:[44, 43, 7] Operation: 48-41=7 Moving to Node #0,1 Current State: 70:[43, 41, 4], Operations: ['48-44=4'] Exploring Operation: 43+4=47, Resulting Numbers: [41, 47] Generated Node #0,1,0: 70:[41, 47] Operation: 43+4=47 Exploring Operation: 43-4=39, Resulting Numbers: [41, 39] Generated Node #0,1,1: 70:[41, 39] Operation: 43-4=39 Exploring Operation: 41-4=37, Resulting Numbers: [43, 37] Generated Node #0,1,2: 70:[43, 37] Operation: 41-4=37 Exploring Operation: 43-41=2, Resulting Numbers: [4, 2] Generated Node #0,1,3: 70:[4, 2] Operation: 43-41=2 Exploring Operation: 43+41=84, Resulting Numbers: [4, 84] Generated Node #0,1,4: 70:[4, 84] Operation: 43+41=84 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 70:[4, 2], Operations: ['48-44=4', '43-41=2'] Exploring Operation: 4*2=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 4/2=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 4-2=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 4+2=6, Resulting Numbers: [6] 6,70 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 #0,1,1 Current State: 70:[41, 39], Operations: ['48-44=4', '43-4=39'] Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,70 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 #0,1,2 Current State: 70:[43, 37], Operations: ['48-44=4', '41-4=37'] Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 43*37=1591, Resulting Numbers: [1591] 1591,70 unequal: No Solution Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,70 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 #0,1,4 Current State: 70:[4, 84], Operations: ['48-44=4', '43+41=84'] Exploring Operation: 84/4=21, Resulting Numbers: [21] 21,70 unequal: No Solution Exploring Operation: 84-4=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 4*84=336, Resulting Numbers: [336] 336,70 unequal: No Solution Exploring Operation: 4+84=88, Resulting Numbers: [88] 88,70 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 #0,1,0 Current State: 70:[41, 47], Operations: ['48-44=4', '43+4=47'] Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,70 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,70 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:[44, 41, 5], Operations: ['48-43=5'] Exploring Operation: 44-41=3, Resulting Numbers: [5, 3] Generated Node #0,3,0: 70:[5, 3] Operation: 44-41=3 Exploring Operation: 44-5=39, Resulting Numbers: [41, 39] Generated Node #0,3,1: 70:[41, 39] Operation: 44-5=39 Exploring Operation: 44+41=85, Resulting Numbers: [5, 85] Generated Node #0,3,2: 70:[5, 85] Operation: 44+41=85 Exploring Operation: 41-5=36, Resulting Numbers: [44, 36] Generated Node #0,3,3: 70:[44, 36] Operation: 41-5=36 Exploring Operation: 44+5=49, Resulting Numbers: [41, 49] Generated Node #0,3,4: 70:[41, 49] Operation: 44+5=49 Moving to Node #0,4 Current State: 70:[44, 43, 7], Operations: ['48-41=7'] Exploring Operation: 44+43=87, Resulting Numbers: [7, 87] Generated Node #0,4,0: 70:[7, 87] Operation: 44+43=87 Exploring Operation: 44+7=51, Resulting Numbers: [43, 51] Generated Node #0,4,1: 70:[43, 51] Operation: 44+7=51 Exploring Operation: 44-7=37, Resulting Numbers: [43, 37] Generated Node #0,4,2: 70:[43, 37] Operation: 44-7=37 Exploring Operation: 43-7=36, Resulting Numbers: [44, 36] Generated Node #0,4,3: 70:[44, 36] Operation: 43-7=36 Exploring Operation: 44-43=1, Resulting Numbers: [7, 1] Generated Node #0,4,4: 70:[7, 1] Operation: 44-43=1 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 70:[7, 1], Operations: ['48-41=7', '44-43=1'] Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 7+1=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,70 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 #0,4,2 Current State: 70:[43, 37], Operations: ['48-41=7', '44-7=37'] Exploring Operation: 43+37=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 43*37=1591, Resulting Numbers: [1591] 1591,70 unequal: No Solution Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,70 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 #0,4,3 Current State: 70:[44, 36], Operations: ['48-41=7', '43-7=36'] Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,70 unequal: No Solution Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,70 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 #0,4,0 Current State: 70:[7, 87], Operations: ['48-41=7', '44+43=87'] Exploring Operation: 7+87=94, Resulting Numbers: [94] 94,70 unequal: No Solution Exploring Operation: 7*87=609, Resulting Numbers: [609] 609,70 unequal: No Solution Exploring Operation: 87-7=80, Resulting Numbers: [80] 80,70 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 #0,4,1 Current State: 70:[43, 51], Operations: ['48-41=7', '44+7=51'] Exploring Operation: 43*51=2193, Resulting Numbers: [2193] 2193,70 unequal: No Solution Exploring Operation: 51-43=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 43+51=94, Resulting Numbers: [94] 94,70 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: 70:[48, 41, 1], Operations: ['44-43=1'] Exploring Operation: 48-1=47, Resulting Numbers: [41, 47] Generated Node #0,0,0: 70:[41, 47] Operation: 48-1=47 Exploring Operation: 48*1=48, Resulting Numbers: [41, 48] Generated Node #0,0,1: 70:[41, 48] Operation: 48*1=48 Exploring Operation: 48-41=7, Resulting Numbers: [1, 7] Generated Node #0,0,2: 70:[1, 7] Operation: 48-41=7 Exploring Operation: 48/1=48, Resulting Numbers: [41, 48] Generated Node #0,0,3: 70:[41, 48] Operation: 48/1=48 Exploring Operation: 41-1=40, Resulting Numbers: [48, 40] Generated Node #0,0,4: 70:[48, 40] Operation: 41-1=40 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 70:[1, 7], Operations: ['44-43=1', '48-41=7'] Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,70 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[41, 47], Operations: ['44-43=1', '48-1=47'] Exploring Operation: 41+47=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 41*47=1927, Resulting Numbers: [1927] 1927,70 unequal: No Solution Exploring Operation: 47-41=6, Resulting Numbers: [6] 6,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 70:[48, 40], Operations: ['44-43=1', '41-1=40'] Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,70 unequal: No Solution Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 70:[41, 48], Operations: ['44-43=1', '48*1=48'] Exploring Operation: 41+48=89, Resulting Numbers: [89] 89,70 unequal: No Solution Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 41*48=1968, Resulting Numbers: [1968] 1968,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 70:[41, 48], Operations: ['44-43=1', '48/1=48'] Exploring Operation: 48-41=7, Resulting Numbers: [7] 7,70 unequal: No Solution Exploring Operation: 41+48=89, Resulting Numbers: [89] 89,70 unequal: No Solution Exploring Operation: 41*48=1968, Resulting Numbers: [1968] 1968,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 70:[48, 43, 3], Operations: ['44-41=3'] Exploring Operation: 48+43=91, Resulting Numbers: [3, 91] Generated Node #0,2,0: 70:[3, 91] Operation: 48+43=91 Exploring Operation: 48-3=45, Resulting Numbers: [43, 45] Generated Node #0,2,1: 70:[43, 45] Operation: 48-3=45 Exploring Operation: 48-43=5, Resulting Numbers: [3, 5] Generated Node #0,2,2: 70:[3, 5] Operation: 48-43=5 Exploring Operation: 43-3=40, Resulting Numbers: [48, 40] Generated Node #0,2,3: 70:[48, 40] Operation: 43-3=40 Exploring Operation: 48/3=16, Resulting Numbers: [43, 16] Generated Node #0,2,4: 70:[43, 16] Operation: 48/3=16 Moving to Node #0,3,0 Current State: 70:[5, 3], Operations: ['48-43=5', '44-41=3'] Exploring Operation: 5+3=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,70 unequal: No Solution Moving to Node #0,2,2 Current State: 70:[3, 5], Operations: ['44-41=3', '48-43=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,70 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,70 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,70 unequal: No Solution Moving to Node #0,2,4 Current State: 70:[43, 16], Operations: ['44-41=3', '48/3=16'] Exploring Operation: 43-16=27, Resulting Numbers: [27] 27,70 unequal: No Solution Exploring Operation: 43+16=59, Resulting Numbers: [59] 59,70 unequal: No Solution Exploring Operation: 43*16=688, Resulting Numbers: [688] 688,70 unequal: No Solution Moving to Node #0,3,3 Current State: 70:[44, 36], Operations: ['48-43=5', '41-5=36'] Exploring Operation: 44*36=1584, Resulting Numbers: [1584] 1584,70 unequal: No Solution Exploring Operation: 44+36=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 44-36=8, Resulting Numbers: [8] 8,70 unequal: No Solution Moving to Node #0,3,1 Current State: 70:[41, 39], Operations: ['48-43=5', '44-5=39'] Exploring Operation: 41+39=80, Resulting Numbers: [80] 80,70 unequal: No Solution Exploring Operation: 41*39=1599, Resulting Numbers: [1599] 1599,70 unequal: No Solution Exploring Operation: 41-39=2, Resulting Numbers: [2] 2,70 unequal: No Solution Moving to Node #0,3,2 Current State: 70:[5, 85], Operations: ['48-43=5', '44+41=85'] Exploring Operation: 5+85=90, Resulting Numbers: [90] 90,70 unequal: No Solution Exploring Operation: 5*85=425, Resulting Numbers: [425] 425,70 unequal: No Solution Exploring Operation: 85/5=17, Resulting Numbers: [17] 17,70 unequal: No Solution Exploring Operation: 85-5=80, Resulting Numbers: [80] 80,70 unequal: No Solution Moving to Node #0,2,3 Current State: 70:[48, 40], Operations: ['44-41=3', '43-3=40'] Exploring Operation: 48+40=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 48*40=1920, Resulting Numbers: [1920] 1920,70 unequal: No Solution Exploring Operation: 48-40=8, Resulting Numbers: [8] 8,70 unequal: No Solution Moving to Node #0,2,1 Current State: 70:[43, 45], Operations: ['44-41=3', '48-3=45'] Exploring Operation: 43+45=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 43*45=1935, Resulting Numbers: [1935] 1935,70 unequal: No Solution Exploring Operation: 45-43=2, Resulting Numbers: [2] 2,70 unequal: No Solution Moving to Node #0,3,4 Current State: 70:[41, 49], Operations: ['48-43=5', '44+5=49'] Exploring Operation: 41+49=90, Resulting Numbers: [90] 90,70 unequal: No Solution Exploring Operation: 49-41=8, Resulting Numbers: [8] 8,70 unequal: No Solution Exploring Operation: 41*49=2009, Resulting Numbers: [2009] 2009,70 unequal: No Solution Moving to Node #0,2,0 Current State: 70:[3, 91], Operations: ['44-41=3', '48+43=91'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,70 unequal: No Solution Exploring Operation: 3*91=273, Resulting Numbers: [273] 273,70 unequal: No Solution Exploring Operation: 3+91=94, Resulting Numbers: [94] 94,70 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 62, 18, 90, 73 ]
97
[ "62+18=80", "90-73=17", "80+17=97" ]
Current State: 97:[62, 18, 90, 73], Operations: [] Exploring Operation: 62+18=80, Resulting Numbers: [90, 73, 80] Generated Node #2: [90, 73, 80] from Operation: 62+18=80 Current State: 97:[90, 73, 80], Operations: ['62+18=80'] Exploring Operation: 90-73=17, Resulting Numbers: [80, 17] Generated Node #3: [80, 17] from Operation: 90-73=17 Current State: 97:[80, 17], Operations: ['62+18=80', '90-73=17'] Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[62, 18, 90, 73], Operations: [] Exploring Operation: 18+90=108, Resulting Numbers: [62, 73, 108] Generated Node #0,0: 97:[62, 73, 108] Operation: 18+90=108 Exploring Operation: 62+18=80, Resulting Numbers: [90, 73, 80] Generated Node #0,1: 97:[90, 73, 80] Operation: 62+18=80 Exploring Operation: 18+73=91, Resulting Numbers: [62, 90, 91] Generated Node #0,2: 97:[62, 90, 91] Operation: 18+73=91 Start Sub Search at level 1: Moving to Node #0,1 Current State: 97:[90, 73, 80], Operations: ['62+18=80'] Exploring Operation: 73+80=153, Resulting Numbers: [90, 153] Generated Node #0,1,0: 97:[90, 153] Operation: 73+80=153 Exploring Operation: 90-73=17, Resulting Numbers: [80, 17] Generated Node #0,1,1: 97:[80, 17] Operation: 90-73=17 Exploring Operation: 90+73=163, Resulting Numbers: [80, 163] Generated Node #0,1,2: 97:[80, 163] Operation: 90+73=163 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 97:[90, 153], Operations: ['62+18=80', '73+80=153'] Exploring Operation: 90+153=243, Resulting Numbers: [243] 243,97 unequal: No Solution Exploring Operation: 153-90=63, Resulting Numbers: [63] 63,97 unequal: No Solution Exploring Operation: 90*153=13770, Resulting Numbers: [13770] 13770,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 97:[80, 163], Operations: ['62+18=80', '90+73=163'] Exploring Operation: 80*163=13040, Resulting Numbers: [13040] 13040,97 unequal: No Solution Exploring Operation: 163-80=83, Resulting Numbers: [83] 83,97 unequal: No Solution Exploring Operation: 80+163=243, Resulting Numbers: [243] 243,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 97:[80, 17], Operations: ['62+18=80', '90-73=17'] Exploring Operation: 80*17=1360, Resulting Numbers: [1360] 1360,97 unequal: No Solution Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Moving to Node #0 Current State: 97:[62, 18, 90, 73], Operations: [] Exploring Operation: 62+18=80, Resulting Numbers: [90, 73, 80] Generated Node #0,1: 97:[90, 73, 80] Operation: 62+18=80 Moving to Node #0,1 Current State: 97:[90, 73, 80], Operations: ['62+18=80'] Exploring Operation: 90-73=17, Resulting Numbers: [80, 17] Generated Node #0,1,1: 97:[80, 17] Operation: 90-73=17 Moving to Node #0,1,1 Current State: 97:[80, 17], Operations: ['62+18=80', '90-73=17'] Exploring Operation: 80+17=97, Resulting Numbers: [97] 97,97 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.984375
hs_3
sum_heuristic
[ 17, 6, 63, 94 ]
55
[ "17*6=102", "63+94=157", "157-102=55" ]
Current State: 55:[17, 6, 63, 94], Operations: [] Exploring Operation: 17*6=102, Resulting Numbers: [63, 94, 102] Generated Node #2: [63, 94, 102] from Operation: 17*6=102 Current State: 55:[63, 94, 102], Operations: ['17*6=102'] Exploring Operation: 63+94=157, Resulting Numbers: [102, 157] Generated Node #3: [102, 157] from Operation: 63+94=157 Current State: 55:[102, 157], Operations: ['17*6=102', '63+94=157'] Exploring Operation: 157-102=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[17, 6, 63, 94], Operations: [] Exploring Operation: 94-63=31, Resulting Numbers: [17, 6, 31] Generated Node #0,0: 55:[17, 6, 31] Operation: 94-63=31 Exploring Operation: 17-6=11, Resulting Numbers: [63, 94, 11] Generated Node #0,1: 55:[63, 94, 11] Operation: 17-6=11 Exploring Operation: 94-17=77, Resulting Numbers: [6, 63, 77] Generated Node #0,2: 55:[6, 63, 77] Operation: 94-17=77 Exploring Operation: 63-6=57, Resulting Numbers: [17, 94, 57] Generated Node #0,3: 55:[17, 94, 57] Operation: 63-6=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 55:[17, 6, 31], Operations: ['94-63=31'] Exploring Operation: 31-6=25, Resulting Numbers: [17, 25] Generated Node #0,0,0: 55:[17, 25] Operation: 31-6=25 Exploring Operation: 17-6=11, Resulting Numbers: [31, 11] Generated Node #0,0,1: 55:[31, 11] Operation: 17-6=11 Exploring Operation: 31-17=14, Resulting Numbers: [6, 14] Generated Node #0,0,2: 55:[6, 14] Operation: 31-17=14 Exploring Operation: 17+31=48, Resulting Numbers: [6, 48] Generated Node #0,0,3: 55:[6, 48] Operation: 17+31=48 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 55:[6, 14], Operations: ['94-63=31', '31-17=14'] Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 55:[6, 48], Operations: ['94-63=31', '17+31=48'] Exploring Operation: 48-6=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 48/6=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 6+48=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 6*48=288, Resulting Numbers: [288] 288,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 55:[17, 25], Operations: ['94-63=31', '31-6=25'] Exploring Operation: 17*25=425, Resulting Numbers: [425] 425,55 unequal: No Solution Exploring Operation: 25-17=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 17+25=42, Resulting Numbers: [42] 42,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 55:[31, 11], Operations: ['94-63=31', '17-6=11'] Exploring Operation: 31+11=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 31*11=341, Resulting Numbers: [341] 341,55 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 55:[6, 63, 77], Operations: ['94-17=77'] Exploring Operation: 6+63=69, Resulting Numbers: [77, 69] Generated Node #0,2,0: 55:[77, 69] Operation: 6+63=69 Exploring Operation: 63-6=57, Resulting Numbers: [77, 57] Generated Node #0,2,1: 55:[77, 57] Operation: 63-6=57 Exploring Operation: 77-6=71, Resulting Numbers: [63, 71] Generated Node #0,2,2: 55:[63, 71] Operation: 77-6=71 Exploring Operation: 77-63=14, Resulting Numbers: [6, 14] Generated Node #0,2,3: 55:[6, 14] Operation: 77-63=14 Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 55:[6, 14], Operations: ['94-17=77', '77-63=14'] Exploring Operation: 6*14=84, Resulting Numbers: [84] 84,55 unequal: No Solution Exploring Operation: 14-6=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 6+14=20, Resulting Numbers: [20] 20,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 55:[77, 57], Operations: ['94-17=77', '63-6=57'] Exploring Operation: 77*57=4389, Resulting Numbers: [4389] 4389,55 unequal: No Solution Exploring Operation: 77+57=134, Resulting Numbers: [134] 134,55 unequal: No Solution Exploring Operation: 77-57=20, Resulting Numbers: [20] 20,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 55:[63, 71], Operations: ['94-17=77', '77-6=71'] Exploring Operation: 71-63=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 63*71=4473, Resulting Numbers: [4473] 4473,55 unequal: No Solution Exploring Operation: 63+71=134, Resulting Numbers: [134] 134,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 55:[77, 69], Operations: ['94-17=77', '6+63=69'] Exploring Operation: 77+69=146, Resulting Numbers: [146] 146,55 unequal: No Solution Exploring Operation: 77-69=8, Resulting Numbers: [8] 8,55 unequal: No Solution Exploring Operation: 77*69=5313, Resulting Numbers: [5313] 5313,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 55:[63, 94, 11], Operations: ['17-6=11'] Exploring Operation: 63+11=74, Resulting Numbers: [94, 74] Generated Node #0,1,0: 55:[94, 74] Operation: 63+11=74 Exploring Operation: 63-11=52, Resulting Numbers: [94, 52] Generated Node #0,1,1: 55:[94, 52] Operation: 63-11=52 Exploring Operation: 94-63=31, Resulting Numbers: [11, 31] Generated Node #0,1,2: 55:[11, 31] Operation: 94-63=31 Exploring Operation: 94-11=83, Resulting Numbers: [63, 83] Generated Node #0,1,3: 55:[63, 83] Operation: 94-11=83 Moving to Node #0,1,2 Current State: 55:[11, 31], Operations: ['17-6=11', '94-63=31'] Exploring Operation: 11*31=341, Resulting Numbers: [341] 341,55 unequal: No Solution Exploring Operation: 11+31=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 31-11=20, Resulting Numbers: [20] 20,55 unequal: No Solution Moving to Node #0,1,3 Current State: 55:[63, 83], Operations: ['17-6=11', '94-11=83'] Exploring Operation: 63*83=5229, Resulting Numbers: [5229] 5229,55 unequal: No Solution Exploring Operation: 63+83=146, Resulting Numbers: [146] 146,55 unequal: No Solution Exploring Operation: 83-63=20, Resulting Numbers: [20] 20,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[94, 52], Operations: ['17-6=11', '63-11=52'] Exploring Operation: 94*52=4888, Resulting Numbers: [4888] 4888,55 unequal: No Solution Exploring Operation: 94-52=42, Resulting Numbers: [42] 42,55 unequal: No Solution Exploring Operation: 94+52=146, Resulting Numbers: [146] 146,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[94, 74], Operations: ['17-6=11', '63+11=74'] Exploring Operation: 94*74=6956, Resulting Numbers: [6956] 6956,55 unequal: No Solution Exploring Operation: 94-74=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 94+74=168, Resulting Numbers: [168] 168,55 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 55:[17, 94, 57], Operations: ['63-6=57'] Exploring Operation: 94-17=77, Resulting Numbers: [57, 77] Generated Node #0,3,0: 55:[57, 77] Operation: 94-17=77 Exploring Operation: 94-57=37, Resulting Numbers: [17, 37] Generated Node #0,3,1: 55:[17, 37] Operation: 94-57=37 Exploring Operation: 17+94=111, Resulting Numbers: [57, 111] Generated Node #0,3,2: 55:[57, 111] Operation: 17+94=111 Exploring Operation: 57-17=40, Resulting Numbers: [94, 40] Generated Node #0,3,3: 55:[94, 40] Operation: 57-17=40 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 55:[57, 77], Operations: ['63-6=57', '94-17=77'] Exploring Operation: 77-57=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 57+77=134, Resulting Numbers: [134] 134,55 unequal: No Solution Exploring Operation: 57*77=4389, Resulting Numbers: [4389] 4389,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 55:[17, 37], Operations: ['63-6=57', '94-57=37'] Exploring Operation: 37-17=20, Resulting Numbers: [20] 20,55 unequal: No Solution Exploring Operation: 17+37=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 17*37=629, Resulting Numbers: [629] 629,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 55:[94, 40], Operations: ['63-6=57', '57-17=40'] Exploring Operation: 94-40=54, Resulting Numbers: [54] 54,55 unequal: No Solution Exploring Operation: 94*40=3760, Resulting Numbers: [3760] 3760,55 unequal: No Solution Exploring Operation: 94+40=134, Resulting Numbers: [134] 134,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 55:[57, 111], Operations: ['63-6=57', '17+94=111'] Exploring Operation: 57*111=6327, Resulting Numbers: [6327] 6327,55 unequal: No Solution Exploring Operation: 57+111=168, Resulting Numbers: [168] 168,55 unequal: No Solution Exploring Operation: 111-57=54, Resulting Numbers: [54] 54,55 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 7, 92, 23, 51 ]
23
[ "7*92=644", "51-23=28", "644/28=23" ]
Current State: 23:[7, 92, 23, 51], Operations: [] Exploring Operation: 7*92=644, Resulting Numbers: [23, 51, 644] Generated Node #2: [23, 51, 644] from Operation: 7*92=644 Current State: 23:[23, 51, 644], Operations: ['7*92=644'] Exploring Operation: 51-23=28, Resulting Numbers: [644, 28] Generated Node #3: [644, 28] from Operation: 51-23=28 Current State: 23:[644, 28], Operations: ['7*92=644', '51-23=28'] Exploring Operation: 644/28=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[7, 92, 23, 51], Operations: [] Exploring Operation: 92-51=41, Resulting Numbers: [7, 23, 41] Generated Node #0,0: 23:[7, 23, 41] Operation: 92-51=41 Moving to Node #0,0 Current State: 23:[7, 23, 41], Operations: ['92-51=41'] Exploring Operation: 41-7=34, Resulting Numbers: [23, 34] Generated Node #0,0,0: 23:[23, 34] Operation: 41-7=34 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 23:[23, 34], Operations: ['92-51=41', '41-7=34'] Exploring Operation: 34-23=11, Resulting Numbers: [11] 11,23 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
[ 21, 70, 77, 42 ]
45
[ "77-70=7", "21/7=3", "42+3=45" ]
Current State: 45:[21, 70, 77, 42], Operations: [] Exploring Operation: 77-70=7, Resulting Numbers: [21, 42, 7] Generated Node #2: [21, 42, 7] from Operation: 77-70=7 Current State: 45:[21, 42, 7], Operations: ['77-70=7'] Exploring Operation: 21/7=3, Resulting Numbers: [42, 3] Generated Node #3: [42, 3] from Operation: 21/7=3 Current State: 45:[42, 3], Operations: ['77-70=7', '21/7=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached
4
Current State: 45:[21, 70, 77, 42], Operations: [] Exploring Operation: 70-21=49, Resulting Numbers: [77, 42, 49] Generated Node #0,0: 45:[77, 42, 49] Operation: 70-21=49 Exploring Operation: 77-70=7, Resulting Numbers: [21, 42, 7] Generated Node #0,1: 45:[21, 42, 7] Operation: 77-70=7 Moving to Node #0,1 Current State: 45:[21, 42, 7], Operations: ['77-70=7'] Exploring Operation: 42/21=2, Resulting Numbers: [7, 2] Generated Node #0,1,0: 45:[7, 2] Operation: 42/21=2 Exploring Operation: 21/7=3, Resulting Numbers: [42, 3] Generated Node #0,1,1: 45:[42, 3] Operation: 21/7=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 45:[7, 2], Operations: ['77-70=7', '42/21=2'] Exploring Operation: 7-2=5, Resulting Numbers: [5] 5,45 unequal: No Solution Exploring Operation: 7+2=9, Resulting Numbers: [9] 9,45 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 45:[42, 3], Operations: ['77-70=7', '21/7=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Moving to Node #0 Current State: 45:[21, 70, 77, 42], Operations: [] Exploring Operation: 77-70=7, Resulting Numbers: [21, 42, 7] Generated Node #0,1: 45:[21, 42, 7] Operation: 77-70=7 Moving to Node #0,1 Current State: 45:[21, 42, 7], Operations: ['77-70=7'] Exploring Operation: 21/7=3, Resulting Numbers: [42, 3] Generated Node #0,1,1: 45:[42, 3] Operation: 21/7=3 Moving to Node #0,1,1 Current State: 45:[42, 3], Operations: ['77-70=7', '21/7=3'] Exploring Operation: 42+3=45, Resulting Numbers: [45] 45,45 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 18, 23, 93, 75 ]
24
[ "93-18=75", "75/75=1", "23+1=24" ]
Current State: 24:[18, 23, 93, 75], Operations: [] Exploring Operation: 93-18=75, Resulting Numbers: [23, 75, 75] Generated Node #2: [23, 75, 75] from Operation: 93-18=75 Current State: 24:[23, 75, 75], Operations: ['93-18=75'] Exploring Operation: 75/75=1, Resulting Numbers: [23, 1] Generated Node #3: [23, 1] from Operation: 75/75=1 Current State: 24:[23, 1], Operations: ['93-18=75', '75/75=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached
4
Current State: 24:[18, 23, 93, 75], Operations: [] Exploring Operation: 75-23=52, Resulting Numbers: [18, 93, 52] Generated Node #0,0: 24:[18, 93, 52] Operation: 75-23=52 Exploring Operation: 93-23=70, Resulting Numbers: [18, 75, 70] Generated Node #0,1: 24:[18, 75, 70] Operation: 93-23=70 Exploring Operation: 93-75=18, Resulting Numbers: [18, 23, 18] Generated Node #0,2: 24:[18, 23, 18] Operation: 93-75=18 Exploring Operation: 93-18=75, Resulting Numbers: [23, 75, 75] Generated Node #0,3: 24:[23, 75, 75] Operation: 93-18=75 Exploring Operation: 75-18=57, Resulting Numbers: [23, 93, 57] Generated Node #0,4: 24:[23, 93, 57] Operation: 75-18=57 Start Sub Search at level 1: Moving to Node #0,2 Current State: 24:[18, 23, 18], Operations: ['93-75=18'] Exploring Operation: 18-18=0, Resulting Numbers: [23, 0] Generated Node #0,2,0: 24:[23, 0] Operation: 18-18=0 Exploring Operation: 18+18=36, Resulting Numbers: [23, 36] Generated Node #0,2,1: 24:[23, 36] Operation: 18+18=36 Exploring Operation: 18/18=1, Resulting Numbers: [23, 1] Generated Node #0,2,2: 24:[23, 1] Operation: 18/18=1 Exploring Operation: 23-18=5, Resulting Numbers: [18, 5] Generated Node #0,2,3: 24:[18, 5] Operation: 23-18=5 Exploring Operation: 23-18=5, Resulting Numbers: [18, 5] Generated Node #0,2,4: 24:[18, 5] Operation: 23-18=5 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 24:[23, 1], Operations: ['93-75=18', '18/18=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Moving to Node #0 Current State: 24:[18, 23, 93, 75], Operations: [] Exploring Operation: 93-75=18, Resulting Numbers: [18, 23, 18] Generated Node #0,2: 24:[18, 23, 18] Operation: 93-75=18 Moving to Node #0,2 Current State: 24:[18, 23, 18], Operations: ['93-75=18'] Exploring Operation: 18/18=1, Resulting Numbers: [23, 1] Generated Node #0,2,2: 24:[23, 1] Operation: 18/18=1 Moving to Node #0,2,2 Current State: 24:[23, 1], Operations: ['93-75=18', '18/18=1'] Exploring Operation: 23+1=24, Resulting Numbers: [24] 24,24 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 46, 41, 53, 98 ]
50
[ "46-41=5", "98-53=45", "5+45=50" ]
Current State: 50:[46, 41, 53, 98], Operations: [] Exploring Operation: 46-41=5, Resulting Numbers: [53, 98, 5] Generated Node #2: [53, 98, 5] from Operation: 46-41=5 Current State: 50:[53, 98, 5], Operations: ['46-41=5'] Exploring Operation: 98-53=45, Resulting Numbers: [5, 45] Generated Node #3: [5, 45] from Operation: 98-53=45 Current State: 50:[5, 45], Operations: ['46-41=5', '98-53=45'] Exploring Operation: 5+45=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[46, 41, 53, 98], Operations: [] Exploring Operation: 98-46=52, Resulting Numbers: [41, 53, 52] Generated Node #0,0: 50:[41, 53, 52] Operation: 98-46=52 Exploring Operation: 98-41=57, Resulting Numbers: [46, 53, 57] Generated Node #0,1: 50:[46, 53, 57] Operation: 98-41=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 50:[41, 53, 52], Operations: ['98-46=52'] Exploring Operation: 52-41=11, Resulting Numbers: [53, 11] Generated Node #0,0,0: 50:[53, 11] Operation: 52-41=11 Exploring Operation: 53-41=12, Resulting Numbers: [52, 12] Generated Node #0,0,1: 50:[52, 12] Operation: 53-41=12 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 50:[53, 11], Operations: ['98-46=52', '52-41=11'] Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,50 unequal: No Solution Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 50:[52, 12], Operations: ['98-46=52', '53-41=12'] Exploring Operation: 52-12=40, Resulting Numbers: [40] 40,50 unequal: No Solution Exploring Operation: 52+12=64, Resulting Numbers: [64] 64,50 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: 50:[46, 53, 57], Operations: ['98-41=57'] Exploring Operation: 57-46=11, Resulting Numbers: [53, 11] Generated Node #0,1,0: 50:[53, 11] Operation: 57-46=11 Exploring Operation: 57-53=4, Resulting Numbers: [46, 4] Generated Node #0,1,1: 50:[46, 4] Operation: 57-53=4 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 50:[53, 11], Operations: ['98-41=57', '57-46=11'] Exploring Operation: 53-11=42, Resulting Numbers: [42] 42,50 unequal: No Solution Exploring Operation: 53+11=64, Resulting Numbers: [64] 64,50 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[46, 4], Operations: ['98-41=57', '57-53=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[46, 41, 53, 98], Operations: [] Exploring Operation: 98-41=57, Resulting Numbers: [46, 53, 57] Generated Node #0,1: 50:[46, 53, 57] Operation: 98-41=57 Moving to Node #0,1 Current State: 50:[46, 53, 57], Operations: ['98-41=57'] Exploring Operation: 57-53=4, Resulting Numbers: [46, 4] Generated Node #0,1,1: 50:[46, 4] Operation: 57-53=4 Moving to Node #0,1,1 Current State: 50:[46, 4], Operations: ['98-41=57', '57-53=4'] Exploring Operation: 46+4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.985243
hs_2
mult_heuristic
[ 46, 9, 44, 62 ]
80
[ "46-44=2", "9*2=18", "62+18=80" ]
Current State: 80:[46, 9, 44, 62], Operations: [] Exploring Operation: 46-44=2, Resulting Numbers: [9, 62, 2] Generated Node #2: [9, 62, 2] from Operation: 46-44=2 Current State: 80:[9, 62, 2], Operations: ['46-44=2'] Exploring Operation: 9*2=18, Resulting Numbers: [62, 18] Generated Node #3: [62, 18] from Operation: 9*2=18 Current State: 80:[62, 18], Operations: ['46-44=2', '9*2=18'] Exploring Operation: 62+18=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[46, 9, 44, 62], Operations: [] Exploring Operation: 9+62=71, Resulting Numbers: [46, 44, 71] Generated Node #0,0: 80:[46, 44, 71] Operation: 9+62=71 Exploring Operation: 46-44=2, Resulting Numbers: [9, 62, 2] Generated Node #0,1: 80:[9, 62, 2] Operation: 46-44=2 Exploring Operation: 62-46=16, Resulting Numbers: [9, 44, 16] Generated Node #0,2: 80:[9, 44, 16] Operation: 62-46=16 Exploring Operation: 62-44=18, Resulting Numbers: [46, 9, 18] Generated Node #0,3: 80:[46, 9, 18] Operation: 62-44=18 Moving to Node #0,2 Current State: 80:[9, 44, 16], Operations: ['62-46=16'] Exploring Operation: 9+16=25, Resulting Numbers: [44, 25] Generated Node #0,2,0: 80:[44, 25] Operation: 9+16=25 Exploring Operation: 44-16=28, Resulting Numbers: [9, 28] Generated Node #0,2,1: 80:[9, 28] Operation: 44-16=28 Exploring Operation: 16-9=7, Resulting Numbers: [44, 7] Generated Node #0,2,2: 80:[44, 7] Operation: 16-9=7 Exploring Operation: 44-9=35, Resulting Numbers: [16, 35] Generated Node #0,2,3: 80:[16, 35] Operation: 44-9=35 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 80:[44, 7], Operations: ['62-46=16', '16-9=7'] Exploring Operation: 44+7=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 44*7=308, Resulting Numbers: [308] 308,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 80:[16, 35], Operations: ['62-46=16', '44-9=35'] Exploring Operation: 16*35=560, Resulting Numbers: [560] 560,80 unequal: No Solution Exploring Operation: 16+35=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 35-16=19, Resulting Numbers: [19] 19,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 80:[44, 25], Operations: ['62-46=16', '9+16=25'] Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 44*25=1100, Resulting Numbers: [1100] 1100,80 unequal: No Solution Exploring Operation: 44+25=69, Resulting Numbers: [69] 69,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 80:[9, 28], Operations: ['62-46=16', '44-16=28'] Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,80 unequal: No Solution Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,80 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: 80:[46, 9, 18], Operations: ['62-44=18'] Exploring Operation: 46-9=37, Resulting Numbers: [18, 37] Generated Node #0,3,0: 80:[18, 37] Operation: 46-9=37 Exploring Operation: 18-9=9, Resulting Numbers: [46, 9] Generated Node #0,3,1: 80:[46, 9] Operation: 18-9=9 Exploring Operation: 46-18=28, Resulting Numbers: [9, 28] Generated Node #0,3,2: 80:[9, 28] Operation: 46-18=28 Exploring Operation: 18/9=2, Resulting Numbers: [46, 2] Generated Node #0,3,3: 80:[46, 2] Operation: 18/9=2 Moving to Node #0,1 Current State: 80:[9, 62, 2], Operations: ['46-44=2'] Exploring Operation: 62/2=31, Resulting Numbers: [9, 31] Generated Node #0,1,0: 80:[9, 31] Operation: 62/2=31 Exploring Operation: 62+2=64, Resulting Numbers: [9, 64] Generated Node #0,1,1: 80:[9, 64] Operation: 62+2=64 Exploring Operation: 9+62=71, Resulting Numbers: [2, 71] Generated Node #0,1,2: 80:[2, 71] Operation: 9+62=71 Exploring Operation: 62-9=53, Resulting Numbers: [2, 53] Generated Node #0,1,3: 80:[2, 53] Operation: 62-9=53 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 80:[2, 71], Operations: ['46-44=2', '9+62=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 2*71=142, Resulting Numbers: [142] 142,80 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 80:[9, 31], Operations: ['46-44=2', '62/2=31'] Exploring Operation: 9+31=40, Resulting Numbers: [40] 40,80 unequal: No Solution Exploring Operation: 9*31=279, Resulting Numbers: [279] 279,80 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 80:[2, 53], Operations: ['46-44=2', '62-9=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,80 unequal: No Solution Exploring Operation: 2+53=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 2*53=106, Resulting Numbers: [106] 106,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 80:[9, 64], Operations: ['46-44=2', '62+2=64'] Exploring Operation: 64-9=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 9*64=576, Resulting Numbers: [576] 576,80 unequal: No Solution Exploring Operation: 9+64=73, Resulting Numbers: [73] 73,80 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: 80:[46, 44, 71], Operations: ['9+62=71'] Exploring Operation: 71-46=25, Resulting Numbers: [44, 25] Generated Node #0,0,0: 80:[44, 25] Operation: 71-46=25 Exploring Operation: 46-44=2, Resulting Numbers: [71, 2] Generated Node #0,0,1: 80:[71, 2] Operation: 46-44=2 Exploring Operation: 46+44=90, Resulting Numbers: [71, 90] Generated Node #0,0,2: 80:[71, 90] Operation: 46+44=90 Exploring Operation: 71-44=27, Resulting Numbers: [46, 27] Generated Node #0,0,3: 80:[46, 27] Operation: 71-44=27 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[44, 25], Operations: ['9+62=71', '71-46=25'] Exploring Operation: 44*25=1100, Resulting Numbers: [1100] 1100,80 unequal: No Solution Exploring Operation: 44+25=69, Resulting Numbers: [69] 69,80 unequal: No Solution Exploring Operation: 44-25=19, Resulting Numbers: [19] 19,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 80:[71, 2], Operations: ['9+62=71', '46-44=2'] Exploring Operation: 71*2=142, Resulting Numbers: [142] 142,80 unequal: No Solution Exploring Operation: 71+2=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 80:[46, 27], Operations: ['9+62=71', '71-44=27'] Exploring Operation: 46+27=73, Resulting Numbers: [73] 73,80 unequal: No Solution Exploring Operation: 46*27=1242, Resulting Numbers: [1242] 1242,80 unequal: No Solution Exploring Operation: 46-27=19, Resulting Numbers: [19] 19,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 80:[71, 90], Operations: ['9+62=71', '46+44=90'] Exploring Operation: 71*90=6390, Resulting Numbers: [6390] 6390,80 unequal: No Solution Exploring Operation: 90-71=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 71+90=161, Resulting Numbers: [161] 161,80 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,0 Current State: 80:[18, 37], Operations: ['62-44=18', '46-9=37'] Exploring Operation: 18*37=666, Resulting Numbers: [666] 666,80 unequal: No Solution Exploring Operation: 18+37=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 37-18=19, Resulting Numbers: [19] 19,80 unequal: No Solution Moving to Node #0,3,3 Current State: 80:[46, 2], Operations: ['62-44=18', '18/9=2'] Exploring Operation: 46/2=23, Resulting Numbers: [23] 23,80 unequal: No Solution Exploring Operation: 46+2=48, Resulting Numbers: [48] 48,80 unequal: No Solution Exploring Operation: 46*2=92, Resulting Numbers: [92] 92,80 unequal: No Solution Exploring Operation: 46-2=44, Resulting Numbers: [44] 44,80 unequal: No Solution Moving to Node #0,3,1 Current State: 80:[46, 9], Operations: ['62-44=18', '18-9=9'] Exploring Operation: 46*9=414, Resulting Numbers: [414] 414,80 unequal: No Solution Exploring Operation: 46+9=55, Resulting Numbers: [55] 55,80 unequal: No Solution Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,80 unequal: No Solution Moving to Node #0,3,2 Current State: 80:[9, 28], Operations: ['62-44=18', '46-18=28'] Exploring Operation: 9+28=37, Resulting Numbers: [37] 37,80 unequal: No Solution Exploring Operation: 28-9=19, Resulting Numbers: [19] 19,80 unequal: No Solution Exploring Operation: 9*28=252, Resulting Numbers: [252] 252,80 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 12, 86, 43, 89 ]
83
[ "12*43=516", "516/86=6", "89-6=83" ]
Current State: 83:[12, 86, 43, 89], Operations: [] Exploring Operation: 12*43=516, Resulting Numbers: [86, 89, 516] Generated Node #2: [86, 89, 516] from Operation: 12*43=516 Current State: 83:[86, 89, 516], Operations: ['12*43=516'] Exploring Operation: 516/86=6, Resulting Numbers: [89, 6] Generated Node #3: [89, 6] from Operation: 516/86=6 Current State: 83:[89, 6], Operations: ['12*43=516', '516/86=6'] Exploring Operation: 89-6=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[12, 86, 43, 89], Operations: [] Exploring Operation: 12+43=55, Resulting Numbers: [86, 89, 55] Generated Node #0,0: 83:[86, 89, 55] Operation: 12+43=55 Exploring Operation: 89-12=77, Resulting Numbers: [86, 43, 77] Generated Node #0,1: 83:[86, 43, 77] Operation: 89-12=77 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[86, 89, 55], Operations: ['12+43=55'] Exploring Operation: 86-55=31, Resulting Numbers: [89, 31] Generated Node #0,0,0: 83:[89, 31] Operation: 86-55=31 Exploring Operation: 89-55=34, Resulting Numbers: [86, 34] Generated Node #0,0,1: 83:[86, 34] Operation: 89-55=34 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 83:[86, 34], Operations: ['12+43=55', '89-55=34'] Exploring Operation: 86+34=120, Resulting Numbers: [120] 120,83 unequal: No Solution Exploring Operation: 86-34=52, Resulting Numbers: [52] 52,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[89, 31], Operations: ['12+43=55', '86-55=31'] Exploring Operation: 89-31=58, Resulting Numbers: [58] 58,83 unequal: No Solution Exploring Operation: 89+31=120, Resulting Numbers: [120] 120,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 83:[86, 43, 77], Operations: ['89-12=77'] Exploring Operation: 43+77=120, Resulting Numbers: [86, 120] Generated Node #0,1,0: 83:[86, 120] Operation: 43+77=120 Exploring Operation: 86-43=43, Resulting Numbers: [77, 43] Generated Node #0,1,1: 83:[77, 43] Operation: 86-43=43 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 83:[86, 120], Operations: ['89-12=77', '43+77=120'] Exploring Operation: 86+120=206, Resulting Numbers: [206] 206,83 unequal: No Solution Exploring Operation: 120-86=34, Resulting Numbers: [34] 34,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 83:[77, 43], Operations: ['89-12=77', '86-43=43'] Exploring Operation: 77-43=34, Resulting Numbers: [34] 34,83 unequal: No Solution Exploring Operation: 77+43=120, Resulting Numbers: [120] 120,83 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 73, 45, 40, 18 ]
17
[ "45-40=5", "18*5=90", "90-73=17" ]
Current State: 17:[73, 45, 40, 18], Operations: [] Exploring Operation: 45-40=5, Resulting Numbers: [73, 18, 5] Generated Node #2: [73, 18, 5] from Operation: 45-40=5 Current State: 17:[73, 18, 5], Operations: ['45-40=5'] Exploring Operation: 18*5=90, Resulting Numbers: [73, 90] Generated Node #3: [73, 90] from Operation: 18*5=90 Current State: 17:[73, 90], Operations: ['45-40=5', '18*5=90'] Exploring Operation: 90-73=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[73, 45, 40, 18], Operations: [] Exploring Operation: 73-45=28, Resulting Numbers: [40, 18, 28] Generated Node #0,0: 17:[40, 18, 28] Operation: 73-45=28 Exploring Operation: 45-40=5, Resulting Numbers: [73, 18, 5] Generated Node #0,1: 17:[73, 18, 5] Operation: 45-40=5 Exploring Operation: 73-40=33, Resulting Numbers: [45, 18, 33] Generated Node #0,2: 17:[45, 18, 33] Operation: 73-40=33 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[40, 18, 28], Operations: ['73-45=28'] Exploring Operation: 40-18=22, Resulting Numbers: [28, 22] Generated Node #0,0,0: 17:[28, 22] Operation: 40-18=22 Exploring Operation: 28-18=10, Resulting Numbers: [40, 10] Generated Node #0,0,1: 17:[40, 10] Operation: 28-18=10 Exploring Operation: 40-28=12, Resulting Numbers: [18, 12] Generated Node #0,0,2: 17:[18, 12] Operation: 40-28=12 Moving to Node #0,0,2 Current State: 17:[18, 12], Operations: ['73-45=28', '40-28=12'] Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,17 unequal: No Solution Moving to Node #0,0,0 Current State: 17:[28, 22], Operations: ['73-45=28', '40-18=22'] Exploring Operation: 28*22=616, Resulting Numbers: [616] 616,17 unequal: No Solution Exploring Operation: 28+22=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 28-22=6, Resulting Numbers: [6] 6,17 unequal: No Solution Moving to Node #0,0,1 Current State: 17:[40, 10], Operations: ['73-45=28', '28-18=10'] Exploring Operation: 40-10=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 40/10=4, Resulting Numbers: [4] 4,17 unequal: No Solution Exploring Operation: 40+10=50, Resulting Numbers: [50] 50,17 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:[45, 18, 33], Operations: ['73-40=33'] Exploring Operation: 45-33=12, Resulting Numbers: [18, 12] Generated Node #0,2,0: 17:[18, 12] Operation: 45-33=12 Exploring Operation: 33-18=15, Resulting Numbers: [45, 15] Generated Node #0,2,1: 17:[45, 15] Operation: 33-18=15 Exploring Operation: 45-18=27, Resulting Numbers: [33, 27] Generated Node #0,2,2: 17:[33, 27] Operation: 45-18=27 Moving to Node #0,2,0 Current State: 17:[18, 12], Operations: ['73-40=33', '45-33=12'] Exploring Operation: 18+12=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 18-12=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 18*12=216, Resulting Numbers: [216] 216,17 unequal: No Solution Moving to Node #0,2,2 Current State: 17:[33, 27], Operations: ['73-40=33', '45-18=27'] Exploring Operation: 33+27=60, Resulting Numbers: [60] 60,17 unequal: No Solution Exploring Operation: 33-27=6, Resulting Numbers: [6] 6,17 unequal: No Solution Exploring Operation: 33*27=891, Resulting Numbers: [891] 891,17 unequal: No Solution Moving to Node #0,2,1 Current State: 17:[45, 15], Operations: ['73-40=33', '33-18=15'] Exploring Operation: 45/15=3, Resulting Numbers: [3] 3,17 unequal: No Solution Exploring Operation: 45-15=30, Resulting Numbers: [30] 30,17 unequal: No Solution Exploring Operation: 45+15=60, Resulting Numbers: [60] 60,17 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 17:[73, 18, 5], Operations: ['45-40=5'] Exploring Operation: 18-5=13, Resulting Numbers: [73, 13] Generated Node #0,1,0: 17:[73, 13] Operation: 18-5=13 Exploring Operation: 73-18=55, Resulting Numbers: [5, 55] Generated Node #0,1,1: 17:[5, 55] Operation: 73-18=55 Exploring Operation: 73-5=68, Resulting Numbers: [18, 68] Generated Node #0,1,2: 17:[18, 68] Operation: 73-5=68 Moving to Node #0,1,1 Current State: 17:[5, 55], Operations: ['45-40=5', '73-18=55'] Exploring Operation: 5+55=60, Resulting Numbers: [60] 60,17 unequal: No Solution Exploring Operation: 55-5=50, Resulting Numbers: [50] 50,17 unequal: No Solution Exploring Operation: 55/5=11, Resulting Numbers: [11] 11,17 unequal: No Solution Moving to Node #0,1,2 Current State: 17:[18, 68], Operations: ['45-40=5', '73-5=68'] Exploring Operation: 18*68=1224, Resulting Numbers: [1224] 1224,17 unequal: No Solution Exploring Operation: 18+68=86, Resulting Numbers: [86] 86,17 unequal: No Solution Exploring Operation: 68-18=50, Resulting Numbers: [50] 50,17 unequal: No Solution Moving to Node #0,1,0 Current State: 17:[73, 13], Operations: ['45-40=5', '18-5=13'] Exploring Operation: 73-13=60, Resulting Numbers: [60] 60,17 unequal: No Solution Exploring Operation: 73*13=949, Resulting Numbers: [949] 949,17 unequal: No Solution Exploring Operation: 73+13=86, Resulting Numbers: [86] 86,17 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
[ 12, 29, 23, 57 ]
59
[ "29-23=6", "12/6=2", "57+2=59" ]
Current State: 59:[12, 29, 23, 57], Operations: [] Exploring Operation: 29-23=6, Resulting Numbers: [12, 57, 6] Generated Node #2: [12, 57, 6] from Operation: 29-23=6 Current State: 59:[12, 57, 6], Operations: ['29-23=6'] Exploring Operation: 12/6=2, Resulting Numbers: [57, 2] Generated Node #3: [57, 2] from Operation: 12/6=2 Current State: 59:[57, 2], Operations: ['29-23=6', '12/6=2'] Exploring Operation: 57+2=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[12, 29, 23, 57], Operations: [] Exploring Operation: 12+29=41, Resulting Numbers: [23, 57, 41] Generated Node #0,0: 59:[23, 57, 41] Operation: 12+29=41 Moving to Node #0,0 Current State: 59:[23, 57, 41], Operations: ['12+29=41'] Exploring Operation: 23+41=64, Resulting Numbers: [57, 64] Generated Node #0,0,0: 59:[57, 64] Operation: 23+41=64 Moving to Node #0,0,0 Current State: 59:[57, 64], Operations: ['12+29=41', '23+41=64'] Exploring Operation: 64-57=7, Resulting Numbers: [7] 7,59 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 6, 19, 27, 19 ]
27
[ "19-19=0", "6*0=0", "27+0=27" ]
Current State: 27:[6, 19, 27, 19], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [6, 27, 0] Generated Node #2: [6, 27, 0] from Operation: 19-19=0 Current State: 27:[6, 27, 0], Operations: ['19-19=0'] Exploring Operation: 6*0=0, Resulting Numbers: [27, 0] Generated Node #3: [27, 0] from Operation: 6*0=0 Current State: 27:[27, 0], Operations: ['19-19=0', '6*0=0'] Exploring Operation: 27+0=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[6, 19, 27, 19], Operations: [] Exploring Operation: 19/19=1, Resulting Numbers: [6, 27, 1] Generated Node #0,0: 27:[6, 27, 1] Operation: 19/19=1 Exploring Operation: 19-19=0, Resulting Numbers: [6, 27, 0] Generated Node #0,1: 27:[6, 27, 0] Operation: 19-19=0 Moving to Node #0,0 Current State: 27:[6, 27, 1], Operations: ['19/19=1'] Exploring Operation: 6-1=5, Resulting Numbers: [27, 5] Generated Node #0,0,0: 27:[27, 5] Operation: 6-1=5 Exploring Operation: 6+1=7, Resulting Numbers: [27, 7] Generated Node #0,0,1: 27:[27, 7] Operation: 6+1=7 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 27:[27, 5], Operations: ['19/19=1', '6-1=5'] Exploring Operation: 27-5=22, Resulting Numbers: [22] 22,27 unequal: No Solution Exploring Operation: 27+5=32, Resulting Numbers: [32] 32,27 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 27:[27, 7], Operations: ['19/19=1', '6+1=7'] Exploring Operation: 27-7=20, Resulting Numbers: [20] 20,27 unequal: No Solution Exploring Operation: 27+7=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 #0,1 Current State: 27:[6, 27, 0], Operations: ['19-19=0'] Exploring Operation: 6+0=6, Resulting Numbers: [27, 6] Generated Node #0,1,0: 27:[27, 6] Operation: 6+0=6 Exploring Operation: 6*0=0, Resulting Numbers: [27, 0] Generated Node #0,1,1: 27:[27, 0] Operation: 6*0=0 Moving to Node #0,1,0 Current State: 27:[27, 6], Operations: ['19-19=0', '6+0=6'] Exploring Operation: 27+6=33, Resulting Numbers: [33] 33,27 unequal: No Solution Exploring Operation: 27-6=21, Resulting Numbers: [21] 21,27 unequal: No Solution Moving to Node #0,1,1 Current State: 27:[27, 0], Operations: ['19-19=0', '6*0=0'] Exploring Operation: 27+0=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[6, 19, 27, 19], Operations: [] Exploring Operation: 19-19=0, Resulting Numbers: [6, 27, 0] Generated Node #0,1: 27:[6, 27, 0] Operation: 19-19=0 Moving to Node #0,1 Current State: 27:[6, 27, 0], Operations: ['19-19=0'] Exploring Operation: 6*0=0, Resulting Numbers: [27, 0] Generated Node #0,1,1: 27:[27, 0] Operation: 6*0=0 Moving to Node #0,1,1 Current State: 27:[27, 0], Operations: ['19-19=0', '6*0=0'] Exploring Operation: 27+0=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
0.985243
hs_2
mult_heuristic
[ 6, 1, 12, 19 ]
17
[ "6*1=6", "12/6=2", "19-2=17" ]
Current State: 17:[6, 1, 12, 19], Operations: [] Exploring Operation: 6*1=6, Resulting Numbers: [12, 19, 6] Generated Node #2: [12, 19, 6] from Operation: 6*1=6 Current State: 17:[12, 19, 6], Operations: ['6*1=6'] Exploring Operation: 12/6=2, Resulting Numbers: [19, 2] Generated Node #3: [19, 2] from Operation: 12/6=2 Current State: 17:[19, 2], Operations: ['6*1=6', '12/6=2'] Exploring Operation: 19-2=17, Resulting Numbers: [17] 17,17 equal: Goal Reached
4
Current State: 17:[6, 1, 12, 19], Operations: [] Exploring Operation: 6+1=7, Resulting Numbers: [12, 19, 7] Generated Node #0,0: 17:[12, 19, 7] Operation: 6+1=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 17:[12, 19, 7], Operations: ['6+1=7'] Exploring Operation: 12+7=19, Resulting Numbers: [19, 19] Generated Node #0,0,0: 17:[19, 19] Operation: 12+7=19 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 17:[19, 19], Operations: ['6+1=7', '12+7=19'] Exploring Operation: 19/19=1, Resulting Numbers: [1] 1,17 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_1
mult_heuristic
[ 42, 14, 2, 35 ]
70
[ "42-2=40", "40-35=5", "14*5=70" ]
Current State: 70:[42, 14, 2, 35], Operations: [] Exploring Operation: 42-2=40, Resulting Numbers: [14, 35, 40] Generated Node #2: [14, 35, 40] from Operation: 42-2=40 Current State: 70:[14, 35, 40], Operations: ['42-2=40'] Exploring Operation: 40-35=5, Resulting Numbers: [14, 5] Generated Node #3: [14, 5] from Operation: 40-35=5 Current State: 70:[14, 5], Operations: ['42-2=40', '40-35=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[42, 14, 2, 35], Operations: [] Exploring Operation: 42-35=7, Resulting Numbers: [14, 2, 7] Generated Node #0,0: 70:[14, 2, 7] Operation: 42-35=7 Exploring Operation: 42-2=40, Resulting Numbers: [14, 35, 40] Generated Node #0,1: 70:[14, 35, 40] Operation: 42-2=40 Exploring Operation: 42-14=28, Resulting Numbers: [2, 35, 28] Generated Node #0,2: 70:[2, 35, 28] Operation: 42-14=28 Exploring Operation: 42/2=21, Resulting Numbers: [14, 35, 21] Generated Node #0,3: 70:[14, 35, 21] Operation: 42/2=21 Exploring Operation: 42/14=3, Resulting Numbers: [2, 35, 3] Generated Node #0,4: 70:[2, 35, 3] Operation: 42/14=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[14, 2, 7], Operations: ['42-35=7'] Exploring Operation: 7-2=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 70:[14, 5] Operation: 7-2=5 Exploring Operation: 2*7=14, Resulting Numbers: [14, 14] Generated Node #0,0,1: 70:[14, 14] Operation: 2*7=14 Exploring Operation: 14/7=2, Resulting Numbers: [2, 2] Generated Node #0,0,2: 70:[2, 2] Operation: 14/7=2 Exploring Operation: 14-7=7, Resulting Numbers: [2, 7] Generated Node #0,0,3: 70:[2, 7] Operation: 14-7=7 Exploring Operation: 14/2=7, Resulting Numbers: [7, 7] Generated Node #0,0,4: 70:[7, 7] Operation: 14/2=7 Moving to Node #0,0,0 Current State: 70:[14, 5], Operations: ['42-35=7', '7-2=5'] Exploring Operation: 14+5=19, Resulting Numbers: [19] 19,70 unequal: No Solution Exploring Operation: 14-5=9, Resulting Numbers: [9] 9,70 unequal: No Solution Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Moving to Node #0 Current State: 70:[42, 14, 2, 35], Operations: [] Exploring Operation: 42-35=7, Resulting Numbers: [14, 2, 7] Generated Node #0,0: 70:[14, 2, 7] Operation: 42-35=7 Moving to Node #0,0 Current State: 70:[14, 2, 7], Operations: ['42-35=7'] Exploring Operation: 7-2=5, Resulting Numbers: [14, 5] Generated Node #0,0,0: 70:[14, 5] Operation: 7-2=5 Moving to Node #0,0,0 Current State: 70:[14, 5], Operations: ['42-35=7', '7-2=5'] Exploring Operation: 14*5=70, Resulting Numbers: [70] 70,70 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 14, 2, 6, 96 ]
68
[ "14+6=20", "96/2=48", "20+48=68" ]
Current State: 68:[14, 2, 6, 96], Operations: [] Exploring Operation: 14+6=20, Resulting Numbers: [2, 96, 20] Generated Node #2: [2, 96, 20] from Operation: 14+6=20 Current State: 68:[2, 96, 20], Operations: ['14+6=20'] Exploring Operation: 96/2=48, Resulting Numbers: [20, 48] Generated Node #3: [20, 48] from Operation: 96/2=48 Current State: 68:[20, 48], Operations: ['14+6=20', '96/2=48'] Exploring Operation: 20+48=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[14, 2, 6, 96], Operations: [] Exploring Operation: 96-6=90, Resulting Numbers: [14, 2, 90] Generated Node #0,0: 68:[14, 2, 90] Operation: 96-6=90 Exploring Operation: 96/6=16, Resulting Numbers: [14, 2, 16] Generated Node #0,1: 68:[14, 2, 16] Operation: 96/6=16 Exploring Operation: 96/2=48, Resulting Numbers: [14, 6, 48] Generated Node #0,2: 68:[14, 6, 48] Operation: 96/2=48 Exploring Operation: 96-14=82, Resulting Numbers: [2, 6, 82] Generated Node #0,3: 68:[2, 6, 82] Operation: 96-14=82 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[14, 2, 16], Operations: ['96/6=16'] Exploring Operation: 14/2=7, Resulting Numbers: [16, 7] Generated Node #0,1,0: 68:[16, 7] Operation: 14/2=7 Exploring Operation: 16-14=2, Resulting Numbers: [2, 2] Generated Node #0,1,1: 68:[2, 2] Operation: 16-14=2 Exploring Operation: 14+2=16, Resulting Numbers: [16, 16] Generated Node #0,1,2: 68:[16, 16] Operation: 14+2=16 Exploring Operation: 14+16=30, Resulting Numbers: [2, 30] Generated Node #0,1,3: 68:[2, 30] Operation: 14+16=30 Moving to Node #0,1,1 Current State: 68:[2, 2], Operations: ['96/6=16', '16-14=2'] Exploring Operation: 2-2=0, Resulting Numbers: [0] 0,68 unequal: No Solution Exploring Operation: 2+2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 2*2=4, Resulting Numbers: [4] 4,68 unequal: No Solution Exploring Operation: 2/2=1, Resulting Numbers: [1] 1,68 unequal: No Solution Moving to Node #0,1,2 Current State: 68:[16, 16], Operations: ['96/6=16', '14+2=16'] Exploring Operation: 16-16=0, Resulting Numbers: [0] 0,68 unequal: No Solution Exploring Operation: 16*16=256, Resulting Numbers: [256] 256,68 unequal: No Solution Exploring Operation: 16/16=1, Resulting Numbers: [1] 1,68 unequal: No Solution Exploring Operation: 16+16=32, Resulting Numbers: [32] 32,68 unequal: No Solution Moving to Node #0,1,3 Current State: 68:[2, 30], Operations: ['96/6=16', '14+16=30'] Exploring Operation: 30/2=15, Resulting Numbers: [15] 15,68 unequal: No Solution Exploring Operation: 30-2=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 2+30=32, Resulting Numbers: [32] 32,68 unequal: No Solution Exploring Operation: 2*30=60, Resulting Numbers: [60] 60,68 unequal: No Solution Moving to Node #0,1,0 Current State: 68:[16, 7], Operations: ['96/6=16', '14/2=7'] Exploring Operation: 16-7=9, Resulting Numbers: [9] 9,68 unequal: No Solution Exploring Operation: 16*7=112, Resulting Numbers: [112] 112,68 unequal: No Solution Exploring Operation: 16+7=23, Resulting Numbers: [23] 23,68 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 68:[2, 6, 82], Operations: ['96-14=82'] Exploring Operation: 6-2=4, Resulting Numbers: [82, 4] Generated Node #0,3,0: 68:[82, 4] Operation: 6-2=4 Exploring Operation: 82-2=80, Resulting Numbers: [6, 80] Generated Node #0,3,1: 68:[6, 80] Operation: 82-2=80 Exploring Operation: 82/2=41, Resulting Numbers: [6, 41] Generated Node #0,3,2: 68:[6, 41] Operation: 82/2=41 Exploring Operation: 82-6=76, Resulting Numbers: [2, 76] Generated Node #0,3,3: 68:[2, 76] Operation: 82-6=76 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 68:[2, 76], Operations: ['96-14=82', '82-6=76'] Exploring Operation: 76-2=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 76/2=38, Resulting Numbers: [38] 38,68 unequal: No Solution Exploring Operation: 2+76=78, Resulting Numbers: [78] 78,68 unequal: No Solution Exploring Operation: 2*76=152, Resulting Numbers: [152] 152,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 68:[6, 41], Operations: ['96-14=82', '82/2=41'] Exploring Operation: 41-6=35, Resulting Numbers: [35] 35,68 unequal: No Solution Exploring Operation: 6+41=47, Resulting Numbers: [47] 47,68 unequal: No Solution Exploring Operation: 6*41=246, Resulting Numbers: [246] 246,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 68:[82, 4], Operations: ['96-14=82', '6-2=4'] Exploring Operation: 82+4=86, Resulting Numbers: [86] 86,68 unequal: No Solution Exploring Operation: 82-4=78, Resulting Numbers: [78] 78,68 unequal: No Solution Exploring Operation: 82*4=328, Resulting Numbers: [328] 328,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 68:[6, 80], Operations: ['96-14=82', '82-2=80'] Exploring Operation: 80-6=74, Resulting Numbers: [74] 74,68 unequal: No Solution Exploring Operation: 6+80=86, Resulting Numbers: [86] 86,68 unequal: No Solution Exploring Operation: 6*80=480, Resulting Numbers: [480] 480,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 68:[14, 6, 48], Operations: ['96/2=48'] Exploring Operation: 48-14=34, Resulting Numbers: [6, 34] Generated Node #0,2,0: 68:[6, 34] Operation: 48-14=34 Exploring Operation: 14+48=62, Resulting Numbers: [6, 62] Generated Node #0,2,1: 68:[6, 62] Operation: 14+48=62 Exploring Operation: 48-6=42, Resulting Numbers: [14, 42] Generated Node #0,2,2: 68:[14, 42] Operation: 48-6=42 Exploring Operation: 48/6=8, Resulting Numbers: [14, 8] Generated Node #0,2,3: 68:[14, 8] Operation: 48/6=8 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 68:[6, 34], Operations: ['96/2=48', '48-14=34'] Exploring Operation: 6+34=40, Resulting Numbers: [40] 40,68 unequal: No Solution Exploring Operation: 34-6=28, Resulting Numbers: [28] 28,68 unequal: No Solution Exploring Operation: 6*34=204, Resulting Numbers: [204] 204,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 68:[14, 8], Operations: ['96/2=48', '48/6=8'] Exploring Operation: 14*8=112, Resulting Numbers: [112] 112,68 unequal: No Solution Exploring Operation: 14+8=22, Resulting Numbers: [22] 22,68 unequal: No Solution Exploring Operation: 14-8=6, Resulting Numbers: [6] 6,68 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 68:[6, 62], Operations: ['96/2=48', '14+48=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[14, 2, 6, 96], Operations: [] Exploring Operation: 96/2=48, Resulting Numbers: [14, 6, 48] Generated Node #0,2: 68:[14, 6, 48] Operation: 96/2=48 Moving to Node #0,2 Current State: 68:[14, 6, 48], Operations: ['96/2=48'] Exploring Operation: 14+48=62, Resulting Numbers: [6, 62] Generated Node #0,2,1: 68:[6, 62] Operation: 14+48=62 Moving to Node #0,2,1 Current State: 68:[6, 62], Operations: ['96/2=48', '14+48=62'] Exploring Operation: 6+62=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.952257
hs_4
sum_heuristic
[ 66, 44, 64, 62 ]
29
[ "66*62=4092", "4092/44=93", "93-64=29" ]
Current State: 29:[66, 44, 64, 62], Operations: [] Exploring Operation: 66*62=4092, Resulting Numbers: [44, 64, 4092] Generated Node #2: [44, 64, 4092] from Operation: 66*62=4092 Current State: 29:[44, 64, 4092], Operations: ['66*62=4092'] Exploring Operation: 4092/44=93, Resulting Numbers: [64, 93] Generated Node #3: [64, 93] from Operation: 4092/44=93 Current State: 29:[64, 93], Operations: ['66*62=4092', '4092/44=93'] Exploring Operation: 93-64=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[66, 44, 64, 62], Operations: [] Exploring Operation: 66-44=22, Resulting Numbers: [64, 62, 22] Generated Node #0,0: 29:[64, 62, 22] Operation: 66-44=22 Moving to Node #0,0 Current State: 29:[64, 62, 22], Operations: ['66-44=22'] Exploring Operation: 64-62=2, Resulting Numbers: [22, 2] Generated Node #0,0,0: 29:[22, 2] Operation: 64-62=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 29:[22, 2], Operations: ['66-44=22', '64-62=2'] Exploring Operation: 22+2=24, Resulting Numbers: [24] 24,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 88, 41, 86, 12 ]
31
[ "88+41=129", "86+12=98", "129-98=31" ]
Current State: 31:[88, 41, 86, 12], Operations: [] Exploring Operation: 88+41=129, Resulting Numbers: [86, 12, 129] Generated Node #2: [86, 12, 129] from Operation: 88+41=129 Current State: 31:[86, 12, 129], Operations: ['88+41=129'] Exploring Operation: 86+12=98, Resulting Numbers: [129, 98] Generated Node #3: [129, 98] from Operation: 86+12=98 Current State: 31:[129, 98], Operations: ['88+41=129', '86+12=98'] Exploring Operation: 129-98=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[88, 41, 86, 12], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [41, 12, 2] Generated Node #0,0: 31:[41, 12, 2] Operation: 88-86=2 Exploring Operation: 86-41=45, Resulting Numbers: [88, 12, 45] Generated Node #0,1: 31:[88, 12, 45] Operation: 86-41=45 Exploring Operation: 88-41=47, Resulting Numbers: [86, 12, 47] Generated Node #0,2: 31:[86, 12, 47] Operation: 88-41=47 Exploring Operation: 88-12=76, Resulting Numbers: [41, 86, 76] Generated Node #0,3: 31:[41, 86, 76] Operation: 88-12=76 Start Sub Search at level 1: Moving to Node #0,0 Current State: 31:[41, 12, 2], Operations: ['88-86=2'] Exploring Operation: 12+2=14, Resulting Numbers: [41, 14] Generated Node #0,0,0: 31:[41, 14] Operation: 12+2=14 Exploring Operation: 12*2=24, Resulting Numbers: [41, 24] Generated Node #0,0,1: 31:[41, 24] Operation: 12*2=24 Exploring Operation: 41-2=39, Resulting Numbers: [12, 39] Generated Node #0,0,2: 31:[12, 39] Operation: 41-2=39 Exploring Operation: 41-12=29, Resulting Numbers: [2, 29] Generated Node #0,0,3: 31:[2, 29] Operation: 41-12=29 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 31:[41, 24], Operations: ['88-86=2', '12*2=24'] Exploring Operation: 41+24=65, Resulting Numbers: [65] 65,31 unequal: No Solution Exploring Operation: 41*24=984, Resulting Numbers: [984] 984,31 unequal: No Solution Exploring Operation: 41-24=17, Resulting Numbers: [17] 17,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 31:[41, 14], Operations: ['88-86=2', '12+2=14'] Exploring Operation: 41+14=55, Resulting Numbers: [55] 55,31 unequal: No Solution Exploring Operation: 41*14=574, Resulting Numbers: [574] 574,31 unequal: No Solution Exploring Operation: 41-14=27, Resulting Numbers: [27] 27,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 31:[12, 39], Operations: ['88-86=2', '41-2=39'] Exploring Operation: 12*39=468, Resulting Numbers: [468] 468,31 unequal: No Solution Exploring Operation: 12+39=51, Resulting Numbers: [51] 51,31 unequal: No Solution Exploring Operation: 39-12=27, Resulting Numbers: [27] 27,31 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 31:[2, 29], Operations: ['88-86=2', '41-12=29'] Exploring Operation: 29-2=27, Resulting Numbers: [27] 27,31 unequal: No Solution Exploring Operation: 2*29=58, Resulting Numbers: [58] 58,31 unequal: No Solution Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Moving to Node #0 Current State: 31:[88, 41, 86, 12], Operations: [] Exploring Operation: 88-86=2, Resulting Numbers: [41, 12, 2] Generated Node #0,0: 31:[41, 12, 2] Operation: 88-86=2 Moving to Node #0,0 Current State: 31:[41, 12, 2], Operations: ['88-86=2'] Exploring Operation: 41-12=29, Resulting Numbers: [2, 29] Generated Node #0,0,3: 31:[2, 29] Operation: 41-12=29 Moving to Node #0,0,3 Current State: 31:[2, 29], Operations: ['88-86=2', '41-12=29'] Exploring Operation: 2+29=31, Resulting Numbers: [31] 31,31 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.979167
hs_4
sum_heuristic
[ 81, 77, 86, 5 ]
76
[ "86-81=5", "5/5=1", "77-1=76" ]
Current State: 76:[81, 77, 86, 5], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [77, 5, 5] Generated Node #2: [77, 5, 5] from Operation: 86-81=5 Current State: 76:[77, 5, 5], Operations: ['86-81=5'] Exploring Operation: 5/5=1, Resulting Numbers: [77, 1] Generated Node #3: [77, 1] from Operation: 5/5=1 Current State: 76:[77, 1], Operations: ['86-81=5', '5/5=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[81, 77, 86, 5], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [77, 5, 5] Generated Node #0,0: 76:[77, 5, 5] Operation: 86-81=5 Exploring Operation: 81-5=76, Resulting Numbers: [77, 86, 76] Generated Node #0,1: 76:[77, 86, 76] Operation: 81-5=76 Exploring Operation: 81-77=4, Resulting Numbers: [86, 5, 4] Generated Node #0,2: 76:[86, 5, 4] Operation: 81-77=4 Exploring Operation: 86-77=9, Resulting Numbers: [81, 5, 9] Generated Node #0,3: 76:[81, 5, 9] Operation: 86-77=9 Moving to Node #0,0 Current State: 76:[77, 5, 5], Operations: ['86-81=5'] Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,0: 76:[5, 72] Operation: 77-5=72 Exploring Operation: 5-5=0, Resulting Numbers: [77, 0] Generated Node #0,0,1: 76:[77, 0] Operation: 5-5=0 Exploring Operation: 5/5=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 76:[77, 1] Operation: 5/5=1 Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,3: 76:[5, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 76:[77, 1], Operations: ['86-81=5', '5/5=1'] Exploring Operation: 77+1=78, Resulting Numbers: [78] 78,76 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,76 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[81, 77, 86, 5], Operations: [] Exploring Operation: 86-81=5, Resulting Numbers: [77, 5, 5] Generated Node #0,0: 76:[77, 5, 5] Operation: 86-81=5 Moving to Node #0,0 Current State: 76:[77, 5, 5], Operations: ['86-81=5'] Exploring Operation: 5/5=1, Resulting Numbers: [77, 1] Generated Node #0,0,2: 76:[77, 1] Operation: 5/5=1 Moving to Node #0,0,2 Current State: 76:[77, 1], Operations: ['86-81=5', '5/5=1'] Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 17, 36, 90, 6 ]
65
[ "36-17=19", "90-6=84", "84-19=65" ]
Current State: 65:[17, 36, 90, 6], Operations: [] Exploring Operation: 36-17=19, Resulting Numbers: [90, 6, 19] Generated Node #2: [90, 6, 19] from Operation: 36-17=19 Current State: 65:[90, 6, 19], Operations: ['36-17=19'] Exploring Operation: 90-6=84, Resulting Numbers: [19, 84] Generated Node #3: [19, 84] from Operation: 90-6=84 Current State: 65:[19, 84], Operations: ['36-17=19', '90-6=84'] Exploring Operation: 84-19=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[17, 36, 90, 6], Operations: [] Exploring Operation: 36/6=6, Resulting Numbers: [17, 90, 6] Generated Node #0,0: 65:[17, 90, 6] Operation: 36/6=6 Exploring Operation: 36-17=19, Resulting Numbers: [90, 6, 19] Generated Node #0,1: 65:[90, 6, 19] Operation: 36-17=19 Exploring Operation: 90-36=54, Resulting Numbers: [17, 6, 54] Generated Node #0,2: 65:[17, 6, 54] Operation: 90-36=54 Exploring Operation: 90-17=73, Resulting Numbers: [36, 6, 73] Generated Node #0,3: 65:[36, 6, 73] Operation: 90-17=73 Exploring Operation: 90/6=15, Resulting Numbers: [17, 36, 15] Generated Node #0,4: 65:[17, 36, 15] Operation: 90/6=15 Moving to Node #0,2 Current State: 65:[17, 6, 54], Operations: ['90-36=54'] Exploring Operation: 17+54=71, Resulting Numbers: [6, 71] Generated Node #0,2,0: 65:[6, 71] Operation: 17+54=71 Exploring Operation: 6+54=60, Resulting Numbers: [17, 60] Generated Node #0,2,1: 65:[17, 60] Operation: 6+54=60 Exploring Operation: 17-6=11, Resulting Numbers: [54, 11] Generated Node #0,2,2: 65:[54, 11] Operation: 17-6=11 Exploring Operation: 54/6=9, Resulting Numbers: [17, 9] Generated Node #0,2,3: 65:[17, 9] Operation: 54/6=9 Exploring Operation: 17+6=23, Resulting Numbers: [54, 23] Generated Node #0,2,4: 65:[54, 23] Operation: 17+6=23 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[6, 71], Operations: ['90-36=54', '17+54=71'] Exploring Operation: 6+71=77, Resulting Numbers: [77] 77,65 unequal: No Solution Exploring Operation: 6*71=426, Resulting Numbers: [426] 426,65 unequal: No Solution Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[17, 36, 90, 6], Operations: [] Exploring Operation: 90-36=54, Resulting Numbers: [17, 6, 54] Generated Node #0,2: 65:[17, 6, 54] Operation: 90-36=54 Moving to Node #0,2 Current State: 65:[17, 6, 54], Operations: ['90-36=54'] Exploring Operation: 17+54=71, Resulting Numbers: [6, 71] Generated Node #0,2,0: 65:[6, 71] Operation: 17+54=71 Moving to Node #0,2,0 Current State: 65:[6, 71], Operations: ['90-36=54', '17+54=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.985243
hs_5
mult_heuristic
[ 86, 44, 37, 87 ]
74
[ "86*37=3182", "87-44=43", "3182/43=74" ]
Current State: 74:[86, 44, 37, 87], Operations: [] Exploring Operation: 86*37=3182, Resulting Numbers: [44, 87, 3182] Generated Node #2: [44, 87, 3182] from Operation: 86*37=3182 Current State: 74:[44, 87, 3182], Operations: ['86*37=3182'] Exploring Operation: 87-44=43, Resulting Numbers: [3182, 43] Generated Node #3: [3182, 43] from Operation: 87-44=43 Current State: 74:[3182, 43], Operations: ['86*37=3182', '87-44=43'] Exploring Operation: 3182/43=74, Resulting Numbers: [74] 74,74 equal: Goal Reached
4
Current State: 74:[86, 44, 37, 87], Operations: [] Exploring Operation: 44-37=7, Resulting Numbers: [86, 87, 7] Generated Node #0,0: 74:[86, 87, 7] Operation: 44-37=7 Exploring Operation: 86-37=49, Resulting Numbers: [44, 87, 49] Generated Node #0,1: 74:[44, 87, 49] Operation: 86-37=49 Exploring Operation: 87-86=1, Resulting Numbers: [44, 37, 1] Generated Node #0,2: 74:[44, 37, 1] Operation: 87-86=1 Exploring Operation: 87-44=43, Resulting Numbers: [86, 37, 43] Generated Node #0,3: 74:[86, 37, 43] Operation: 87-44=43 Exploring Operation: 86-44=42, Resulting Numbers: [37, 87, 42] Generated Node #0,4: 74:[37, 87, 42] Operation: 86-44=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 74:[44, 37, 1], Operations: ['87-86=1'] Exploring Operation: 44/1=44, Resulting Numbers: [37, 44] Generated Node #0,2,0: 74:[37, 44] Operation: 44/1=44 Exploring Operation: 44-37=7, Resulting Numbers: [1, 7] Generated Node #0,2,1: 74:[1, 7] Operation: 44-37=7 Exploring Operation: 44*1=44, Resulting Numbers: [37, 44] Generated Node #0,2,2: 74:[37, 44] Operation: 44*1=44 Exploring Operation: 37*1=37, Resulting Numbers: [44, 37] Generated Node #0,2,3: 74:[44, 37] Operation: 37*1=37 Exploring Operation: 44-1=43, Resulting Numbers: [37, 43] Generated Node #0,2,4: 74:[37, 43] Operation: 44-1=43 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 74:[1, 7], Operations: ['87-86=1', '44-37=7'] Exploring Operation: 1*7=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 1+7=8, Resulting Numbers: [8] 8,74 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,74 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 #0,2,4 Current State: 74:[37, 43], Operations: ['87-86=1', '44-1=43'] Exploring Operation: 43-37=6, Resulting Numbers: [6] 6,74 unequal: No Solution Exploring Operation: 37+43=80, Resulting Numbers: [80] 80,74 unequal: No Solution Exploring Operation: 37*43=1591, Resulting Numbers: [1591] 1591,74 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 #0,2,0 Current State: 74:[37, 44], Operations: ['87-86=1', '44/1=44'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 37*44=1628, Resulting Numbers: [1628] 1628,74 unequal: No Solution Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,74 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:[37, 44], Operations: ['87-86=1', '44*1=44'] Exploring Operation: 37*44=1628, Resulting Numbers: [1628] 1628,74 unequal: No Solution Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 37+44=81, Resulting Numbers: [81] 81,74 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 #0,2,3 Current State: 74:[44, 37], Operations: ['87-86=1', '37*1=37'] Exploring Operation: 44-37=7, Resulting Numbers: [7] 7,74 unequal: No Solution Exploring Operation: 44+37=81, Resulting Numbers: [81] 81,74 unequal: No Solution Exploring Operation: 44*37=1628, Resulting Numbers: [1628] 1628,74 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 #0,3 Current State: 74:[86, 37, 43], Operations: ['87-44=43'] Exploring Operation: 86/43=2, Resulting Numbers: [37, 2] Generated Node #0,3,0: 74:[37, 2] Operation: 86/43=2 Exploring Operation: 86-43=43, Resulting Numbers: [37, 43] Generated Node #0,3,1: 74:[37, 43] Operation: 86-43=43 Exploring Operation: 86-37=49, Resulting Numbers: [43, 49] Generated Node #0,3,2: 74:[43, 49] Operation: 86-37=49 Exploring Operation: 37+43=80, Resulting Numbers: [86, 80] Generated Node #0,3,3: 74:[86, 80] Operation: 37+43=80 Exploring Operation: 43-37=6, Resulting Numbers: [86, 6] Generated Node #0,3,4: 74:[86, 6] Operation: 43-37=6 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 74:[37, 2], Operations: ['87-44=43', '86/43=2'] Exploring Operation: 37-2=35, Resulting Numbers: [35] 35,74 unequal: No Solution Exploring Operation: 37+2=39, Resulting Numbers: [39] 39,74 unequal: No Solution Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Moving to Node #0 Current State: 74:[86, 44, 37, 87], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [86, 37, 43] Generated Node #0,3: 74:[86, 37, 43] Operation: 87-44=43 Moving to Node #0,3 Current State: 74:[86, 37, 43], Operations: ['87-44=43'] Exploring Operation: 86/43=2, Resulting Numbers: [37, 2] Generated Node #0,3,0: 74:[37, 2] Operation: 86/43=2 Moving to Node #0,3,0 Current State: 74:[37, 2], Operations: ['87-44=43', '86/43=2'] Exploring Operation: 37*2=74, Resulting Numbers: [74] 74,74 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967014
hs_5
mult_heuristic
[ 56, 2, 3, 72 ]
50
[ "72-56=16", "3*16=48", "2+48=50" ]
Current State: 50:[56, 2, 3, 72], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [2, 3, 16] Generated Node #2: [2, 3, 16] from Operation: 72-56=16 Current State: 50:[2, 3, 16], Operations: ['72-56=16'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #3: [2, 48] from Operation: 3*16=48 Current State: 50:[2, 48], Operations: ['72-56=16', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[56, 2, 3, 72], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [2, 3, 16] Generated Node #0,0: 50:[2, 3, 16] Operation: 72-56=16 Moving to Node #0,0 Current State: 50:[2, 3, 16], Operations: ['72-56=16'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 3*16=48 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['72-56=16', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[56, 2, 3, 72], Operations: [] Exploring Operation: 72-56=16, Resulting Numbers: [2, 3, 16] Generated Node #0,0: 50:[2, 3, 16] Operation: 72-56=16 Moving to Node #0,0 Current State: 50:[2, 3, 16], Operations: ['72-56=16'] Exploring Operation: 3*16=48, Resulting Numbers: [2, 48] Generated Node #0,0,0: 50:[2, 48] Operation: 3*16=48 Moving to Node #0,0,0 Current State: 50:[2, 48], Operations: ['72-56=16', '3*16=48'] Exploring Operation: 2+48=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 55, 73, 30, 88 ]
25
[ "30*88=2640", "2640/55=48", "73-48=25" ]
Current State: 25:[55, 73, 30, 88], Operations: [] Exploring Operation: 30*88=2640, Resulting Numbers: [55, 73, 2640] Generated Node #2: [55, 73, 2640] from Operation: 30*88=2640 Current State: 25:[55, 73, 2640], Operations: ['30*88=2640'] Exploring Operation: 2640/55=48, Resulting Numbers: [73, 48] Generated Node #3: [73, 48] from Operation: 2640/55=48 Current State: 25:[73, 48], Operations: ['30*88=2640', '2640/55=48'] Exploring Operation: 73-48=25, Resulting Numbers: [25] 25,25 equal: Goal Reached
4
Current State: 25:[55, 73, 30, 88], Operations: [] Exploring Operation: 88-55=33, Resulting Numbers: [73, 30, 33] Generated Node #0,0: 25:[73, 30, 33] Operation: 88-55=33 Exploring Operation: 88-73=15, Resulting Numbers: [55, 30, 15] Generated Node #0,1: 25:[55, 30, 15] Operation: 88-73=15 Moving to Node #0,1 Current State: 25:[55, 30, 15], Operations: ['88-73=15'] Exploring Operation: 55-30=25, Resulting Numbers: [15, 25] Generated Node #0,1,0: 25:[15, 25] Operation: 55-30=25 Exploring Operation: 55-15=40, Resulting Numbers: [30, 40] Generated Node #0,1,1: 25:[30, 40] Operation: 55-15=40 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 25:[15, 25], Operations: ['88-73=15', '55-30=25'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 15+25=40, Resulting Numbers: [40] 40,25 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 #0,1,1 Current State: 25:[30, 40], Operations: ['88-73=15', '55-15=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,25 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: 25:[73, 30, 33], Operations: ['88-55=33'] Exploring Operation: 73-33=40, Resulting Numbers: [30, 40] Generated Node #0,0,0: 25:[30, 40] Operation: 73-33=40 Exploring Operation: 73-30=43, Resulting Numbers: [33, 43] Generated Node #0,0,1: 25:[33, 43] Operation: 73-30=43 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 25:[30, 40], Operations: ['88-55=33', '73-33=40'] Exploring Operation: 40-30=10, Resulting Numbers: [10] 10,25 unequal: No Solution Exploring Operation: 30+40=70, Resulting Numbers: [70] 70,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 25:[33, 43], Operations: ['88-55=33', '73-30=43'] Exploring Operation: 33+43=76, Resulting Numbers: [76] 76,25 unequal: No Solution Exploring Operation: 43-33=10, Resulting Numbers: [10] 10,25 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 95, 79, 34, 17 ]
67
[ "95-79=16", "34+17=51", "16+51=67" ]
Current State: 67:[95, 79, 34, 17], Operations: [] Exploring Operation: 95-79=16, Resulting Numbers: [34, 17, 16] Generated Node #2: [34, 17, 16] from Operation: 95-79=16 Current State: 67:[34, 17, 16], Operations: ['95-79=16'] Exploring Operation: 34+17=51, Resulting Numbers: [16, 51] Generated Node #3: [16, 51] from Operation: 34+17=51 Current State: 67:[16, 51], Operations: ['95-79=16', '34+17=51'] Exploring Operation: 16+51=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[95, 79, 34, 17], Operations: [] Exploring Operation: 95-34=61, Resulting Numbers: [79, 17, 61] Generated Node #0,0: 67:[79, 17, 61] Operation: 95-34=61 Exploring Operation: 95-17=78, Resulting Numbers: [79, 34, 78] Generated Node #0,1: 67:[79, 34, 78] Operation: 95-17=78 Exploring Operation: 95+17=112, Resulting Numbers: [79, 34, 112] Generated Node #0,2: 67:[79, 34, 112] Operation: 95+17=112 Exploring Operation: 34+17=51, Resulting Numbers: [95, 79, 51] Generated Node #0,3: 67:[95, 79, 51] Operation: 34+17=51 Exploring Operation: 79-17=62, Resulting Numbers: [95, 34, 62] Generated Node #0,4: 67:[95, 34, 62] Operation: 79-17=62 Start Sub Search at level 1: Moving to Node #0,1 Current State: 67:[79, 34, 78], Operations: ['95-17=78'] Exploring Operation: 79-78=1, Resulting Numbers: [34, 1] Generated Node #0,1,0: 67:[34, 1] Operation: 79-78=1 Exploring Operation: 79-34=45, Resulting Numbers: [78, 45] Generated Node #0,1,1: 67:[78, 45] Operation: 79-34=45 Exploring Operation: 34+78=112, Resulting Numbers: [79, 112] Generated Node #0,1,2: 67:[79, 112] Operation: 34+78=112 Exploring Operation: 78-34=44, Resulting Numbers: [79, 44] Generated Node #0,1,3: 67:[79, 44] Operation: 78-34=44 Exploring Operation: 79+34=113, Resulting Numbers: [78, 113] Generated Node #0,1,4: 67:[78, 113] Operation: 79+34=113 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 67:[78, 45], Operations: ['95-17=78', '79-34=45'] Exploring Operation: 78*45=3510, Resulting Numbers: [3510] 3510,67 unequal: No Solution Exploring Operation: 78+45=123, Resulting Numbers: [123] 123,67 unequal: No Solution Exploring Operation: 78-45=33, Resulting Numbers: [33] 33,67 unequal: No Solution No 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: 67:[79, 44], Operations: ['95-17=78', '78-34=44'] Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,67 unequal: No Solution Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,67 unequal: No Solution No 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: 67:[79, 112], Operations: ['95-17=78', '34+78=112'] Exploring Operation: 112-79=33, Resulting Numbers: [33] 33,67 unequal: No Solution Exploring Operation: 79+112=191, Resulting Numbers: [191] 191,67 unequal: No Solution Exploring Operation: 79*112=8848, Resulting Numbers: [8848] 8848,67 unequal: No Solution No 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: 67:[78, 113], Operations: ['95-17=78', '79+34=113'] Exploring Operation: 78+113=191, Resulting Numbers: [191] 191,67 unequal: No Solution Exploring Operation: 113-78=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 78*113=8814, Resulting Numbers: [8814] 8814,67 unequal: No Solution No 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: 67:[34, 1], Operations: ['95-17=78', '79-78=1'] Exploring Operation: 34*1=34, Resulting Numbers: [34] 34,67 unequal: No Solution Exploring Operation: 34/1=34, Resulting Numbers: [34] 34,67 unequal: No Solution Exploring Operation: 34+1=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 34-1=33, Resulting Numbers: [33] 33,67 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: 67:[95, 79, 51], Operations: ['34+17=51'] Exploring Operation: 79-51=28, Resulting Numbers: [95, 28] Generated Node #0,3,0: 67:[95, 28] Operation: 79-51=28 Exploring Operation: 95-79=16, Resulting Numbers: [51, 16] Generated Node #0,3,1: 67:[51, 16] Operation: 95-79=16 Exploring Operation: 79+51=130, Resulting Numbers: [95, 130] Generated Node #0,3,2: 67:[95, 130] Operation: 79+51=130 Exploring Operation: 95-51=44, Resulting Numbers: [79, 44] Generated Node #0,3,3: 67:[79, 44] Operation: 95-51=44 Exploring Operation: 95+51=146, Resulting Numbers: [79, 146] Generated Node #0,3,4: 67:[79, 146] Operation: 95+51=146 Moving to Node #0,3,3 Current State: 67:[79, 44], Operations: ['34+17=51', '95-51=44'] Exploring Operation: 79+44=123, Resulting Numbers: [123] 123,67 unequal: No Solution Exploring Operation: 79-44=35, Resulting Numbers: [35] 35,67 unequal: No Solution Exploring Operation: 79*44=3476, Resulting Numbers: [3476] 3476,67 unequal: No Solution Moving to Node #0,3,1 Current State: 67:[51, 16], Operations: ['34+17=51', '95-79=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[95, 79, 34, 17], Operations: [] Exploring Operation: 34+17=51, Resulting Numbers: [95, 79, 51] Generated Node #0,3: 67:[95, 79, 51] Operation: 34+17=51 Moving to Node #0,3 Current State: 67:[95, 79, 51], Operations: ['34+17=51'] Exploring Operation: 95-79=16, Resulting Numbers: [51, 16] Generated Node #0,3,1: 67:[51, 16] Operation: 95-79=16 Moving to Node #0,3,1 Current State: 67:[51, 16], Operations: ['34+17=51', '95-79=16'] Exploring Operation: 51+16=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.966146
hs_5
mult_heuristic
[ 1, 74, 91, 18 ]
79
[ "91-1=90", "90/18=5", "74+5=79" ]
Current State: 79:[1, 74, 91, 18], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [74, 18, 90] Generated Node #2: [74, 18, 90] from Operation: 91-1=90 Current State: 79:[74, 18, 90], Operations: ['91-1=90'] Exploring Operation: 90/18=5, Resulting Numbers: [74, 5] Generated Node #3: [74, 5] from Operation: 90/18=5 Current State: 79:[74, 5], Operations: ['91-1=90', '90/18=5'] Exploring Operation: 74+5=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[1, 74, 91, 18], Operations: [] Exploring Operation: 91-1=90, Resulting Numbers: [74, 18, 90] Generated Node #0,0: 79:[74, 18, 90] Operation: 91-1=90 Exploring Operation: 1+74=75, Resulting Numbers: [91, 18, 75] Generated Node #0,1: 79:[91, 18, 75] Operation: 1+74=75 Exploring Operation: 1+18=19, Resulting Numbers: [74, 91, 19] Generated Node #0,2: 79:[74, 91, 19] Operation: 1+18=19 Moving to Node #0,0 Current State: 79:[74, 18, 90], Operations: ['91-1=90'] Exploring Operation: 74+18=92, Resulting Numbers: [90, 92] Generated Node #0,0,0: 79:[90, 92] Operation: 74+18=92 Exploring Operation: 74-18=56, Resulting Numbers: [90, 56] Generated Node #0,0,1: 79:[90, 56] Operation: 74-18=56 Exploring Operation: 90-18=72, Resulting Numbers: [74, 72] Generated Node #0,0,2: 79:[74, 72] Operation: 90-18=72 Moving to Node #0,1 Current State: 79:[91, 18, 75], Operations: ['1+74=75'] Exploring Operation: 91-18=73, Resulting Numbers: [75, 73] Generated Node #0,1,0: 79:[75, 73] Operation: 91-18=73 Exploring Operation: 91+18=109, Resulting Numbers: [75, 109] Generated Node #0,1,1: 79:[75, 109] Operation: 91+18=109 Exploring Operation: 18+75=93, Resulting Numbers: [91, 93] Generated Node #0,1,2: 79:[91, 93] Operation: 18+75=93 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 79:[75, 73], Operations: ['1+74=75', '91-18=73'] Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 75*73=5475, Resulting Numbers: [5475] 5475,79 unequal: No Solution Exploring Operation: 75+73=148, Resulting Numbers: [148] 148,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 79:[91, 93], Operations: ['1+74=75', '18+75=93'] Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,79 unequal: No Solution Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 79:[75, 109], Operations: ['1+74=75', '91+18=109'] Exploring Operation: 109-75=34, Resulting Numbers: [34] 34,79 unequal: No Solution Exploring Operation: 75*109=8175, Resulting Numbers: [8175] 8175,79 unequal: No Solution Exploring Operation: 75+109=184, Resulting Numbers: [184] 184,79 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: 79:[74, 91, 19], Operations: ['1+18=19'] Exploring Operation: 74+19=93, Resulting Numbers: [91, 93] Generated Node #0,2,0: 79:[91, 93] Operation: 74+19=93 Exploring Operation: 74-19=55, Resulting Numbers: [91, 55] Generated Node #0,2,1: 79:[91, 55] Operation: 74-19=55 Exploring Operation: 91-19=72, Resulting Numbers: [74, 72] Generated Node #0,2,2: 79:[74, 72] Operation: 91-19=72 Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 79:[74, 72], Operations: ['1+18=19', '91-19=72'] Exploring Operation: 74*72=5328, Resulting Numbers: [5328] 5328,79 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 74+72=146, Resulting Numbers: [146] 146,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 79:[91, 93], Operations: ['1+18=19', '74+19=93'] Exploring Operation: 93-91=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 91+93=184, Resulting Numbers: [184] 184,79 unequal: No Solution Exploring Operation: 91*93=8463, Resulting Numbers: [8463] 8463,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 79:[91, 55], Operations: ['1+18=19', '74-19=55'] Exploring Operation: 91+55=146, Resulting Numbers: [146] 146,79 unequal: No Solution Exploring Operation: 91*55=5005, Resulting Numbers: [5005] 5005,79 unequal: No Solution Exploring Operation: 91-55=36, Resulting Numbers: [36] 36,79 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,2 Current State: 79:[74, 72], Operations: ['91-1=90', '90-18=72'] Exploring Operation: 74+72=146, Resulting Numbers: [146] 146,79 unequal: No Solution Exploring Operation: 74-72=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 74*72=5328, Resulting Numbers: [5328] 5328,79 unequal: No Solution Moving to Node #0,0,0 Current State: 79:[90, 92], Operations: ['91-1=90', '74+18=92'] Exploring Operation: 92-90=2, Resulting Numbers: [2] 2,79 unequal: No Solution Exploring Operation: 90+92=182, Resulting Numbers: [182] 182,79 unequal: No Solution Exploring Operation: 90*92=8280, Resulting Numbers: [8280] 8280,79 unequal: No Solution Moving to Node #0,0,1 Current State: 79:[90, 56], Operations: ['91-1=90', '74-18=56'] Exploring Operation: 90*56=5040, Resulting Numbers: [5040] 5040,79 unequal: No Solution Exploring Operation: 90+56=146, Resulting Numbers: [146] 146,79 unequal: No Solution Exploring Operation: 90-56=34, Resulting Numbers: [34] 34,79 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 80, 65, 28, 15 ]
75
[ "28-15=13", "65/13=5", "80-5=75" ]
Current State: 75:[80, 65, 28, 15], Operations: [] Exploring Operation: 28-15=13, Resulting Numbers: [80, 65, 13] Generated Node #2: [80, 65, 13] from Operation: 28-15=13 Current State: 75:[80, 65, 13], Operations: ['28-15=13'] Exploring Operation: 65/13=5, Resulting Numbers: [80, 5] Generated Node #3: [80, 5] from Operation: 65/13=5 Current State: 75:[80, 5], Operations: ['28-15=13', '65/13=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[80, 65, 28, 15], Operations: [] Exploring Operation: 28-15=13, Resulting Numbers: [80, 65, 13] Generated Node #0,0: 75:[80, 65, 13] Operation: 28-15=13 Exploring Operation: 65-28=37, Resulting Numbers: [80, 15, 37] Generated Node #0,1: 75:[80, 15, 37] Operation: 65-28=37 Exploring Operation: 80-15=65, Resulting Numbers: [65, 28, 65] Generated Node #0,2: 75:[65, 28, 65] Operation: 80-15=65 Exploring Operation: 65+15=80, Resulting Numbers: [80, 28, 80] Generated Node #0,3: 75:[80, 28, 80] Operation: 65+15=80 Exploring Operation: 80-65=15, Resulting Numbers: [28, 15, 15] Generated Node #0,4: 75:[28, 15, 15] Operation: 80-65=15 Start Sub Search at level 1: Moving to Node #0,4 Current State: 75:[28, 15, 15], Operations: ['80-65=15'] Exploring Operation: 15+15=30, Resulting Numbers: [28, 30] Generated Node #0,4,0: 75:[28, 30] Operation: 15+15=30 Exploring Operation: 28-15=13, Resulting Numbers: [15, 13] Generated Node #0,4,1: 75:[15, 13] Operation: 28-15=13 Exploring Operation: 28-15=13, Resulting Numbers: [15, 13] Generated Node #0,4,2: 75:[15, 13] Operation: 28-15=13 Exploring Operation: 15/15=1, Resulting Numbers: [28, 1] Generated Node #0,4,3: 75:[28, 1] Operation: 15/15=1 Exploring Operation: 15-15=0, Resulting Numbers: [28, 0] Generated Node #0,4,4: 75:[28, 0] Operation: 15-15=0 Moving to Node #0,4,1 Current State: 75:[15, 13], Operations: ['80-65=15', '28-15=13'] Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,75 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,75 unequal: No Solution Moving to Node #0,4,2 Current State: 75:[15, 13], Operations: ['80-65=15', '28-15=13'] Exploring Operation: 15*13=195, Resulting Numbers: [195] 195,75 unequal: No Solution Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 15+13=28, Resulting Numbers: [28] 28,75 unequal: No Solution Moving to Node #0,4,3 Current State: 75:[28, 1], Operations: ['80-65=15', '15/15=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,75 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,75 unequal: No Solution Moving to Node #0,4,4 Current State: 75:[28, 0], Operations: ['80-65=15', '15-15=0'] Exploring Operation: 28-0=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Moving to Node #0,4,0 Current State: 75:[28, 30], Operations: ['80-65=15', '15+15=30'] Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,75 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 75:[80, 28, 80], Operations: ['65+15=80'] Exploring Operation: 80-28=52, Resulting Numbers: [80, 52] Generated Node #0,3,0: 75:[80, 52] Operation: 80-28=52 Exploring Operation: 80+28=108, Resulting Numbers: [80, 108] Generated Node #0,3,1: 75:[80, 108] Operation: 80+28=108 Exploring Operation: 80/80=1, Resulting Numbers: [28, 1] Generated Node #0,3,2: 75:[28, 1] Operation: 80/80=1 Exploring Operation: 80-28=52, Resulting Numbers: [80, 52] Generated Node #0,3,3: 75:[80, 52] Operation: 80-28=52 Exploring Operation: 80-80=0, Resulting Numbers: [28, 0] Generated Node #0,3,4: 75:[28, 0] Operation: 80-80=0 Moving to Node #0,3,2 Current State: 75:[28, 1], Operations: ['65+15=80', '80/80=1'] Exploring Operation: 28*1=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28/1=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28+1=29, Resulting Numbers: [29] 29,75 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,75 unequal: No Solution Moving to Node #0,3,4 Current State: 75:[28, 0], Operations: ['65+15=80', '80-80=0'] Exploring Operation: 28-0=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28+0=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 28*0=0, Resulting Numbers: [0] 0,75 unequal: No Solution Moving to Node #0,3,0 Current State: 75:[80, 52], Operations: ['65+15=80', '80-28=52'] Exploring Operation: 80*52=4160, Resulting Numbers: [4160] 4160,75 unequal: No Solution Exploring Operation: 80-52=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 80+52=132, Resulting Numbers: [132] 132,75 unequal: No Solution Moving to Node #0,3,3 Current State: 75:[80, 52], Operations: ['65+15=80', '80-28=52'] Exploring Operation: 80*52=4160, Resulting Numbers: [4160] 4160,75 unequal: No Solution Exploring Operation: 80+52=132, Resulting Numbers: [132] 132,75 unequal: No Solution Exploring Operation: 80-52=28, Resulting Numbers: [28] 28,75 unequal: No Solution Moving to Node #0,3,1 Current State: 75:[80, 108], Operations: ['65+15=80', '80+28=108'] Exploring Operation: 108-80=28, Resulting Numbers: [28] 28,75 unequal: No Solution Exploring Operation: 80*108=8640, Resulting Numbers: [8640] 8640,75 unequal: No Solution Exploring Operation: 80+108=188, Resulting Numbers: [188] 188,75 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 75:[80, 65, 13], Operations: ['28-15=13'] Exploring Operation: 80+13=93, Resulting Numbers: [65, 93] Generated Node #0,0,0: 75:[65, 93] Operation: 80+13=93 Exploring Operation: 65/13=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 75:[80, 5] Operation: 65/13=5 Exploring Operation: 80-13=67, Resulting Numbers: [65, 67] Generated Node #0,0,2: 75:[65, 67] Operation: 80-13=67 Exploring Operation: 80-65=15, Resulting Numbers: [13, 15] Generated Node #0,0,3: 75:[13, 15] Operation: 80-65=15 Exploring Operation: 65+13=78, Resulting Numbers: [80, 78] Generated Node #0,0,4: 75:[80, 78] Operation: 65+13=78 Moving to Node #0,0,3 Current State: 75:[13, 15], Operations: ['28-15=13', '80-65=15'] Exploring Operation: 15-13=2, Resulting Numbers: [2] 2,75 unequal: No Solution Exploring Operation: 13*15=195, Resulting Numbers: [195] 195,75 unequal: No Solution Exploring Operation: 13+15=28, Resulting Numbers: [28] 28,75 unequal: No Solution Moving to Node #0,0,1 Current State: 75:[80, 5], Operations: ['28-15=13', '65/13=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[80, 65, 28, 15], Operations: [] Exploring Operation: 28-15=13, Resulting Numbers: [80, 65, 13] Generated Node #0,0: 75:[80, 65, 13] Operation: 28-15=13 Moving to Node #0,0 Current State: 75:[80, 65, 13], Operations: ['28-15=13'] Exploring Operation: 65/13=5, Resulting Numbers: [80, 5] Generated Node #0,0,1: 75:[80, 5] Operation: 65/13=5 Moving to Node #0,0,1 Current State: 75:[80, 5], Operations: ['28-15=13', '65/13=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.947917
hs_5
mult_heuristic
[ 92, 88, 2, 99 ]
70
[ "99-88=11", "2*11=22", "92-22=70" ]
Current State: 70:[92, 88, 2, 99], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [92, 2, 11] Generated Node #2: [92, 2, 11] from Operation: 99-88=11 Current State: 70:[92, 2, 11], Operations: ['99-88=11'] Exploring Operation: 2*11=22, Resulting Numbers: [92, 22] Generated Node #3: [92, 22] from Operation: 2*11=22 Current State: 70:[92, 22], Operations: ['99-88=11', '2*11=22'] Exploring Operation: 92-22=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[92, 88, 2, 99], Operations: [] Exploring Operation: 99-92=7, Resulting Numbers: [88, 2, 7] Generated Node #0,0: 70:[88, 2, 7] Operation: 99-92=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 70:[88, 2, 7], Operations: ['99-92=7'] Exploring Operation: 88/2=44, Resulting Numbers: [7, 44] Generated Node #0,0,0: 70:[7, 44] Operation: 88/2=44 Moving to Node #0,0,0 Current State: 70:[7, 44], Operations: ['99-92=7', '88/2=44'] Exploring Operation: 44-7=37, Resulting Numbers: [37] 37,70 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 80, 40, 87, 7 ]
96
[ "80/40=2", "87+7=94", "2+94=96" ]
Current State: 96:[80, 40, 87, 7], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [87, 7, 2] Generated Node #2: [87, 7, 2] from Operation: 80/40=2 Current State: 96:[87, 7, 2], Operations: ['80/40=2'] Exploring Operation: 87+7=94, Resulting Numbers: [2, 94] Generated Node #3: [2, 94] from Operation: 87+7=94 Current State: 96:[2, 94], Operations: ['80/40=2', '87+7=94'] Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[80, 40, 87, 7], Operations: [] Exploring Operation: 87-80=7, Resulting Numbers: [40, 7, 7] Generated Node #0,0: 96:[40, 7, 7] Operation: 87-80=7 Exploring Operation: 80-40=40, Resulting Numbers: [87, 7, 40] Generated Node #0,1: 96:[87, 7, 40] Operation: 80-40=40 Exploring Operation: 80/40=2, Resulting Numbers: [87, 7, 2] Generated Node #0,2: 96:[87, 7, 2] Operation: 80/40=2 Moving to Node #0,0 Current State: 96:[40, 7, 7], Operations: ['87-80=7'] Exploring Operation: 40+7=47, Resulting Numbers: [7, 47] Generated Node #0,0,0: 96:[7, 47] Operation: 40+7=47 Exploring Operation: 40+7=47, Resulting Numbers: [7, 47] Generated Node #0,0,1: 96:[7, 47] Operation: 40+7=47 Exploring Operation: 40-7=33, Resulting Numbers: [7, 33] Generated Node #0,0,2: 96:[7, 33] Operation: 40-7=33 Moving to Node #0,2 Current State: 96:[87, 7, 2], Operations: ['80/40=2'] Exploring Operation: 87+7=94, Resulting Numbers: [2, 94] Generated Node #0,2,0: 96:[2, 94] Operation: 87+7=94 Exploring Operation: 7+2=9, Resulting Numbers: [87, 9] Generated Node #0,2,1: 96:[87, 9] Operation: 7+2=9 Exploring Operation: 87+2=89, Resulting Numbers: [7, 89] Generated Node #0,2,2: 96:[7, 89] Operation: 87+2=89 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 96:[2, 94], Operations: ['80/40=2', '87+7=94'] Exploring Operation: 94-2=92, Resulting Numbers: [92] 92,96 unequal: No Solution Exploring Operation: 94/2=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[80, 40, 87, 7], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [87, 7, 2] Generated Node #0,2: 96:[87, 7, 2] Operation: 80/40=2 Moving to Node #0,2 Current State: 96:[87, 7, 2], Operations: ['80/40=2'] Exploring Operation: 87+7=94, Resulting Numbers: [2, 94] Generated Node #0,2,0: 96:[2, 94] Operation: 87+7=94 Moving to Node #0,2,0 Current State: 96:[2, 94], Operations: ['80/40=2', '87+7=94'] Exploring Operation: 2+94=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_3
mult_heuristic
[ 32, 67, 68, 19 ]
12
[ "32+67=99", "68+19=87", "99-87=12" ]
Current State: 12:[32, 67, 68, 19], Operations: [] Exploring Operation: 32+67=99, Resulting Numbers: [68, 19, 99] Generated Node #2: [68, 19, 99] from Operation: 32+67=99 Current State: 12:[68, 19, 99], Operations: ['32+67=99'] Exploring Operation: 68+19=87, Resulting Numbers: [99, 87] Generated Node #3: [99, 87] from Operation: 68+19=87 Current State: 12:[99, 87], Operations: ['32+67=99', '68+19=87'] Exploring Operation: 99-87=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[32, 67, 68, 19], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [32, 19, 1] Generated Node #0,0: 12:[32, 19, 1] Operation: 68-67=1 Exploring Operation: 67-32=35, Resulting Numbers: [68, 19, 35] Generated Node #0,1: 12:[68, 19, 35] Operation: 67-32=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[32, 19, 1], Operations: ['68-67=1'] Exploring Operation: 32-1=31, Resulting Numbers: [19, 31] Generated Node #0,0,0: 12:[19, 31] Operation: 32-1=31 Exploring Operation: 32-19=13, Resulting Numbers: [1, 13] Generated Node #0,0,1: 12:[1, 13] Operation: 32-19=13 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[1, 13], Operations: ['68-67=1', '32-19=13'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[32, 67, 68, 19], Operations: [] Exploring Operation: 68-67=1, Resulting Numbers: [32, 19, 1] Generated Node #0,0: 12:[32, 19, 1] Operation: 68-67=1 Moving to Node #0,0 Current State: 12:[32, 19, 1], Operations: ['68-67=1'] Exploring Operation: 32-19=13, Resulting Numbers: [1, 13] Generated Node #0,0,1: 12:[1, 13] Operation: 32-19=13 Moving to Node #0,0,1 Current State: 12:[1, 13], Operations: ['68-67=1', '32-19=13'] Exploring Operation: 13-1=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 86, 30, 95, 94 ]
57
[ "86-30=56", "95-94=1", "56+1=57" ]
Current State: 57:[86, 30, 95, 94], Operations: [] Exploring Operation: 86-30=56, Resulting Numbers: [95, 94, 56] Generated Node #2: [95, 94, 56] from Operation: 86-30=56 Current State: 57:[95, 94, 56], Operations: ['86-30=56'] Exploring Operation: 95-94=1, Resulting Numbers: [56, 1] Generated Node #3: [56, 1] from Operation: 95-94=1 Current State: 57:[56, 1], Operations: ['86-30=56', '95-94=1'] Exploring Operation: 56+1=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[86, 30, 95, 94], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [86, 30, 1] Generated Node #0,0: 57:[86, 30, 1] Operation: 95-94=1 Exploring Operation: 95-86=9, Resulting Numbers: [30, 94, 9] Generated Node #0,1: 57:[30, 94, 9] Operation: 95-86=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 57:[86, 30, 1], Operations: ['95-94=1'] Exploring Operation: 86-30=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 57:[1, 56] Operation: 86-30=56 Exploring Operation: 86-1=85, Resulting Numbers: [30, 85] Generated Node #0,0,1: 57:[30, 85] Operation: 86-1=85 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 57:[1, 56], Operations: ['95-94=1', '86-30=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[86, 30, 95, 94], Operations: [] Exploring Operation: 95-94=1, Resulting Numbers: [86, 30, 1] Generated Node #0,0: 57:[86, 30, 1] Operation: 95-94=1 Moving to Node #0,0 Current State: 57:[86, 30, 1], Operations: ['95-94=1'] Exploring Operation: 86-30=56, Resulting Numbers: [1, 56] Generated Node #0,0,0: 57:[1, 56] Operation: 86-30=56 Moving to Node #0,0,0 Current State: 57:[1, 56], Operations: ['95-94=1', '86-30=56'] Exploring Operation: 1+56=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
sum_heuristic
[ 28, 90, 31, 55 ]
32
[ "28+90=118", "31+55=86", "118-86=32" ]
Current State: 32:[28, 90, 31, 55], Operations: [] Exploring Operation: 28+90=118, Resulting Numbers: [31, 55, 118] Generated Node #2: [31, 55, 118] from Operation: 28+90=118 Current State: 32:[31, 55, 118], Operations: ['28+90=118'] Exploring Operation: 31+55=86, Resulting Numbers: [118, 86] Generated Node #3: [118, 86] from Operation: 31+55=86 Current State: 32:[118, 86], Operations: ['28+90=118', '31+55=86'] Exploring Operation: 118-86=32, Resulting Numbers: [32] 32,32 equal: Goal Reached
4
Current State: 32:[28, 90, 31, 55], Operations: [] Exploring Operation: 55-31=24, Resulting Numbers: [28, 90, 24] Generated Node #0,0: 32:[28, 90, 24] Operation: 55-31=24 Exploring Operation: 55-28=27, Resulting Numbers: [90, 31, 27] Generated Node #0,1: 32:[90, 31, 27] Operation: 55-28=27 Exploring Operation: 90-28=62, Resulting Numbers: [31, 55, 62] Generated Node #0,2: 32:[31, 55, 62] Operation: 90-28=62 Exploring Operation: 90-55=35, Resulting Numbers: [28, 31, 35] Generated Node #0,3: 32:[28, 31, 35] Operation: 90-55=35 Exploring Operation: 90-31=59, Resulting Numbers: [28, 55, 59] Generated Node #0,4: 32:[28, 55, 59] Operation: 90-31=59 Moving to Node #0,3 Current State: 32:[28, 31, 35], Operations: ['90-55=35'] Exploring Operation: 28+31=59, Resulting Numbers: [35, 59] Generated Node #0,3,0: 32:[35, 59] Operation: 28+31=59 Exploring Operation: 31-28=3, Resulting Numbers: [35, 3] Generated Node #0,3,1: 32:[35, 3] Operation: 31-28=3 Exploring Operation: 35-28=7, Resulting Numbers: [31, 7] Generated Node #0,3,2: 32:[31, 7] Operation: 35-28=7 Exploring Operation: 35-31=4, Resulting Numbers: [28, 4] Generated Node #0,3,3: 32:[28, 4] Operation: 35-31=4 Exploring Operation: 28+35=63, Resulting Numbers: [31, 63] Generated Node #0,3,4: 32:[31, 63] Operation: 28+35=63 Moving to Node #0,4 Current State: 32:[28, 55, 59], Operations: ['90-31=59'] Exploring Operation: 28+59=87, Resulting Numbers: [55, 87] Generated Node #0,4,0: 32:[55, 87] Operation: 28+59=87 Exploring Operation: 28+55=83, Resulting Numbers: [59, 83] Generated Node #0,4,1: 32:[59, 83] Operation: 28+55=83 Exploring Operation: 59-55=4, Resulting Numbers: [28, 4] Generated Node #0,4,2: 32:[28, 4] Operation: 59-55=4 Exploring Operation: 55-28=27, Resulting Numbers: [59, 27] Generated Node #0,4,3: 32:[59, 27] Operation: 55-28=27 Exploring Operation: 59-28=31, Resulting Numbers: [55, 31] Generated Node #0,4,4: 32:[55, 31] Operation: 59-28=31 Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 32:[28, 4], Operations: ['90-31=59', '59-55=4'] Exploring Operation: 28*4=112, Resulting Numbers: [112] 112,32 unequal: No Solution Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Moving to Node #0 Current State: 32:[28, 90, 31, 55], Operations: [] Exploring Operation: 90-31=59, Resulting Numbers: [28, 55, 59] Generated Node #0,4: 32:[28, 55, 59] Operation: 90-31=59 Moving to Node #0,4 Current State: 32:[28, 55, 59], Operations: ['90-31=59'] Exploring Operation: 59-55=4, Resulting Numbers: [28, 4] Generated Node #0,4,2: 32:[28, 4] Operation: 59-55=4 Moving to Node #0,4,2 Current State: 32:[28, 4], Operations: ['90-31=59', '59-55=4'] Exploring Operation: 28+4=32, Resulting Numbers: [32] 32,32 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
mult_heuristic
[ 8, 66, 63, 12 ]
36
[ "66-63=3", "8*3=24", "12+24=36" ]
Current State: 36:[8, 66, 63, 12], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [8, 12, 3] Generated Node #2: [8, 12, 3] from Operation: 66-63=3 Current State: 36:[8, 12, 3], Operations: ['66-63=3'] Exploring Operation: 8*3=24, Resulting Numbers: [12, 24] Generated Node #3: [12, 24] from Operation: 8*3=24 Current State: 36:[12, 24], Operations: ['66-63=3', '8*3=24'] Exploring Operation: 12+24=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[8, 66, 63, 12], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [8, 12, 3] Generated Node #0,0: 36:[8, 12, 3] Operation: 66-63=3 Exploring Operation: 63-12=51, Resulting Numbers: [8, 66, 51] Generated Node #0,1: 36:[8, 66, 51] Operation: 63-12=51 Exploring Operation: 66-12=54, Resulting Numbers: [8, 63, 54] Generated Node #0,2: 36:[8, 63, 54] Operation: 66-12=54 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[8, 12, 3], Operations: ['66-63=3'] Exploring Operation: 8-3=5, Resulting Numbers: [12, 5] Generated Node #0,0,0: 36:[12, 5] Operation: 8-3=5 Exploring Operation: 12-8=4, Resulting Numbers: [3, 4] Generated Node #0,0,1: 36:[3, 4] Operation: 12-8=4 Exploring Operation: 8+3=11, Resulting Numbers: [12, 11] Generated Node #0,0,2: 36:[12, 11] Operation: 8+3=11 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 36:[3, 4], Operations: ['66-63=3', '12-8=4'] Exploring Operation: 3+4=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 4-3=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 3*4=12, Resulting Numbers: [12] 12,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 36:[12, 5], Operations: ['66-63=3', '8-3=5'] Exploring Operation: 12*5=60, Resulting Numbers: [60] 60,36 unequal: No Solution Exploring Operation: 12-5=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 12+5=17, Resulting Numbers: [17] 17,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 36:[12, 11], Operations: ['66-63=3', '8+3=11'] Exploring Operation: 12+11=23, Resulting Numbers: [23] 23,36 unequal: No Solution Exploring Operation: 12-11=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 12*11=132, Resulting Numbers: [132] 132,36 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: 36:[8, 66, 51], Operations: ['63-12=51'] Exploring Operation: 66-51=15, Resulting Numbers: [8, 15] Generated Node #0,1,0: 36:[8, 15] Operation: 66-51=15 Exploring Operation: 66-8=58, Resulting Numbers: [51, 58] Generated Node #0,1,1: 36:[51, 58] Operation: 66-8=58 Exploring Operation: 51-8=43, Resulting Numbers: [66, 43] Generated Node #0,1,2: 36:[66, 43] Operation: 51-8=43 Moving to Node #0,1,0 Current State: 36:[8, 15], Operations: ['63-12=51', '66-51=15'] Exploring Operation: 8*15=120, Resulting Numbers: [120] 120,36 unequal: No Solution Exploring Operation: 8+15=23, Resulting Numbers: [23] 23,36 unequal: No Solution Exploring Operation: 15-8=7, Resulting Numbers: [7] 7,36 unequal: No Solution Moving to Node #0,1,1 Current State: 36:[51, 58], Operations: ['63-12=51', '66-8=58'] Exploring Operation: 51+58=109, Resulting Numbers: [109] 109,36 unequal: No Solution Exploring Operation: 58-51=7, Resulting Numbers: [7] 7,36 unequal: No Solution Exploring Operation: 51*58=2958, Resulting Numbers: [2958] 2958,36 unequal: No Solution Moving to Node #0,1,2 Current State: 36:[66, 43], Operations: ['63-12=51', '51-8=43'] Exploring Operation: 66*43=2838, Resulting Numbers: [2838] 2838,36 unequal: No Solution Exploring Operation: 66-43=23, Resulting Numbers: [23] 23,36 unequal: No Solution Exploring Operation: 66+43=109, Resulting Numbers: [109] 109,36 unequal: No Solution No 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: 36:[8, 63, 54], Operations: ['66-12=54'] Exploring Operation: 63-54=9, Resulting Numbers: [8, 9] Generated Node #0,2,0: 36:[8, 9] Operation: 63-54=9 Exploring Operation: 54-8=46, Resulting Numbers: [63, 46] Generated Node #0,2,1: 36:[63, 46] Operation: 54-8=46 Exploring Operation: 63-8=55, Resulting Numbers: [54, 55] Generated Node #0,2,2: 36:[54, 55] Operation: 63-8=55 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 36:[8, 9], Operations: ['66-12=54', '63-54=9'] Exploring Operation: 9-8=1, Resulting Numbers: [1] 1,36 unequal: No Solution Exploring Operation: 8*9=72, Resulting Numbers: [72] 72,36 unequal: No Solution Exploring Operation: 8+9=17, Resulting Numbers: [17] 17,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 36:[63, 46], Operations: ['66-12=54', '54-8=46'] Exploring Operation: 63*46=2898, Resulting Numbers: [2898] 2898,36 unequal: No Solution Exploring Operation: 63-46=17, Resulting Numbers: [17] 17,36 unequal: No Solution Exploring Operation: 63+46=109, Resulting Numbers: [109] 109,36 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 36:[54, 55], Operations: ['66-12=54', '63-8=55'] Exploring Operation: 54*55=2970, Resulting Numbers: [2970] 2970,36 unequal: No Solution Exploring Operation: 54+55=109, Resulting Numbers: [109] 109,36 unequal: No Solution Exploring Operation: 55-54=1, Resulting Numbers: [1] 1,36 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
[ 22, 49, 80, 31 ]
84
[ "49-22=27", "80+31=111", "111-27=84" ]
Current State: 84:[22, 49, 80, 31], Operations: [] Exploring Operation: 49-22=27, Resulting Numbers: [80, 31, 27] Generated Node #2: [80, 31, 27] from Operation: 49-22=27 Current State: 84:[80, 31, 27], Operations: ['49-22=27'] Exploring Operation: 80+31=111, Resulting Numbers: [27, 111] Generated Node #3: [27, 111] from Operation: 80+31=111 Current State: 84:[27, 111], Operations: ['49-22=27', '80+31=111'] Exploring Operation: 111-27=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[22, 49, 80, 31], Operations: [] Exploring Operation: 80-49=31, Resulting Numbers: [22, 31, 31] Generated Node #0,0: 84:[22, 31, 31] Operation: 80-49=31 Exploring Operation: 49-22=27, Resulting Numbers: [80, 31, 27] Generated Node #0,1: 84:[80, 31, 27] Operation: 49-22=27 Exploring Operation: 49-31=18, Resulting Numbers: [22, 80, 18] Generated Node #0,2: 84:[22, 80, 18] Operation: 49-31=18 Start Sub Search at level 1: Moving to Node #0,0 Current State: 84:[22, 31, 31], Operations: ['80-49=31'] Exploring Operation: 31/31=1, Resulting Numbers: [22, 1] Generated Node #0,0,0: 84:[22, 1] Operation: 31/31=1 Exploring Operation: 31-31=0, Resulting Numbers: [22, 0] Generated Node #0,0,1: 84:[22, 0] Operation: 31-31=0 Exploring Operation: 31-22=9, Resulting Numbers: [31, 9] Generated Node #0,0,2: 84:[31, 9] Operation: 31-22=9 Moving to Node #0,0,0 Current State: 84:[22, 1], Operations: ['80-49=31', '31/31=1'] Exploring Operation: 22*1=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,84 unequal: No Solution Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,84 unequal: No Solution Moving to Node #0,0,1 Current State: 84:[22, 0], Operations: ['80-49=31', '31-31=0'] Exploring Operation: 22+0=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 22*0=0, Resulting Numbers: [0] 0,84 unequal: No Solution Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,84 unequal: No Solution Moving to Node #0,0,2 Current State: 84:[31, 9], Operations: ['80-49=31', '31-22=9'] Exploring Operation: 31+9=40, Resulting Numbers: [40] 40,84 unequal: No Solution Exploring Operation: 31*9=279, Resulting Numbers: [279] 279,84 unequal: No Solution Exploring Operation: 31-9=22, Resulting Numbers: [22] 22,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 84:[80, 31, 27], Operations: ['49-22=27'] Exploring Operation: 80-27=53, Resulting Numbers: [31, 53] Generated Node #0,1,0: 84:[31, 53] Operation: 80-27=53 Exploring Operation: 80-31=49, Resulting Numbers: [27, 49] Generated Node #0,1,1: 84:[27, 49] Operation: 80-31=49 Exploring Operation: 31-27=4, Resulting Numbers: [80, 4] Generated Node #0,1,2: 84:[80, 4] Operation: 31-27=4 Moving to Node #0,1,2 Current State: 84:[80, 4], Operations: ['49-22=27', '31-27=4'] Exploring Operation: 80/4=20, Resulting Numbers: [20] 20,84 unequal: No Solution Exploring Operation: 80-4=76, Resulting Numbers: [76] 76,84 unequal: No Solution Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[22, 49, 80, 31], Operations: [] Exploring Operation: 49-22=27, Resulting Numbers: [80, 31, 27] Generated Node #0,1: 84:[80, 31, 27] Operation: 49-22=27 Moving to Node #0,1 Current State: 84:[80, 31, 27], Operations: ['49-22=27'] Exploring Operation: 31-27=4, Resulting Numbers: [80, 4] Generated Node #0,1,2: 84:[80, 4] Operation: 31-27=4 Moving to Node #0,1,2 Current State: 84:[80, 4], Operations: ['49-22=27', '31-27=4'] Exploring Operation: 80+4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.978299
hs_3
sum_heuristic
[ 94, 26, 73, 81 ]
76
[ "94-26=68", "81-73=8", "68+8=76" ]
Current State: 76:[94, 26, 73, 81], Operations: [] Exploring Operation: 94-26=68, Resulting Numbers: [73, 81, 68] Generated Node #2: [73, 81, 68] from Operation: 94-26=68 Current State: 76:[73, 81, 68], Operations: ['94-26=68'] Exploring Operation: 81-73=8, Resulting Numbers: [68, 8] Generated Node #3: [68, 8] from Operation: 81-73=8 Current State: 76:[68, 8], Operations: ['94-26=68', '81-73=8'] Exploring Operation: 68+8=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[94, 26, 73, 81], Operations: [] Exploring Operation: 94-81=13, Resulting Numbers: [26, 73, 13] Generated Node #0,0: 76:[26, 73, 13] Operation: 94-81=13 Exploring Operation: 94-26=68, Resulting Numbers: [73, 81, 68] Generated Node #0,1: 76:[73, 81, 68] Operation: 94-26=68 Exploring Operation: 94-73=21, Resulting Numbers: [26, 81, 21] Generated Node #0,2: 76:[26, 81, 21] Operation: 94-73=21 Moving to Node #0,2 Current State: 76:[26, 81, 21], Operations: ['94-73=21'] Exploring Operation: 26-21=5, Resulting Numbers: [81, 5] Generated Node #0,2,0: 76:[81, 5] Operation: 26-21=5 Exploring Operation: 81-26=55, Resulting Numbers: [21, 55] Generated Node #0,2,1: 76:[21, 55] Operation: 81-26=55 Exploring Operation: 26+21=47, Resulting Numbers: [81, 47] Generated Node #0,2,2: 76:[81, 47] Operation: 26+21=47 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 76:[81, 5], Operations: ['94-73=21', '26-21=5'] Exploring Operation: 81*5=405, Resulting Numbers: [405] 405,76 unequal: No Solution Exploring Operation: 81+5=86, Resulting Numbers: [86] 86,76 unequal: No Solution Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[94, 26, 73, 81], Operations: [] Exploring Operation: 94-73=21, Resulting Numbers: [26, 81, 21] Generated Node #0,2: 76:[26, 81, 21] Operation: 94-73=21 Moving to Node #0,2 Current State: 76:[26, 81, 21], Operations: ['94-73=21'] Exploring Operation: 26-21=5, Resulting Numbers: [81, 5] Generated Node #0,2,0: 76:[81, 5] Operation: 26-21=5 Moving to Node #0,2,0 Current State: 76:[81, 5], Operations: ['94-73=21', '26-21=5'] Exploring Operation: 81-5=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.988715
hs_3
sum_heuristic
[ 26, 71, 41, 76 ]
62
[ "26+71=97", "76-41=35", "97-35=62" ]
Current State: 62:[26, 71, 41, 76], Operations: [] Exploring Operation: 26+71=97, Resulting Numbers: [41, 76, 97] Generated Node #2: [41, 76, 97] from Operation: 26+71=97 Current State: 62:[41, 76, 97], Operations: ['26+71=97'] Exploring Operation: 76-41=35, Resulting Numbers: [97, 35] Generated Node #3: [97, 35] from Operation: 76-41=35 Current State: 62:[97, 35], Operations: ['26+71=97', '76-41=35'] Exploring Operation: 97-35=62, Resulting Numbers: [62] 62,62 equal: Goal Reached
4
Current State: 62:[26, 71, 41, 76], Operations: [] Exploring Operation: 76-71=5, Resulting Numbers: [26, 41, 5] Generated Node #0,0: 62:[26, 41, 5] Operation: 76-71=5 Exploring Operation: 71-41=30, Resulting Numbers: [26, 76, 30] Generated Node #0,1: 62:[26, 76, 30] Operation: 71-41=30 Exploring Operation: 76-26=50, Resulting Numbers: [71, 41, 50] Generated Node #0,2: 62:[71, 41, 50] Operation: 76-26=50 Exploring Operation: 26+41=67, Resulting Numbers: [71, 76, 67] Generated Node #0,3: 62:[71, 76, 67] Operation: 26+41=67 Exploring Operation: 76-41=35, Resulting Numbers: [26, 71, 35] Generated Node #0,4: 62:[26, 71, 35] Operation: 76-41=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 62:[26, 41, 5], Operations: ['76-71=5'] Exploring Operation: 26-5=21, Resulting Numbers: [41, 21] Generated Node #0,0,0: 62:[41, 21] Operation: 26-5=21 Exploring Operation: 41-5=36, Resulting Numbers: [26, 36] Generated Node #0,0,1: 62:[26, 36] Operation: 41-5=36 Exploring Operation: 41-26=15, Resulting Numbers: [5, 15] Generated Node #0,0,2: 62:[5, 15] Operation: 41-26=15 Exploring Operation: 26+5=31, Resulting Numbers: [41, 31] Generated Node #0,0,3: 62:[41, 31] Operation: 26+5=31 Exploring Operation: 26+41=67, Resulting Numbers: [5, 67] Generated Node #0,0,4: 62:[5, 67] Operation: 26+41=67 Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 62:[5, 67], Operations: ['76-71=5', '26+41=67'] Exploring Operation: 5*67=335, Resulting Numbers: [335] 335,62 unequal: No Solution Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Moving to Node #0 Current State: 62:[26, 71, 41, 76], Operations: [] Exploring Operation: 76-71=5, Resulting Numbers: [26, 41, 5] Generated Node #0,0: 62:[26, 41, 5] Operation: 76-71=5 Moving to Node #0,0 Current State: 62:[26, 41, 5], Operations: ['76-71=5'] Exploring Operation: 26+41=67, Resulting Numbers: [5, 67] Generated Node #0,0,4: 62:[5, 67] Operation: 26+41=67 Moving to Node #0,0,4 Current State: 62:[5, 67], Operations: ['76-71=5', '26+41=67'] Exploring Operation: 67-5=62, Resulting Numbers: [62] 62,62 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_5
mult_heuristic
[ 95, 4, 69, 54 ]
76
[ "95-4=91", "69-54=15", "91-15=76" ]
Current State: 76:[95, 4, 69, 54], Operations: [] Exploring Operation: 95-4=91, Resulting Numbers: [69, 54, 91] Generated Node #2: [69, 54, 91] from Operation: 95-4=91 Current State: 76:[69, 54, 91], Operations: ['95-4=91'] Exploring Operation: 69-54=15, Resulting Numbers: [91, 15] Generated Node #3: [91, 15] from Operation: 69-54=15 Current State: 76:[91, 15], Operations: ['95-4=91', '69-54=15'] Exploring Operation: 91-15=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[95, 4, 69, 54], Operations: [] Exploring Operation: 95-54=41, Resulting Numbers: [4, 69, 41] Generated Node #0,0: 76:[4, 69, 41] Operation: 95-54=41 Start Sub Search at level 1: Moving to Node #0,0 Current State: 76:[4, 69, 41], Operations: ['95-54=41'] Exploring Operation: 4+69=73, Resulting Numbers: [41, 73] Generated Node #0,0,0: 76:[41, 73] Operation: 4+69=73 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 76:[41, 73], Operations: ['95-54=41', '4+69=73'] Exploring Operation: 73-41=32, Resulting Numbers: [32] 32,76 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
[ 54, 8, 18, 17 ]
27
[ "54+8=62", "18+17=35", "62-35=27" ]
Current State: 27:[54, 8, 18, 17], Operations: [] Exploring Operation: 54+8=62, Resulting Numbers: [18, 17, 62] Generated Node #2: [18, 17, 62] from Operation: 54+8=62 Current State: 27:[18, 17, 62], Operations: ['54+8=62'] Exploring Operation: 18+17=35, Resulting Numbers: [62, 35] Generated Node #3: [62, 35] from Operation: 18+17=35 Current State: 27:[62, 35], Operations: ['54+8=62', '18+17=35'] Exploring Operation: 62-35=27, Resulting Numbers: [27] 27,27 equal: Goal Reached
4
Current State: 27:[54, 8, 18, 17], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [8, 17, 3] Generated Node #0,0: 27:[8, 17, 3] Operation: 54/18=3 Exploring Operation: 54-17=37, Resulting Numbers: [8, 18, 37] Generated Node #0,1: 27:[8, 18, 37] Operation: 54-17=37 Exploring Operation: 54-8=46, Resulting Numbers: [18, 17, 46] Generated Node #0,2: 27:[18, 17, 46] Operation: 54-8=46 Exploring Operation: 54-18=36, Resulting Numbers: [8, 17, 36] Generated Node #0,3: 27:[8, 17, 36] Operation: 54-18=36 Exploring Operation: 18-17=1, Resulting Numbers: [54, 8, 1] Generated Node #0,4: 27:[54, 8, 1] Operation: 18-17=1 Moving to Node #0,0 Current State: 27:[8, 17, 3], Operations: ['54/18=3'] Exploring Operation: 17-3=14, Resulting Numbers: [8, 14] Generated Node #0,0,0: 27:[8, 14] Operation: 17-3=14 Exploring Operation: 8+3=11, Resulting Numbers: [17, 11] Generated Node #0,0,1: 27:[17, 11] Operation: 8+3=11 Exploring Operation: 8+17=25, Resulting Numbers: [3, 25] Generated Node #0,0,2: 27:[3, 25] Operation: 8+17=25 Exploring Operation: 17+3=20, Resulting Numbers: [8, 20] Generated Node #0,0,3: 27:[8, 20] Operation: 17+3=20 Exploring Operation: 17-8=9, Resulting Numbers: [3, 9] Generated Node #0,0,4: 27:[3, 9] Operation: 17-8=9 Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 27:[3, 9], Operations: ['54/18=3', '17-8=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Moving to Node #0 Current State: 27:[54, 8, 18, 17], Operations: [] Exploring Operation: 54/18=3, Resulting Numbers: [8, 17, 3] Generated Node #0,0: 27:[8, 17, 3] Operation: 54/18=3 Moving to Node #0,0 Current State: 27:[8, 17, 3], Operations: ['54/18=3'] Exploring Operation: 17-8=9, Resulting Numbers: [3, 9] Generated Node #0,0,4: 27:[3, 9] Operation: 17-8=9 Moving to Node #0,0,4 Current State: 27:[3, 9], Operations: ['54/18=3', '17-8=9'] Exploring Operation: 3*9=27, Resulting Numbers: [27] 27,27 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 34, 51, 29, 10 ]
26
[ "51+29=80", "80/10=8", "34-8=26" ]
Current State: 26:[34, 51, 29, 10], Operations: [] Exploring Operation: 51+29=80, Resulting Numbers: [34, 10, 80] Generated Node #2: [34, 10, 80] from Operation: 51+29=80 Current State: 26:[34, 10, 80], Operations: ['51+29=80'] Exploring Operation: 80/10=8, Resulting Numbers: [34, 8] Generated Node #3: [34, 8] from Operation: 80/10=8 Current State: 26:[34, 8], Operations: ['51+29=80', '80/10=8'] Exploring Operation: 34-8=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[34, 51, 29, 10], Operations: [] Exploring Operation: 51-29=22, Resulting Numbers: [34, 10, 22] Generated Node #0,0: 26:[34, 10, 22] Operation: 51-29=22 Exploring Operation: 51-34=17, Resulting Numbers: [29, 10, 17] Generated Node #0,1: 26:[29, 10, 17] Operation: 51-34=17 Moving to Node #0,1 Current State: 26:[29, 10, 17], Operations: ['51-34=17'] Exploring Operation: 29-17=12, Resulting Numbers: [10, 12] Generated Node #0,1,0: 26:[10, 12] Operation: 29-17=12 Exploring Operation: 10+17=27, Resulting Numbers: [29, 27] Generated Node #0,1,1: 26:[29, 27] Operation: 10+17=27 Moving to Node #0,0 Current State: 26:[34, 10, 22], Operations: ['51-29=22'] Exploring Operation: 34-22=12, Resulting Numbers: [10, 12] Generated Node #0,0,0: 26:[10, 12] Operation: 34-22=12 Exploring Operation: 34-10=24, Resulting Numbers: [22, 24] Generated Node #0,0,1: 26:[22, 24] Operation: 34-10=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 26:[10, 12], Operations: ['51-29=22', '34-22=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 26:[22, 24], Operations: ['51-29=22', '34-10=24'] Exploring Operation: 24-22=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 22+24=46, Resulting Numbers: [46] 46,26 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,0 Current State: 26:[10, 12], Operations: ['51-34=17', '29-17=12'] Exploring Operation: 10+12=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 12-10=2, Resulting Numbers: [2] 2,26 unequal: No Solution Moving to Node #0,1,1 Current State: 26:[29, 27], Operations: ['51-34=17', '10+17=27'] Exploring Operation: 29-27=2, Resulting Numbers: [2] 2,26 unequal: No Solution Exploring Operation: 29+27=56, Resulting Numbers: [56] 56,26 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 78, 36, 6, 43 ]
65
[ "78+36=114", "6+43=49", "114-49=65" ]
Current State: 65:[78, 36, 6, 43], Operations: [] Exploring Operation: 78+36=114, Resulting Numbers: [6, 43, 114] Generated Node #2: [6, 43, 114] from Operation: 78+36=114 Current State: 65:[6, 43, 114], Operations: ['78+36=114'] Exploring Operation: 6+43=49, Resulting Numbers: [114, 49] Generated Node #3: [114, 49] from Operation: 6+43=49 Current State: 65:[114, 49], Operations: ['78+36=114', '6+43=49'] Exploring Operation: 114-49=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[78, 36, 6, 43], Operations: [] Exploring Operation: 36+43=79, Resulting Numbers: [78, 6, 79] Generated Node #0,0: 65:[78, 6, 79] Operation: 36+43=79 Exploring Operation: 43-36=7, Resulting Numbers: [78, 6, 7] Generated Node #0,1: 65:[78, 6, 7] Operation: 43-36=7 Moving to Node #0,1 Current State: 65:[78, 6, 7], Operations: ['43-36=7'] Exploring Operation: 78-7=71, Resulting Numbers: [6, 71] Generated Node #0,1,0: 65:[6, 71] Operation: 78-7=71 Exploring Operation: 78/6=13, Resulting Numbers: [7, 13] Generated Node #0,1,1: 65:[7, 13] Operation: 78/6=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[7, 13], Operations: ['43-36=7', '78/6=13'] Exploring Operation: 13-7=6, Resulting Numbers: [6] 6,65 unequal: No Solution Exploring Operation: 7+13=20, Resulting Numbers: [20] 20,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[6, 71], Operations: ['43-36=7', '78-7=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[78, 36, 6, 43], Operations: [] Exploring Operation: 43-36=7, Resulting Numbers: [78, 6, 7] Generated Node #0,1: 65:[78, 6, 7] Operation: 43-36=7 Moving to Node #0,1 Current State: 65:[78, 6, 7], Operations: ['43-36=7'] Exploring Operation: 78-7=71, Resulting Numbers: [6, 71] Generated Node #0,1,0: 65:[6, 71] Operation: 78-7=71 Moving to Node #0,1,0 Current State: 65:[6, 71], Operations: ['43-36=7', '78-7=71'] Exploring Operation: 71-6=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
sum_heuristic
[ 38, 52, 54, 92 ]
65
[ "38+92=130", "54-52=2", "130/2=65" ]
Current State: 65:[38, 52, 54, 92], Operations: [] Exploring Operation: 38+92=130, Resulting Numbers: [52, 54, 130] Generated Node #2: [52, 54, 130] from Operation: 38+92=130 Current State: 65:[52, 54, 130], Operations: ['38+92=130'] Exploring Operation: 54-52=2, Resulting Numbers: [130, 2] Generated Node #3: [130, 2] from Operation: 54-52=2 Current State: 65:[130, 2], Operations: ['38+92=130', '54-52=2'] Exploring Operation: 130/2=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[38, 52, 54, 92], Operations: [] Exploring Operation: 52-38=14, Resulting Numbers: [54, 92, 14] Generated Node #0,0: 65:[54, 92, 14] Operation: 52-38=14 Exploring Operation: 92-38=54, Resulting Numbers: [52, 54, 54] Generated Node #0,1: 65:[52, 54, 54] Operation: 92-38=54 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[52, 54, 54], Operations: ['92-38=54'] Exploring Operation: 54-52=2, Resulting Numbers: [54, 2] Generated Node #0,1,0: 65:[54, 2] Operation: 54-52=2 Exploring Operation: 54-52=2, Resulting Numbers: [54, 2] Generated Node #0,1,1: 65:[54, 2] Operation: 54-52=2 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[54, 2], Operations: ['92-38=54', '54-52=2'] Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,65 unequal: No Solution Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,65 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:[54, 2], Operations: ['92-38=54', '54-52=2'] Exploring Operation: 54+2=56, Resulting Numbers: [56] 56,65 unequal: No Solution Exploring Operation: 54-2=52, Resulting Numbers: [52] 52,65 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 #0,0 Current State: 65:[54, 92, 14], Operations: ['52-38=14'] Exploring Operation: 92-14=78, Resulting Numbers: [54, 78] Generated Node #0,0,0: 65:[54, 78] Operation: 92-14=78 Exploring Operation: 92-54=38, Resulting Numbers: [14, 38] Generated Node #0,0,1: 65:[14, 38] Operation: 92-54=38 Moving to Node #0,0,0 Current State: 65:[54, 78], Operations: ['52-38=14', '92-14=78'] Exploring Operation: 78-54=24, Resulting Numbers: [24] 24,65 unequal: No Solution Exploring Operation: 54+78=132, Resulting Numbers: [132] 132,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[14, 38], Operations: ['52-38=14', '92-54=38'] Exploring Operation: 14+38=52, Resulting Numbers: [52] 52,65 unequal: No Solution Exploring Operation: 38-14=24, Resulting Numbers: [24] 24,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 90, 85, 37, 3 ]
14
[ "90-85=5", "37+5=42", "42/3=14" ]
Current State: 14:[90, 85, 37, 3], Operations: [] Exploring Operation: 90-85=5, Resulting Numbers: [37, 3, 5] Generated Node #2: [37, 3, 5] from Operation: 90-85=5 Current State: 14:[37, 3, 5], Operations: ['90-85=5'] Exploring Operation: 37+5=42, Resulting Numbers: [3, 42] Generated Node #3: [3, 42] from Operation: 37+5=42 Current State: 14:[3, 42], Operations: ['90-85=5', '37+5=42'] Exploring Operation: 42/3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[90, 85, 37, 3], Operations: [] Exploring Operation: 90/3=30, Resulting Numbers: [85, 37, 30] Generated Node #0,0: 14:[85, 37, 30] Operation: 90/3=30 Exploring Operation: 90-85=5, Resulting Numbers: [37, 3, 5] Generated Node #0,1: 14:[37, 3, 5] Operation: 90-85=5 Moving to Node #0,1 Current State: 14:[37, 3, 5], Operations: ['90-85=5'] Exploring Operation: 37-3=34, Resulting Numbers: [5, 34] Generated Node #0,1,0: 14:[5, 34] Operation: 37-3=34 Exploring Operation: 37-5=32, Resulting Numbers: [3, 32] Generated Node #0,1,1: 14:[3, 32] Operation: 37-5=32 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 14:[3, 32], Operations: ['90-85=5', '37-5=32'] Exploring Operation: 32-3=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 3+32=35, Resulting Numbers: [35] 35,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 14:[5, 34], Operations: ['90-85=5', '37-3=34'] Exploring Operation: 34-5=29, Resulting Numbers: [29] 29,14 unequal: No Solution Exploring Operation: 5+34=39, Resulting Numbers: [39] 39,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0 Current State: 14:[85, 37, 30], Operations: ['90/3=30'] Exploring Operation: 85-30=55, Resulting Numbers: [37, 55] Generated Node #0,0,0: 14:[37, 55] Operation: 85-30=55 Exploring Operation: 85-37=48, Resulting Numbers: [30, 48] Generated Node #0,0,1: 14:[30, 48] Operation: 85-37=48 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 14:[30, 48], Operations: ['90/3=30', '85-37=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,14 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,14 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[37, 55], Operations: ['90/3=30', '85-30=55'] Exploring Operation: 37+55=92, Resulting Numbers: [92] 92,14 unequal: No Solution Exploring Operation: 55-37=18, Resulting Numbers: [18] 18,14 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
[ 41, 80, 40, 9 ]
72
[ "41+80=121", "40+9=49", "121-49=72" ]
Current State: 72:[41, 80, 40, 9], Operations: [] Exploring Operation: 41+80=121, Resulting Numbers: [40, 9, 121] Generated Node #2: [40, 9, 121] from Operation: 41+80=121 Current State: 72:[40, 9, 121], Operations: ['41+80=121'] Exploring Operation: 40+9=49, Resulting Numbers: [121, 49] Generated Node #3: [121, 49] from Operation: 40+9=49 Current State: 72:[121, 49], Operations: ['41+80=121', '40+9=49'] Exploring Operation: 121-49=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[41, 80, 40, 9], Operations: [] Exploring Operation: 80/40=2, Resulting Numbers: [41, 9, 2] Generated Node #0,0: 72:[41, 9, 2] Operation: 80/40=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[41, 9, 2], Operations: ['80/40=2'] Exploring Operation: 41-2=39, Resulting Numbers: [9, 39] Generated Node #0,0,0: 72:[9, 39] Operation: 41-2=39 Moving to Node #0,0,0 Current State: 72:[9, 39], Operations: ['80/40=2', '41-2=39'] Exploring Operation: 39-9=30, Resulting Numbers: [30] 30,72 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 34, 79, 14, 49 ]
40
[ "34*49=1666", "1666/14=119", "119-79=40" ]
Current State: 40:[34, 79, 14, 49], Operations: [] Exploring Operation: 34*49=1666, Resulting Numbers: [79, 14, 1666] Generated Node #2: [79, 14, 1666] from Operation: 34*49=1666 Current State: 40:[79, 14, 1666], Operations: ['34*49=1666'] Exploring Operation: 1666/14=119, Resulting Numbers: [79, 119] Generated Node #3: [79, 119] from Operation: 1666/14=119 Current State: 40:[79, 119], Operations: ['34*49=1666', '1666/14=119'] Exploring Operation: 119-79=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[34, 79, 14, 49], Operations: [] Exploring Operation: 79-14=65, Resulting Numbers: [34, 49, 65] Generated Node #0,0: 40:[34, 49, 65] Operation: 79-14=65 Exploring Operation: 34-14=20, Resulting Numbers: [79, 49, 20] Generated Node #0,1: 40:[79, 49, 20] Operation: 34-14=20 Exploring Operation: 49-34=15, Resulting Numbers: [79, 14, 15] Generated Node #0,2: 40:[79, 14, 15] Operation: 49-34=15 Exploring Operation: 79-49=30, Resulting Numbers: [34, 14, 30] Generated Node #0,3: 40:[34, 14, 30] Operation: 79-49=30 Exploring Operation: 79-34=45, Resulting Numbers: [14, 49, 45] Generated Node #0,4: 40:[14, 49, 45] Operation: 79-34=45 Start Sub Search at level 1: Moving to Node #0,4 Current State: 40:[14, 49, 45], Operations: ['79-34=45'] Exploring Operation: 49-14=35, Resulting Numbers: [45, 35] Generated Node #0,4,0: 40:[45, 35] Operation: 49-14=35 Exploring Operation: 49-45=4, Resulting Numbers: [14, 4] Generated Node #0,4,1: 40:[14, 4] Operation: 49-45=4 Exploring Operation: 45-14=31, Resulting Numbers: [49, 31] Generated Node #0,4,2: 40:[49, 31] Operation: 45-14=31 Exploring Operation: 14+45=59, Resulting Numbers: [49, 59] Generated Node #0,4,3: 40:[49, 59] Operation: 14+45=59 Exploring Operation: 14+49=63, Resulting Numbers: [45, 63] Generated Node #0,4,4: 40:[45, 63] Operation: 14+49=63 Moving to Node #0,4,1 Current State: 40:[14, 4], Operations: ['79-34=45', '49-45=4'] Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,40 unequal: No Solution Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,40 unequal: No Solution Moving to Node #0,4,0 Current State: 40:[45, 35], Operations: ['79-34=45', '49-14=35'] Exploring Operation: 45+35=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 45-35=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 45*35=1575, Resulting Numbers: [1575] 1575,40 unequal: No Solution Moving to Node #0,4,2 Current State: 40:[49, 31], Operations: ['79-34=45', '45-14=31'] Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 49+31=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 49*31=1519, Resulting Numbers: [1519] 1519,40 unequal: No Solution Moving to Node #0,4,3 Current State: 40:[49, 59], Operations: ['79-34=45', '14+45=59'] Exploring Operation: 49*59=2891, Resulting Numbers: [2891] 2891,40 unequal: No Solution Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,40 unequal: No Solution Moving to Node #0,4,4 Current State: 40:[45, 63], Operations: ['79-34=45', '14+49=63'] Exploring Operation: 63-45=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 45+63=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 45*63=2835, Resulting Numbers: [2835] 2835,40 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 40:[34, 14, 30], Operations: ['79-49=30'] Exploring Operation: 34-14=20, Resulting Numbers: [30, 20] Generated Node #0,3,0: 40:[30, 20] Operation: 34-14=20 Exploring Operation: 14+30=44, Resulting Numbers: [34, 44] Generated Node #0,3,1: 40:[34, 44] Operation: 14+30=44 Exploring Operation: 30-14=16, Resulting Numbers: [34, 16] Generated Node #0,3,2: 40:[34, 16] Operation: 30-14=16 Exploring Operation: 34+14=48, Resulting Numbers: [30, 48] Generated Node #0,3,3: 40:[30, 48] Operation: 34+14=48 Exploring Operation: 34-30=4, Resulting Numbers: [14, 4] Generated Node #0,3,4: 40:[14, 4] Operation: 34-30=4 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 40:[14, 4], Operations: ['79-49=30', '34-30=4'] Exploring Operation: 14+4=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 14-4=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 14*4=56, Resulting Numbers: [56] 56,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 40:[30, 20], Operations: ['79-49=30', '34-14=20'] Exploring Operation: 30+20=50, Resulting Numbers: [50] 50,40 unequal: No Solution Exploring Operation: 30*20=600, Resulting Numbers: [600] 600,40 unequal: No Solution Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 40:[34, 44], Operations: ['79-49=30', '14+30=44'] Exploring Operation: 44-34=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 34+44=78, Resulting Numbers: [78] 78,40 unequal: No Solution Exploring Operation: 34*44=1496, Resulting Numbers: [1496] 1496,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 40:[34, 16], Operations: ['79-49=30', '30-14=16'] Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,40 unequal: No Solution Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 40:[30, 48], Operations: ['79-49=30', '34+14=48'] Exploring Operation: 48-30=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 30+48=78, Resulting Numbers: [78] 78,40 unequal: No Solution Exploring Operation: 30*48=1440, Resulting Numbers: [1440] 1440,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[34, 49, 65], Operations: ['79-14=65'] Exploring Operation: 34+49=83, Resulting Numbers: [65, 83] Generated Node #0,0,0: 40:[65, 83] Operation: 34+49=83 Exploring Operation: 65-49=16, Resulting Numbers: [34, 16] Generated Node #0,0,1: 40:[34, 16] Operation: 65-49=16 Exploring Operation: 49-34=15, Resulting Numbers: [65, 15] Generated Node #0,0,2: 40:[65, 15] Operation: 49-34=15 Exploring Operation: 65-34=31, Resulting Numbers: [49, 31] Generated Node #0,0,3: 40:[49, 31] Operation: 65-34=31 Exploring Operation: 34+65=99, Resulting Numbers: [49, 99] Generated Node #0,0,4: 40:[49, 99] Operation: 34+65=99 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 40:[34, 16], Operations: ['79-14=65', '65-49=16'] Exploring Operation: 34-16=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 34+16=50, Resulting Numbers: [50] 50,40 unequal: No Solution Exploring Operation: 34*16=544, Resulting Numbers: [544] 544,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 40:[49, 31], Operations: ['79-14=65', '65-34=31'] Exploring Operation: 49*31=1519, Resulting Numbers: [1519] 1519,40 unequal: No Solution Exploring Operation: 49+31=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 49-31=18, Resulting Numbers: [18] 18,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 40:[65, 15], Operations: ['79-14=65', '49-34=15'] Exploring Operation: 65+15=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 65*15=975, Resulting Numbers: [975] 975,40 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 40:[65, 83], Operations: ['79-14=65', '34+49=83'] Exploring Operation: 83-65=18, Resulting Numbers: [18] 18,40 unequal: No Solution Exploring Operation: 65*83=5395, Resulting Numbers: [5395] 5395,40 unequal: No Solution Exploring Operation: 65+83=148, Resulting Numbers: [148] 148,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 40:[49, 99], Operations: ['79-14=65', '34+65=99'] Exploring Operation: 49+99=148, Resulting Numbers: [148] 148,40 unequal: No Solution Exploring Operation: 49*99=4851, Resulting Numbers: [4851] 4851,40 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 40:[79, 49, 20], Operations: ['34-14=20'] Exploring Operation: 79-49=30, Resulting Numbers: [20, 30] Generated Node #0,1,0: 40:[20, 30] Operation: 79-49=30 Exploring Operation: 49+20=69, Resulting Numbers: [79, 69] Generated Node #0,1,1: 40:[79, 69] Operation: 49+20=69 Exploring Operation: 79+20=99, Resulting Numbers: [49, 99] Generated Node #0,1,2: 40:[49, 99] Operation: 79+20=99 Exploring Operation: 79-20=59, Resulting Numbers: [49, 59] Generated Node #0,1,3: 40:[49, 59] Operation: 79-20=59 Exploring Operation: 49-20=29, Resulting Numbers: [79, 29] Generated Node #0,1,4: 40:[79, 29] Operation: 49-20=29 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 40:[20, 30], Operations: ['34-14=20', '79-49=30'] Exploring Operation: 30-20=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 20*30=600, Resulting Numbers: [600] 600,40 unequal: No Solution Exploring Operation: 20+30=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 40:[49, 59], Operations: ['34-14=20', '79-20=59'] Exploring Operation: 49*59=2891, Resulting Numbers: [2891] 2891,40 unequal: No Solution Exploring Operation: 59-49=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 49+59=108, Resulting Numbers: [108] 108,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 40:[79, 29], Operations: ['34-14=20', '49-20=29'] Exploring Operation: 79+29=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,40 unequal: No Solution Exploring Operation: 79*29=2291, Resulting Numbers: [2291] 2291,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 40:[79, 69], Operations: ['34-14=20', '49+20=69'] Exploring Operation: 79-69=10, Resulting Numbers: [10] 10,40 unequal: No Solution Exploring Operation: 79*69=5451, Resulting Numbers: [5451] 5451,40 unequal: No Solution Exploring Operation: 79+69=148, Resulting Numbers: [148] 148,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 40:[49, 99], Operations: ['34-14=20', '79+20=99'] Exploring Operation: 49*99=4851, Resulting Numbers: [4851] 4851,40 unequal: No Solution Exploring Operation: 49+99=148, Resulting Numbers: [148] 148,40 unequal: No Solution Exploring Operation: 99-49=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 40:[79, 14, 15], Operations: ['49-34=15'] Exploring Operation: 15-14=1, Resulting Numbers: [79, 1] Generated Node #0,2,0: 40:[79, 1] Operation: 15-14=1 Exploring Operation: 14+15=29, Resulting Numbers: [79, 29] Generated Node #0,2,1: 40:[79, 29] Operation: 14+15=29 Exploring Operation: 79-15=64, Resulting Numbers: [14, 64] Generated Node #0,2,2: 40:[14, 64] Operation: 79-15=64 Exploring Operation: 79+14=93, Resulting Numbers: [15, 93] Generated Node #0,2,3: 40:[15, 93] Operation: 79+14=93 Exploring Operation: 79-14=65, Resulting Numbers: [15, 65] Generated Node #0,2,4: 40:[15, 65] Operation: 79-14=65 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 40:[14, 64], Operations: ['49-34=15', '79-15=64'] Exploring Operation: 64-14=50, Resulting Numbers: [50] 50,40 unequal: No Solution Exploring Operation: 14*64=896, Resulting Numbers: [896] 896,40 unequal: No Solution Exploring Operation: 14+64=78, Resulting Numbers: [78] 78,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 40:[15, 65], Operations: ['49-34=15', '79-14=65'] Exploring Operation: 15*65=975, Resulting Numbers: [975] 975,40 unequal: No Solution Exploring Operation: 15+65=80, Resulting Numbers: [80] 80,40 unequal: No Solution Exploring Operation: 65-15=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 40:[79, 1], Operations: ['49-34=15', '15-14=1'] Exploring Operation: 79/1=79, Resulting Numbers: [79] 79,40 unequal: No Solution Exploring Operation: 79-1=78, Resulting Numbers: [78] 78,40 unequal: No Solution Exploring Operation: 79*1=79, Resulting Numbers: [79] 79,40 unequal: No Solution Exploring Operation: 79+1=80, Resulting Numbers: [80] 80,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 40:[79, 29], Operations: ['49-34=15', '14+15=29'] Exploring Operation: 79*29=2291, Resulting Numbers: [2291] 2291,40 unequal: No Solution Exploring Operation: 79+29=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 79-29=50, Resulting Numbers: [50] 50,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 40:[15, 93], Operations: ['49-34=15', '79+14=93'] Exploring Operation: 15*93=1395, Resulting Numbers: [1395] 1395,40 unequal: No Solution Exploring Operation: 15+93=108, Resulting Numbers: [108] 108,40 unequal: No Solution Exploring Operation: 93-15=78, Resulting Numbers: [78] 78,40 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
sum_heuristic
[ 85, 95, 82, 91 ]
55
[ "85*91=7735", "95*82=7790", "7790-7735=55" ]
Current State: 55:[85, 95, 82, 91], Operations: [] Exploring Operation: 85*91=7735, Resulting Numbers: [95, 82, 7735] Generated Node #2: [95, 82, 7735] from Operation: 85*91=7735 Current State: 55:[95, 82, 7735], Operations: ['85*91=7735'] Exploring Operation: 95*82=7790, Resulting Numbers: [7735, 7790] Generated Node #3: [7735, 7790] from Operation: 95*82=7790 Current State: 55:[7735, 7790], Operations: ['85*91=7735', '95*82=7790'] Exploring Operation: 7790-7735=55, Resulting Numbers: [55] 55,55 equal: Goal Reached
4
Current State: 55:[85, 95, 82, 91], Operations: [] Exploring Operation: 95-91=4, Resulting Numbers: [85, 82, 4] Generated Node #0,0: 55:[85, 82, 4] Operation: 95-91=4 Exploring Operation: 95-85=10, Resulting Numbers: [82, 91, 10] Generated Node #0,1: 55:[82, 91, 10] Operation: 95-85=10 Moving to Node #0,0 Current State: 55:[85, 82, 4], Operations: ['95-91=4'] Exploring Operation: 85-4=81, Resulting Numbers: [82, 81] Generated Node #0,0,0: 55:[82, 81] Operation: 85-4=81 Exploring Operation: 85-82=3, Resulting Numbers: [4, 3] Generated Node #0,0,1: 55:[4, 3] Operation: 85-82=3 Moving to Node #0,1 Current State: 55:[82, 91, 10], Operations: ['95-85=10'] Exploring Operation: 91-82=9, Resulting Numbers: [10, 9] Generated Node #0,1,0: 55:[10, 9] Operation: 91-82=9 Exploring Operation: 82-10=72, Resulting Numbers: [91, 72] Generated Node #0,1,1: 55:[91, 72] Operation: 82-10=72 Moving to Node #0,0,1 Current State: 55:[4, 3], Operations: ['95-91=4', '85-82=3'] Exploring Operation: 4+3=7, Resulting Numbers: [7] 7,55 unequal: No Solution Exploring Operation: 4*3=12, Resulting Numbers: [12] 12,55 unequal: No Solution Moving to Node #0,1,0 Current State: 55:[10, 9], Operations: ['95-85=10', '91-82=9'] Exploring Operation: 10-9=1, Resulting Numbers: [1] 1,55 unequal: No Solution Exploring Operation: 10+9=19, Resulting Numbers: [19] 19,55 unequal: No Solution Moving to Node #0,0,0 Current State: 55:[82, 81], Operations: ['95-91=4', '85-4=81'] Exploring Operation: 82+81=163, Resulting Numbers: [163] 163,55 unequal: No Solution Exploring Operation: 82-81=1, Resulting Numbers: [1] 1,55 unequal: No Solution Moving to Node #0,1,1 Current State: 55:[91, 72], Operations: ['95-85=10', '82-10=72'] Exploring Operation: 91+72=163, Resulting Numbers: [163] 163,55 unequal: No Solution Exploring Operation: 91-72=19, Resulting Numbers: [19] 19,55 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 94, 36, 98, 97 ]
86
[ "97-94=3", "36/3=12", "98-12=86" ]
Current State: 86:[94, 36, 98, 97], Operations: [] Exploring Operation: 97-94=3, Resulting Numbers: [36, 98, 3] Generated Node #2: [36, 98, 3] from Operation: 97-94=3 Current State: 86:[36, 98, 3], Operations: ['97-94=3'] Exploring Operation: 36/3=12, Resulting Numbers: [98, 12] Generated Node #3: [98, 12] from Operation: 36/3=12 Current State: 86:[98, 12], Operations: ['97-94=3', '36/3=12'] Exploring Operation: 98-12=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[94, 36, 98, 97], Operations: [] Exploring Operation: 98-94=4, Resulting Numbers: [36, 97, 4] Generated Node #0,0: 86:[36, 97, 4] Operation: 98-94=4 Exploring Operation: 98-97=1, Resulting Numbers: [94, 36, 1] Generated Node #0,1: 86:[94, 36, 1] Operation: 98-97=1 Moving to Node #0,1 Current State: 86:[94, 36, 1], Operations: ['98-97=1'] Exploring Operation: 36+1=37, Resulting Numbers: [94, 37] Generated Node #0,1,0: 86:[94, 37] Operation: 36+1=37 Exploring Operation: 94-1=93, Resulting Numbers: [36, 93] Generated Node #0,1,1: 86:[36, 93] Operation: 94-1=93 Moving to Node #0,0 Current State: 86:[36, 97, 4], Operations: ['98-94=4'] Exploring Operation: 36+4=40, Resulting Numbers: [97, 40] Generated Node #0,0,0: 86:[97, 40] Operation: 36+4=40 Exploring Operation: 97-4=93, Resulting Numbers: [36, 93] Generated Node #0,0,1: 86:[36, 93] Operation: 97-4=93 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 86:[97, 40], Operations: ['98-94=4', '36+4=40'] Exploring Operation: 97+40=137, Resulting Numbers: [137] 137,86 unequal: No Solution Exploring Operation: 97-40=57, Resulting Numbers: [57] 57,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 86:[36, 93], Operations: ['98-94=4', '97-4=93'] Exploring Operation: 93-36=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 36+93=129, Resulting Numbers: [129] 129,86 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: 86:[94, 37], Operations: ['98-97=1', '36+1=37'] Exploring Operation: 94+37=131, Resulting Numbers: [131] 131,86 unequal: No Solution Exploring Operation: 94-37=57, Resulting Numbers: [57] 57,86 unequal: No Solution Moving to Node #0,1,1 Current State: 86:[36, 93], Operations: ['98-97=1', '94-1=93'] Exploring Operation: 93-36=57, Resulting Numbers: [57] 57,86 unequal: No Solution Exploring Operation: 36+93=129, Resulting Numbers: [129] 129,86 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 91, 65, 28, 61 ]
67
[ "91+65=156", "28+61=89", "156-89=67" ]
Current State: 67:[91, 65, 28, 61], Operations: [] Exploring Operation: 91+65=156, Resulting Numbers: [28, 61, 156] Generated Node #2: [28, 61, 156] from Operation: 91+65=156 Current State: 67:[28, 61, 156], Operations: ['91+65=156'] Exploring Operation: 28+61=89, Resulting Numbers: [156, 89] Generated Node #3: [156, 89] from Operation: 28+61=89 Current State: 67:[156, 89], Operations: ['91+65=156', '28+61=89'] Exploring Operation: 156-89=67, Resulting Numbers: [67] 67,67 equal: Goal Reached
4
Current State: 67:[91, 65, 28, 61], Operations: [] Exploring Operation: 28+61=89, Resulting Numbers: [91, 65, 89] Generated Node #0,0: 67:[91, 65, 89] Operation: 28+61=89 Exploring Operation: 65+28=93, Resulting Numbers: [91, 61, 93] Generated Node #0,1: 67:[91, 61, 93] Operation: 65+28=93 Exploring Operation: 91-28=63, Resulting Numbers: [65, 61, 63] Generated Node #0,2: 67:[65, 61, 63] Operation: 91-28=63 Start Sub Search at level 1: Moving to Node #0,2 Current State: 67:[65, 61, 63], Operations: ['91-28=63'] Exploring Operation: 61+63=124, Resulting Numbers: [65, 124] Generated Node #0,2,0: 67:[65, 124] Operation: 61+63=124 Exploring Operation: 65+61=126, Resulting Numbers: [63, 126] Generated Node #0,2,1: 67:[63, 126] Operation: 65+61=126 Exploring Operation: 65-61=4, Resulting Numbers: [63, 4] Generated Node #0,2,2: 67:[63, 4] Operation: 65-61=4 Moving to Node #0,2,0 Current State: 67:[65, 124], Operations: ['91-28=63', '61+63=124'] Exploring Operation: 65*124=8060, Resulting Numbers: [8060] 8060,67 unequal: No Solution Exploring Operation: 124-65=59, Resulting Numbers: [59] 59,67 unequal: No Solution Exploring Operation: 65+124=189, Resulting Numbers: [189] 189,67 unequal: No Solution Moving to Node #0,2,1 Current State: 67:[63, 126], Operations: ['91-28=63', '65+61=126'] Exploring Operation: 126-63=63, Resulting Numbers: [63] 63,67 unequal: No Solution Exploring Operation: 63+126=189, Resulting Numbers: [189] 189,67 unequal: No Solution Exploring Operation: 126/63=2, Resulting Numbers: [2] 2,67 unequal: No Solution Moving to Node #0,2,2 Current State: 67:[63, 4], Operations: ['91-28=63', '65-61=4'] Exploring Operation: 63-4=59, Resulting Numbers: [59] 59,67 unequal: No Solution Exploring Operation: 63*4=252, Resulting Numbers: [252] 252,67 unequal: No Solution Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Moving to Node #0 Current State: 67:[91, 65, 28, 61], Operations: [] Exploring Operation: 91-28=63, Resulting Numbers: [65, 61, 63] Generated Node #0,2: 67:[65, 61, 63] Operation: 91-28=63 Moving to Node #0,2 Current State: 67:[65, 61, 63], Operations: ['91-28=63'] Exploring Operation: 65-61=4, Resulting Numbers: [63, 4] Generated Node #0,2,2: 67:[63, 4] Operation: 65-61=4 Moving to Node #0,2,2 Current State: 67:[63, 4], Operations: ['91-28=63', '65-61=4'] Exploring Operation: 63+4=67, Resulting Numbers: [67] 67,67 equal: Goal Reached Exit Sub Search at level 1
0.983507
hs_3
sum_heuristic