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
[ 16, 59, 75, 18 ]
43
[ "18-16=2", "59*2=118", "118-75=43" ]
Current State: 43:[16, 59, 75, 18], Operations: [] Exploring Operation: 18-16=2, Resulting Numbers: [59, 75, 2] Generated Node #2: [59, 75, 2] from Operation: 18-16=2 Current State: 43:[59, 75, 2], Operations: ['18-16=2'] Exploring Operation: 59*2=118, Resulting Numbers: [75, 118] Generated Node #3: [75, 118] from Operation: 59*2=118 Current State: 43:[75, 118], Operations: ['18-16=2', '59*2=118'] Exploring Operation: 118-75=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[16, 59, 75, 18], Operations: [] Exploring Operation: 59-16=43, Resulting Numbers: [75, 18, 43] Generated Node #0,0: 43:[75, 18, 43] Operation: 59-16=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[75, 18, 43], Operations: ['59-16=43'] Exploring Operation: 75-18=57, Resulting Numbers: [43, 57] Generated Node #0,0,0: 43:[43, 57] Operation: 75-18=57 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[43, 57], Operations: ['59-16=43', '75-18=57'] Exploring Operation: 57-43=14, Resulting Numbers: [14] 14,43 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 63, 66, 7, 34 ]
30
[ "66-63=3", "34-7=27", "3+27=30" ]
Current State: 30:[63, 66, 7, 34], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [7, 34, 3] Generated Node #2: [7, 34, 3] from Operation: 66-63=3 Current State: 30:[7, 34, 3], Operations: ['66-63=3'] Exploring Operation: 34-7=27, Resulting Numbers: [3, 27] Generated Node #3: [3, 27] from Operation: 34-7=27 Current State: 30:[3, 27], Operations: ['66-63=3', '34-7=27'] Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[63, 66, 7, 34], Operations: [] Exploring Operation: 66-34=32, Resulting Numbers: [63, 7, 32] Generated Node #0,0: 30:[63, 7, 32] Operation: 66-34=32 Exploring Operation: 66-63=3, Resulting Numbers: [7, 34, 3] Generated Node #0,1: 30:[7, 34, 3] Operation: 66-63=3 Exploring Operation: 63-34=29, Resulting Numbers: [66, 7, 29] Generated Node #0,2: 30:[66, 7, 29] Operation: 63-34=29 Start Sub Search at level 1: Moving to Node #0,1 Current State: 30:[7, 34, 3], Operations: ['66-63=3'] Exploring Operation: 34-3=31, Resulting Numbers: [7, 31] Generated Node #0,1,0: 30:[7, 31] Operation: 34-3=31 Exploring Operation: 34-7=27, Resulting Numbers: [3, 27] Generated Node #0,1,1: 30:[3, 27] Operation: 34-7=27 Exploring Operation: 7+3=10, Resulting Numbers: [34, 10] Generated Node #0,1,2: 30:[34, 10] Operation: 7+3=10 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 30:[7, 31], Operations: ['66-63=3', '34-3=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,30 unequal: No Solution Exploring Operation: 31-7=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 7*31=217, Resulting Numbers: [217] 217,30 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 30:[3, 27], Operations: ['66-63=3', '34-7=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,30 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,30 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Moving to Node #0 Current State: 30:[63, 66, 7, 34], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [7, 34, 3] Generated Node #0,1: 30:[7, 34, 3] Operation: 66-63=3 Moving to Node #0,1 Current State: 30:[7, 34, 3], Operations: ['66-63=3'] Exploring Operation: 34-7=27, Resulting Numbers: [3, 27] Generated Node #0,1,1: 30:[3, 27] Operation: 34-7=27 Moving to Node #0,1,1 Current State: 30:[3, 27], Operations: ['66-63=3', '34-7=27'] Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,30 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986111
hs_3
sum_heuristic
[ 75, 13, 50, 33 ]
69
[ "13+33=46", "75*46=3450", "3450/50=69" ]
Current State: 69:[75, 13, 50, 33], Operations: [] Exploring Operation: 13+33=46, Resulting Numbers: [75, 50, 46] Generated Node #2: [75, 50, 46] from Operation: 13+33=46 Current State: 69:[75, 50, 46], Operations: ['13+33=46'] Exploring Operation: 75*46=3450, Resulting Numbers: [50, 3450] Generated Node #3: [50, 3450] from Operation: 75*46=3450 Current State: 69:[50, 3450], Operations: ['13+33=46', '75*46=3450'] Exploring Operation: 3450/50=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[75, 13, 50, 33], Operations: [] Exploring Operation: 33-13=20, Resulting Numbers: [75, 50, 20] Generated Node #0,0: 69:[75, 50, 20] Operation: 33-13=20 Exploring Operation: 50-33=17, Resulting Numbers: [75, 13, 17] Generated Node #0,1: 69:[75, 13, 17] Operation: 50-33=17 Exploring Operation: 75-50=25, Resulting Numbers: [13, 33, 25] Generated Node #0,2: 69:[13, 33, 25] Operation: 75-50=25 Exploring Operation: 13+50=63, Resulting Numbers: [75, 33, 63] Generated Node #0,3: 69:[75, 33, 63] Operation: 13+50=63 Moving to Node #0,1 Current State: 69:[75, 13, 17], Operations: ['50-33=17'] Exploring Operation: 17-13=4, Resulting Numbers: [75, 4] Generated Node #0,1,0: 69:[75, 4] Operation: 17-13=4 Exploring Operation: 13+17=30, Resulting Numbers: [75, 30] Generated Node #0,1,1: 69:[75, 30] Operation: 13+17=30 Exploring Operation: 75-17=58, Resulting Numbers: [13, 58] Generated Node #0,1,2: 69:[13, 58] Operation: 75-17=58 Exploring Operation: 75-13=62, Resulting Numbers: [17, 62] Generated Node #0,1,3: 69:[17, 62] Operation: 75-13=62 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[75, 4], Operations: ['50-33=17', '17-13=4'] Exploring Operation: 75+4=79, Resulting Numbers: [79] 79,69 unequal: No Solution Exploring Operation: 75-4=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 75*4=300, Resulting Numbers: [300] 300,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[75, 30], Operations: ['50-33=17', '13+17=30'] Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[17, 62], Operations: ['50-33=17', '75-13=62'] Exploring Operation: 62-17=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 17*62=1054, Resulting Numbers: [1054] 1054,69 unequal: No Solution Exploring Operation: 17+62=79, Resulting Numbers: [79] 79,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[13, 58], Operations: ['50-33=17', '75-17=58'] Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,69 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: 69:[75, 33, 63], Operations: ['13+50=63'] Exploring Operation: 63-33=30, Resulting Numbers: [75, 30] Generated Node #0,3,0: 69:[75, 30] Operation: 63-33=30 Exploring Operation: 75-63=12, Resulting Numbers: [33, 12] Generated Node #0,3,1: 69:[33, 12] Operation: 75-63=12 Exploring Operation: 33+63=96, Resulting Numbers: [75, 96] Generated Node #0,3,2: 69:[75, 96] Operation: 33+63=96 Exploring Operation: 75-33=42, Resulting Numbers: [63, 42] Generated Node #0,3,3: 69:[63, 42] Operation: 75-33=42 Moving to Node #0,2 Current State: 69:[13, 33, 25], Operations: ['75-50=25'] Exploring Operation: 33-25=8, Resulting Numbers: [13, 8] Generated Node #0,2,0: 69:[13, 8] Operation: 33-25=8 Exploring Operation: 33-13=20, Resulting Numbers: [25, 20] Generated Node #0,2,1: 69:[25, 20] Operation: 33-13=20 Exploring Operation: 25-13=12, Resulting Numbers: [33, 12] Generated Node #0,2,2: 69:[33, 12] Operation: 25-13=12 Exploring Operation: 33+25=58, Resulting Numbers: [13, 58] Generated Node #0,2,3: 69:[13, 58] Operation: 33+25=58 Moving to Node #0,0 Current State: 69:[75, 50, 20], Operations: ['33-13=20'] Exploring Operation: 75-20=55, Resulting Numbers: [50, 55] Generated Node #0,0,0: 69:[50, 55] Operation: 75-20=55 Exploring Operation: 50-20=30, Resulting Numbers: [75, 30] Generated Node #0,0,1: 69:[75, 30] Operation: 50-20=30 Exploring Operation: 50+20=70, Resulting Numbers: [75, 70] Generated Node #0,0,2: 69:[75, 70] Operation: 50+20=70 Exploring Operation: 75-50=25, Resulting Numbers: [20, 25] Generated Node #0,0,3: 69:[20, 25] Operation: 75-50=25 Moving to Node #0,2,1 Current State: 69:[25, 20], Operations: ['75-50=25', '33-13=20'] Exploring Operation: 25+20=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 25*20=500, Resulting Numbers: [500] 500,69 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,0,3 Current State: 69:[20, 25], Operations: ['33-13=20', '75-50=25'] Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,69 unequal: No Solution Moving to Node #0,0,2 Current State: 69:[75, 70], Operations: ['33-13=20', '50+20=70'] Exploring Operation: 75*70=5250, Resulting Numbers: [5250] 5250,69 unequal: No Solution Exploring Operation: 75+70=145, Resulting Numbers: [145] 145,69 unequal: No Solution Exploring Operation: 75-70=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,0,1 Current State: 69:[75, 30], Operations: ['33-13=20', '50-20=30'] Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,69 unequal: No Solution Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[75, 30], Operations: ['13+50=63', '63-33=30'] Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,69 unequal: No Solution Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,69 unequal: No Solution Moving to Node #0,2,0 Current State: 69:[13, 8], Operations: ['75-50=25', '33-25=8'] Exploring Operation: 13+8=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 13*8=104, Resulting Numbers: [104] 104,69 unequal: No Solution Exploring Operation: 13-8=5, Resulting Numbers: [5] 5,69 unequal: No Solution Moving to Node #0,2,2 Current State: 69:[33, 12], Operations: ['75-50=25', '25-13=12'] Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,69 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[33, 12], Operations: ['13+50=63', '75-63=12'] Exploring Operation: 33+12=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 33*12=396, Resulting Numbers: [396] 396,69 unequal: No Solution Exploring Operation: 33-12=21, Resulting Numbers: [21] 21,69 unequal: No Solution Moving to Node #0,2,3 Current State: 69:[13, 58], Operations: ['75-50=25', '33+25=58'] Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,69 unequal: No Solution Exploring Operation: 13*58=754, Resulting Numbers: [754] 754,69 unequal: No Solution Exploring Operation: 13+58=71, Resulting Numbers: [71] 71,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[63, 42], Operations: ['13+50=63', '75-33=42'] Exploring Operation: 63-42=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 63+42=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 63*42=2646, Resulting Numbers: [2646] 2646,69 unequal: No Solution Moving to Node #0,3,2 Current State: 69:[75, 96], Operations: ['13+50=63', '33+63=96'] Exploring Operation: 96-75=21, Resulting Numbers: [21] 21,69 unequal: No Solution Exploring Operation: 75+96=171, Resulting Numbers: [171] 171,69 unequal: No Solution Exploring Operation: 75*96=7200, Resulting Numbers: [7200] 7200,69 unequal: No Solution Moving to Node #0,0,0 Current State: 69:[50, 55], Operations: ['33-13=20', '75-20=55'] Exploring Operation: 50+55=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,69 unequal: No Solution Exploring Operation: 50*55=2750, Resulting Numbers: [2750] 2750,69 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 26, 99, 90 ]
57
[ "90/15=6", "26*6=156", "156-99=57" ]
Current State: 57:[15, 26, 99, 90], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [26, 99, 6] Generated Node #2: [26, 99, 6] from Operation: 90/15=6 Current State: 57:[26, 99, 6], Operations: ['90/15=6'] Exploring Operation: 26*6=156, Resulting Numbers: [99, 156] Generated Node #3: [99, 156] from Operation: 26*6=156 Current State: 57:[99, 156], Operations: ['90/15=6', '26*6=156'] Exploring Operation: 156-99=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[15, 26, 99, 90], Operations: [] Exploring Operation: 90/15=6, Resulting Numbers: [26, 99, 6] Generated Node #0,0: 57:[26, 99, 6] Operation: 90/15=6 Exploring Operation: 99-90=9, Resulting Numbers: [15, 26, 9] Generated Node #0,1: 57:[15, 26, 9] Operation: 99-90=9 Exploring Operation: 99-26=73, Resulting Numbers: [15, 90, 73] Generated Node #0,2: 57:[15, 90, 73] Operation: 99-26=73 Moving to Node #0,1 Current State: 57:[15, 26, 9], Operations: ['99-90=9'] Exploring Operation: 26-9=17, Resulting Numbers: [15, 17] Generated Node #0,1,0: 57:[15, 17] Operation: 26-9=17 Exploring Operation: 15+9=24, Resulting Numbers: [26, 24] Generated Node #0,1,1: 57:[26, 24] Operation: 15+9=24 Exploring Operation: 15-9=6, Resulting Numbers: [26, 6] Generated Node #0,1,2: 57:[26, 6] Operation: 15-9=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 57:[15, 17], Operations: ['99-90=9', '26-9=17'] Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 57:[26, 6], Operations: ['99-90=9', '15-9=6'] Exploring Operation: 26-6=20, Resulting Numbers: [20] 20,57 unequal: No Solution Exploring Operation: 26+6=32, Resulting Numbers: [32] 32,57 unequal: No Solution Exploring Operation: 26*6=156, Resulting Numbers: [156] 156,57 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 57:[26, 24], Operations: ['99-90=9', '15+9=24'] Exploring Operation: 26+24=50, Resulting Numbers: [50] 50,57 unequal: No Solution Exploring Operation: 26*24=624, Resulting Numbers: [624] 624,57 unequal: No Solution Exploring Operation: 26-24=2, Resulting Numbers: [2] 2,57 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: 57:[26, 99, 6], Operations: ['90/15=6'] Exploring Operation: 99-26=73, Resulting Numbers: [6, 73] Generated Node #0,0,0: 57:[6, 73] Operation: 99-26=73 Exploring Operation: 26-6=20, Resulting Numbers: [99, 20] Generated Node #0,0,1: 57:[99, 20] Operation: 26-6=20 Exploring Operation: 99-6=93, Resulting Numbers: [26, 93] Generated Node #0,0,2: 57:[26, 93] Operation: 99-6=93 Moving to Node #0,2 Current State: 57:[15, 90, 73], Operations: ['99-26=73'] Exploring Operation: 90/15=6, Resulting Numbers: [73, 6] Generated Node #0,2,0: 57:[73, 6] Operation: 90/15=6 Exploring Operation: 90-15=75, Resulting Numbers: [73, 75] Generated Node #0,2,1: 57:[73, 75] Operation: 90-15=75 Exploring Operation: 90-73=17, Resulting Numbers: [15, 17] Generated Node #0,2,2: 57:[15, 17] Operation: 90-73=17 Moving to Node #0,2,2 Current State: 57:[15, 17], Operations: ['99-26=73', '90-73=17'] Exploring Operation: 15*17=255, Resulting Numbers: [255] 255,57 unequal: No Solution Exploring Operation: 17-15=2, Resulting Numbers: [2] 2,57 unequal: No Solution Exploring Operation: 15+17=32, Resulting Numbers: [32] 32,57 unequal: No Solution Moving to Node #0,0,0 Current State: 57:[6, 73], Operations: ['90/15=6', '99-26=73'] Exploring Operation: 6*73=438, Resulting Numbers: [438] 438,57 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 6+73=79, Resulting Numbers: [79] 79,57 unequal: No Solution Moving to Node #0,2,0 Current State: 57:[73, 6], Operations: ['99-26=73', '90/15=6'] Exploring Operation: 73+6=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 73*6=438, Resulting Numbers: [438] 438,57 unequal: No Solution Exploring Operation: 73-6=67, Resulting Numbers: [67] 67,57 unequal: No Solution Moving to Node #0,2,1 Current State: 57:[73, 75], Operations: ['99-26=73', '90-15=75'] Exploring Operation: 73*75=5475, Resulting Numbers: [5475] 5475,57 unequal: No Solution Exploring Operation: 73+75=148, Resulting Numbers: [148] 148,57 unequal: No Solution Exploring Operation: 75-73=2, Resulting Numbers: [2] 2,57 unequal: No Solution Moving to Node #0,0,1 Current State: 57:[99, 20], Operations: ['90/15=6', '26-6=20'] Exploring Operation: 99-20=79, Resulting Numbers: [79] 79,57 unequal: No Solution Exploring Operation: 99+20=119, Resulting Numbers: [119] 119,57 unequal: No Solution Exploring Operation: 99*20=1980, Resulting Numbers: [1980] 1980,57 unequal: No Solution Moving to Node #0,0,2 Current State: 57:[26, 93], Operations: ['90/15=6', '99-6=93'] Exploring Operation: 26+93=119, Resulting Numbers: [119] 119,57 unequal: No Solution Exploring Operation: 93-26=67, Resulting Numbers: [67] 67,57 unequal: No Solution Exploring Operation: 26*93=2418, Resulting Numbers: [2418] 2418,57 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 31, 98, 97, 13 ]
44
[ "31+13=44", "98-97=1", "44*1=44" ]
Current State: 44:[31, 98, 97, 13], Operations: [] Exploring Operation: 31+13=44, Resulting Numbers: [98, 97, 44] Generated Node #2: [98, 97, 44] from Operation: 31+13=44 Current State: 44:[98, 97, 44], Operations: ['31+13=44'] Exploring Operation: 98-97=1, Resulting Numbers: [44, 1] Generated Node #3: [44, 1] from Operation: 98-97=1 Current State: 44:[44, 1], Operations: ['31+13=44', '98-97=1'] Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
4
Current State: 44:[31, 98, 97, 13], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [31, 13, 1] Generated Node #0,0: 44:[31, 13, 1] Operation: 98-97=1 Exploring Operation: 98-31=67, Resulting Numbers: [97, 13, 67] Generated Node #0,1: 44:[97, 13, 67] Operation: 98-31=67 Moving to Node #0,0 Current State: 44:[31, 13, 1], Operations: ['98-97=1'] Exploring Operation: 31-13=18, Resulting Numbers: [1, 18] Generated Node #0,0,0: 44:[1, 18] Operation: 31-13=18 Exploring Operation: 31+13=44, Resulting Numbers: [1, 44] Generated Node #0,0,1: 44:[1, 44] Operation: 31+13=44 Moving to Node #0,1 Current State: 44:[97, 13, 67], Operations: ['98-31=67'] Exploring Operation: 97-67=30, Resulting Numbers: [13, 30] Generated Node #0,1,0: 44:[13, 30] Operation: 97-67=30 Exploring Operation: 97-13=84, Resulting Numbers: [67, 84] Generated Node #0,1,1: 44:[67, 84] Operation: 97-13=84 Moving to Node #0,0,1 Current State: 44:[1, 44], Operations: ['98-97=1', '31+13=44'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached Moving to Node #0 Current State: 44:[31, 98, 97, 13], Operations: [] Exploring Operation: 98-97=1, Resulting Numbers: [31, 13, 1] Generated Node #0,0: 44:[31, 13, 1] Operation: 98-97=1 Moving to Node #0,0 Current State: 44:[31, 13, 1], Operations: ['98-97=1'] Exploring Operation: 31+13=44, Resulting Numbers: [1, 44] Generated Node #0,0,1: 44:[1, 44] Operation: 31+13=44 Moving to Node #0,0,1 Current State: 44:[1, 44], Operations: ['98-97=1', '31+13=44'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,44 equal: Goal Reached
0.990451
hs_2
mult_heuristic
[ 88, 4, 48, 21 ]
76
[ "88-48=40", "40-21=19", "4*19=76" ]
Current State: 76:[88, 4, 48, 21], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [4, 21, 40] Generated Node #2: [4, 21, 40] from Operation: 88-48=40 Current State: 76:[4, 21, 40], Operations: ['88-48=40'] Exploring Operation: 40-21=19, Resulting Numbers: [4, 19] Generated Node #3: [4, 19] from Operation: 40-21=19 Current State: 76:[4, 19], Operations: ['88-48=40', '40-21=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached
4
Current State: 76:[88, 4, 48, 21], Operations: [] Exploring Operation: 88-21=67, Resulting Numbers: [4, 48, 67] Generated Node #0,0: 76:[4, 48, 67] Operation: 88-21=67 Exploring Operation: 88/4=22, Resulting Numbers: [48, 21, 22] Generated Node #0,1: 76:[48, 21, 22] Operation: 88/4=22 Exploring Operation: 88-48=40, Resulting Numbers: [4, 21, 40] Generated Node #0,2: 76:[4, 21, 40] Operation: 88-48=40 Start Sub Search at level 1: Moving to Node #0,2 Current State: 76:[4, 21, 40], Operations: ['88-48=40'] Exploring Operation: 40-4=36, Resulting Numbers: [21, 36] Generated Node #0,2,0: 76:[21, 36] Operation: 40-4=36 Exploring Operation: 40-21=19, Resulting Numbers: [4, 19] Generated Node #0,2,1: 76:[4, 19] Operation: 40-21=19 Exploring Operation: 21-4=17, Resulting Numbers: [40, 17] Generated Node #0,2,2: 76:[40, 17] Operation: 21-4=17 Moving to Node #0,2,1 Current State: 76:[4, 19], Operations: ['88-48=40', '40-21=19'] Exploring Operation: 4+19=23, Resulting Numbers: [23] 23,76 unequal: No Solution Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Moving to Node #0 Current State: 76:[88, 4, 48, 21], Operations: [] Exploring Operation: 88-48=40, Resulting Numbers: [4, 21, 40] Generated Node #0,2: 76:[4, 21, 40] Operation: 88-48=40 Moving to Node #0,2 Current State: 76:[4, 21, 40], Operations: ['88-48=40'] Exploring Operation: 40-21=19, Resulting Numbers: [4, 19] Generated Node #0,2,1: 76:[4, 19] Operation: 40-21=19 Moving to Node #0,2,1 Current State: 76:[4, 19], Operations: ['88-48=40', '40-21=19'] Exploring Operation: 4*19=76, Resulting Numbers: [76] 76,76 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 7, 14, 10, 31 ]
49
[ "14+10=24", "31-24=7", "7*7=49" ]
Current State: 49:[7, 14, 10, 31], Operations: [] Exploring Operation: 14+10=24, Resulting Numbers: [7, 31, 24] Generated Node #2: [7, 31, 24] from Operation: 14+10=24 Current State: 49:[7, 31, 24], Operations: ['14+10=24'] Exploring Operation: 31-24=7, Resulting Numbers: [7, 7] Generated Node #3: [7, 7] from Operation: 31-24=7 Current State: 49:[7, 7], Operations: ['14+10=24', '31-24=7'] Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[7, 14, 10, 31], Operations: [] Exploring Operation: 14+31=45, Resulting Numbers: [7, 10, 45] Generated Node #0,0: 49:[7, 10, 45] Operation: 14+31=45 Moving to Node #0,0 Current State: 49:[7, 10, 45], Operations: ['14+31=45'] Exploring Operation: 7+45=52, Resulting Numbers: [10, 52] Generated Node #0,0,0: 49:[10, 52] Operation: 7+45=52 Moving to Node #0,0,0 Current State: 49:[10, 52], Operations: ['14+31=45', '7+45=52'] Exploring Operation: 52-10=42, Resulting Numbers: [42] 42,49 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 3, 15, 57, 37 ]
69
[ "3*37=111", "57-15=42", "111-42=69" ]
Current State: 69:[3, 15, 57, 37], Operations: [] Exploring Operation: 3*37=111, Resulting Numbers: [15, 57, 111] Generated Node #2: [15, 57, 111] from Operation: 3*37=111 Current State: 69:[15, 57, 111], Operations: ['3*37=111'] Exploring Operation: 57-15=42, Resulting Numbers: [111, 42] Generated Node #3: [111, 42] from Operation: 57-15=42 Current State: 69:[111, 42], Operations: ['3*37=111', '57-15=42'] Exploring Operation: 111-42=69, Resulting Numbers: [69] 69,69 equal: Goal Reached
4
Current State: 69:[3, 15, 57, 37], Operations: [] Exploring Operation: 15/3=5, Resulting Numbers: [57, 37, 5] Generated Node #0,0: 69:[57, 37, 5] Operation: 15/3=5 Exploring Operation: 15+57=72, Resulting Numbers: [3, 37, 72] Generated Node #0,1: 69:[3, 37, 72] Operation: 15+57=72 Exploring Operation: 57-37=20, Resulting Numbers: [3, 15, 20] Generated Node #0,2: 69:[3, 15, 20] Operation: 57-37=20 Exploring Operation: 37-15=22, Resulting Numbers: [3, 57, 22] Generated Node #0,3: 69:[3, 57, 22] Operation: 37-15=22 Exploring Operation: 57/3=19, Resulting Numbers: [15, 37, 19] Generated Node #0,4: 69:[15, 37, 19] Operation: 57/3=19 Moving to Node #0,2 Current State: 69:[3, 15, 20], Operations: ['57-37=20'] Exploring Operation: 15/3=5, Resulting Numbers: [20, 5] Generated Node #0,2,0: 69:[20, 5] Operation: 15/3=5 Exploring Operation: 3+15=18, Resulting Numbers: [20, 18] Generated Node #0,2,1: 69:[20, 18] Operation: 3+15=18 Exploring Operation: 15-3=12, Resulting Numbers: [20, 12] Generated Node #0,2,2: 69:[20, 12] Operation: 15-3=12 Exploring Operation: 20-15=5, Resulting Numbers: [3, 5] Generated Node #0,2,3: 69:[3, 5] Operation: 20-15=5 Exploring Operation: 3+20=23, Resulting Numbers: [15, 23] Generated Node #0,2,4: 69:[15, 23] Operation: 3+20=23 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 69:[3, 5], Operations: ['57-37=20', '20-15=5'] Exploring Operation: 3*5=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 3+5=8, Resulting Numbers: [8] 8,69 unequal: No Solution Exploring Operation: 5-3=2, Resulting Numbers: [2] 2,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 69:[20, 5], Operations: ['57-37=20', '15/3=5'] Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,69 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 69:[20, 18], Operations: ['57-37=20', '3+15=18'] Exploring Operation: 20*18=360, Resulting Numbers: [360] 360,69 unequal: No Solution Exploring Operation: 20+18=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 20-18=2, Resulting Numbers: [2] 2,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 69:[15, 23], Operations: ['57-37=20', '3+20=23'] Exploring Operation: 15*23=345, Resulting Numbers: [345] 345,69 unequal: No Solution Exploring Operation: 15+23=38, Resulting Numbers: [38] 38,69 unequal: No Solution Exploring Operation: 23-15=8, Resulting Numbers: [8] 8,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 69:[20, 12], Operations: ['57-37=20', '15-3=12'] Exploring Operation: 20+12=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 20*12=240, Resulting Numbers: [240] 240,69 unequal: No Solution Exploring Operation: 20-12=8, Resulting Numbers: [8] 8,69 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: 69:[3, 57, 22], Operations: ['37-15=22'] Exploring Operation: 3+57=60, Resulting Numbers: [22, 60] Generated Node #0,3,0: 69:[22, 60] Operation: 3+57=60 Exploring Operation: 3+22=25, Resulting Numbers: [57, 25] Generated Node #0,3,1: 69:[57, 25] Operation: 3+22=25 Exploring Operation: 57/3=19, Resulting Numbers: [22, 19] Generated Node #0,3,2: 69:[22, 19] Operation: 57/3=19 Exploring Operation: 57+22=79, Resulting Numbers: [3, 79] Generated Node #0,3,3: 69:[3, 79] Operation: 57+22=79 Exploring Operation: 57-22=35, Resulting Numbers: [3, 35] Generated Node #0,3,4: 69:[3, 35] Operation: 57-22=35 Moving to Node #0,1 Current State: 69:[3, 37, 72], Operations: ['15+57=72'] Exploring Operation: 37-3=34, Resulting Numbers: [72, 34] Generated Node #0,1,0: 69:[72, 34] Operation: 37-3=34 Exploring Operation: 3+37=40, Resulting Numbers: [72, 40] Generated Node #0,1,1: 69:[72, 40] Operation: 3+37=40 Exploring Operation: 72/3=24, Resulting Numbers: [37, 24] Generated Node #0,1,2: 69:[37, 24] Operation: 72/3=24 Exploring Operation: 72-3=69, Resulting Numbers: [37, 69] Generated Node #0,1,3: 69:[37, 69] Operation: 72-3=69 Exploring Operation: 72-37=35, Resulting Numbers: [3, 35] Generated Node #0,1,4: 69:[3, 35] Operation: 72-37=35 Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 69:[3, 35], Operations: ['15+57=72', '72-37=35'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 69:[72, 34], Operations: ['15+57=72', '37-3=34'] Exploring Operation: 72*34=2448, Resulting Numbers: [2448] 2448,69 unequal: No Solution Exploring Operation: 72+34=106, Resulting Numbers: [106] 106,69 unequal: No Solution Exploring Operation: 72-34=38, Resulting Numbers: [38] 38,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 69:[37, 69], Operations: ['15+57=72', '72-3=69'] Exploring Operation: 37*69=2553, Resulting Numbers: [2553] 2553,69 unequal: No Solution Exploring Operation: 69-37=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 37+69=106, Resulting Numbers: [106] 106,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 69:[37, 24], Operations: ['15+57=72', '72/3=24'] Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,69 unequal: No Solution Exploring Operation: 37+24=61, Resulting Numbers: [61] 61,69 unequal: No Solution Exploring Operation: 37*24=888, Resulting Numbers: [888] 888,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 69:[72, 40], Operations: ['15+57=72', '3+37=40'] Exploring Operation: 72*40=2880, Resulting Numbers: [2880] 2880,69 unequal: No Solution Exploring Operation: 72-40=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 72+40=112, Resulting Numbers: [112] 112,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 69:[15, 37, 19], Operations: ['57/3=19'] Exploring Operation: 37-19=18, Resulting Numbers: [15, 18] Generated Node #0,4,0: 69:[15, 18] Operation: 37-19=18 Exploring Operation: 37-15=22, Resulting Numbers: [19, 22] Generated Node #0,4,1: 69:[19, 22] Operation: 37-15=22 Exploring Operation: 19-15=4, Resulting Numbers: [37, 4] Generated Node #0,4,2: 69:[37, 4] Operation: 19-15=4 Exploring Operation: 37+19=56, Resulting Numbers: [15, 56] Generated Node #0,4,3: 69:[15, 56] Operation: 37+19=56 Exploring Operation: 15+37=52, Resulting Numbers: [19, 52] Generated Node #0,4,4: 69:[19, 52] Operation: 15+37=52 Moving to Node #0,0 Current State: 69:[57, 37, 5], Operations: ['15/3=5'] Exploring Operation: 57-37=20, Resulting Numbers: [5, 20] Generated Node #0,0,0: 69:[5, 20] Operation: 57-37=20 Exploring Operation: 57+5=62, Resulting Numbers: [37, 62] Generated Node #0,0,1: 69:[37, 62] Operation: 57+5=62 Exploring Operation: 57+37=94, Resulting Numbers: [5, 94] Generated Node #0,0,2: 69:[5, 94] Operation: 57+37=94 Exploring Operation: 37-5=32, Resulting Numbers: [57, 32] Generated Node #0,0,3: 69:[57, 32] Operation: 37-5=32 Exploring Operation: 57-5=52, Resulting Numbers: [37, 52] Generated Node #0,0,4: 69:[37, 52] Operation: 57-5=52 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 69:[5, 20], Operations: ['15/3=5', '57-37=20'] Exploring Operation: 5+20=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,69 unequal: No Solution Exploring Operation: 5*20=100, Resulting Numbers: [100] 100,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 69:[37, 62], Operations: ['15/3=5', '57+5=62'] Exploring Operation: 62-37=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 37*62=2294, Resulting Numbers: [2294] 2294,69 unequal: No Solution Exploring Operation: 37+62=99, Resulting Numbers: [99] 99,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 69:[57, 32], Operations: ['15/3=5', '37-5=32'] Exploring Operation: 57*32=1824, Resulting Numbers: [1824] 1824,69 unequal: No Solution Exploring Operation: 57-32=25, Resulting Numbers: [25] 25,69 unequal: No Solution Exploring Operation: 57+32=89, Resulting Numbers: [89] 89,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 69:[5, 94], Operations: ['15/3=5', '57+37=94'] Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,69 unequal: No Solution Exploring Operation: 5+94=99, Resulting Numbers: [99] 99,69 unequal: No Solution Exploring Operation: 5*94=470, Resulting Numbers: [470] 470,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 69:[37, 52], Operations: ['15/3=5', '57-5=52'] Exploring Operation: 52-37=15, Resulting Numbers: [15] 15,69 unequal: No Solution Exploring Operation: 37+52=89, Resulting Numbers: [89] 89,69 unequal: No Solution Exploring Operation: 37*52=1924, Resulting Numbers: [1924] 1924,69 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3,2 Current State: 69:[22, 19], Operations: ['37-15=22', '57/3=19'] Exploring Operation: 22*19=418, Resulting Numbers: [418] 418,69 unequal: No Solution Exploring Operation: 22+19=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,69 unequal: No Solution Moving to Node #0,4,1 Current State: 69:[19, 22], Operations: ['57/3=19', '37-15=22'] Exploring Operation: 19+22=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 22-19=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 19*22=418, Resulting Numbers: [418] 418,69 unequal: No Solution Moving to Node #0,3,3 Current State: 69:[3, 79], Operations: ['37-15=22', '57+22=79'] Exploring Operation: 79-3=76, Resulting Numbers: [76] 76,69 unequal: No Solution Exploring Operation: 3+79=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 3*79=237, Resulting Numbers: [237] 237,69 unequal: No Solution Moving to Node #0,3,0 Current State: 69:[22, 60], Operations: ['37-15=22', '3+57=60'] Exploring Operation: 22*60=1320, Resulting Numbers: [1320] 1320,69 unequal: No Solution Exploring Operation: 22+60=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 60-22=38, Resulting Numbers: [38] 38,69 unequal: No Solution Moving to Node #0,3,4 Current State: 69:[3, 35], Operations: ['37-15=22', '57-22=35'] Exploring Operation: 3*35=105, Resulting Numbers: [105] 105,69 unequal: No Solution Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,69 unequal: No Solution Exploring Operation: 3+35=38, Resulting Numbers: [38] 38,69 unequal: No Solution Moving to Node #0,4,0 Current State: 69:[15, 18], Operations: ['57/3=19', '37-19=18'] Exploring Operation: 15*18=270, Resulting Numbers: [270] 270,69 unequal: No Solution Exploring Operation: 18-15=3, Resulting Numbers: [3] 3,69 unequal: No Solution Exploring Operation: 15+18=33, Resulting Numbers: [33] 33,69 unequal: No Solution Moving to Node #0,3,1 Current State: 69:[57, 25], Operations: ['37-15=22', '3+22=25'] Exploring Operation: 57+25=82, Resulting Numbers: [82] 82,69 unequal: No Solution Exploring Operation: 57*25=1425, Resulting Numbers: [1425] 1425,69 unequal: No Solution Exploring Operation: 57-25=32, Resulting Numbers: [32] 32,69 unequal: No Solution Moving to Node #0,4,2 Current State: 69:[37, 4], Operations: ['57/3=19', '19-15=4'] Exploring Operation: 37-4=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 37*4=148, Resulting Numbers: [148] 148,69 unequal: No Solution Exploring Operation: 37+4=41, Resulting Numbers: [41] 41,69 unequal: No Solution Moving to Node #0,4,3 Current State: 69:[15, 56], Operations: ['57/3=19', '37+19=56'] Exploring Operation: 15+56=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 56-15=41, Resulting Numbers: [41] 41,69 unequal: No Solution Exploring Operation: 15*56=840, Resulting Numbers: [840] 840,69 unequal: No Solution Moving to Node #0,4,4 Current State: 69:[19, 52], Operations: ['57/3=19', '15+37=52'] Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,69 unequal: No Solution Exploring Operation: 19+52=71, Resulting Numbers: [71] 71,69 unequal: No Solution Exploring Operation: 19*52=988, Resulting Numbers: [988] 988,69 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 11, 50, 40, 98 ]
97
[ "50-11=39", "98-40=58", "39+58=97" ]
Current State: 97:[11, 50, 40, 98], Operations: [] Exploring Operation: 50-11=39, Resulting Numbers: [40, 98, 39] Generated Node #2: [40, 98, 39] from Operation: 50-11=39 Current State: 97:[40, 98, 39], Operations: ['50-11=39'] Exploring Operation: 98-40=58, Resulting Numbers: [39, 58] Generated Node #3: [39, 58] from Operation: 98-40=58 Current State: 97:[39, 58], Operations: ['50-11=39', '98-40=58'] Exploring Operation: 39+58=97, Resulting Numbers: [97] 97,97 equal: Goal Reached
4
Current State: 97:[11, 50, 40, 98], Operations: [] Exploring Operation: 11+50=61, Resulting Numbers: [40, 98, 61] Generated Node #0,0: 97:[40, 98, 61] Operation: 11+50=61 Start Sub Search at level 1: Moving to Node #0,0 Current State: 97:[40, 98, 61], Operations: ['11+50=61'] Exploring Operation: 40+61=101, Resulting Numbers: [98, 101] Generated Node #0,0,0: 97:[98, 101] Operation: 40+61=101 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 97:[98, 101], Operations: ['11+50=61', '40+61=101'] Exploring Operation: 101-98=3, Resulting Numbers: [3] 3,97 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 44, 83, 4, 40 ]
49
[ "83-44=39", "40/4=10", "39+10=49" ]
Current State: 49:[44, 83, 4, 40], Operations: [] Exploring Operation: 83-44=39, Resulting Numbers: [4, 40, 39] Generated Node #2: [4, 40, 39] from Operation: 83-44=39 Current State: 49:[4, 40, 39], Operations: ['83-44=39'] Exploring Operation: 40/4=10, Resulting Numbers: [39, 10] Generated Node #3: [39, 10] from Operation: 40/4=10 Current State: 49:[39, 10], Operations: ['83-44=39', '40/4=10'] Exploring Operation: 39+10=49, Resulting Numbers: [49] 49,49 equal: Goal Reached
4
Current State: 49:[44, 83, 4, 40], Operations: [] Exploring Operation: 83-40=43, Resulting Numbers: [44, 4, 43] Generated Node #0,0: 49:[44, 4, 43] Operation: 83-40=43 Start Sub Search at level 1: Moving to Node #0,0 Current State: 49:[44, 4, 43], Operations: ['83-40=43'] Exploring Operation: 44+4=48, Resulting Numbers: [43, 48] Generated Node #0,0,0: 49:[43, 48] Operation: 44+4=48 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 49:[43, 48], Operations: ['83-40=43', '44+4=48'] Exploring Operation: 48-43=5, Resulting Numbers: [5] 5,49 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
mult_heuristic
[ 12, 69, 72, 24 ]
78
[ "12+69=81", "72/24=3", "81-3=78" ]
Current State: 78:[12, 69, 72, 24], Operations: [] Exploring Operation: 12+69=81, Resulting Numbers: [72, 24, 81] Generated Node #2: [72, 24, 81] from Operation: 12+69=81 Current State: 78:[72, 24, 81], Operations: ['12+69=81'] Exploring Operation: 72/24=3, Resulting Numbers: [81, 3] Generated Node #3: [81, 3] from Operation: 72/24=3 Current State: 78:[81, 3], Operations: ['12+69=81', '72/24=3'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[12, 69, 72, 24], Operations: [] Exploring Operation: 72/12=6, Resulting Numbers: [69, 24, 6] Generated Node #0,0: 78:[69, 24, 6] Operation: 72/12=6 Exploring Operation: 12+69=81, Resulting Numbers: [72, 24, 81] Generated Node #0,1: 78:[72, 24, 81] Operation: 12+69=81 Exploring Operation: 72-69=3, Resulting Numbers: [12, 24, 3] Generated Node #0,2: 78:[12, 24, 3] Operation: 72-69=3 Exploring Operation: 72/24=3, Resulting Numbers: [12, 69, 3] Generated Node #0,3: 78:[12, 69, 3] Operation: 72/24=3 Start Sub Search at level 1: Moving to Node #0,2 Current State: 78:[12, 24, 3], Operations: ['72-69=3'] Exploring Operation: 24+3=27, Resulting Numbers: [12, 27] Generated Node #0,2,0: 78:[12, 27] Operation: 24+3=27 Exploring Operation: 24/12=2, Resulting Numbers: [3, 2] Generated Node #0,2,1: 78:[3, 2] Operation: 24/12=2 Exploring Operation: 12+24=36, Resulting Numbers: [3, 36] Generated Node #0,2,2: 78:[3, 36] Operation: 12+24=36 Exploring Operation: 24-12=12, Resulting Numbers: [3, 12] Generated Node #0,2,3: 78:[3, 12] Operation: 24-12=12 Moving to Node #0,2,1 Current State: 78:[3, 2], Operations: ['72-69=3', '24/12=2'] Exploring Operation: 3+2=5, Resulting Numbers: [5] 5,78 unequal: No Solution Exploring Operation: 3*2=6, Resulting Numbers: [6] 6,78 unequal: No Solution Exploring Operation: 3-2=1, Resulting Numbers: [1] 1,78 unequal: No Solution Moving to Node #0,2,3 Current State: 78:[3, 12], Operations: ['72-69=3', '24-12=12'] Exploring Operation: 3*12=36, Resulting Numbers: [36] 36,78 unequal: No Solution Exploring Operation: 3+12=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 12-3=9, Resulting Numbers: [9] 9,78 unequal: No Solution Exploring Operation: 12/3=4, Resulting Numbers: [4] 4,78 unequal: No Solution Moving to Node #0,2,0 Current State: 78:[12, 27], Operations: ['72-69=3', '24+3=27'] Exploring Operation: 27-12=15, Resulting Numbers: [15] 15,78 unequal: No Solution Exploring Operation: 12*27=324, Resulting Numbers: [324] 324,78 unequal: No Solution Exploring Operation: 12+27=39, Resulting Numbers: [39] 39,78 unequal: No Solution Moving to Node #0,2,2 Current State: 78:[3, 36], Operations: ['72-69=3', '12+24=36'] Exploring Operation: 3+36=39, Resulting Numbers: [39] 39,78 unequal: No Solution Exploring Operation: 36/3=12, Resulting Numbers: [12] 12,78 unequal: No Solution Exploring Operation: 3*36=108, Resulting Numbers: [108] 108,78 unequal: No Solution Exploring Operation: 36-3=33, Resulting Numbers: [33] 33,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 78:[12, 69, 3], Operations: ['72/24=3'] Exploring Operation: 12/3=4, Resulting Numbers: [69, 4] Generated Node #0,3,0: 78:[69, 4] Operation: 12/3=4 Exploring Operation: 69/3=23, Resulting Numbers: [12, 23] Generated Node #0,3,1: 78:[12, 23] Operation: 69/3=23 Exploring Operation: 69+3=72, Resulting Numbers: [12, 72] Generated Node #0,3,2: 78:[12, 72] Operation: 69+3=72 Exploring Operation: 12+69=81, Resulting Numbers: [3, 81] Generated Node #0,3,3: 78:[3, 81] Operation: 12+69=81 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 78:[3, 81], Operations: ['72/24=3', '12+69=81'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[12, 69, 72, 24], Operations: [] Exploring Operation: 72/24=3, Resulting Numbers: [12, 69, 3] Generated Node #0,3: 78:[12, 69, 3] Operation: 72/24=3 Moving to Node #0,3 Current State: 78:[12, 69, 3], Operations: ['72/24=3'] Exploring Operation: 12+69=81, Resulting Numbers: [3, 81] Generated Node #0,3,3: 78:[3, 81] Operation: 12+69=81 Moving to Node #0,3,3 Current State: 78:[3, 81], Operations: ['72/24=3', '12+69=81'] Exploring Operation: 81-3=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.97309
hs_4
sum_heuristic
[ 2, 17, 52, 11 ]
26
[ "17-2=15", "52-11=41", "41-15=26" ]
Current State: 26:[2, 17, 52, 11], Operations: [] Exploring Operation: 17-2=15, Resulting Numbers: [52, 11, 15] Generated Node #2: [52, 11, 15] from Operation: 17-2=15 Current State: 26:[52, 11, 15], Operations: ['17-2=15'] Exploring Operation: 52-11=41, Resulting Numbers: [15, 41] Generated Node #3: [15, 41] from Operation: 52-11=41 Current State: 26:[15, 41], Operations: ['17-2=15', '52-11=41'] Exploring Operation: 41-15=26, Resulting Numbers: [26] 26,26 equal: Goal Reached
4
Current State: 26:[2, 17, 52, 11], Operations: [] Exploring Operation: 52/2=26, Resulting Numbers: [17, 11, 26] Generated Node #0,0: 26:[17, 11, 26] Operation: 52/2=26 Exploring Operation: 52-17=35, Resulting Numbers: [2, 11, 35] Generated Node #0,1: 26:[2, 11, 35] Operation: 52-17=35 Exploring Operation: 17+11=28, Resulting Numbers: [2, 52, 28] Generated Node #0,2: 26:[2, 52, 28] Operation: 17+11=28 Exploring Operation: 52-11=41, Resulting Numbers: [2, 17, 41] Generated Node #0,3: 26:[2, 17, 41] Operation: 52-11=41 Exploring Operation: 17-2=15, Resulting Numbers: [52, 11, 15] Generated Node #0,4: 26:[52, 11, 15] Operation: 17-2=15 Moving to Node #0,0 Current State: 26:[17, 11, 26], Operations: ['52/2=26'] Exploring Operation: 26-17=9, Resulting Numbers: [11, 9] Generated Node #0,0,0: 26:[11, 9] Operation: 26-17=9 Exploring Operation: 26-11=15, Resulting Numbers: [17, 15] Generated Node #0,0,1: 26:[17, 15] Operation: 26-11=15 Exploring Operation: 17+11=28, Resulting Numbers: [26, 28] Generated Node #0,0,2: 26:[26, 28] Operation: 17+11=28 Exploring Operation: 11+26=37, Resulting Numbers: [17, 37] Generated Node #0,0,3: 26:[17, 37] Operation: 11+26=37 Exploring Operation: 17-11=6, Resulting Numbers: [26, 6] Generated Node #0,0,4: 26:[26, 6] Operation: 17-11=6 Moving to Node #0,1 Current State: 26:[2, 11, 35], Operations: ['52-17=35'] Exploring Operation: 35-2=33, Resulting Numbers: [11, 33] Generated Node #0,1,0: 26:[11, 33] Operation: 35-2=33 Exploring Operation: 35-11=24, Resulting Numbers: [2, 24] Generated Node #0,1,1: 26:[2, 24] Operation: 35-11=24 Exploring Operation: 11-2=9, Resulting Numbers: [35, 9] Generated Node #0,1,2: 26:[35, 9] Operation: 11-2=9 Exploring Operation: 2*11=22, Resulting Numbers: [35, 22] Generated Node #0,1,3: 26:[35, 22] Operation: 2*11=22 Exploring Operation: 2+11=13, Resulting Numbers: [35, 13] Generated Node #0,1,4: 26:[35, 13] Operation: 2+11=13 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 26:[2, 24], Operations: ['52-17=35', '35-11=24'] Exploring Operation: 24-2=22, Resulting Numbers: [22] 22,26 unequal: No Solution Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Moving to Node #0 Current State: 26:[2, 17, 52, 11], Operations: [] Exploring Operation: 52-17=35, Resulting Numbers: [2, 11, 35] Generated Node #0,1: 26:[2, 11, 35] Operation: 52-17=35 Moving to Node #0,1 Current State: 26:[2, 11, 35], Operations: ['52-17=35'] Exploring Operation: 35-11=24, Resulting Numbers: [2, 24] Generated Node #0,1,1: 26:[2, 24] Operation: 35-11=24 Moving to Node #0,1,1 Current State: 26:[2, 24], Operations: ['52-17=35', '35-11=24'] Exploring Operation: 2+24=26, Resulting Numbers: [26] 26,26 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 15, 67, 68, 69 ]
51
[ "67-15=52", "69-68=1", "52-1=51" ]
Current State: 51:[15, 67, 68, 69], Operations: [] Exploring Operation: 67-15=52, Resulting Numbers: [68, 69, 52] Generated Node #2: [68, 69, 52] from Operation: 67-15=52 Current State: 51:[68, 69, 52], Operations: ['67-15=52'] Exploring Operation: 69-68=1, Resulting Numbers: [52, 1] Generated Node #3: [52, 1] from Operation: 69-68=1 Current State: 51:[52, 1], Operations: ['67-15=52', '69-68=1'] Exploring Operation: 52-1=51, Resulting Numbers: [51] 51,51 equal: Goal Reached
4
Current State: 51:[15, 67, 68, 69], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [15, 68, 2] Generated Node #0,0: 51:[15, 68, 2] Operation: 69-67=2 Exploring Operation: 69-68=1, Resulting Numbers: [15, 67, 1] Generated Node #0,1: 51:[15, 67, 1] Operation: 69-68=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 51:[15, 68, 2], Operations: ['69-67=2'] Exploring Operation: 68-15=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 51:[2, 53] Operation: 68-15=53 Exploring Operation: 15+2=17, Resulting Numbers: [68, 17] Generated Node #0,0,1: 51:[68, 17] Operation: 15+2=17 Moving to Node #0,0,0 Current State: 51:[2, 53], Operations: ['69-67=2', '68-15=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Moving to Node #0 Current State: 51:[15, 67, 68, 69], Operations: [] Exploring Operation: 69-67=2, Resulting Numbers: [15, 68, 2] Generated Node #0,0: 51:[15, 68, 2] Operation: 69-67=2 Moving to Node #0,0 Current State: 51:[15, 68, 2], Operations: ['69-67=2'] Exploring Operation: 68-15=53, Resulting Numbers: [2, 53] Generated Node #0,0,0: 51:[2, 53] Operation: 68-15=53 Moving to Node #0,0,0 Current State: 51:[2, 53], Operations: ['69-67=2', '68-15=53'] Exploring Operation: 53-2=51, Resulting Numbers: [51] 51,51 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 88, 15, 37, 88 ]
84
[ "37-15=22", "88/22=4", "88-4=84" ]
Current State: 84:[88, 15, 37, 88], Operations: [] Exploring Operation: 37-15=22, Resulting Numbers: [88, 88, 22] Generated Node #2: [88, 88, 22] from Operation: 37-15=22 Current State: 84:[88, 88, 22], Operations: ['37-15=22'] Exploring Operation: 88/22=4, Resulting Numbers: [4] 4,84 equal: Goal Reached Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[88, 15, 37, 88], Operations: [] Exploring Operation: 88/88=1, Resulting Numbers: [15, 37, 1] Generated Node #0,0: 84:[15, 37, 1] Operation: 88/88=1 Exploring Operation: 88-37=51, Resulting Numbers: [15, 88, 51] Generated Node #0,1: 84:[15, 88, 51] Operation: 88-37=51 Exploring Operation: 88-88=0, Resulting Numbers: [15, 37, 0] Generated Node #0,2: 84:[15, 37, 0] Operation: 88-88=0 Exploring Operation: 88-37=51, Resulting Numbers: [88, 15, 51] Generated Node #0,3: 84:[88, 15, 51] Operation: 88-37=51 Exploring Operation: 37-15=22, Resulting Numbers: [88, 88, 22] Generated Node #0,4: 84:[88, 88, 22] Operation: 37-15=22 Moving to Node #0,0 Current State: 84:[15, 37, 1], Operations: ['88/88=1'] Exploring Operation: 37+1=38, Resulting Numbers: [15, 38] Generated Node #0,0,0: 84:[15, 38] Operation: 37+1=38 Exploring Operation: 15*1=15, Resulting Numbers: [37, 15] Generated Node #0,0,1: 84:[37, 15] Operation: 15*1=15 Exploring Operation: 37-15=22, Resulting Numbers: [1, 22] Generated Node #0,0,2: 84:[1, 22] Operation: 37-15=22 Exploring Operation: 15-1=14, Resulting Numbers: [37, 14] Generated Node #0,0,3: 84:[37, 14] Operation: 15-1=14 Exploring Operation: 15/1=15, Resulting Numbers: [37, 15] Generated Node #0,0,4: 84:[37, 15] Operation: 15/1=15 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 84:[1, 22], Operations: ['88/88=1', '37-15=22'] Exploring Operation: 1*22=22, Resulting Numbers: [22] 22,84 unequal: No Solution 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: 1+22=23, Resulting Numbers: [23] 23,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 84:[15, 38], Operations: ['88/88=1', '37+1=38'] Exploring Operation: 38-15=23, Resulting Numbers: [23] 23,84 unequal: No Solution Exploring Operation: 15*38=570, Resulting Numbers: [570] 570,84 unequal: No Solution Exploring Operation: 15+38=53, Resulting Numbers: [53] 53,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 84:[37, 14], Operations: ['88/88=1', '15-1=14'] Exploring Operation: 37*14=518, Resulting Numbers: [518] 518,84 unequal: No Solution Exploring Operation: 37+14=51, Resulting Numbers: [51] 51,84 unequal: No Solution Exploring Operation: 37-14=23, Resulting Numbers: [23] 23,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 84:[37, 15], Operations: ['88/88=1', '15*1=15'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 37*15=555, Resulting Numbers: [555] 555,84 unequal: No Solution Exploring Operation: 37+15=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 84:[37, 15], Operations: ['88/88=1', '15/1=15'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 37*15=555, Resulting Numbers: [555] 555,84 unequal: No Solution Exploring Operation: 37+15=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2 Current State: 84:[15, 37, 0], Operations: ['88-88=0'] Exploring Operation: 37*0=0, Resulting Numbers: [15, 0] Generated Node #0,2,0: 84:[15, 0] Operation: 37*0=0 Exploring Operation: 15+0=15, Resulting Numbers: [37, 15] Generated Node #0,2,1: 84:[37, 15] Operation: 15+0=15 Exploring Operation: 15-0=15, Resulting Numbers: [37, 15] Generated Node #0,2,2: 84:[37, 15] Operation: 15-0=15 Exploring Operation: 37-15=22, Resulting Numbers: [0, 22] Generated Node #0,2,3: 84:[0, 22] Operation: 37-15=22 Exploring Operation: 37+0=37, Resulting Numbers: [15, 37] Generated Node #0,2,4: 84:[15, 37] Operation: 37+0=37 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 84:[15, 0], Operations: ['88-88=0', '37*0=0'] Exploring Operation: 15*0=0, Resulting Numbers: [0] 0,84 unequal: No Solution Exploring Operation: 15-0=15, Resulting Numbers: [15] 15,84 unequal: No Solution Exploring Operation: 15+0=15, Resulting Numbers: [15] 15,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 84:[0, 22], Operations: ['88-88=0', '37-15=22'] Exploring Operation: 22-0=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 0*22=0, Resulting Numbers: [0] 0,84 unequal: No Solution Exploring Operation: 0+22=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 #0,2,1 Current State: 84:[37, 15], Operations: ['88-88=0', '15+0=15'] Exploring Operation: 37*15=555, Resulting Numbers: [555] 555,84 unequal: No Solution Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 37+15=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 84:[37, 15], Operations: ['88-88=0', '15-0=15'] Exploring Operation: 37+15=52, Resulting Numbers: [52] 52,84 unequal: No Solution Exploring Operation: 37*15=555, Resulting Numbers: [555] 555,84 unequal: No Solution Exploring Operation: 37-15=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 #0,2,4 Current State: 84:[15, 37], Operations: ['88-88=0', '37+0=37'] Exploring Operation: 37-15=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 15*37=555, Resulting Numbers: [555] 555,84 unequal: No Solution Exploring Operation: 15+37=52, Resulting Numbers: [52] 52,84 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 84:[88, 88, 22], Operations: ['37-15=22'] Exploring Operation: 88-22=66, Resulting Numbers: [88, 66] Generated Node #0,4,0: 84:[88, 66] Operation: 88-22=66 Exploring Operation: 88/22=4, Resulting Numbers: [88, 4] Generated Node #0,4,1: 84:[88, 4] Operation: 88/22=4 Exploring Operation: 88/22=4, Resulting Numbers: [88, 4] Generated Node #0,4,2: 84:[88, 4] Operation: 88/22=4 Exploring Operation: 88/88=1, Resulting Numbers: [22, 1] Generated Node #0,4,3: 84:[22, 1] Operation: 88/88=1 Exploring Operation: 88-88=0, Resulting Numbers: [22, 0] Generated Node #0,4,4: 84:[22, 0] Operation: 88-88=0 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 84:[22, 1], Operations: ['37-15=22', '88/88=1'] Exploring Operation: 22/1=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 22+1=23, Resulting Numbers: [23] 23,84 unequal: No Solution 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 No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 84:[22, 0], Operations: ['37-15=22', '88-88=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 No 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: 84:[88, 4], Operations: ['37-15=22', '88/22=4'] Exploring Operation: 88/4=22, Resulting Numbers: [22] 22,84 unequal: No Solution Exploring Operation: 88+4=92, Resulting Numbers: [92] 92,84 unequal: No Solution Exploring Operation: 88*4=352, Resulting Numbers: [352] 352,84 unequal: No Solution Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Moving to Node #0 Current State: 84:[88, 15, 37, 88], Operations: [] Exploring Operation: 37-15=22, Resulting Numbers: [88, 88, 22] Generated Node #0,4: 84:[88, 88, 22] Operation: 37-15=22 Moving to Node #0,4 Current State: 84:[88, 88, 22], Operations: ['37-15=22'] Exploring Operation: 88/22=4, Resulting Numbers: [88, 4] Generated Node #0,4,1: 84:[88, 4] Operation: 88/22=4 Moving to Node #0,4,1 Current State: 84:[88, 4], Operations: ['37-15=22', '88/22=4'] Exploring Operation: 88-4=84, Resulting Numbers: [84] 84,84 equal: Goal Reached Exit Sub Search at level 1
0.942708
hs_5
mult_heuristic
[ 4, 27, 69, 89 ]
88
[ "4*27=108", "89-69=20", "108-20=88" ]
Current State: 88:[4, 27, 69, 89], Operations: [] Exploring Operation: 4*27=108, Resulting Numbers: [69, 89, 108] Generated Node #2: [69, 89, 108] from Operation: 4*27=108 Current State: 88:[69, 89, 108], Operations: ['4*27=108'] Exploring Operation: 89-69=20, Resulting Numbers: [108, 20] Generated Node #3: [108, 20] from Operation: 89-69=20 Current State: 88:[108, 20], Operations: ['4*27=108', '89-69=20'] Exploring Operation: 108-20=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[4, 27, 69, 89], Operations: [] Exploring Operation: 89-69=20, Resulting Numbers: [4, 27, 20] Generated Node #0,0: 88:[4, 27, 20] Operation: 89-69=20 Exploring Operation: 69-27=42, Resulting Numbers: [4, 89, 42] Generated Node #0,1: 88:[4, 89, 42] Operation: 69-27=42 Start Sub Search at level 1: Moving to Node #0,1 Current State: 88:[4, 89, 42], Operations: ['69-27=42'] Exploring Operation: 4+42=46, Resulting Numbers: [89, 46] Generated Node #0,1,0: 88:[89, 46] Operation: 4+42=46 Exploring Operation: 89-42=47, Resulting Numbers: [4, 47] Generated Node #0,1,1: 88:[4, 47] Operation: 89-42=47 Moving to Node #0,1,0 Current State: 88:[89, 46], Operations: ['69-27=42', '4+42=46'] Exploring Operation: 89-46=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 89+46=135, Resulting Numbers: [135] 135,88 unequal: No Solution Moving to Node #0,1,1 Current State: 88:[4, 47], Operations: ['69-27=42', '89-42=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 88:[4, 27, 20], Operations: ['89-69=20'] Exploring Operation: 27-20=7, Resulting Numbers: [4, 7] Generated Node #0,0,0: 88:[4, 7] Operation: 27-20=7 Exploring Operation: 27-4=23, Resulting Numbers: [20, 23] Generated Node #0,0,1: 88:[20, 23] Operation: 27-4=23 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 88:[4, 7], Operations: ['89-69=20', '27-20=7'] Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,88 unequal: No Solution Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,88 unequal: No Solution No 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: 88:[20, 23], Operations: ['89-69=20', '27-4=23'] Exploring Operation: 23-20=3, Resulting Numbers: [3] 3,88 unequal: No Solution Exploring Operation: 20+23=43, Resulting Numbers: [43] 43,88 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
[ 94, 50, 74, 54 ]
80
[ "94-74=20", "54-50=4", "20*4=80" ]
Current State: 80:[94, 50, 74, 54], Operations: [] Exploring Operation: 94-74=20, Resulting Numbers: [50, 54, 20] Generated Node #2: [50, 54, 20] from Operation: 94-74=20 Current State: 80:[50, 54, 20], Operations: ['94-74=20'] Exploring Operation: 54-50=4, Resulting Numbers: [20, 4] Generated Node #3: [20, 4] from Operation: 54-50=4 Current State: 80:[20, 4], Operations: ['94-74=20', '54-50=4'] Exploring Operation: 20*4=80, Resulting Numbers: [80] 80,80 equal: Goal Reached
4
Current State: 80:[94, 50, 74, 54], Operations: [] Exploring Operation: 94-54=40, Resulting Numbers: [50, 74, 40] Generated Node #0,0: 80:[50, 74, 40] Operation: 94-54=40 Moving to Node #0,0 Current State: 80:[50, 74, 40], Operations: ['94-54=40'] Exploring Operation: 74-50=24, Resulting Numbers: [40, 24] Generated Node #0,0,0: 80:[40, 24] Operation: 74-50=24 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 80:[40, 24], Operations: ['94-54=40', '74-50=24'] Exploring Operation: 40-24=16, Resulting Numbers: [16] 16,80 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
[ 32, 11, 1, 71 ]
50
[ "32-11=21", "1*71=71", "71-21=50" ]
Current State: 50:[32, 11, 1, 71], Operations: [] Exploring Operation: 32-11=21, Resulting Numbers: [1, 71, 21] Generated Node #2: [1, 71, 21] from Operation: 32-11=21 Current State: 50:[1, 71, 21], Operations: ['32-11=21'] Exploring Operation: 1*71=71, Resulting Numbers: [21, 71] Generated Node #3: [21, 71] from Operation: 1*71=71 Current State: 50:[21, 71], Operations: ['32-11=21', '1*71=71'] Exploring Operation: 71-21=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[32, 11, 1, 71], Operations: [] Exploring Operation: 71-32=39, Resulting Numbers: [11, 1, 39] Generated Node #0,0: 50:[11, 1, 39] Operation: 71-32=39 Exploring Operation: 71-11=60, Resulting Numbers: [32, 1, 60] Generated Node #0,1: 50:[32, 1, 60] Operation: 71-11=60 Moving to Node #0,0 Current State: 50:[11, 1, 39], Operations: ['71-32=39'] Exploring Operation: 11+39=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 50:[1, 50] Operation: 11+39=50 Exploring Operation: 39-11=28, Resulting Numbers: [1, 28] Generated Node #0,0,1: 50:[1, 28] Operation: 39-11=28 Moving to Node #0,1 Current State: 50:[32, 1, 60], Operations: ['71-11=60'] Exploring Operation: 32-1=31, Resulting Numbers: [60, 31] Generated Node #0,1,0: 50:[60, 31] Operation: 32-1=31 Exploring Operation: 60-32=28, Resulting Numbers: [1, 28] Generated Node #0,1,1: 50:[1, 28] Operation: 60-32=28 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 50:[1, 28], Operations: ['71-11=60', '60-32=28'] Exploring Operation: 1*28=28, Resulting Numbers: [28] 28,50 unequal: No Solution Exploring Operation: 28-1=27, Resulting Numbers: [27] 27,50 unequal: No Solution No 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: 50:[60, 31], Operations: ['71-11=60', '32-1=31'] Exploring Operation: 60+31=91, Resulting Numbers: [91] 91,50 unequal: No Solution Exploring Operation: 60-31=29, Resulting Numbers: [29] 29,50 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 50:[1, 50], Operations: ['71-32=39', '11+39=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[32, 11, 1, 71], Operations: [] Exploring Operation: 71-32=39, Resulting Numbers: [11, 1, 39] Generated Node #0,0: 50:[11, 1, 39] Operation: 71-32=39 Moving to Node #0,0 Current State: 50:[11, 1, 39], Operations: ['71-32=39'] Exploring Operation: 11+39=50, Resulting Numbers: [1, 50] Generated Node #0,0,0: 50:[1, 50] Operation: 11+39=50 Moving to Node #0,0,0 Current State: 50:[1, 50], Operations: ['71-32=39', '11+39=50'] Exploring Operation: 1*50=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
0.986979
hs_2
sum_heuristic
[ 33, 63, 4, 9 ]
36
[ "33-4=29", "63/9=7", "29+7=36" ]
Current State: 36:[33, 63, 4, 9], Operations: [] Exploring Operation: 33-4=29, Resulting Numbers: [63, 9, 29] Generated Node #2: [63, 9, 29] from Operation: 33-4=29 Current State: 36:[63, 9, 29], Operations: ['33-4=29'] Exploring Operation: 63/9=7, Resulting Numbers: [29, 7] Generated Node #3: [29, 7] from Operation: 63/9=7 Current State: 36:[29, 7], Operations: ['33-4=29', '63/9=7'] Exploring Operation: 29+7=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[33, 63, 4, 9], Operations: [] Exploring Operation: 63-33=30, Resulting Numbers: [4, 9, 30] Generated Node #0,0: 36:[4, 9, 30] Operation: 63-33=30 Exploring Operation: 63/9=7, Resulting Numbers: [33, 4, 7] Generated Node #0,1: 36:[33, 4, 7] Operation: 63/9=7 Start Sub Search at level 1: Moving to Node #0,1 Current State: 36:[33, 4, 7], Operations: ['63/9=7'] Exploring Operation: 7-4=3, Resulting Numbers: [33, 3] Generated Node #0,1,0: 36:[33, 3] Operation: 7-4=3 Exploring Operation: 33+4=37, Resulting Numbers: [7, 37] Generated Node #0,1,1: 36:[7, 37] Operation: 33+4=37 Moving to Node #0,1,1 Current State: 36:[7, 37], Operations: ['63/9=7', '33+4=37'] Exploring Operation: 37-7=30, Resulting Numbers: [30] 30,36 unequal: No Solution Exploring Operation: 7+37=44, Resulting Numbers: [44] 44,36 unequal: No Solution Moving to Node #0,1,0 Current State: 36:[33, 3], Operations: ['63/9=7', '7-4=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[33, 63, 4, 9], Operations: [] Exploring Operation: 63/9=7, Resulting Numbers: [33, 4, 7] Generated Node #0,1: 36:[33, 4, 7] Operation: 63/9=7 Moving to Node #0,1 Current State: 36:[33, 4, 7], Operations: ['63/9=7'] Exploring Operation: 7-4=3, Resulting Numbers: [33, 3] Generated Node #0,1,0: 36:[33, 3] Operation: 7-4=3 Moving to Node #0,1,0 Current State: 36:[33, 3], Operations: ['63/9=7', '7-4=3'] Exploring Operation: 33+3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 1
0.990451
hs_2
mult_heuristic
[ 83, 4, 71, 27 ]
81
[ "83-71=12", "12/4=3", "27*3=81" ]
Current State: 81:[83, 4, 71, 27], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [4, 27, 12] Generated Node #2: [4, 27, 12] from Operation: 83-71=12 Current State: 81:[4, 27, 12], Operations: ['83-71=12'] Exploring Operation: 12/4=3, Resulting Numbers: [27, 3] Generated Node #3: [27, 3] from Operation: 12/4=3 Current State: 81:[27, 3], Operations: ['83-71=12', '12/4=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached
4
Current State: 81:[83, 4, 71, 27], Operations: [] Exploring Operation: 4+71=75, Resulting Numbers: [83, 27, 75] Generated Node #0,0: 81:[83, 27, 75] Operation: 4+71=75 Exploring Operation: 83-71=12, Resulting Numbers: [4, 27, 12] Generated Node #0,1: 81:[4, 27, 12] Operation: 83-71=12 Exploring Operation: 83-4=79, Resulting Numbers: [71, 27, 79] Generated Node #0,2: 81:[71, 27, 79] Operation: 83-4=79 Exploring Operation: 83+4=87, Resulting Numbers: [71, 27, 87] Generated Node #0,3: 81:[71, 27, 87] Operation: 83+4=87 Start Sub Search at level 1: Moving to Node #0,1 Current State: 81:[4, 27, 12], Operations: ['83-71=12'] Exploring Operation: 27-4=23, Resulting Numbers: [12, 23] Generated Node #0,1,0: 81:[12, 23] Operation: 27-4=23 Exploring Operation: 12-4=8, Resulting Numbers: [27, 8] Generated Node #0,1,1: 81:[27, 8] Operation: 12-4=8 Exploring Operation: 4+27=31, Resulting Numbers: [12, 31] Generated Node #0,1,2: 81:[12, 31] Operation: 4+27=31 Exploring Operation: 12/4=3, Resulting Numbers: [27, 3] Generated Node #0,1,3: 81:[27, 3] Operation: 12/4=3 Moving to Node #0,1,3 Current State: 81:[27, 3], Operations: ['83-71=12', '12/4=3'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,81 unequal: No Solution Exploring Operation: 27+3=30, Resulting Numbers: [30] 30,81 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,81 unequal: No Solution Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Moving to Node #0 Current State: 81:[83, 4, 71, 27], Operations: [] Exploring Operation: 83-71=12, Resulting Numbers: [4, 27, 12] Generated Node #0,1: 81:[4, 27, 12] Operation: 83-71=12 Moving to Node #0,1 Current State: 81:[4, 27, 12], Operations: ['83-71=12'] Exploring Operation: 12/4=3, Resulting Numbers: [27, 3] Generated Node #0,1,3: 81:[27, 3] Operation: 12/4=3 Moving to Node #0,1,3 Current State: 81:[27, 3], Operations: ['83-71=12', '12/4=3'] Exploring Operation: 27*3=81, Resulting Numbers: [81] 81,81 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_4
mult_heuristic
[ 39, 49, 78, 99 ]
39
[ "39*99=3861", "49*78=3822", "3861-3822=39" ]
Current State: 39:[39, 49, 78, 99], Operations: [] Exploring Operation: 39*99=3861, Resulting Numbers: [49, 78, 3861] Generated Node #2: [49, 78, 3861] from Operation: 39*99=3861 Current State: 39:[49, 78, 3861], Operations: ['39*99=3861'] Exploring Operation: 49*78=3822, Resulting Numbers: [3861, 3822] Generated Node #3: [3861, 3822] from Operation: 49*78=3822 Current State: 39:[3861, 3822], Operations: ['39*99=3861', '49*78=3822'] Exploring Operation: 3861-3822=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[39, 49, 78, 99], Operations: [] Exploring Operation: 78-39=39, Resulting Numbers: [49, 99, 39] Generated Node #0,0: 39:[49, 99, 39] Operation: 78-39=39 Exploring Operation: 99-39=60, Resulting Numbers: [49, 78, 60] Generated Node #0,1: 39:[49, 78, 60] Operation: 99-39=60 Exploring Operation: 99-49=50, Resulting Numbers: [39, 78, 50] Generated Node #0,2: 39:[39, 78, 50] Operation: 99-49=50 Exploring Operation: 99-78=21, Resulting Numbers: [39, 49, 21] Generated Node #0,3: 39:[39, 49, 21] Operation: 99-78=21 Start Sub Search at level 1: Moving to Node #0,3 Current State: 39:[39, 49, 21], Operations: ['99-78=21'] Exploring Operation: 49-21=28, Resulting Numbers: [39, 28] Generated Node #0,3,0: 39:[39, 28] Operation: 49-21=28 Exploring Operation: 39+21=60, Resulting Numbers: [49, 60] Generated Node #0,3,1: 39:[49, 60] Operation: 39+21=60 Exploring Operation: 49-39=10, Resulting Numbers: [21, 10] Generated Node #0,3,2: 39:[21, 10] Operation: 49-39=10 Exploring Operation: 39-21=18, Resulting Numbers: [49, 18] Generated Node #0,3,3: 39:[49, 18] Operation: 39-21=18 Moving to Node #0,3,0 Current State: 39:[39, 28], Operations: ['99-78=21', '49-21=28'] Exploring Operation: 39*28=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution Exploring Operation: 39+28=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,39 unequal: No Solution Moving to Node #0,3,2 Current State: 39:[21, 10], Operations: ['99-78=21', '49-39=10'] Exploring Operation: 21-10=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 21+10=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 21*10=210, Resulting Numbers: [210] 210,39 unequal: No Solution Moving to Node #0,3,3 Current State: 39:[49, 18], Operations: ['99-78=21', '39-21=18'] Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,39 unequal: No Solution Moving to Node #0,3,1 Current State: 39:[49, 60], Operations: ['99-78=21', '39+21=60'] Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,39 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 39:[39, 78, 50], Operations: ['99-49=50'] Exploring Operation: 78-39=39, Resulting Numbers: [50, 39] Generated Node #0,2,0: 39:[50, 39] Operation: 78-39=39 Exploring Operation: 78/39=2, Resulting Numbers: [50, 2] Generated Node #0,2,1: 39:[50, 2] Operation: 78/39=2 Exploring Operation: 50-39=11, Resulting Numbers: [78, 11] Generated Node #0,2,2: 39:[78, 11] Operation: 50-39=11 Exploring Operation: 78-50=28, Resulting Numbers: [39, 28] Generated Node #0,2,3: 39:[39, 28] Operation: 78-50=28 Moving to Node #0,2,0 Current State: 39:[50, 39], Operations: ['99-49=50', '78-39=39'] Exploring Operation: 50+39=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 50*39=1950, Resulting Numbers: [1950] 1950,39 unequal: No Solution Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,39 unequal: No Solution Moving to Node #0,2,3 Current State: 39:[39, 28], Operations: ['99-49=50', '78-50=28'] Exploring Operation: 39-28=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 39*28=1092, Resulting Numbers: [1092] 1092,39 unequal: No Solution Exploring Operation: 39+28=67, Resulting Numbers: [67] 67,39 unequal: No Solution Moving to Node #0,2,1 Current State: 39:[50, 2], Operations: ['99-49=50', '78/39=2'] Exploring Operation: 50+2=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 50*2=100, Resulting Numbers: [100] 100,39 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,39 unequal: No Solution Moving to Node #0,2,2 Current State: 39:[78, 11], Operations: ['99-49=50', '50-39=11'] Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 78*11=858, Resulting Numbers: [858] 858,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[49, 99, 39], Operations: ['78-39=39'] Exploring Operation: 49-39=10, Resulting Numbers: [99, 10] Generated Node #0,0,0: 39:[99, 10] Operation: 49-39=10 Exploring Operation: 99-39=60, Resulting Numbers: [49, 60] Generated Node #0,0,1: 39:[49, 60] Operation: 99-39=60 Exploring Operation: 99-49=50, Resulting Numbers: [39, 50] Generated Node #0,0,2: 39:[39, 50] Operation: 99-49=50 Exploring Operation: 49+99=148, Resulting Numbers: [39, 148] Generated Node #0,0,3: 39:[39, 148] Operation: 49+99=148 Moving to Node #0,0,2 Current State: 39:[39, 50], Operations: ['78-39=39', '99-49=50'] Exploring Operation: 39*50=1950, Resulting Numbers: [1950] 1950,39 unequal: No Solution Exploring Operation: 50-39=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 39+50=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[49, 60], Operations: ['78-39=39', '99-39=60'] Exploring Operation: 49*60=2940, Resulting Numbers: [2940] 2940,39 unequal: No Solution Exploring Operation: 60-49=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 49+60=109, Resulting Numbers: [109] 109,39 unequal: No Solution Moving to Node #0,0,0 Current State: 39:[99, 10], Operations: ['78-39=39', '49-39=10'] Exploring Operation: 99+10=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 99*10=990, Resulting Numbers: [990] 990,39 unequal: No Solution Exploring Operation: 99-10=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,0,3 Current State: 39:[39, 148], Operations: ['78-39=39', '49+99=148'] Exploring Operation: 148-39=109, Resulting Numbers: [109] 109,39 unequal: No Solution Exploring Operation: 39+148=187, Resulting Numbers: [187] 187,39 unequal: No Solution Exploring Operation: 39*148=5772, Resulting Numbers: [5772] 5772,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[49, 78, 60], Operations: ['99-39=60'] Exploring Operation: 78-60=18, Resulting Numbers: [49, 18] Generated Node #0,1,0: 39:[49, 18] Operation: 78-60=18 Exploring Operation: 78-49=29, Resulting Numbers: [60, 29] Generated Node #0,1,1: 39:[60, 29] Operation: 78-49=29 Exploring Operation: 60-49=11, Resulting Numbers: [78, 11] Generated Node #0,1,2: 39:[78, 11] Operation: 60-49=11 Exploring Operation: 49+78=127, Resulting Numbers: [60, 127] Generated Node #0,1,3: 39:[60, 127] Operation: 49+78=127 Moving to Node #0,1,0 Current State: 39:[49, 18], Operations: ['99-39=60', '78-60=18'] Exploring Operation: 49+18=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 49*18=882, Resulting Numbers: [882] 882,39 unequal: No Solution Exploring Operation: 49-18=31, Resulting Numbers: [31] 31,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[60, 29], Operations: ['99-39=60', '78-49=29'] Exploring Operation: 60-29=31, Resulting Numbers: [31] 31,39 unequal: No Solution Exploring Operation: 60*29=1740, Resulting Numbers: [1740] 1740,39 unequal: No Solution Exploring Operation: 60+29=89, Resulting Numbers: [89] 89,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[78, 11], Operations: ['99-39=60', '60-49=11'] Exploring Operation: 78+11=89, Resulting Numbers: [89] 89,39 unequal: No Solution Exploring Operation: 78-11=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 78*11=858, Resulting Numbers: [858] 858,39 unequal: No Solution Moving to Node #0,1,3 Current State: 39:[60, 127], Operations: ['99-39=60', '49+78=127'] Exploring Operation: 60+127=187, Resulting Numbers: [187] 187,39 unequal: No Solution Exploring Operation: 127-60=67, Resulting Numbers: [67] 67,39 unequal: No Solution Exploring Operation: 60*127=7620, Resulting Numbers: [7620] 7620,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
mult_heuristic
[ 96, 24, 36, 23 ]
14
[ "96/24=4", "36/4=9", "23-9=14" ]
Current State: 14:[96, 24, 36, 23], Operations: [] Exploring Operation: 96/24=4, Resulting Numbers: [36, 23, 4] Generated Node #2: [36, 23, 4] from Operation: 96/24=4 Current State: 14:[36, 23, 4], Operations: ['96/24=4'] Exploring Operation: 36/4=9, Resulting Numbers: [23, 9] Generated Node #3: [23, 9] from Operation: 36/4=9 Current State: 14:[23, 9], Operations: ['96/24=4', '36/4=9'] Exploring Operation: 23-9=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[96, 24, 36, 23], Operations: [] Exploring Operation: 96/24=4, Resulting Numbers: [36, 23, 4] Generated Node #0,0: 14:[36, 23, 4] Operation: 96/24=4 Moving to Node #0,0 Current State: 14:[36, 23, 4], Operations: ['96/24=4'] Exploring Operation: 36-23=13, Resulting Numbers: [4, 13] Generated Node #0,0,0: 14:[4, 13] Operation: 36-23=13 Moving to Node #0,0,0 Current State: 14:[4, 13], Operations: ['96/24=4', '36-23=13'] Exploring Operation: 13-4=9, Resulting Numbers: [9] 9,14 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 1, 32, 24, 35 ]
72
[ "1*32=32", "35-32=3", "24*3=72" ]
Current State: 72:[1, 32, 24, 35], Operations: [] Exploring Operation: 1*32=32, Resulting Numbers: [24, 35, 32] Generated Node #2: [24, 35, 32] from Operation: 1*32=32 Current State: 72:[24, 35, 32], Operations: ['1*32=32'] Exploring Operation: 35-32=3, Resulting Numbers: [24, 3] Generated Node #3: [24, 3] from Operation: 35-32=3 Current State: 72:[24, 3], Operations: ['1*32=32', '35-32=3'] Exploring Operation: 24*3=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[1, 32, 24, 35], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [1, 24, 3] Generated Node #0,0: 72:[1, 24, 3] Operation: 35-32=3 Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[1, 24, 3], Operations: ['35-32=3'] Exploring Operation: 1*24=24, Resulting Numbers: [3, 24] Generated Node #0,0,0: 72:[3, 24] Operation: 1*24=24 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 72:[3, 24], Operations: ['35-32=3', '1*24=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[1, 32, 24, 35], Operations: [] Exploring Operation: 35-32=3, Resulting Numbers: [1, 24, 3] Generated Node #0,0: 72:[1, 24, 3] Operation: 35-32=3 Moving to Node #0,0 Current State: 72:[1, 24, 3], Operations: ['35-32=3'] Exploring Operation: 1*24=24, Resulting Numbers: [3, 24] Generated Node #0,0,0: 72:[3, 24] Operation: 1*24=24 Moving to Node #0,0,0 Current State: 72:[3, 24], Operations: ['35-32=3', '1*24=24'] Exploring Operation: 3*24=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 21, 60, 39, 3 ]
39
[ "21+60=81", "39+3=42", "81-42=39" ]
Current State: 39:[21, 60, 39, 3], Operations: [] Exploring Operation: 21+60=81, Resulting Numbers: [39, 3, 81] Generated Node #2: [39, 3, 81] from Operation: 21+60=81 Current State: 39:[39, 3, 81], Operations: ['21+60=81'] Exploring Operation: 39+3=42, Resulting Numbers: [81, 42] Generated Node #3: [81, 42] from Operation: 39+3=42 Current State: 39:[81, 42], Operations: ['21+60=81', '39+3=42'] Exploring Operation: 81-42=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[21, 60, 39, 3], Operations: [] Exploring Operation: 60-21=39, Resulting Numbers: [39, 3, 39] Generated Node #0,0: 39:[39, 3, 39] Operation: 60-21=39 Exploring Operation: 60/3=20, Resulting Numbers: [21, 39, 20] Generated Node #0,1: 39:[21, 39, 20] Operation: 60/3=20 Start Sub Search at level 1: Moving to Node #0,0 Current State: 39:[39, 3, 39], Operations: ['60-21=39'] Exploring Operation: 39/3=13, Resulting Numbers: [39, 13] Generated Node #0,0,0: 39:[39, 13] Operation: 39/3=13 Exploring Operation: 39/3=13, Resulting Numbers: [39, 13] Generated Node #0,0,1: 39:[39, 13] Operation: 39/3=13 Moving to Node #0,0,0 Current State: 39:[39, 13], Operations: ['60-21=39', '39/3=13'] Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,39 unequal: No Solution Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,39 unequal: No Solution Moving to Node #0,0,1 Current State: 39:[39, 13], Operations: ['60-21=39', '39/3=13'] Exploring Operation: 39/13=3, Resulting Numbers: [3] 3,39 unequal: No Solution Exploring Operation: 39+13=52, Resulting Numbers: [52] 52,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 39:[21, 39, 20], Operations: ['60/3=20'] Exploring Operation: 21-20=1, Resulting Numbers: [39, 1] Generated Node #0,1,0: 39:[39, 1] Operation: 21-20=1 Exploring Operation: 21+20=41, Resulting Numbers: [39, 41] Generated Node #0,1,1: 39:[39, 41] Operation: 21+20=41 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 39:[39, 1], Operations: ['60/3=20', '21-20=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Moving to Node #0 Current State: 39:[21, 60, 39, 3], Operations: [] Exploring Operation: 60/3=20, Resulting Numbers: [21, 39, 20] Generated Node #0,1: 39:[21, 39, 20] Operation: 60/3=20 Moving to Node #0,1 Current State: 39:[21, 39, 20], Operations: ['60/3=20'] Exploring Operation: 21-20=1, Resulting Numbers: [39, 1] Generated Node #0,1,0: 39:[39, 1] Operation: 21-20=1 Moving to Node #0,1,0 Current State: 39:[39, 1], Operations: ['60/3=20', '21-20=1'] Exploring Operation: 39*1=39, Resulting Numbers: [39] 39,39 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 47, 10, 15, 18 ]
85
[ "47+18=65", "10*15=150", "150-65=85" ]
Current State: 85:[47, 10, 15, 18], Operations: [] Exploring Operation: 47+18=65, Resulting Numbers: [10, 15, 65] Generated Node #2: [10, 15, 65] from Operation: 47+18=65 Current State: 85:[10, 15, 65], Operations: ['47+18=65'] Exploring Operation: 10*15=150, Resulting Numbers: [65, 150] Generated Node #3: [65, 150] from Operation: 10*15=150 Current State: 85:[65, 150], Operations: ['47+18=65', '10*15=150'] Exploring Operation: 150-65=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[47, 10, 15, 18], Operations: [] Exploring Operation: 47-18=29, Resulting Numbers: [10, 15, 29] Generated Node #0,0: 85:[10, 15, 29] Operation: 47-18=29 Start Sub Search at level 1: Moving to Node #0,0 Current State: 85:[10, 15, 29], Operations: ['47-18=29'] Exploring Operation: 29-10=19, Resulting Numbers: [15, 19] Generated Node #0,0,0: 85:[15, 19] Operation: 29-10=19 Moving to Node #0,0,0 Current State: 85:[15, 19], Operations: ['47-18=29', '29-10=19'] Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,85 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
[ 28, 3, 22, 80 ]
70
[ "28+22=50", "3*50=150", "150-80=70" ]
Current State: 70:[28, 3, 22, 80], Operations: [] Exploring Operation: 28+22=50, Resulting Numbers: [3, 80, 50] Generated Node #2: [3, 80, 50] from Operation: 28+22=50 Current State: 70:[3, 80, 50], Operations: ['28+22=50'] Exploring Operation: 3*50=150, Resulting Numbers: [80, 150] Generated Node #3: [80, 150] from Operation: 3*50=150 Current State: 70:[80, 150], Operations: ['28+22=50', '3*50=150'] Exploring Operation: 150-80=70, Resulting Numbers: [70] 70,70 equal: Goal Reached
4
Current State: 70:[28, 3, 22, 80], Operations: [] Exploring Operation: 28-22=6, Resulting Numbers: [3, 80, 6] Generated Node #0,0: 70:[3, 80, 6] Operation: 28-22=6 Exploring Operation: 80-22=58, Resulting Numbers: [28, 3, 58] Generated Node #0,1: 70:[28, 3, 58] Operation: 80-22=58 Moving to Node #0,0 Current State: 70:[3, 80, 6], Operations: ['28-22=6'] Exploring Operation: 80-6=74, Resulting Numbers: [3, 74] Generated Node #0,0,0: 70:[3, 74] Operation: 80-6=74 Exploring Operation: 80-3=77, Resulting Numbers: [6, 77] Generated Node #0,0,1: 70:[6, 77] Operation: 80-3=77 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 70:[3, 74], Operations: ['28-22=6', '80-6=74'] Exploring Operation: 74-3=71, Resulting Numbers: [71] 71,70 unequal: No Solution Exploring Operation: 3+74=77, Resulting Numbers: [77] 77,70 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:[6, 77], Operations: ['28-22=6', '80-3=77'] Exploring Operation: 6+77=83, Resulting Numbers: [83] 83,70 unequal: No Solution Exploring Operation: 77-6=71, Resulting Numbers: [71] 71,70 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: 70:[28, 3, 58], Operations: ['80-22=58'] Exploring Operation: 58-28=30, Resulting Numbers: [3, 30] Generated Node #0,1,0: 70:[3, 30] Operation: 58-28=30 Exploring Operation: 28+3=31, Resulting Numbers: [58, 31] Generated Node #0,1,1: 70:[58, 31] Operation: 28+3=31 Moving to Node #0,1,0 Current State: 70:[3, 30], Operations: ['80-22=58', '58-28=30'] Exploring Operation: 30/3=10, Resulting Numbers: [10] 10,70 unequal: No Solution Exploring Operation: 3+30=33, Resulting Numbers: [33] 33,70 unequal: No Solution Moving to Node #0,1,1 Current State: 70:[58, 31], Operations: ['80-22=58', '28+3=31'] Exploring Operation: 58+31=89, Resulting Numbers: [89] 89,70 unequal: No Solution Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,70 unequal: No Solution No solution found.
0
hs_2
mult_heuristic
[ 2, 46, 28, 47 ]
63
[ "46-2=44", "47-28=19", "44+19=63" ]
Current State: 63:[2, 46, 28, 47], Operations: [] Exploring Operation: 46-2=44, Resulting Numbers: [28, 47, 44] Generated Node #2: [28, 47, 44] from Operation: 46-2=44 Current State: 63:[28, 47, 44], Operations: ['46-2=44'] Exploring Operation: 47-28=19, Resulting Numbers: [44, 19] Generated Node #3: [44, 19] from Operation: 47-28=19 Current State: 63:[44, 19], Operations: ['46-2=44', '47-28=19'] Exploring Operation: 44+19=63, Resulting Numbers: [63] 63,63 equal: Goal Reached
4
Current State: 63:[2, 46, 28, 47], Operations: [] Exploring Operation: 47-46=1, Resulting Numbers: [2, 28, 1] Generated Node #0,0: 63:[2, 28, 1] Operation: 47-46=1 Start Sub Search at level 1: Moving to Node #0,0 Current State: 63:[2, 28, 1], Operations: ['47-46=1'] Exploring Operation: 28-2=26, Resulting Numbers: [1, 26] Generated Node #0,0,0: 63:[1, 26] Operation: 28-2=26 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 63:[1, 26], Operations: ['47-46=1', '28-2=26'] Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,63 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 No solution found.
0
hs_1
sum_heuristic
[ 91, 12, 49, 28 ]
88
[ "91*12=1092", "1092/28=39", "49+39=88" ]
Current State: 88:[91, 12, 49, 28], Operations: [] Exploring Operation: 91*12=1092, Resulting Numbers: [49, 28, 1092] Generated Node #2: [49, 28, 1092] from Operation: 91*12=1092 Current State: 88:[49, 28, 1092], Operations: ['91*12=1092'] Exploring Operation: 1092/28=39, Resulting Numbers: [49, 39] Generated Node #3: [49, 39] from Operation: 1092/28=39 Current State: 88:[49, 39], Operations: ['91*12=1092', '1092/28=39'] Exploring Operation: 49+39=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[91, 12, 49, 28], Operations: [] Exploring Operation: 49-28=21, Resulting Numbers: [91, 12, 21] Generated Node #0,0: 88:[91, 12, 21] Operation: 49-28=21 Exploring Operation: 91-49=42, Resulting Numbers: [12, 28, 42] Generated Node #0,1: 88:[12, 28, 42] Operation: 91-49=42 Exploring Operation: 28-12=16, Resulting Numbers: [91, 49, 16] Generated Node #0,2: 88:[91, 49, 16] Operation: 28-12=16 Exploring Operation: 12+28=40, Resulting Numbers: [91, 49, 40] Generated Node #0,3: 88:[91, 49, 40] Operation: 12+28=40 Moving to Node #0,0 Current State: 88:[91, 12, 21], Operations: ['49-28=21'] Exploring Operation: 91-12=79, Resulting Numbers: [21, 79] Generated Node #0,0,0: 88:[21, 79] Operation: 91-12=79 Exploring Operation: 91+12=103, Resulting Numbers: [21, 103] Generated Node #0,0,1: 88:[21, 103] Operation: 91+12=103 Exploring Operation: 12+21=33, Resulting Numbers: [91, 33] Generated Node #0,0,2: 88:[91, 33] Operation: 12+21=33 Exploring Operation: 21-12=9, Resulting Numbers: [91, 9] Generated Node #0,0,3: 88:[91, 9] Operation: 21-12=9 Moving to Node #0,1 Current State: 88:[12, 28, 42], Operations: ['91-49=42'] Exploring Operation: 42-12=30, Resulting Numbers: [28, 30] Generated Node #0,1,0: 88:[28, 30] Operation: 42-12=30 Exploring Operation: 12+28=40, Resulting Numbers: [42, 40] Generated Node #0,1,1: 88:[42, 40] Operation: 12+28=40 Exploring Operation: 42-28=14, Resulting Numbers: [12, 14] Generated Node #0,1,2: 88:[12, 14] Operation: 42-28=14 Exploring Operation: 28-12=16, Resulting Numbers: [42, 16] Generated Node #0,1,3: 88:[42, 16] Operation: 28-12=16 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[12, 14], Operations: ['91-49=42', '42-28=14'] Exploring Operation: 12+14=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 12*14=168, Resulting Numbers: [168] 168,88 unequal: No Solution Exploring Operation: 14-12=2, Resulting Numbers: [2] 2,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[42, 40], Operations: ['91-49=42', '12+28=40'] Exploring Operation: 42+40=82, Resulting Numbers: [82] 82,88 unequal: No Solution Exploring Operation: 42*40=1680, Resulting Numbers: [1680] 1680,88 unequal: No Solution Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[42, 16], Operations: ['91-49=42', '28-12=16'] Exploring Operation: 42+16=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 42*16=672, Resulting Numbers: [672] 672,88 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[28, 30], Operations: ['91-49=42', '42-12=30'] Exploring Operation: 28+30=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 30-28=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 28*30=840, Resulting Numbers: [840] 840,88 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: 88:[91, 49, 40], Operations: ['12+28=40'] Exploring Operation: 49-40=9, Resulting Numbers: [91, 9] Generated Node #0,3,0: 88:[91, 9] Operation: 49-40=9 Exploring Operation: 49+40=89, Resulting Numbers: [91, 89] Generated Node #0,3,1: 88:[91, 89] Operation: 49+40=89 Exploring Operation: 91-49=42, Resulting Numbers: [40, 42] Generated Node #0,3,2: 88:[40, 42] Operation: 91-49=42 Exploring Operation: 91-40=51, Resulting Numbers: [49, 51] Generated Node #0,3,3: 88:[49, 51] Operation: 91-40=51 Moving to Node #0,2 Current State: 88:[91, 49, 16], Operations: ['28-12=16'] Exploring Operation: 91-16=75, Resulting Numbers: [49, 75] Generated Node #0,2,0: 88:[49, 75] Operation: 91-16=75 Exploring Operation: 91+16=107, Resulting Numbers: [49, 107] Generated Node #0,2,1: 88:[49, 107] Operation: 91+16=107 Exploring Operation: 49-16=33, Resulting Numbers: [91, 33] Generated Node #0,2,2: 88:[91, 33] Operation: 49-16=33 Exploring Operation: 91-49=42, Resulting Numbers: [16, 42] Generated Node #0,2,3: 88:[16, 42] Operation: 91-49=42 Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[16, 42], Operations: ['28-12=16', '91-49=42'] Exploring Operation: 16*42=672, Resulting Numbers: [672] 672,88 unequal: No Solution Exploring Operation: 16+42=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 42-16=26, Resulting Numbers: [26] 26,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[91, 33], Operations: ['28-12=16', '49-16=33'] Exploring Operation: 91-33=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 91+33=124, Resulting Numbers: [124] 124,88 unequal: No Solution Exploring Operation: 91*33=3003, Resulting Numbers: [3003] 3003,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[49, 75], Operations: ['28-12=16', '91-16=75'] Exploring Operation: 49+75=124, Resulting Numbers: [124] 124,88 unequal: No Solution Exploring Operation: 75-49=26, Resulting Numbers: [26] 26,88 unequal: No Solution Exploring Operation: 49*75=3675, Resulting Numbers: [3675] 3675,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[49, 107], Operations: ['28-12=16', '91+16=107'] Exploring Operation: 107-49=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 49*107=5243, Resulting Numbers: [5243] 5243,88 unequal: No Solution Exploring Operation: 49+107=156, Resulting Numbers: [156] 156,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,3 Current State: 88:[91, 9], Operations: ['49-28=21', '21-12=9'] Exploring Operation: 91+9=100, Resulting Numbers: [100] 100,88 unequal: No Solution Exploring Operation: 91*9=819, Resulting Numbers: [819] 819,88 unequal: No Solution Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[91, 89], Operations: ['12+28=40', '49+40=89'] Exploring Operation: 91*89=8099, Resulting Numbers: [8099] 8099,88 unequal: No Solution Exploring Operation: 91-89=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 91+89=180, Resulting Numbers: [180] 180,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[91, 9], Operations: ['12+28=40', '49-40=9'] Exploring Operation: 91+9=100, Resulting Numbers: [100] 100,88 unequal: No Solution Exploring Operation: 91*9=819, Resulting Numbers: [819] 819,88 unequal: No Solution Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[40, 42], Operations: ['12+28=40', '91-49=42'] Exploring Operation: 42-40=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 40*42=1680, Resulting Numbers: [1680] 1680,88 unequal: No Solution Exploring Operation: 40+42=82, Resulting Numbers: [82] 82,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[21, 79], Operations: ['49-28=21', '91-12=79'] Exploring Operation: 21*79=1659, Resulting Numbers: [1659] 1659,88 unequal: No Solution Exploring Operation: 79-21=58, Resulting Numbers: [58] 58,88 unequal: No Solution Exploring Operation: 21+79=100, Resulting Numbers: [100] 100,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[49, 51], Operations: ['12+28=40', '91-40=51'] Exploring Operation: 49*51=2499, Resulting Numbers: [2499] 2499,88 unequal: No Solution Exploring Operation: 51-49=2, Resulting Numbers: [2] 2,88 unequal: No Solution Exploring Operation: 49+51=100, Resulting Numbers: [100] 100,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[91, 33], Operations: ['49-28=21', '12+21=33'] Exploring Operation: 91*33=3003, Resulting Numbers: [3003] 3003,88 unequal: No Solution Exploring Operation: 91+33=124, Resulting Numbers: [124] 124,88 unequal: No Solution Exploring Operation: 91-33=58, Resulting Numbers: [58] 58,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[21, 103], Operations: ['49-28=21', '91+12=103'] Exploring Operation: 103-21=82, Resulting Numbers: [82] 82,88 unequal: No Solution Exploring Operation: 21+103=124, Resulting Numbers: [124] 124,88 unequal: No Solution Exploring Operation: 21*103=2163, Resulting Numbers: [2163] 2163,88 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 60, 30, 24, 23 ]
52
[ "60*30=1800", "1800/24=75", "75-23=52" ]
Current State: 52:[60, 30, 24, 23], Operations: [] Exploring Operation: 60*30=1800, Resulting Numbers: [24, 23, 1800] Generated Node #2: [24, 23, 1800] from Operation: 60*30=1800 Current State: 52:[24, 23, 1800], Operations: ['60*30=1800'] Exploring Operation: 1800/24=75, Resulting Numbers: [23, 75] Generated Node #3: [23, 75] from Operation: 1800/24=75 Current State: 52:[23, 75], Operations: ['60*30=1800', '1800/24=75'] Exploring Operation: 75-23=52, Resulting Numbers: [52] 52,52 equal: Goal Reached
4
Current State: 52:[60, 30, 24, 23], Operations: [] Exploring Operation: 60/30=2, Resulting Numbers: [24, 23, 2] Generated Node #0,0: 52:[24, 23, 2] Operation: 60/30=2 Start Sub Search at level 1: Moving to Node #0,0 Current State: 52:[24, 23, 2], Operations: ['60/30=2'] Exploring Operation: 24-23=1, Resulting Numbers: [2, 1] Generated Node #0,0,0: 52:[2, 1] Operation: 24-23=1 Moving to Node #0,0,0 Current State: 52:[2, 1], Operations: ['60/30=2', '24-23=1'] Exploring Operation: 2*1=2, Resulting Numbers: [2] 2,52 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
[ 40, 16, 64, 45 ]
88
[ "64*45=2880", "2880/40=72", "16+72=88" ]
Current State: 88:[40, 16, 64, 45], Operations: [] Exploring Operation: 64*45=2880, Resulting Numbers: [40, 16, 2880] Generated Node #2: [40, 16, 2880] from Operation: 64*45=2880 Current State: 88:[40, 16, 2880], Operations: ['64*45=2880'] Exploring Operation: 2880/40=72, Resulting Numbers: [16, 72] Generated Node #3: [16, 72] from Operation: 2880/40=72 Current State: 88:[16, 72], Operations: ['64*45=2880', '2880/40=72'] Exploring Operation: 16+72=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[40, 16, 64, 45], Operations: [] Exploring Operation: 64-45=19, Resulting Numbers: [40, 16, 19] Generated Node #0,0: 88:[40, 16, 19] Operation: 64-45=19 Exploring Operation: 64-40=24, Resulting Numbers: [16, 45, 24] Generated Node #0,1: 88:[16, 45, 24] Operation: 64-40=24 Exploring Operation: 64-16=48, Resulting Numbers: [40, 45, 48] Generated Node #0,2: 88:[40, 45, 48] Operation: 64-16=48 Exploring Operation: 16+64=80, Resulting Numbers: [40, 45, 80] Generated Node #0,3: 88:[40, 45, 80] Operation: 16+64=80 Exploring Operation: 64/16=4, Resulting Numbers: [40, 45, 4] Generated Node #0,4: 88:[40, 45, 4] Operation: 64/16=4 Moving to Node #0,4 Current State: 88:[40, 45, 4], Operations: ['64/16=4'] Exploring Operation: 40+4=44, Resulting Numbers: [45, 44] Generated Node #0,4,0: 88:[45, 44] Operation: 40+4=44 Exploring Operation: 45-4=41, Resulting Numbers: [40, 41] Generated Node #0,4,1: 88:[40, 41] Operation: 45-4=41 Exploring Operation: 40/4=10, Resulting Numbers: [45, 10] Generated Node #0,4,2: 88:[45, 10] Operation: 40/4=10 Exploring Operation: 40+45=85, Resulting Numbers: [4, 85] Generated Node #0,4,3: 88:[4, 85] Operation: 40+45=85 Exploring Operation: 45-40=5, Resulting Numbers: [4, 5] Generated Node #0,4,4: 88:[4, 5] Operation: 45-40=5 Moving to Node #0,1 Current State: 88:[16, 45, 24], Operations: ['64-40=24'] Exploring Operation: 45-24=21, Resulting Numbers: [16, 21] Generated Node #0,1,0: 88:[16, 21] Operation: 45-24=21 Exploring Operation: 16+45=61, Resulting Numbers: [24, 61] Generated Node #0,1,1: 88:[24, 61] Operation: 16+45=61 Exploring Operation: 24-16=8, Resulting Numbers: [45, 8] Generated Node #0,1,2: 88:[45, 8] Operation: 24-16=8 Exploring Operation: 16+24=40, Resulting Numbers: [45, 40] Generated Node #0,1,3: 88:[45, 40] Operation: 16+24=40 Exploring Operation: 45-16=29, Resulting Numbers: [24, 29] Generated Node #0,1,4: 88:[24, 29] Operation: 45-16=29 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[45, 8], Operations: ['64-40=24', '24-16=8'] Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,88 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[45, 40], Operations: ['64-40=24', '16+24=40'] Exploring Operation: 45*40=1800, Resulting Numbers: [1800] 1800,88 unequal: No Solution Exploring Operation: 45+40=85, Resulting Numbers: [85] 85,88 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[16, 21], Operations: ['64-40=24', '45-24=21'] Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,88 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 88:[24, 29], Operations: ['64-40=24', '45-16=29'] Exploring Operation: 24+29=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 29-24=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 24*29=696, Resulting Numbers: [696] 696,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[24, 61], Operations: ['64-40=24', '16+45=61'] Exploring Operation: 24+61=85, Resulting Numbers: [85] 85,88 unequal: No Solution Exploring Operation: 61-24=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 24*61=1464, Resulting Numbers: [1464] 1464,88 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: 88:[40, 45, 48], Operations: ['64-16=48'] Exploring Operation: 48-40=8, Resulting Numbers: [45, 8] Generated Node #0,2,0: 88:[45, 8] Operation: 48-40=8 Exploring Operation: 45-40=5, Resulting Numbers: [48, 5] Generated Node #0,2,1: 88:[48, 5] Operation: 45-40=5 Exploring Operation: 48-45=3, Resulting Numbers: [40, 3] Generated Node #0,2,2: 88:[40, 3] Operation: 48-45=3 Exploring Operation: 40+48=88, Resulting Numbers: [45, 88] Generated Node #0,2,3: 88:[45, 88] Operation: 40+48=88 Exploring Operation: 40+45=85, Resulting Numbers: [48, 85] Generated Node #0,2,4: 88:[48, 85] Operation: 40+45=85 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 88:[45, 8], Operations: ['64-16=48', '48-40=8'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 45*8=360, Resulting Numbers: [360] 360,88 unequal: No Solution Exploring Operation: 45+8=53, Resulting Numbers: [53] 53,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 88:[45, 88], Operations: ['64-16=48', '40+48=88'] Exploring Operation: 45*88=3960, Resulting Numbers: [3960] 3960,88 unequal: No Solution Exploring Operation: 88-45=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 45+88=133, Resulting Numbers: [133] 133,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 88:[48, 5], Operations: ['64-16=48', '45-40=5'] Exploring Operation: 48*5=240, Resulting Numbers: [240] 240,88 unequal: No Solution Exploring Operation: 48+5=53, Resulting Numbers: [53] 53,88 unequal: No Solution Exploring Operation: 48-5=43, Resulting Numbers: [43] 43,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 88:[40, 3], Operations: ['64-16=48', '48-45=3'] Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 88:[48, 85], Operations: ['64-16=48', '40+45=85'] Exploring Operation: 48+85=133, Resulting Numbers: [133] 133,88 unequal: No Solution Exploring Operation: 48*85=4080, Resulting Numbers: [4080] 4080,88 unequal: No Solution Exploring Operation: 85-48=37, Resulting Numbers: [37] 37,88 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: 88:[40, 16, 19], Operations: ['64-45=19'] Exploring Operation: 40-16=24, Resulting Numbers: [19, 24] Generated Node #0,0,0: 88:[19, 24] Operation: 40-16=24 Exploring Operation: 40-19=21, Resulting Numbers: [16, 21] Generated Node #0,0,1: 88:[16, 21] Operation: 40-19=21 Exploring Operation: 16+19=35, Resulting Numbers: [40, 35] Generated Node #0,0,2: 88:[40, 35] Operation: 16+19=35 Exploring Operation: 19-16=3, Resulting Numbers: [40, 3] Generated Node #0,0,3: 88:[40, 3] Operation: 19-16=3 Exploring Operation: 40+16=56, Resulting Numbers: [19, 56] Generated Node #0,0,4: 88:[19, 56] Operation: 40+16=56 Moving to Node #0,3 Current State: 88:[40, 45, 80], Operations: ['16+64=80'] Exploring Operation: 45-40=5, Resulting Numbers: [80, 5] Generated Node #0,3,0: 88:[80, 5] Operation: 45-40=5 Exploring Operation: 40+45=85, Resulting Numbers: [80, 85] Generated Node #0,3,1: 88:[80, 85] Operation: 40+45=85 Exploring Operation: 80/40=2, Resulting Numbers: [45, 2] Generated Node #0,3,2: 88:[45, 2] Operation: 80/40=2 Exploring Operation: 80-40=40, Resulting Numbers: [45, 40] Generated Node #0,3,3: 88:[45, 40] Operation: 80-40=40 Exploring Operation: 80-45=35, Resulting Numbers: [40, 35] Generated Node #0,3,4: 88:[40, 35] Operation: 80-45=35 Moving to Node #0,4,0 Current State: 88:[45, 44], Operations: ['64/16=4', '40+4=44'] Exploring Operation: 45*44=1980, Resulting Numbers: [1980] 1980,88 unequal: No Solution Exploring Operation: 45+44=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 45-44=1, Resulting Numbers: [1] 1,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[4, 5], Operations: ['64/16=4', '45-40=5'] Exploring Operation: 4+5=9, Resulting Numbers: [9] 9,88 unequal: No Solution Exploring Operation: 5-4=1, Resulting Numbers: [1] 1,88 unequal: No Solution Exploring Operation: 4*5=20, Resulting Numbers: [20] 20,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[45, 2], Operations: ['16+64=80', '80/40=2'] Exploring Operation: 45*2=90, Resulting Numbers: [90] 90,88 unequal: No Solution Exploring Operation: 45+2=47, Resulting Numbers: [47] 47,88 unequal: No Solution Exploring Operation: 45-2=43, Resulting Numbers: [43] 43,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[45, 10], Operations: ['64/16=4', '40/4=10'] Exploring Operation: 45+10=55, Resulting Numbers: [55] 55,88 unequal: No Solution Exploring Operation: 45*10=450, Resulting Numbers: [450] 450,88 unequal: No Solution Exploring Operation: 45-10=35, Resulting Numbers: [35] 35,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[4, 85], Operations: ['64/16=4', '40+45=85'] Exploring Operation: 4*85=340, Resulting Numbers: [340] 340,88 unequal: No Solution Exploring Operation: 4+85=89, Resulting Numbers: [89] 89,88 unequal: No Solution Exploring Operation: 85-4=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[40, 3], Operations: ['64-45=19', '19-16=3'] Exploring Operation: 40*3=120, Resulting Numbers: [120] 120,88 unequal: No Solution Exploring Operation: 40-3=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 40+3=43, Resulting Numbers: [43] 43,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[19, 24], Operations: ['64-45=19', '40-16=24'] Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,88 unequal: No Solution Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,88 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[45, 40], Operations: ['16+64=80', '80-40=40'] Exploring Operation: 45*40=1800, Resulting Numbers: [1800] 1800,88 unequal: No Solution Exploring Operation: 45+40=85, Resulting Numbers: [85] 85,88 unequal: No Solution Exploring Operation: 45-40=5, Resulting Numbers: [5] 5,88 unequal: No Solution Moving to Node #0,0,1 Current State: 88:[16, 21], Operations: ['64-45=19', '40-19=21'] Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[40, 41], Operations: ['64/16=4', '45-4=41'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,88 unequal: No Solution Exploring Operation: 40+41=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 40*41=1640, Resulting Numbers: [1640] 1640,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[80, 5], Operations: ['16+64=80', '45-40=5'] Exploring Operation: 80-5=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 80*5=400, Resulting Numbers: [400] 400,88 unequal: No Solution Exploring Operation: 80/5=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 80+5=85, Resulting Numbers: [85] 85,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[80, 85], Operations: ['16+64=80', '40+45=85'] Exploring Operation: 80+85=165, Resulting Numbers: [165] 165,88 unequal: No Solution Exploring Operation: 85-80=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 80*85=6800, Resulting Numbers: [6800] 6800,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[40, 35], Operations: ['16+64=80', '80-45=35'] Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 40*35=1400, Resulting Numbers: [1400] 1400,88 unequal: No Solution Exploring Operation: 40+35=75, Resulting Numbers: [75] 75,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[40, 35], Operations: ['64-45=19', '16+19=35'] Exploring Operation: 40-35=5, Resulting Numbers: [5] 5,88 unequal: No Solution Exploring Operation: 40+35=75, Resulting Numbers: [75] 75,88 unequal: No Solution Exploring Operation: 40*35=1400, Resulting Numbers: [1400] 1400,88 unequal: No Solution Moving to Node #0,0,4 Current State: 88:[19, 56], Operations: ['64-45=19', '40+16=56'] Exploring Operation: 19*56=1064, Resulting Numbers: [1064] 1064,88 unequal: No Solution Exploring Operation: 56-19=37, Resulting Numbers: [37] 37,88 unequal: No Solution Exploring Operation: 19+56=75, Resulting Numbers: [75] 75,88 unequal: No Solution No solution found.
0
hs_5
mult_heuristic
[ 73, 37, 37, 6 ]
43
[ "73-37=36", "36/6=6", "37+6=43" ]
Current State: 43:[73, 37, 37, 6], Operations: [] Exploring Operation: 73-37=36, Resulting Numbers: [6, 36] Generated Node #2: [6, 36] from Operation: 73-37=36 Current State: 43:[6, 36], Operations: ['73-37=36'] Exploring Operation: 36/6=6, Resulting Numbers: [6] 6,43 equal: Goal Reached Exploring Operation: 37+6=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[73, 37, 37, 6], Operations: [] Exploring Operation: 73-6=67, Resulting Numbers: [37, 37, 67] Generated Node #0,0: 43:[37, 37, 67] Operation: 73-6=67 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[37, 37, 67], Operations: ['73-6=67'] Exploring Operation: 67-37=30, Resulting Numbers: [37, 30] Generated Node #0,0,0: 43:[37, 30] Operation: 67-37=30 Moving to Node #0,0,0 Current State: 43:[37, 30], Operations: ['73-6=67', '67-37=30'] Exploring Operation: 37+30=67, Resulting Numbers: [67] 67,43 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 39, 8, 41, 29 ]
42
[ "41-39=2", "29-8=21", "2*21=42" ]
Current State: 42:[39, 8, 41, 29], Operations: [] Exploring Operation: 41-39=2, Resulting Numbers: [8, 29, 2] Generated Node #2: [8, 29, 2] from Operation: 41-39=2 Current State: 42:[8, 29, 2], Operations: ['41-39=2'] Exploring Operation: 29-8=21, Resulting Numbers: [2, 21] Generated Node #3: [2, 21] from Operation: 29-8=21 Current State: 42:[2, 21], Operations: ['41-39=2', '29-8=21'] Exploring Operation: 2*21=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
4
Current State: 42:[39, 8, 41, 29], Operations: [] Exploring Operation: 41-29=12, Resulting Numbers: [39, 8, 12] Generated Node #0,0: 42:[39, 8, 12] Operation: 41-29=12 Exploring Operation: 39-29=10, Resulting Numbers: [8, 41, 10] Generated Node #0,1: 42:[8, 41, 10] Operation: 39-29=10 Exploring Operation: 29-8=21, Resulting Numbers: [39, 41, 21] Generated Node #0,2: 42:[39, 41, 21] Operation: 29-8=21 Moving to Node #0,2 Current State: 42:[39, 41, 21], Operations: ['29-8=21'] Exploring Operation: 39-21=18, Resulting Numbers: [41, 18] Generated Node #0,2,0: 42:[41, 18] Operation: 39-21=18 Exploring Operation: 41-21=20, Resulting Numbers: [39, 20] Generated Node #0,2,1: 42:[39, 20] Operation: 41-21=20 Exploring Operation: 41-39=2, Resulting Numbers: [21, 2] Generated Node #0,2,2: 42:[21, 2] Operation: 41-39=2 Moving to Node #0,1 Current State: 42:[8, 41, 10], Operations: ['39-29=10'] Exploring Operation: 8+10=18, Resulting Numbers: [41, 18] Generated Node #0,1,0: 42:[41, 18] Operation: 8+10=18 Exploring Operation: 8+41=49, Resulting Numbers: [10, 49] Generated Node #0,1,1: 42:[10, 49] Operation: 8+41=49 Exploring Operation: 10-8=2, Resulting Numbers: [41, 2] Generated Node #0,1,2: 42:[41, 2] Operation: 10-8=2 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 42:[41, 2], Operations: ['39-29=10', '10-8=2'] Exploring Operation: 41*2=82, Resulting Numbers: [82] 82,42 unequal: No Solution Exploring Operation: 41-2=39, Resulting Numbers: [39] 39,42 unequal: No Solution Exploring Operation: 41+2=43, Resulting Numbers: [43] 43,42 unequal: No Solution No 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: 42:[41, 18], Operations: ['39-29=10', '8+10=18'] Exploring Operation: 41-18=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 41*18=738, Resulting Numbers: [738] 738,42 unequal: No Solution Exploring Operation: 41+18=59, Resulting Numbers: [59] 59,42 unequal: No Solution No 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: 42:[10, 49], Operations: ['39-29=10', '8+41=49'] Exploring Operation: 10+49=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 49-10=39, Resulting Numbers: [39] 39,42 unequal: No Solution Exploring Operation: 10*49=490, Resulting Numbers: [490] 490,42 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: 42:[39, 8, 12], Operations: ['41-29=12'] Exploring Operation: 12-8=4, Resulting Numbers: [39, 4] Generated Node #0,0,0: 42:[39, 4] Operation: 12-8=4 Exploring Operation: 8+12=20, Resulting Numbers: [39, 20] Generated Node #0,0,1: 42:[39, 20] Operation: 8+12=20 Exploring Operation: 39+8=47, Resulting Numbers: [12, 47] Generated Node #0,0,2: 42:[12, 47] Operation: 39+8=47 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 42:[39, 4], Operations: ['41-29=12', '12-8=4'] Exploring Operation: 39-4=35, Resulting Numbers: [35] 35,42 unequal: No Solution Exploring Operation: 39*4=156, Resulting Numbers: [156] 156,42 unequal: No Solution Exploring Operation: 39+4=43, Resulting Numbers: [43] 43,42 unequal: No Solution No 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: 42:[39, 20], Operations: ['41-29=12', '8+12=20'] Exploring Operation: 39+20=59, Resulting Numbers: [59] 59,42 unequal: No Solution Exploring Operation: 39-20=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 39*20=780, Resulting Numbers: [780] 780,42 unequal: No Solution No 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: 42:[12, 47], Operations: ['41-29=12', '39+8=47'] Exploring Operation: 12*47=564, Resulting Numbers: [564] 564,42 unequal: No Solution Exploring Operation: 47-12=35, Resulting Numbers: [35] 35,42 unequal: No Solution Exploring Operation: 12+47=59, Resulting Numbers: [59] 59,42 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,2 Current State: 42:[21, 2], Operations: ['29-8=21', '41-39=2'] Exploring Operation: 21+2=23, Resulting Numbers: [23] 23,42 unequal: No Solution Exploring Operation: 21-2=19, Resulting Numbers: [19] 19,42 unequal: No Solution Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached Moving to Node #0 Current State: 42:[39, 8, 41, 29], Operations: [] Exploring Operation: 29-8=21, Resulting Numbers: [39, 41, 21] Generated Node #0,2: 42:[39, 41, 21] Operation: 29-8=21 Moving to Node #0,2 Current State: 42:[39, 41, 21], Operations: ['29-8=21'] Exploring Operation: 41-39=2, Resulting Numbers: [21, 2] Generated Node #0,2,2: 42:[21, 2] Operation: 41-39=2 Moving to Node #0,2,2 Current State: 42:[21, 2], Operations: ['29-8=21', '41-39=2'] Exploring Operation: 21*2=42, Resulting Numbers: [42] 42,42 equal: Goal Reached
0.967882
hs_3
mult_heuristic
[ 27, 3, 34, 93 ]
38
[ "34-27=7", "93/3=31", "7+31=38" ]
Current State: 38:[27, 3, 34, 93], Operations: [] Exploring Operation: 34-27=7, Resulting Numbers: [3, 93, 7] Generated Node #2: [3, 93, 7] from Operation: 34-27=7 Current State: 38:[3, 93, 7], Operations: ['34-27=7'] Exploring Operation: 93/3=31, Resulting Numbers: [7, 31] Generated Node #3: [7, 31] from Operation: 93/3=31 Current State: 38:[7, 31], Operations: ['34-27=7', '93/3=31'] Exploring Operation: 7+31=38, Resulting Numbers: [38] 38,38 equal: Goal Reached
4
Current State: 38:[27, 3, 34, 93], Operations: [] Exploring Operation: 93-34=59, Resulting Numbers: [27, 3, 59] Generated Node #0,0: 38:[27, 3, 59] Operation: 93-34=59 Exploring Operation: 93/3=31, Resulting Numbers: [27, 34, 31] Generated Node #0,1: 38:[27, 34, 31] Operation: 93/3=31 Moving to Node #0,1 Current State: 38:[27, 34, 31], Operations: ['93/3=31'] Exploring Operation: 31-27=4, Resulting Numbers: [34, 4] Generated Node #0,1,0: 38:[34, 4] Operation: 31-27=4 Exploring Operation: 34-31=3, Resulting Numbers: [27, 3] Generated Node #0,1,1: 38:[27, 3] Operation: 34-31=3 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 38:[34, 4], Operations: ['93/3=31', '31-27=4'] Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Moving to Node #0 Current State: 38:[27, 3, 34, 93], Operations: [] Exploring Operation: 93/3=31, Resulting Numbers: [27, 34, 31] Generated Node #0,1: 38:[27, 34, 31] Operation: 93/3=31 Moving to Node #0,1 Current State: 38:[27, 34, 31], Operations: ['93/3=31'] Exploring Operation: 31-27=4, Resulting Numbers: [34, 4] Generated Node #0,1,0: 38:[34, 4] Operation: 31-27=4 Moving to Node #0,1,0 Current State: 38:[34, 4], Operations: ['93/3=31', '31-27=4'] Exploring Operation: 34+4=38, Resulting Numbers: [38] 38,38 equal: Goal Reached Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 27, 32, 20, 25 ]
13
[ "32*25=800", "800/20=40", "40-27=13" ]
Current State: 13:[27, 32, 20, 25], Operations: [] Exploring Operation: 32*25=800, Resulting Numbers: [27, 20, 800] Generated Node #2: [27, 20, 800] from Operation: 32*25=800 Current State: 13:[27, 20, 800], Operations: ['32*25=800'] Exploring Operation: 800/20=40, Resulting Numbers: [27, 40] Generated Node #3: [27, 40] from Operation: 800/20=40 Current State: 13:[27, 40], Operations: ['32*25=800', '800/20=40'] Exploring Operation: 40-27=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[27, 32, 20, 25], Operations: [] Exploring Operation: 32-27=5, Resulting Numbers: [20, 25, 5] Generated Node #0,0: 13:[20, 25, 5] Operation: 32-27=5 Exploring Operation: 32-20=12, Resulting Numbers: [27, 25, 12] Generated Node #0,1: 13:[27, 25, 12] Operation: 32-20=12 Exploring Operation: 27-20=7, Resulting Numbers: [32, 25, 7] Generated Node #0,2: 13:[32, 25, 7] Operation: 27-20=7 Exploring Operation: 32-25=7, Resulting Numbers: [27, 20, 7] Generated Node #0,3: 13:[27, 20, 7] Operation: 32-25=7 Start Sub Search at level 1: Moving to Node #0,0 Current State: 13:[20, 25, 5], Operations: ['32-27=5'] Exploring Operation: 25-5=20, Resulting Numbers: [20, 20] Generated Node #0,0,0: 13:[20, 20] Operation: 25-5=20 Exploring Operation: 20-5=15, Resulting Numbers: [25, 15] Generated Node #0,0,1: 13:[25, 15] Operation: 20-5=15 Exploring Operation: 25-20=5, Resulting Numbers: [5, 5] Generated Node #0,0,2: 13:[5, 5] Operation: 25-20=5 Exploring Operation: 25/5=5, Resulting Numbers: [20, 5] Generated Node #0,0,3: 13:[20, 5] Operation: 25/5=5 Moving to Node #0,0,0 Current State: 13:[20, 20], Operations: ['32-27=5', '25-5=20'] Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,13 unequal: No Solution Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,13 unequal: No Solution Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,13 unequal: No Solution Moving to Node #0,0,1 Current State: 13:[25, 15], Operations: ['32-27=5', '20-5=15'] Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,13 unequal: No Solution Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,13 unequal: No Solution Moving to Node #0,0,3 Current State: 13:[20, 5], Operations: ['32-27=5', '25/5=5'] Exploring Operation: 20-5=15, Resulting Numbers: [15] 15,13 unequal: No Solution Exploring Operation: 20/5=4, Resulting Numbers: [4] 4,13 unequal: No Solution Exploring Operation: 20+5=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 20*5=100, Resulting Numbers: [100] 100,13 unequal: No Solution Moving to Node #0,0,2 Current State: 13:[5, 5], Operations: ['32-27=5', '25-20=5'] Exploring Operation: 5/5=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 5*5=25, Resulting Numbers: [25] 25,13 unequal: No Solution Exploring Operation: 5+5=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 5-5=0, Resulting Numbers: [0] 0,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 13:[27, 25, 12], Operations: ['32-20=12'] Exploring Operation: 25-12=13, Resulting Numbers: [27, 13] Generated Node #0,1,0: 13:[27, 13] Operation: 25-12=13 Exploring Operation: 27+12=39, Resulting Numbers: [25, 39] Generated Node #0,1,1: 13:[25, 39] Operation: 27+12=39 Exploring Operation: 27-25=2, Resulting Numbers: [12, 2] Generated Node #0,1,2: 13:[12, 2] Operation: 27-25=2 Exploring Operation: 27-12=15, Resulting Numbers: [25, 15] Generated Node #0,1,3: 13:[25, 15] Operation: 27-12=15 Moving to Node #0,1,2 Current State: 13:[12, 2], Operations: ['32-20=12', '27-25=2'] Exploring Operation: 12+2=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 12/2=6, Resulting Numbers: [6] 6,13 unequal: No Solution Exploring Operation: 12-2=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 12*2=24, Resulting Numbers: [24] 24,13 unequal: No Solution Moving to Node #0,1,3 Current State: 13:[25, 15], Operations: ['32-20=12', '27-12=15'] Exploring Operation: 25-15=10, Resulting Numbers: [10] 10,13 unequal: No Solution Exploring Operation: 25+15=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 25*15=375, Resulting Numbers: [375] 375,13 unequal: No Solution Moving to Node #0,1,0 Current State: 13:[27, 13], Operations: ['32-20=12', '25-12=13'] Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,13 unequal: No Solution Moving to Node #0,1,1 Current State: 13:[25, 39], Operations: ['32-20=12', '27+12=39'] Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,13 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 13:[27, 20, 7], Operations: ['32-25=7'] Exploring Operation: 27-20=7, Resulting Numbers: [7, 7] Generated Node #0,3,0: 13:[7, 7] Operation: 27-20=7 Exploring Operation: 27+7=34, Resulting Numbers: [20, 34] Generated Node #0,3,1: 13:[20, 34] Operation: 27+7=34 Exploring Operation: 27-7=20, Resulting Numbers: [20, 20] Generated Node #0,3,2: 13:[20, 20] Operation: 27-7=20 Exploring Operation: 20-7=13, Resulting Numbers: [27, 13] Generated Node #0,3,3: 13:[27, 13] Operation: 20-7=13 Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 13:[7, 7], Operations: ['32-25=7', '27-20=7'] Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,13 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,13 unequal: No Solution No 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: 13:[20, 20], Operations: ['32-25=7', '27-7=20'] Exploring Operation: 20*20=400, Resulting Numbers: [400] 400,13 unequal: No Solution Exploring Operation: 20/20=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 20+20=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 20-20=0, Resulting Numbers: [0] 0,13 unequal: No Solution No 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: 13:[27, 13], Operations: ['32-25=7', '20-7=13'] Exploring Operation: 27+13=40, Resulting Numbers: [40] 40,13 unequal: No Solution Exploring Operation: 27*13=351, Resulting Numbers: [351] 351,13 unequal: No Solution Exploring Operation: 27-13=14, Resulting Numbers: [14] 14,13 unequal: No Solution No 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: 13:[20, 34], Operations: ['32-25=7', '27+7=34'] Exploring Operation: 34-20=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 20*34=680, Resulting Numbers: [680] 680,13 unequal: No Solution Exploring Operation: 20+34=54, Resulting Numbers: [54] 54,13 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 13:[32, 25, 7], Operations: ['27-20=7'] Exploring Operation: 32+7=39, Resulting Numbers: [25, 39] Generated Node #0,2,0: 13:[25, 39] Operation: 32+7=39 Exploring Operation: 32-7=25, Resulting Numbers: [25, 25] Generated Node #0,2,1: 13:[25, 25] Operation: 32-7=25 Exploring Operation: 25-7=18, Resulting Numbers: [32, 18] Generated Node #0,2,2: 13:[32, 18] Operation: 25-7=18 Exploring Operation: 32-25=7, Resulting Numbers: [7, 7] Generated Node #0,2,3: 13:[7, 7] Operation: 32-25=7 Moving to Node #0,2,3 Current State: 13:[7, 7], Operations: ['27-20=7', '32-25=7'] Exploring Operation: 7+7=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 7*7=49, Resulting Numbers: [49] 49,13 unequal: No Solution Exploring Operation: 7/7=1, Resulting Numbers: [1] 1,13 unequal: No Solution Exploring Operation: 7-7=0, Resulting Numbers: [0] 0,13 unequal: No Solution Moving to Node #0,2,2 Current State: 13:[32, 18], Operations: ['27-20=7', '25-7=18'] Exploring Operation: 32*18=576, Resulting Numbers: [576] 576,13 unequal: No Solution Exploring Operation: 32+18=50, Resulting Numbers: [50] 50,13 unequal: No Solution Exploring Operation: 32-18=14, Resulting Numbers: [14] 14,13 unequal: No Solution Moving to Node #0,2,1 Current State: 13:[25, 25], Operations: ['27-20=7', '32-7=25'] Exploring Operation: 25+25=50, Resulting Numbers: [50] 50,13 unequal: No Solution Exploring Operation: 25-25=0, Resulting Numbers: [0] 0,13 unequal: No Solution Exploring Operation: 25*25=625, Resulting Numbers: [625] 625,13 unequal: No Solution Exploring Operation: 25/25=1, Resulting Numbers: [1] 1,13 unequal: No Solution Moving to Node #0,2,0 Current State: 13:[25, 39], Operations: ['27-20=7', '32+7=39'] Exploring Operation: 25+39=64, Resulting Numbers: [64] 64,13 unequal: No Solution Exploring Operation: 39-25=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 25*39=975, Resulting Numbers: [975] 975,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 29, 76, 87, 83 ]
43
[ "76-29=47", "87-83=4", "47-4=43" ]
Current State: 43:[29, 76, 87, 83], Operations: [] Exploring Operation: 76-29=47, Resulting Numbers: [87, 83, 47] Generated Node #2: [87, 83, 47] from Operation: 76-29=47 Current State: 43:[87, 83, 47], Operations: ['76-29=47'] Exploring Operation: 87-83=4, Resulting Numbers: [47, 4] Generated Node #3: [47, 4] from Operation: 87-83=4 Current State: 43:[47, 4], Operations: ['76-29=47', '87-83=4'] Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,43 equal: Goal Reached
4
Current State: 43:[29, 76, 87, 83], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [29, 83, 11] Generated Node #0,0: 43:[29, 83, 11] Operation: 87-76=11 Exploring Operation: 87-83=4, Resulting Numbers: [29, 76, 4] Generated Node #0,1: 43:[29, 76, 4] Operation: 87-83=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 43:[29, 83, 11], Operations: ['87-76=11'] Exploring Operation: 83-29=54, Resulting Numbers: [11, 54] Generated Node #0,0,0: 43:[11, 54] Operation: 83-29=54 Exploring Operation: 29+11=40, Resulting Numbers: [83, 40] Generated Node #0,0,1: 43:[83, 40] Operation: 29+11=40 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 43:[11, 54], Operations: ['87-76=11', '83-29=54'] Exploring Operation: 11+54=65, Resulting Numbers: [65] 65,43 unequal: No Solution Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Moving to Node #0 Current State: 43:[29, 76, 87, 83], Operations: [] Exploring Operation: 87-76=11, Resulting Numbers: [29, 83, 11] Generated Node #0,0: 43:[29, 83, 11] Operation: 87-76=11 Moving to Node #0,0 Current State: 43:[29, 83, 11], Operations: ['87-76=11'] Exploring Operation: 83-29=54, Resulting Numbers: [11, 54] Generated Node #0,0,0: 43:[11, 54] Operation: 83-29=54 Moving to Node #0,0,0 Current State: 43:[11, 54], Operations: ['87-76=11', '83-29=54'] Exploring Operation: 54-11=43, Resulting Numbers: [43] 43,43 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 44, 1, 61, 94 ]
11
[ "44*1=44", "94-61=33", "44-33=11" ]
Current State: 11:[44, 1, 61, 94], Operations: [] Exploring Operation: 44*1=44, Resulting Numbers: [61, 94, 44] Generated Node #2: [61, 94, 44] from Operation: 44*1=44 Current State: 11:[61, 94, 44], Operations: ['44*1=44'] Exploring Operation: 94-61=33, Resulting Numbers: [44, 33] Generated Node #3: [44, 33] from Operation: 94-61=33 Current State: 11:[44, 33], Operations: ['44*1=44', '94-61=33'] Exploring Operation: 44-33=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[44, 1, 61, 94], Operations: [] Exploring Operation: 61-1=60, Resulting Numbers: [44, 94, 60] Generated Node #0,0: 11:[44, 94, 60] Operation: 61-1=60 Exploring Operation: 61-44=17, Resulting Numbers: [1, 94, 17] Generated Node #0,1: 11:[1, 94, 17] Operation: 61-44=17 Exploring Operation: 94-44=50, Resulting Numbers: [1, 61, 50] Generated Node #0,2: 11:[1, 61, 50] Operation: 94-44=50 Exploring Operation: 94-61=33, Resulting Numbers: [44, 1, 33] Generated Node #0,3: 11:[44, 1, 33] Operation: 94-61=33 Exploring Operation: 44-1=43, Resulting Numbers: [61, 94, 43] Generated Node #0,4: 11:[61, 94, 43] Operation: 44-1=43 Moving to Node #0,3 Current State: 11:[44, 1, 33], Operations: ['94-61=33'] Exploring Operation: 44-33=11, Resulting Numbers: [1, 11] Generated Node #0,3,0: 11:[1, 11] Operation: 44-33=11 Exploring Operation: 44/1=44, Resulting Numbers: [33, 44] Generated Node #0,3,1: 11:[33, 44] Operation: 44/1=44 Exploring Operation: 44*1=44, Resulting Numbers: [33, 44] Generated Node #0,3,2: 11:[33, 44] Operation: 44*1=44 Exploring Operation: 44-1=43, Resulting Numbers: [33, 43] Generated Node #0,3,3: 11:[33, 43] Operation: 44-1=43 Exploring Operation: 33-1=32, Resulting Numbers: [44, 32] Generated Node #0,3,4: 11:[44, 32] Operation: 33-1=32 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 11:[1, 11], Operations: ['94-61=33', '44-33=11'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Moving to Node #0 Current State: 11:[44, 1, 61, 94], Operations: [] Exploring Operation: 94-61=33, Resulting Numbers: [44, 1, 33] Generated Node #0,3: 11:[44, 1, 33] Operation: 94-61=33 Moving to Node #0,3 Current State: 11:[44, 1, 33], Operations: ['94-61=33'] Exploring Operation: 44-33=11, Resulting Numbers: [1, 11] Generated Node #0,3,0: 11:[1, 11] Operation: 44-33=11 Moving to Node #0,3,0 Current State: 11:[1, 11], Operations: ['94-61=33', '44-33=11'] Exploring Operation: 11/1=11, Resulting Numbers: [11] 11,11 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
sum_heuristic
[ 10, 76, 73, 58 ]
88
[ "76-73=3", "10*3=30", "58+30=88" ]
Current State: 88:[10, 76, 73, 58], Operations: [] Exploring Operation: 76-73=3, Resulting Numbers: [10, 58, 3] Generated Node #2: [10, 58, 3] from Operation: 76-73=3 Current State: 88:[10, 58, 3], Operations: ['76-73=3'] Exploring Operation: 10*3=30, Resulting Numbers: [58, 30] Generated Node #3: [58, 30] from Operation: 10*3=30 Current State: 88:[58, 30], Operations: ['76-73=3', '10*3=30'] Exploring Operation: 58+30=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[10, 76, 73, 58], Operations: [] Exploring Operation: 73-58=15, Resulting Numbers: [10, 76, 15] Generated Node #0,0: 88:[10, 76, 15] Operation: 73-58=15 Exploring Operation: 76-73=3, Resulting Numbers: [10, 58, 3] Generated Node #0,1: 88:[10, 58, 3] Operation: 76-73=3 Exploring Operation: 76-58=18, Resulting Numbers: [10, 73, 18] Generated Node #0,2: 88:[10, 73, 18] Operation: 76-58=18 Exploring Operation: 10+76=86, Resulting Numbers: [73, 58, 86] Generated Node #0,3: 88:[73, 58, 86] Operation: 10+76=86 Exploring Operation: 10+73=83, Resulting Numbers: [76, 58, 83] Generated Node #0,4: 88:[76, 58, 83] Operation: 10+73=83 Moving to Node #0,1 Current State: 88:[10, 58, 3], Operations: ['76-73=3'] Exploring Operation: 10-3=7, Resulting Numbers: [58, 7] Generated Node #0,1,0: 88:[58, 7] Operation: 10-3=7 Exploring Operation: 58-3=55, Resulting Numbers: [10, 55] Generated Node #0,1,1: 88:[10, 55] Operation: 58-3=55 Exploring Operation: 58-10=48, Resulting Numbers: [3, 48] Generated Node #0,1,2: 88:[3, 48] Operation: 58-10=48 Exploring Operation: 10+3=13, Resulting Numbers: [58, 13] Generated Node #0,1,3: 88:[58, 13] Operation: 10+3=13 Exploring Operation: 58+3=61, Resulting Numbers: [10, 61] Generated Node #0,1,4: 88:[10, 61] Operation: 58+3=61 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 88:[3, 48], Operations: ['76-73=3', '58-10=48'] Exploring Operation: 48/3=16, Resulting Numbers: [16] 16,88 unequal: No Solution Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 48-3=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 3*48=144, Resulting Numbers: [144] 144,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 88:[10, 55], Operations: ['76-73=3', '58-3=55'] Exploring Operation: 10+55=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 10*55=550, Resulting Numbers: [550] 550,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 88:[58, 7], Operations: ['76-73=3', '10-3=7'] Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 58*7=406, Resulting Numbers: [406] 406,88 unequal: No Solution Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 88:[58, 13], Operations: ['76-73=3', '10+3=13'] Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,88 unequal: No Solution Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,88 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,4 Current State: 88:[10, 61], Operations: ['76-73=3', '58+3=61'] Exploring Operation: 10+61=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 10*61=610, Resulting Numbers: [610] 610,88 unequal: No Solution Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,88 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: 88:[10, 76, 15], Operations: ['73-58=15'] Exploring Operation: 10+76=86, Resulting Numbers: [15, 86] Generated Node #0,0,0: 88:[15, 86] Operation: 10+76=86 Exploring Operation: 76+15=91, Resulting Numbers: [10, 91] Generated Node #0,0,1: 88:[10, 91] Operation: 76+15=91 Exploring Operation: 10+15=25, Resulting Numbers: [76, 25] Generated Node #0,0,2: 88:[76, 25] Operation: 10+15=25 Exploring Operation: 15-10=5, Resulting Numbers: [76, 5] Generated Node #0,0,3: 88:[76, 5] Operation: 15-10=5 Exploring Operation: 76-15=61, Resulting Numbers: [10, 61] Generated Node #0,0,4: 88:[10, 61] Operation: 76-15=61 Moving to Node #0,2 Current State: 88:[10, 73, 18], Operations: ['76-58=18'] Exploring Operation: 10+73=83, Resulting Numbers: [18, 83] Generated Node #0,2,0: 88:[18, 83] Operation: 10+73=83 Exploring Operation: 10+18=28, Resulting Numbers: [73, 28] Generated Node #0,2,1: 88:[73, 28] Operation: 10+18=28 Exploring Operation: 73-18=55, Resulting Numbers: [10, 55] Generated Node #0,2,2: 88:[10, 55] Operation: 73-18=55 Exploring Operation: 73+18=91, Resulting Numbers: [10, 91] Generated Node #0,2,3: 88:[10, 91] Operation: 73+18=91 Exploring Operation: 18-10=8, Resulting Numbers: [73, 8] Generated Node #0,2,4: 88:[73, 8] Operation: 18-10=8 Moving to Node #0,3 Current State: 88:[73, 58, 86], Operations: ['10+76=86'] Exploring Operation: 58+86=144, Resulting Numbers: [73, 144] Generated Node #0,3,0: 88:[73, 144] Operation: 58+86=144 Exploring Operation: 86-58=28, Resulting Numbers: [73, 28] Generated Node #0,3,1: 88:[73, 28] Operation: 86-58=28 Exploring Operation: 73+58=131, Resulting Numbers: [86, 131] Generated Node #0,3,2: 88:[86, 131] Operation: 73+58=131 Exploring Operation: 86-73=13, Resulting Numbers: [58, 13] Generated Node #0,3,3: 88:[58, 13] Operation: 86-73=13 Exploring Operation: 73-58=15, Resulting Numbers: [86, 15] Generated Node #0,3,4: 88:[86, 15] Operation: 73-58=15 Moving to Node #0,4 Current State: 88:[76, 58, 83], Operations: ['10+73=83'] Exploring Operation: 76+58=134, Resulting Numbers: [83, 134] Generated Node #0,4,0: 88:[83, 134] Operation: 76+58=134 Exploring Operation: 83-76=7, Resulting Numbers: [58, 7] Generated Node #0,4,1: 88:[58, 7] Operation: 83-76=7 Exploring Operation: 83-58=25, Resulting Numbers: [76, 25] Generated Node #0,4,2: 88:[76, 25] Operation: 83-58=25 Exploring Operation: 58+83=141, Resulting Numbers: [76, 141] Generated Node #0,4,3: 88:[76, 141] Operation: 58+83=141 Exploring Operation: 76-58=18, Resulting Numbers: [83, 18] Generated Node #0,4,4: 88:[83, 18] Operation: 76-58=18 Moving to Node #0,0,1 Current State: 88:[10, 91], Operations: ['73-58=15', '76+15=91'] Exploring Operation: 10*91=910, Resulting Numbers: [910] 910,88 unequal: No Solution Exploring Operation: 10+91=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 91-10=81, Resulting Numbers: [81] 81,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[10, 91], Operations: ['76-58=18', '73+18=91'] Exploring Operation: 10+91=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 91-10=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 10*91=910, Resulting Numbers: [910] 910,88 unequal: No Solution Moving to Node #0,0,0 Current State: 88:[15, 86], Operations: ['73-58=15', '10+76=86'] Exploring Operation: 15+86=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 15*86=1290, Resulting Numbers: [1290] 1290,88 unequal: No Solution Moving to Node #0,3,4 Current State: 88:[86, 15], Operations: ['10+76=86', '73-58=15'] Exploring Operation: 86-15=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 86*15=1290, Resulting Numbers: [1290] 1290,88 unequal: No Solution Exploring Operation: 86+15=101, Resulting Numbers: [101] 101,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[18, 83], Operations: ['76-58=18', '10+73=83'] Exploring Operation: 18*83=1494, Resulting Numbers: [1494] 1494,88 unequal: No Solution Exploring Operation: 18+83=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,4,4 Current State: 88:[83, 18], Operations: ['10+73=83', '76-58=18'] Exploring Operation: 83*18=1494, Resulting Numbers: [1494] 1494,88 unequal: No Solution Exploring Operation: 83-18=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 83+18=101, Resulting Numbers: [101] 101,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[10, 55], Operations: ['76-58=18', '73-18=55'] Exploring Operation: 10+55=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 55-10=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 10*55=550, Resulting Numbers: [550] 550,88 unequal: No Solution Moving to Node #0,0,3 Current State: 88:[76, 5], Operations: ['73-58=15', '15-10=5'] Exploring Operation: 76-5=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 76+5=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 76*5=380, Resulting Numbers: [380] 380,88 unequal: No Solution Moving to Node #0,4,2 Current State: 88:[76, 25], Operations: ['10+73=83', '83-58=25'] Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,88 unequal: No Solution Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,88 unequal: No Solution Moving to Node #0,2,4 Current State: 88:[73, 8], Operations: ['76-58=18', '18-10=8'] Exploring Operation: 73*8=584, Resulting Numbers: [584] 584,88 unequal: No Solution Exploring Operation: 73+8=81, Resulting Numbers: [81] 81,88 unequal: No Solution Exploring Operation: 73-8=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,0,2 Current State: 88:[76, 25], Operations: ['73-58=15', '10+15=25'] Exploring Operation: 76+25=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 76*25=1900, Resulting Numbers: [1900] 1900,88 unequal: No Solution Exploring Operation: 76-25=51, Resulting Numbers: [51] 51,88 unequal: No Solution Moving to Node #0,4,1 Current State: 88:[58, 7], Operations: ['10+73=83', '83-76=7'] Exploring Operation: 58-7=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 58*7=406, Resulting Numbers: [406] 406,88 unequal: No Solution Exploring Operation: 58+7=65, Resulting Numbers: [65] 65,88 unequal: No Solution Moving to Node #0,3,3 Current State: 88:[58, 13], Operations: ['10+76=86', '86-73=13'] Exploring Operation: 58+13=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 58-13=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 58*13=754, Resulting Numbers: [754] 754,88 unequal: No Solution Moving to Node #0,0,4 Current State: 88:[10, 61], Operations: ['73-58=15', '76-15=61'] Exploring Operation: 61-10=51, Resulting Numbers: [51] 51,88 unequal: No Solution Exploring Operation: 10*61=610, Resulting Numbers: [610] 610,88 unequal: No Solution Exploring Operation: 10+61=71, Resulting Numbers: [71] 71,88 unequal: No Solution Moving to Node #0,3,1 Current State: 88:[73, 28], Operations: ['10+76=86', '86-58=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,88 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,88 unequal: No Solution Moving to Node #0,2,1 Current State: 88:[73, 28], Operations: ['76-58=18', '10+18=28'] Exploring Operation: 73-28=45, Resulting Numbers: [45] 45,88 unequal: No Solution Exploring Operation: 73+28=101, Resulting Numbers: [101] 101,88 unequal: No Solution Exploring Operation: 73*28=2044, Resulting Numbers: [2044] 2044,88 unequal: No Solution Moving to Node #0,3,2 Current State: 88:[86, 131], Operations: ['10+76=86', '73+58=131'] Exploring Operation: 86+131=217, Resulting Numbers: [217] 217,88 unequal: No Solution Exploring Operation: 86*131=11266, Resulting Numbers: [11266] 11266,88 unequal: No Solution Exploring Operation: 131-86=45, Resulting Numbers: [45] 45,88 unequal: No Solution Moving to Node #0,4,0 Current State: 88:[83, 134], Operations: ['10+73=83', '76+58=134'] Exploring Operation: 83+134=217, Resulting Numbers: [217] 217,88 unequal: No Solution Exploring Operation: 83*134=11122, Resulting Numbers: [11122] 11122,88 unequal: No Solution Exploring Operation: 134-83=51, Resulting Numbers: [51] 51,88 unequal: No Solution Moving to Node #0,4,3 Current State: 88:[76, 141], Operations: ['10+73=83', '58+83=141'] Exploring Operation: 141-76=65, Resulting Numbers: [65] 65,88 unequal: No Solution Exploring Operation: 76*141=10716, Resulting Numbers: [10716] 10716,88 unequal: No Solution Exploring Operation: 76+141=217, Resulting Numbers: [217] 217,88 unequal: No Solution Moving to Node #0,3,0 Current State: 88:[73, 144], Operations: ['10+76=86', '58+86=144'] Exploring Operation: 73*144=10512, Resulting Numbers: [10512] 10512,88 unequal: No Solution Exploring Operation: 144-73=71, Resulting Numbers: [71] 71,88 unequal: No Solution Exploring Operation: 73+144=217, Resulting Numbers: [217] 217,88 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 85, 5, 57, 79 ]
56
[ "85-5=80", "57+79=136", "136-80=56" ]
Current State: 56:[85, 5, 57, 79], Operations: [] Exploring Operation: 85-5=80, Resulting Numbers: [57, 79, 80] Generated Node #2: [57, 79, 80] from Operation: 85-5=80 Current State: 56:[57, 79, 80], Operations: ['85-5=80'] Exploring Operation: 57+79=136, Resulting Numbers: [80, 136] Generated Node #3: [80, 136] from Operation: 57+79=136 Current State: 56:[80, 136], Operations: ['85-5=80', '57+79=136'] Exploring Operation: 136-80=56, Resulting Numbers: [56] 56,56 equal: Goal Reached
4
Current State: 56:[85, 5, 57, 79], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [5, 57, 6] Generated Node #0,0: 56:[5, 57, 6] Operation: 85-79=6 Moving to Node #0,0 Current State: 56:[5, 57, 6], Operations: ['85-79=6'] Exploring Operation: 6-5=1, Resulting Numbers: [57, 1] Generated Node #0,0,0: 56:[57, 1] Operation: 6-5=1 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 56:[57, 1], Operations: ['85-79=6', '6-5=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Moving to Node #0 Current State: 56:[85, 5, 57, 79], Operations: [] Exploring Operation: 85-79=6, Resulting Numbers: [5, 57, 6] Generated Node #0,0: 56:[5, 57, 6] Operation: 85-79=6 Moving to Node #0,0 Current State: 56:[5, 57, 6], Operations: ['85-79=6'] Exploring Operation: 6-5=1, Resulting Numbers: [57, 1] Generated Node #0,0,0: 56:[57, 1] Operation: 6-5=1 Moving to Node #0,0,0 Current State: 56:[57, 1], Operations: ['85-79=6', '6-5=1'] Exploring Operation: 57-1=56, Resulting Numbers: [56] 56,56 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
sum_heuristic
[ 17, 25, 51, 38 ]
100
[ "51-17=34", "38-34=4", "25*4=100" ]
Current State: 100:[17, 25, 51, 38], Operations: [] Exploring Operation: 51-17=34, Resulting Numbers: [25, 38, 34] Generated Node #2: [25, 38, 34] from Operation: 51-17=34 Current State: 100:[25, 38, 34], Operations: ['51-17=34'] Exploring Operation: 38-34=4, Resulting Numbers: [25, 4] Generated Node #3: [25, 4] from Operation: 38-34=4 Current State: 100:[25, 4], Operations: ['51-17=34', '38-34=4'] Exploring Operation: 25*4=100, Resulting Numbers: [100] 100,100 equal: Goal Reached
4
Current State: 100:[17, 25, 51, 38], Operations: [] Exploring Operation: 38-17=21, Resulting Numbers: [25, 51, 21] Generated Node #0,0: 100:[25, 51, 21] Operation: 38-17=21 Start Sub Search at level 1: Moving to Node #0,0 Current State: 100:[25, 51, 21], Operations: ['38-17=21'] Exploring Operation: 25-21=4, Resulting Numbers: [51, 4] Generated Node #0,0,0: 100:[51, 4] Operation: 25-21=4 Moving to Node #0,0,0 Current State: 100:[51, 4], Operations: ['38-17=21', '25-21=4'] Exploring Operation: 51-4=47, Resulting Numbers: [47] 47,100 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
[ 83, 42, 85, 17 ]
57
[ "83+42=125", "85-17=68", "125-68=57" ]
Current State: 57:[83, 42, 85, 17], Operations: [] Exploring Operation: 83+42=125, Resulting Numbers: [85, 17, 125] Generated Node #2: [85, 17, 125] from Operation: 83+42=125 Current State: 57:[85, 17, 125], Operations: ['83+42=125'] Exploring Operation: 85-17=68, Resulting Numbers: [125, 68] Generated Node #3: [125, 68] from Operation: 85-17=68 Current State: 57:[125, 68], Operations: ['83+42=125', '85-17=68'] Exploring Operation: 125-68=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
4
Current State: 57:[83, 42, 85, 17], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [42, 17, 2] Generated Node #0,0: 57:[42, 17, 2] Operation: 85-83=2 Moving to Node #0,0 Current State: 57:[42, 17, 2], Operations: ['85-83=2'] Exploring Operation: 42+17=59, Resulting Numbers: [2, 59] Generated Node #0,0,0: 57:[2, 59] Operation: 42+17=59 Moving to Node #0,0,0 Current State: 57:[2, 59], Operations: ['85-83=2', '42+17=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached Moving to Node #0 Current State: 57:[83, 42, 85, 17], Operations: [] Exploring Operation: 85-83=2, Resulting Numbers: [42, 17, 2] Generated Node #0,0: 57:[42, 17, 2] Operation: 85-83=2 Moving to Node #0,0 Current State: 57:[42, 17, 2], Operations: ['85-83=2'] Exploring Operation: 42+17=59, Resulting Numbers: [2, 59] Generated Node #0,0,0: 57:[2, 59] Operation: 42+17=59 Moving to Node #0,0,0 Current State: 57:[2, 59], Operations: ['85-83=2', '42+17=59'] Exploring Operation: 59-2=57, Resulting Numbers: [57] 57,57 equal: Goal Reached
0.993924
hs_1
sum_heuristic
[ 93, 61, 51, 9 ]
93
[ "61-51=10", "10-9=1", "93*1=93" ]
Current State: 93:[93, 61, 51, 9], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [93, 9, 10] Generated Node #2: [93, 9, 10] from Operation: 61-51=10 Current State: 93:[93, 9, 10], Operations: ['61-51=10'] Exploring Operation: 10-9=1, Resulting Numbers: [93, 1] Generated Node #3: [93, 1] from Operation: 10-9=1 Current State: 93:[93, 1], Operations: ['61-51=10', '10-9=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached
4
Current State: 93:[93, 61, 51, 9], Operations: [] Exploring Operation: 93-61=32, Resulting Numbers: [51, 9, 32] Generated Node #0,0: 93:[51, 9, 32] Operation: 93-61=32 Exploring Operation: 61+51=112, Resulting Numbers: [93, 9, 112] Generated Node #0,1: 93:[93, 9, 112] Operation: 61+51=112 Exploring Operation: 61-51=10, Resulting Numbers: [93, 9, 10] Generated Node #0,2: 93:[93, 9, 10] Operation: 61-51=10 Exploring Operation: 61-9=52, Resulting Numbers: [93, 51, 52] Generated Node #0,3: 93:[93, 51, 52] Operation: 61-9=52 Exploring Operation: 51-9=42, Resulting Numbers: [93, 61, 42] Generated Node #0,4: 93:[93, 61, 42] Operation: 51-9=42 Start Sub Search at level 1: Moving to Node #0,2 Current State: 93:[93, 9, 10], Operations: ['61-51=10'] Exploring Operation: 10-9=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 93:[93, 1] Operation: 10-9=1 Exploring Operation: 93+9=102, Resulting Numbers: [10, 102] Generated Node #0,2,1: 93:[10, 102] Operation: 93+9=102 Exploring Operation: 9+10=19, Resulting Numbers: [93, 19] Generated Node #0,2,2: 93:[93, 19] Operation: 9+10=19 Exploring Operation: 93-9=84, Resulting Numbers: [10, 84] Generated Node #0,2,3: 93:[10, 84] Operation: 93-9=84 Exploring Operation: 9*10=90, Resulting Numbers: [93, 90] Generated Node #0,2,4: 93:[93, 90] Operation: 9*10=90 Moving to Node #0,2,0 Current State: 93:[93, 1], Operations: ['61-51=10', '10-9=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Moving to Node #0 Current State: 93:[93, 61, 51, 9], Operations: [] Exploring Operation: 61-51=10, Resulting Numbers: [93, 9, 10] Generated Node #0,2: 93:[93, 9, 10] Operation: 61-51=10 Moving to Node #0,2 Current State: 93:[93, 9, 10], Operations: ['61-51=10'] Exploring Operation: 10-9=1, Resulting Numbers: [93, 1] Generated Node #0,2,0: 93:[93, 1] Operation: 10-9=1 Moving to Node #0,2,0 Current State: 93:[93, 1], Operations: ['61-51=10', '10-9=1'] Exploring Operation: 93*1=93, Resulting Numbers: [93] 93,93 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 74, 50, 29, 98 ]
58
[ "50+98=148", "148/74=2", "29*2=58" ]
Current State: 58:[74, 50, 29, 98], Operations: [] Exploring Operation: 50+98=148, Resulting Numbers: [74, 29, 148] Generated Node #2: [74, 29, 148] from Operation: 50+98=148 Current State: 58:[74, 29, 148], Operations: ['50+98=148'] Exploring Operation: 148/74=2, Resulting Numbers: [29, 2] Generated Node #3: [29, 2] from Operation: 148/74=2 Current State: 58:[29, 2], Operations: ['50+98=148', '148/74=2'] Exploring Operation: 29*2=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[74, 50, 29, 98], Operations: [] Exploring Operation: 98-74=24, Resulting Numbers: [50, 29, 24] Generated Node #0,0: 58:[50, 29, 24] Operation: 98-74=24 Exploring Operation: 98-29=69, Resulting Numbers: [74, 50, 69] Generated Node #0,1: 58:[74, 50, 69] Operation: 98-29=69 Exploring Operation: 98-50=48, Resulting Numbers: [74, 29, 48] Generated Node #0,2: 58:[74, 29, 48] Operation: 98-50=48 Exploring Operation: 74-50=24, Resulting Numbers: [29, 98, 24] Generated Node #0,3: 58:[29, 98, 24] Operation: 74-50=24 Exploring Operation: 74-29=45, Resulting Numbers: [50, 98, 45] Generated Node #0,4: 58:[50, 98, 45] Operation: 74-29=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 58:[50, 29, 24], Operations: ['98-74=24'] Exploring Operation: 29+24=53, Resulting Numbers: [50, 53] Generated Node #0,0,0: 58:[50, 53] Operation: 29+24=53 Exploring Operation: 50+24=74, Resulting Numbers: [29, 74] Generated Node #0,0,1: 58:[29, 74] Operation: 50+24=74 Exploring Operation: 50-29=21, Resulting Numbers: [24, 21] Generated Node #0,0,2: 58:[24, 21] Operation: 50-29=21 Exploring Operation: 29-24=5, Resulting Numbers: [50, 5] Generated Node #0,0,3: 58:[50, 5] Operation: 29-24=5 Exploring Operation: 50-24=26, Resulting Numbers: [29, 26] Generated Node #0,0,4: 58:[29, 26] Operation: 50-24=26 Moving to Node #0,0,4 Current State: 58:[29, 26], Operations: ['98-74=24', '50-24=26'] Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,58 unequal: No Solution Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,58 unequal: No Solution Moving to Node #0,0,3 Current State: 58:[50, 5], Operations: ['98-74=24', '29-24=5'] Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,58 unequal: No Solution Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,58 unequal: No Solution Moving to Node #0,0,0 Current State: 58:[50, 53], Operations: ['98-74=24', '29+24=53'] Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,58 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,58 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,0,2 Current State: 58:[24, 21], Operations: ['98-74=24', '50-29=21'] Exploring Operation: 24-21=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 24*21=504, Resulting Numbers: [504] 504,58 unequal: No Solution Exploring Operation: 24+21=45, Resulting Numbers: [45] 45,58 unequal: No Solution Moving to Node #0,0,1 Current State: 58:[29, 74], Operations: ['98-74=24', '50+24=74'] Exploring Operation: 29*74=2146, Resulting Numbers: [2146] 2146,58 unequal: No Solution Exploring Operation: 29+74=103, Resulting Numbers: [103] 103,58 unequal: No Solution Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,58 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 #0,2 Current State: 58:[74, 29, 48], Operations: ['98-50=48'] Exploring Operation: 29+48=77, Resulting Numbers: [74, 77] Generated Node #0,2,0: 58:[74, 77] Operation: 29+48=77 Exploring Operation: 74-29=45, Resulting Numbers: [48, 45] Generated Node #0,2,1: 58:[48, 45] Operation: 74-29=45 Exploring Operation: 48-29=19, Resulting Numbers: [74, 19] Generated Node #0,2,2: 58:[74, 19] Operation: 48-29=19 Exploring Operation: 74+29=103, Resulting Numbers: [48, 103] Generated Node #0,2,3: 58:[48, 103] Operation: 74+29=103 Exploring Operation: 74-48=26, Resulting Numbers: [29, 26] Generated Node #0,2,4: 58:[29, 26] Operation: 74-48=26 Moving to Node #0,2,4 Current State: 58:[29, 26], Operations: ['98-50=48', '74-48=26'] Exploring Operation: 29-26=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 29*26=754, Resulting Numbers: [754] 754,58 unequal: No Solution Exploring Operation: 29+26=55, Resulting Numbers: [55] 55,58 unequal: No Solution Moving to Node #0,2,1 Current State: 58:[48, 45], Operations: ['98-50=48', '74-29=45'] Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 48+45=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 48*45=2160, Resulting Numbers: [2160] 2160,58 unequal: No Solution Moving to Node #0,2,2 Current State: 58:[74, 19], Operations: ['98-50=48', '48-29=19'] Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,58 unequal: No Solution Moving to Node #0,2,0 Current State: 58:[74, 77], Operations: ['98-50=48', '29+48=77'] Exploring Operation: 74*77=5698, Resulting Numbers: [5698] 5698,58 unequal: No Solution Exploring Operation: 77-74=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 74+77=151, Resulting Numbers: [151] 151,58 unequal: No Solution Moving to Node #0,2,3 Current State: 58:[48, 103], Operations: ['98-50=48', '74+29=103'] Exploring Operation: 48*103=4944, Resulting Numbers: [4944] 4944,58 unequal: No Solution Exploring Operation: 103-48=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 48+103=151, Resulting Numbers: [151] 151,58 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 #0,1 Current State: 58:[74, 50, 69], Operations: ['98-29=69'] Exploring Operation: 74-69=5, Resulting Numbers: [50, 5] Generated Node #0,1,0: 58:[50, 5] Operation: 74-69=5 Exploring Operation: 69-50=19, Resulting Numbers: [74, 19] Generated Node #0,1,1: 58:[74, 19] Operation: 69-50=19 Exploring Operation: 50+69=119, Resulting Numbers: [74, 119] Generated Node #0,1,2: 58:[74, 119] Operation: 50+69=119 Exploring Operation: 74+50=124, Resulting Numbers: [69, 124] Generated Node #0,1,3: 58:[69, 124] Operation: 74+50=124 Exploring Operation: 74-50=24, Resulting Numbers: [69, 24] Generated Node #0,1,4: 58:[69, 24] Operation: 74-50=24 Moving to Node #0,1,0 Current State: 58:[50, 5], Operations: ['98-29=69', '74-69=5'] Exploring Operation: 50-5=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 50*5=250, Resulting Numbers: [250] 250,58 unequal: No Solution Exploring Operation: 50+5=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 50/5=10, Resulting Numbers: [10] 10,58 unequal: No Solution Moving to Node #0,1,4 Current State: 58:[69, 24], Operations: ['98-29=69', '74-50=24'] Exploring Operation: 69+24=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 69*24=1656, Resulting Numbers: [1656] 1656,58 unequal: No Solution Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,58 unequal: No Solution Moving to Node #0,1,1 Current State: 58:[74, 19], Operations: ['98-29=69', '69-50=19'] Exploring Operation: 74-19=55, Resulting Numbers: [55] 55,58 unequal: No Solution Exploring Operation: 74*19=1406, Resulting Numbers: [1406] 1406,58 unequal: No Solution Exploring Operation: 74+19=93, Resulting Numbers: [93] 93,58 unequal: No Solution Moving to Node #0,1,2 Current State: 58:[74, 119], Operations: ['98-29=69', '50+69=119'] Exploring Operation: 74+119=193, Resulting Numbers: [193] 193,58 unequal: No Solution Exploring Operation: 74*119=8806, Resulting Numbers: [8806] 8806,58 unequal: No Solution Exploring Operation: 119-74=45, Resulting Numbers: [45] 45,58 unequal: No Solution Moving to Node #0,1,3 Current State: 58:[69, 124], Operations: ['98-29=69', '74+50=124'] Exploring Operation: 69+124=193, Resulting Numbers: [193] 193,58 unequal: No Solution Exploring Operation: 69*124=8556, Resulting Numbers: [8556] 8556,58 unequal: No Solution Exploring Operation: 124-69=55, Resulting Numbers: [55] 55,58 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 #0,3 Current State: 58:[29, 98, 24], Operations: ['74-50=24'] Exploring Operation: 98+24=122, Resulting Numbers: [29, 122] Generated Node #0,3,0: 58:[29, 122] Operation: 98+24=122 Exploring Operation: 29-24=5, Resulting Numbers: [98, 5] Generated Node #0,3,1: 58:[98, 5] Operation: 29-24=5 Exploring Operation: 29+24=53, Resulting Numbers: [98, 53] Generated Node #0,3,2: 58:[98, 53] Operation: 29+24=53 Exploring Operation: 98-29=69, Resulting Numbers: [24, 69] Generated Node #0,3,3: 58:[24, 69] Operation: 98-29=69 Exploring Operation: 98-24=74, Resulting Numbers: [29, 74] Generated Node #0,3,4: 58:[29, 74] Operation: 98-24=74 Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 58:[24, 69], Operations: ['74-50=24', '98-29=69'] Exploring Operation: 69-24=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 24*69=1656, Resulting Numbers: [1656] 1656,58 unequal: No Solution Exploring Operation: 24+69=93, Resulting Numbers: [93] 93,58 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 #0,3,4 Current State: 58:[29, 74], Operations: ['74-50=24', '98-24=74'] Exploring Operation: 74-29=45, Resulting Numbers: [45] 45,58 unequal: No Solution Exploring Operation: 29+74=103, Resulting Numbers: [103] 103,58 unequal: No Solution Exploring Operation: 29*74=2146, Resulting Numbers: [2146] 2146,58 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 #0,3,1 Current State: 58:[98, 5], Operations: ['74-50=24', '29-24=5'] Exploring Operation: 98+5=103, Resulting Numbers: [103] 103,58 unequal: No Solution Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 98*5=490, Resulting Numbers: [490] 490,58 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 #0,3,2 Current State: 58:[98, 53], Operations: ['74-50=24', '29+24=53'] Exploring Operation: 98*53=5194, Resulting Numbers: [5194] 5194,58 unequal: No Solution Exploring Operation: 98+53=151, Resulting Numbers: [151] 151,58 unequal: No Solution Exploring Operation: 98-53=45, Resulting Numbers: [45] 45,58 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 #0,3,0 Current State: 58:[29, 122], Operations: ['74-50=24', '98+24=122'] Exploring Operation: 29*122=3538, Resulting Numbers: [3538] 3538,58 unequal: No Solution Exploring Operation: 29+122=151, Resulting Numbers: [151] 151,58 unequal: No Solution Exploring Operation: 122-29=93, Resulting Numbers: [93] 93,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 58:[50, 98, 45], Operations: ['74-29=45'] Exploring Operation: 98-45=53, Resulting Numbers: [50, 53] Generated Node #0,4,0: 58:[50, 53] Operation: 98-45=53 Exploring Operation: 50-45=5, Resulting Numbers: [98, 5] Generated Node #0,4,1: 58:[98, 5] Operation: 50-45=5 Exploring Operation: 98+45=143, Resulting Numbers: [50, 143] Generated Node #0,4,2: 58:[50, 143] Operation: 98+45=143 Exploring Operation: 98-50=48, Resulting Numbers: [45, 48] Generated Node #0,4,3: 58:[45, 48] Operation: 98-50=48 Exploring Operation: 50+45=95, Resulting Numbers: [98, 95] Generated Node #0,4,4: 58:[98, 95] Operation: 50+45=95 Moving to Node #0,4,0 Current State: 58:[50, 53], Operations: ['74-29=45', '98-45=53'] Exploring Operation: 50*53=2650, Resulting Numbers: [2650] 2650,58 unequal: No Solution Exploring Operation: 53-50=3, Resulting Numbers: [3] 3,58 unequal: No Solution Exploring Operation: 50+53=103, Resulting Numbers: [103] 103,58 unequal: No Solution Moving to Node #0,4,3 Current State: 58:[45, 48], Operations: ['74-29=45', '98-50=48'] Exploring Operation: 45+48=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 45*48=2160, Resulting Numbers: [2160] 2160,58 unequal: No Solution Exploring Operation: 48-45=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,4,1 Current State: 58:[98, 5], Operations: ['74-29=45', '50-45=5'] Exploring Operation: 98-5=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 98+5=103, Resulting Numbers: [103] 103,58 unequal: No Solution Exploring Operation: 98*5=490, Resulting Numbers: [490] 490,58 unequal: No Solution Moving to Node #0,4,4 Current State: 58:[98, 95], Operations: ['74-29=45', '50+45=95'] Exploring Operation: 98*95=9310, Resulting Numbers: [9310] 9310,58 unequal: No Solution Exploring Operation: 98+95=193, Resulting Numbers: [193] 193,58 unequal: No Solution Exploring Operation: 98-95=3, Resulting Numbers: [3] 3,58 unequal: No Solution Moving to Node #0,4,2 Current State: 58:[50, 143], Operations: ['74-29=45', '98+45=143'] Exploring Operation: 143-50=93, Resulting Numbers: [93] 93,58 unequal: No Solution Exploring Operation: 50*143=7150, Resulting Numbers: [7150] 7150,58 unequal: No Solution Exploring Operation: 50+143=193, Resulting Numbers: [193] 193,58 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 52, 69, 1, 30 ]
13
[ "69-52=17", "1*30=30", "30-17=13" ]
Current State: 13:[52, 69, 1, 30], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [1, 30, 17] Generated Node #2: [1, 30, 17] from Operation: 69-52=17 Current State: 13:[1, 30, 17], Operations: ['69-52=17'] Exploring Operation: 1*30=30, Resulting Numbers: [17, 30] Generated Node #3: [17, 30] from Operation: 1*30=30 Current State: 13:[17, 30], Operations: ['69-52=17', '1*30=30'] Exploring Operation: 30-17=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[52, 69, 1, 30], Operations: [] Exploring Operation: 52-1=51, Resulting Numbers: [69, 30, 51] Generated Node #0,0: 13:[69, 30, 51] Operation: 52-1=51 Exploring Operation: 69-52=17, Resulting Numbers: [1, 30, 17] Generated Node #0,1: 13:[1, 30, 17] Operation: 69-52=17 Exploring Operation: 52-30=22, Resulting Numbers: [69, 1, 22] Generated Node #0,2: 13:[69, 1, 22] Operation: 52-30=22 Exploring Operation: 69-30=39, Resulting Numbers: [52, 1, 39] Generated Node #0,3: 13:[52, 1, 39] Operation: 69-30=39 Moving to Node #0,1 Current State: 13:[1, 30, 17], Operations: ['69-52=17'] Exploring Operation: 30-1=29, Resulting Numbers: [17, 29] Generated Node #0,1,0: 13:[17, 29] Operation: 30-1=29 Exploring Operation: 30-17=13, Resulting Numbers: [1, 13] Generated Node #0,1,1: 13:[1, 13] Operation: 30-17=13 Exploring Operation: 17-1=16, Resulting Numbers: [30, 16] Generated Node #0,1,2: 13:[30, 16] Operation: 17-1=16 Exploring Operation: 1*30=30, Resulting Numbers: [17, 30] Generated Node #0,1,3: 13:[17, 30] Operation: 1*30=30 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 13:[1, 13], Operations: ['69-52=17', '30-17=13'] Exploring Operation: 1+13=14, Resulting Numbers: [14] 14,13 unequal: No Solution Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[52, 69, 1, 30], Operations: [] Exploring Operation: 69-52=17, Resulting Numbers: [1, 30, 17] Generated Node #0,1: 13:[1, 30, 17] Operation: 69-52=17 Moving to Node #0,1 Current State: 13:[1, 30, 17], Operations: ['69-52=17'] Exploring Operation: 30-17=13, Resulting Numbers: [1, 13] Generated Node #0,1,1: 13:[1, 13] Operation: 30-17=13 Moving to Node #0,1,1 Current State: 13:[1, 13], Operations: ['69-52=17', '30-17=13'] Exploring Operation: 13/1=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 31, 96, 55, 26 ]
85
[ "31-26=5", "55/5=11", "96-11=85" ]
Current State: 85:[31, 96, 55, 26], Operations: [] Exploring Operation: 31-26=5, Resulting Numbers: [96, 55, 5] Generated Node #2: [96, 55, 5] from Operation: 31-26=5 Current State: 85:[96, 55, 5], Operations: ['31-26=5'] Exploring Operation: 55/5=11, Resulting Numbers: [96, 11] Generated Node #3: [96, 11] from Operation: 55/5=11 Current State: 85:[96, 11], Operations: ['31-26=5', '55/5=11'] Exploring Operation: 96-11=85, Resulting Numbers: [85] 85,85 equal: Goal Reached
4
Current State: 85:[31, 96, 55, 26], Operations: [] Exploring Operation: 55-31=24, Resulting Numbers: [96, 26, 24] Generated Node #0,0: 85:[96, 26, 24] Operation: 55-31=24 Exploring Operation: 31+55=86, Resulting Numbers: [96, 26, 86] Generated Node #0,1: 85:[96, 26, 86] Operation: 31+55=86 Moving to Node #0,1 Current State: 85:[96, 26, 86], Operations: ['31+55=86'] Exploring Operation: 96-26=70, Resulting Numbers: [86, 70] Generated Node #0,1,0: 85:[86, 70] Operation: 96-26=70 Exploring Operation: 96-86=10, Resulting Numbers: [26, 10] Generated Node #0,1,1: 85:[26, 10] Operation: 96-86=10 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 85:[26, 10], Operations: ['31+55=86', '96-86=10'] Exploring Operation: 26+10=36, Resulting Numbers: [36] 36,85 unequal: No Solution Exploring Operation: 26-10=16, Resulting Numbers: [16] 16,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 85:[86, 70], Operations: ['31+55=86', '96-26=70'] Exploring Operation: 86-70=16, Resulting Numbers: [16] 16,85 unequal: No Solution Exploring Operation: 86+70=156, Resulting Numbers: [156] 156,85 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:[96, 26, 24], Operations: ['55-31=24'] Exploring Operation: 96/24=4, Resulting Numbers: [26, 4] Generated Node #0,0,0: 85:[26, 4] Operation: 96/24=4 Exploring Operation: 26-24=2, Resulting Numbers: [96, 2] Generated Node #0,0,1: 85:[96, 2] Operation: 26-24=2 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 85:[26, 4], Operations: ['55-31=24', '96/24=4'] Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,85 unequal: No Solution Exploring Operation: 26+4=30, Resulting Numbers: [30] 30,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 85:[96, 2], Operations: ['55-31=24', '26-24=2'] Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,85 unequal: No Solution Exploring Operation: 96+2=98, Resulting Numbers: [98] 98,85 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
mult_heuristic
[ 6, 39, 6, 90 ]
54
[ "6*39=234", "90+234=324", "324/6=54" ]
Current State: 54:[6, 39, 6, 90], Operations: [] Exploring Operation: 6*39=234, Resulting Numbers: [90, 234] Generated Node #2: [90, 234] from Operation: 6*39=234 Current State: 54:[90, 234], Operations: ['6*39=234'] Exploring Operation: 90+234=324, Resulting Numbers: [324] 324,54 equal: Goal Reached Exploring Operation: 324/6=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[6, 39, 6, 90], Operations: [] Exploring Operation: 90-39=51, Resulting Numbers: [6, 6, 51] Generated Node #0,0: 54:[6, 6, 51] Operation: 90-39=51 Exploring Operation: 90/6=15, Resulting Numbers: [6, 39, 15] Generated Node #0,1: 54:[6, 39, 15] Operation: 90/6=15 Exploring Operation: 90/6=15, Resulting Numbers: [39, 6, 15] Generated Node #0,2: 54:[39, 6, 15] Operation: 90/6=15 Start Sub Search at level 1: Moving to Node #0,0 Current State: 54:[6, 6, 51], Operations: ['90-39=51'] Exploring Operation: 6/6=1, Resulting Numbers: [51, 1] Generated Node #0,0,0: 54:[51, 1] Operation: 6/6=1 Exploring Operation: 6+51=57, Resulting Numbers: [6, 57] Generated Node #0,0,1: 54:[6, 57] Operation: 6+51=57 Exploring Operation: 6+51=57, Resulting Numbers: [6, 57] Generated Node #0,0,2: 54:[6, 57] Operation: 6+51=57 Moving to Node #0,0,1 Current State: 54:[6, 57], Operations: ['90-39=51', '6+51=57'] Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,54 unequal: No Solution Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,54 unequal: No Solution Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,54 unequal: No Solution Moving to Node #0,0,2 Current State: 54:[6, 57], Operations: ['90-39=51', '6+51=57'] Exploring Operation: 6+57=63, Resulting Numbers: [63] 63,54 unequal: No Solution Exploring Operation: 6*57=342, Resulting Numbers: [342] 342,54 unequal: No Solution Exploring Operation: 57-6=51, Resulting Numbers: [51] 51,54 unequal: No Solution Moving to Node #0,0,0 Current State: 54:[51, 1], Operations: ['90-39=51', '6/6=1'] Exploring Operation: 51+1=52, Resulting Numbers: [52] 52,54 unequal: No Solution Exploring Operation: 51/1=51, Resulting Numbers: [51] 51,54 unequal: No Solution Exploring Operation: 51*1=51, Resulting Numbers: [51] 51,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 54:[6, 39, 15], Operations: ['90/6=15'] Exploring Operation: 39-6=33, Resulting Numbers: [15, 33] Generated Node #0,1,0: 54:[15, 33] Operation: 39-6=33 Exploring Operation: 39-15=24, Resulting Numbers: [6, 24] Generated Node #0,1,1: 54:[6, 24] Operation: 39-15=24 Exploring Operation: 39+15=54, Resulting Numbers: [6, 54] Generated Node #0,1,2: 54:[6, 54] Operation: 39+15=54 Moving to Node #0,1,2 Current State: 54:[6, 54], Operations: ['90/6=15', '39+15=54'] Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,54 unequal: No Solution Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,54 unequal: No Solution Moving to Node #0,1,1 Current State: 54:[6, 24], Operations: ['90/6=15', '39-15=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,54 unequal: No Solution Moving to Node #0,1,0 Current State: 54:[15, 33], Operations: ['90/6=15', '39-6=33'] Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,54 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,54 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 Current State: 54:[39, 6, 15], Operations: ['90/6=15'] Exploring Operation: 39+15=54, Resulting Numbers: [6, 54] Generated Node #0,2,0: 54:[6, 54] Operation: 39+15=54 Exploring Operation: 39-6=33, Resulting Numbers: [15, 33] Generated Node #0,2,1: 54:[15, 33] Operation: 39-6=33 Exploring Operation: 39-15=24, Resulting Numbers: [6, 24] Generated Node #0,2,2: 54:[6, 24] Operation: 39-15=24 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 54:[6, 54], Operations: ['90/6=15', '39+15=54'] Exploring Operation: 54/6=9, Resulting Numbers: [9] 9,54 unequal: No Solution Exploring Operation: 54-6=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 6+54=60, Resulting Numbers: [60] 60,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 54:[6, 24], Operations: ['90/6=15', '39-15=24'] Exploring Operation: 6+24=30, Resulting Numbers: [30] 30,54 unequal: No Solution Exploring Operation: 24/6=4, Resulting Numbers: [4] 4,54 unequal: No Solution Exploring Operation: 24-6=18, Resulting Numbers: [18] 18,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 54:[15, 33], Operations: ['90/6=15', '39-6=33'] Exploring Operation: 15*33=495, Resulting Numbers: [495] 495,54 unequal: No Solution Exploring Operation: 33-15=18, Resulting Numbers: [18] 18,54 unequal: No Solution Exploring Operation: 15+33=48, Resulting Numbers: [48] 48,54 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 94, 51, 58, 12 ]
54
[ "94-58=36", "36/12=3", "51+3=54" ]
Current State: 54:[94, 51, 58, 12], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [51, 12, 36] Generated Node #2: [51, 12, 36] from Operation: 94-58=36 Current State: 54:[51, 12, 36], Operations: ['94-58=36'] Exploring Operation: 36/12=3, Resulting Numbers: [51, 3] Generated Node #3: [51, 3] from Operation: 36/12=3 Current State: 54:[51, 3], Operations: ['94-58=36', '36/12=3'] Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
4
Current State: 54:[94, 51, 58, 12], Operations: [] Exploring Operation: 58-51=7, Resulting Numbers: [94, 12, 7] Generated Node #0,0: 54:[94, 12, 7] Operation: 58-51=7 Exploring Operation: 94-51=43, Resulting Numbers: [58, 12, 43] Generated Node #0,1: 54:[58, 12, 43] Operation: 94-51=43 Exploring Operation: 94-12=82, Resulting Numbers: [51, 58, 82] Generated Node #0,2: 54:[51, 58, 82] Operation: 94-12=82 Exploring Operation: 58-12=46, Resulting Numbers: [94, 51, 46] Generated Node #0,3: 54:[94, 51, 46] Operation: 58-12=46 Exploring Operation: 94-58=36, Resulting Numbers: [51, 12, 36] Generated Node #0,4: 54:[51, 12, 36] Operation: 94-58=36 Moving to Node #0,4 Current State: 54:[51, 12, 36], Operations: ['94-58=36'] Exploring Operation: 36/12=3, Resulting Numbers: [51, 3] Generated Node #0,4,0: 54:[51, 3] Operation: 36/12=3 Exploring Operation: 12+36=48, Resulting Numbers: [51, 48] Generated Node #0,4,1: 54:[51, 48] Operation: 12+36=48 Exploring Operation: 51+12=63, Resulting Numbers: [36, 63] Generated Node #0,4,2: 54:[36, 63] Operation: 51+12=63 Exploring Operation: 51-36=15, Resulting Numbers: [12, 15] Generated Node #0,4,3: 54:[12, 15] Operation: 51-36=15 Exploring Operation: 36-12=24, Resulting Numbers: [51, 24] Generated Node #0,4,4: 54:[51, 24] Operation: 36-12=24 Moving to Node #0,1 Current State: 54:[58, 12, 43], Operations: ['94-51=43'] Exploring Operation: 58-12=46, Resulting Numbers: [43, 46] Generated Node #0,1,0: 54:[43, 46] Operation: 58-12=46 Exploring Operation: 43-12=31, Resulting Numbers: [58, 31] Generated Node #0,1,1: 54:[58, 31] Operation: 43-12=31 Exploring Operation: 58-43=15, Resulting Numbers: [12, 15] Generated Node #0,1,2: 54:[12, 15] Operation: 58-43=15 Exploring Operation: 58+12=70, Resulting Numbers: [43, 70] Generated Node #0,1,3: 54:[43, 70] Operation: 58+12=70 Exploring Operation: 12+43=55, Resulting Numbers: [58, 55] Generated Node #0,1,4: 54:[58, 55] Operation: 12+43=55 Moving to Node #0,2 Current State: 54:[51, 58, 82], Operations: ['94-12=82'] Exploring Operation: 51+58=109, Resulting Numbers: [82, 109] Generated Node #0,2,0: 54:[82, 109] Operation: 51+58=109 Exploring Operation: 82-58=24, Resulting Numbers: [51, 24] Generated Node #0,2,1: 54:[51, 24] Operation: 82-58=24 Exploring Operation: 51+82=133, Resulting Numbers: [58, 133] Generated Node #0,2,2: 54:[58, 133] Operation: 51+82=133 Exploring Operation: 82-51=31, Resulting Numbers: [58, 31] Generated Node #0,2,3: 54:[58, 31] Operation: 82-51=31 Exploring Operation: 58-51=7, Resulting Numbers: [82, 7] Generated Node #0,2,4: 54:[82, 7] Operation: 58-51=7 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 54:[51, 24], Operations: ['94-12=82', '82-58=24'] Exploring Operation: 51*24=1224, Resulting Numbers: [1224] 1224,54 unequal: No Solution Exploring Operation: 51-24=27, Resulting Numbers: [27] 27,54 unequal: No Solution Exploring Operation: 51+24=75, Resulting Numbers: [75] 75,54 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 #0,2,3 Current State: 54:[58, 31], Operations: ['94-12=82', '82-51=31'] Exploring Operation: 58*31=1798, Resulting Numbers: [1798] 1798,54 unequal: No Solution Exploring Operation: 58+31=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 58-31=27, Resulting Numbers: [27] 27,54 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 #0,2,4 Current State: 54:[82, 7], Operations: ['94-12=82', '58-51=7'] Exploring Operation: 82+7=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 82*7=574, Resulting Numbers: [574] 574,54 unequal: No Solution Exploring Operation: 82-7=75, Resulting Numbers: [75] 75,54 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:[82, 109], Operations: ['94-12=82', '51+58=109'] Exploring Operation: 82+109=191, Resulting Numbers: [191] 191,54 unequal: No Solution Exploring Operation: 82*109=8938, Resulting Numbers: [8938] 8938,54 unequal: No Solution Exploring Operation: 109-82=27, Resulting Numbers: [27] 27,54 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:[58, 133], Operations: ['94-12=82', '51+82=133'] Exploring Operation: 133-58=75, Resulting Numbers: [75] 75,54 unequal: No Solution Exploring Operation: 58*133=7714, Resulting Numbers: [7714] 7714,54 unequal: No Solution Exploring Operation: 58+133=191, Resulting Numbers: [191] 191,54 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: 54:[94, 12, 7], Operations: ['58-51=7'] Exploring Operation: 94-7=87, Resulting Numbers: [12, 87] Generated Node #0,0,0: 54:[12, 87] Operation: 94-7=87 Exploring Operation: 12-7=5, Resulting Numbers: [94, 5] Generated Node #0,0,1: 54:[94, 5] Operation: 12-7=5 Exploring Operation: 94+7=101, Resulting Numbers: [12, 101] Generated Node #0,0,2: 54:[12, 101] Operation: 94+7=101 Exploring Operation: 12+7=19, Resulting Numbers: [94, 19] Generated Node #0,0,3: 54:[94, 19] Operation: 12+7=19 Exploring Operation: 94-12=82, Resulting Numbers: [7, 82] Generated Node #0,0,4: 54:[7, 82] Operation: 94-12=82 Moving to Node #0,3 Current State: 54:[94, 51, 46], Operations: ['58-12=46'] Exploring Operation: 94-46=48, Resulting Numbers: [51, 48] Generated Node #0,3,0: 54:[51, 48] Operation: 94-46=48 Exploring Operation: 51-46=5, Resulting Numbers: [94, 5] Generated Node #0,3,1: 54:[94, 5] Operation: 51-46=5 Exploring Operation: 94+46=140, Resulting Numbers: [51, 140] Generated Node #0,3,2: 54:[51, 140] Operation: 94+46=140 Exploring Operation: 51+46=97, Resulting Numbers: [94, 97] Generated Node #0,3,3: 54:[94, 97] Operation: 51+46=97 Exploring Operation: 94-51=43, Resulting Numbers: [46, 43] Generated Node #0,3,4: 54:[46, 43] Operation: 94-51=43 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 54:[51, 48], Operations: ['58-12=46', '94-46=48'] Exploring Operation: 51*48=2448, Resulting Numbers: [2448] 2448,54 unequal: No Solution Exploring Operation: 51+48=99, Resulting Numbers: [99] 99,54 unequal: No Solution Exploring Operation: 51-48=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 54:[46, 43], Operations: ['58-12=46', '94-51=43'] Exploring Operation: 46+43=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 46*43=1978, Resulting Numbers: [1978] 1978,54 unequal: No Solution Exploring Operation: 46-43=3, Resulting Numbers: [3] 3,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 54:[94, 5], Operations: ['58-12=46', '51-46=5'] Exploring Operation: 94*5=470, Resulting Numbers: [470] 470,54 unequal: No Solution Exploring Operation: 94-5=89, Resulting Numbers: [89] 89,54 unequal: No Solution Exploring Operation: 94+5=99, Resulting Numbers: [99] 99,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 54:[94, 97], Operations: ['58-12=46', '51+46=97'] Exploring Operation: 94+97=191, Resulting Numbers: [191] 191,54 unequal: No Solution Exploring Operation: 97-94=3, Resulting Numbers: [3] 3,54 unequal: No Solution Exploring Operation: 94*97=9118, Resulting Numbers: [9118] 9118,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 54:[51, 140], Operations: ['58-12=46', '94+46=140'] Exploring Operation: 51*140=7140, Resulting Numbers: [7140] 7140,54 unequal: No Solution Exploring Operation: 51+140=191, Resulting Numbers: [191] 191,54 unequal: No Solution Exploring Operation: 140-51=89, Resulting Numbers: [89] 89,54 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4,0 Current State: 54:[51, 3], Operations: ['94-58=36', '36/12=3'] Exploring Operation: 51/3=17, Resulting Numbers: [17] 17,54 unequal: No Solution Exploring Operation: 51-3=48, Resulting Numbers: [48] 48,54 unequal: No Solution Exploring Operation: 51*3=153, Resulting Numbers: [153] 153,54 unequal: No Solution Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached Moving to Node #0 Current State: 54:[94, 51, 58, 12], Operations: [] Exploring Operation: 94-58=36, Resulting Numbers: [51, 12, 36] Generated Node #0,4: 54:[51, 12, 36] Operation: 94-58=36 Moving to Node #0,4 Current State: 54:[51, 12, 36], Operations: ['94-58=36'] Exploring Operation: 36/12=3, Resulting Numbers: [51, 3] Generated Node #0,4,0: 54:[51, 3] Operation: 36/12=3 Moving to Node #0,4,0 Current State: 54:[51, 3], Operations: ['94-58=36', '36/12=3'] Exploring Operation: 51+3=54, Resulting Numbers: [54] 54,54 equal: Goal Reached
0.940972
hs_5
sum_heuristic
[ 55, 7, 16, 91 ]
94
[ "55-7=48", "48/16=3", "91+3=94" ]
Current State: 94:[55, 7, 16, 91], Operations: [] Exploring Operation: 55-7=48, Resulting Numbers: [16, 91, 48] Generated Node #2: [16, 91, 48] from Operation: 55-7=48 Current State: 94:[16, 91, 48], Operations: ['55-7=48'] Exploring Operation: 48/16=3, Resulting Numbers: [91, 3] Generated Node #3: [91, 3] from Operation: 48/16=3 Current State: 94:[91, 3], Operations: ['55-7=48', '48/16=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[55, 7, 16, 91], Operations: [] Exploring Operation: 55-7=48, Resulting Numbers: [16, 91, 48] Generated Node #0,0: 94:[16, 91, 48] Operation: 55-7=48 Exploring Operation: 7+91=98, Resulting Numbers: [55, 16, 98] Generated Node #0,1: 94:[55, 16, 98] Operation: 7+91=98 Exploring Operation: 55-16=39, Resulting Numbers: [7, 91, 39] Generated Node #0,2: 94:[7, 91, 39] Operation: 55-16=39 Exploring Operation: 16-7=9, Resulting Numbers: [55, 91, 9] Generated Node #0,3: 94:[55, 91, 9] Operation: 16-7=9 Start Sub Search at level 1: Moving to Node #0,2 Current State: 94:[7, 91, 39], Operations: ['55-16=39'] Exploring Operation: 7+39=46, Resulting Numbers: [91, 46] Generated Node #0,2,0: 94:[91, 46] Operation: 7+39=46 Exploring Operation: 91-39=52, Resulting Numbers: [7, 52] Generated Node #0,2,1: 94:[7, 52] Operation: 91-39=52 Exploring Operation: 91-7=84, Resulting Numbers: [39, 84] Generated Node #0,2,2: 94:[39, 84] Operation: 91-7=84 Exploring Operation: 7+91=98, Resulting Numbers: [39, 98] Generated Node #0,2,3: 94:[39, 98] Operation: 7+91=98 Moving to Node #0,2,0 Current State: 94:[91, 46], Operations: ['55-16=39', '7+39=46'] Exploring Operation: 91*46=4186, Resulting Numbers: [4186] 4186,94 unequal: No Solution Exploring Operation: 91-46=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 91+46=137, Resulting Numbers: [137] 137,94 unequal: No Solution Moving to Node #0,2,1 Current State: 94:[7, 52], Operations: ['55-16=39', '91-39=52'] Exploring Operation: 7+52=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 52-7=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 7*52=364, Resulting Numbers: [364] 364,94 unequal: No Solution Moving to Node #0,2,3 Current State: 94:[39, 98], Operations: ['55-16=39', '7+91=98'] Exploring Operation: 98-39=59, Resulting Numbers: [59] 59,94 unequal: No Solution Exploring Operation: 39+98=137, Resulting Numbers: [137] 137,94 unequal: No Solution Exploring Operation: 39*98=3822, Resulting Numbers: [3822] 3822,94 unequal: No Solution Moving to Node #0,2,2 Current State: 94:[39, 84], Operations: ['55-16=39', '91-7=84'] Exploring Operation: 84-39=45, Resulting Numbers: [45] 45,94 unequal: No Solution Exploring Operation: 39+84=123, Resulting Numbers: [123] 123,94 unequal: No Solution Exploring Operation: 39*84=3276, Resulting Numbers: [3276] 3276,94 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 94:[16, 91, 48], Operations: ['55-7=48'] Exploring Operation: 91-48=43, Resulting Numbers: [16, 43] Generated Node #0,0,0: 94:[16, 43] Operation: 91-48=43 Exploring Operation: 16+91=107, Resulting Numbers: [48, 107] Generated Node #0,0,1: 94:[48, 107] Operation: 16+91=107 Exploring Operation: 48/16=3, Resulting Numbers: [91, 3] Generated Node #0,0,2: 94:[91, 3] Operation: 48/16=3 Exploring Operation: 48-16=32, Resulting Numbers: [91, 32] Generated Node #0,0,3: 94:[91, 32] Operation: 48-16=32 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 94:[91, 3], Operations: ['55-7=48', '48/16=3'] Exploring Operation: 91-3=88, Resulting Numbers: [88] 88,94 unequal: No Solution Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[55, 7, 16, 91], Operations: [] Exploring Operation: 55-7=48, Resulting Numbers: [16, 91, 48] Generated Node #0,0: 94:[16, 91, 48] Operation: 55-7=48 Moving to Node #0,0 Current State: 94:[16, 91, 48], Operations: ['55-7=48'] Exploring Operation: 48/16=3, Resulting Numbers: [91, 3] Generated Node #0,0,2: 94:[91, 3] Operation: 48/16=3 Moving to Node #0,0,2 Current State: 94:[91, 3], Operations: ['55-7=48', '48/16=3'] Exploring Operation: 91+3=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.973958
hs_4
sum_heuristic
[ 50, 52, 89, 81 ]
94
[ "50+52=102", "89-81=8", "102-8=94" ]
Current State: 94:[50, 52, 89, 81], Operations: [] Exploring Operation: 50+52=102, Resulting Numbers: [89, 81, 102] Generated Node #2: [89, 81, 102] from Operation: 50+52=102 Current State: 94:[89, 81, 102], Operations: ['50+52=102'] Exploring Operation: 89-81=8, Resulting Numbers: [102, 8] Generated Node #3: [102, 8] from Operation: 89-81=8 Current State: 94:[102, 8], Operations: ['50+52=102', '89-81=8'] Exploring Operation: 102-8=94, Resulting Numbers: [94] 94,94 equal: Goal Reached
4
Current State: 94:[50, 52, 89, 81], Operations: [] Exploring Operation: 52-50=2, Resulting Numbers: [89, 81, 2] Generated Node #0,0: 94:[89, 81, 2] Operation: 52-50=2 Exploring Operation: 50+52=102, Resulting Numbers: [89, 81, 102] Generated Node #0,1: 94:[89, 81, 102] Operation: 50+52=102 Exploring Operation: 89-50=39, Resulting Numbers: [52, 81, 39] Generated Node #0,2: 94:[52, 81, 39] Operation: 89-50=39 Exploring Operation: 89-81=8, Resulting Numbers: [50, 52, 8] Generated Node #0,3: 94:[50, 52, 8] Operation: 89-81=8 Start Sub Search at level 1: Moving to Node #0,3 Current State: 94:[50, 52, 8], Operations: ['89-81=8'] Exploring Operation: 52-50=2, Resulting Numbers: [8, 2] Generated Node #0,3,0: 94:[8, 2] Operation: 52-50=2 Exploring Operation: 50+52=102, Resulting Numbers: [8, 102] Generated Node #0,3,1: 94:[8, 102] Operation: 50+52=102 Exploring Operation: 52-8=44, Resulting Numbers: [50, 44] Generated Node #0,3,2: 94:[50, 44] Operation: 52-8=44 Exploring Operation: 50-8=42, Resulting Numbers: [52, 42] Generated Node #0,3,3: 94:[52, 42] Operation: 50-8=42 Moving to Node #0,3,0 Current State: 94:[8, 2], Operations: ['89-81=8', '52-50=2'] Exploring Operation: 8/2=4, Resulting Numbers: [4] 4,94 unequal: No Solution Exploring Operation: 8-2=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 8+2=10, Resulting Numbers: [10] 10,94 unequal: No Solution Exploring Operation: 8*2=16, Resulting Numbers: [16] 16,94 unequal: No Solution Moving to Node #0,3,2 Current State: 94:[50, 44], Operations: ['89-81=8', '52-8=44'] Exploring Operation: 50-44=6, Resulting Numbers: [6] 6,94 unequal: No Solution Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Moving to Node #0 Current State: 94:[50, 52, 89, 81], Operations: [] Exploring Operation: 89-81=8, Resulting Numbers: [50, 52, 8] Generated Node #0,3: 94:[50, 52, 8] Operation: 89-81=8 Moving to Node #0,3 Current State: 94:[50, 52, 8], Operations: ['89-81=8'] Exploring Operation: 52-8=44, Resulting Numbers: [50, 44] Generated Node #0,3,2: 94:[50, 44] Operation: 52-8=44 Moving to Node #0,3,2 Current State: 94:[50, 44], Operations: ['89-81=8', '52-8=44'] Exploring Operation: 50+44=94, Resulting Numbers: [94] 94,94 equal: Goal Reached Exit Sub Search at level 1
0.984375
hs_4
sum_heuristic
[ 78, 7, 8, 71 ]
87
[ "71-8=63", "63/7=9", "78+9=87" ]
Current State: 87:[78, 7, 8, 71], Operations: [] Exploring Operation: 71-8=63, Resulting Numbers: [78, 7, 63] Generated Node #2: [78, 7, 63] from Operation: 71-8=63 Current State: 87:[78, 7, 63], Operations: ['71-8=63'] Exploring Operation: 63/7=9, Resulting Numbers: [78, 9] Generated Node #3: [78, 9] from Operation: 63/7=9 Current State: 87:[78, 9], Operations: ['71-8=63', '63/7=9'] Exploring Operation: 78+9=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[78, 7, 8, 71], Operations: [] Exploring Operation: 78-71=7, Resulting Numbers: [7, 8, 7] Generated Node #0,0: 87:[7, 8, 7] Operation: 78-71=7 Exploring Operation: 78+8=86, Resulting Numbers: [7, 71, 86] Generated Node #0,1: 87:[7, 71, 86] Operation: 78+8=86 Exploring Operation: 8+71=79, Resulting Numbers: [78, 7, 79] Generated Node #0,2: 87:[78, 7, 79] Operation: 8+71=79 Start Sub Search at level 1: Moving to Node #0,0 Current State: 87:[7, 8, 7], Operations: ['78-71=7'] Exploring Operation: 8-7=1, Resulting Numbers: [7, 1] Generated Node #0,0,0: 87:[7, 1] Operation: 8-7=1 Exploring Operation: 8-7=1, Resulting Numbers: [7, 1] Generated Node #0,0,1: 87:[7, 1] Operation: 8-7=1 Exploring Operation: 7/7=1, Resulting Numbers: [8, 1] Generated Node #0,0,2: 87:[8, 1] Operation: 7/7=1 Moving to Node #0,0,0 Current State: 87:[7, 1], Operations: ['78-71=7', '8-7=1'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Moving to Node #0,0,1 Current State: 87:[7, 1], Operations: ['78-71=7', '8-7=1'] Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Moving to Node #0,0,2 Current State: 87:[8, 1], Operations: ['78-71=7', '7/7=1'] Exploring Operation: 8*1=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 8-1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 8/1=8, Resulting Numbers: [8] 8,87 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[7, 71, 86], Operations: ['78+8=86'] Exploring Operation: 7+71=78, Resulting Numbers: [86, 78] Generated Node #0,1,0: 87:[86, 78] Operation: 7+71=78 Exploring Operation: 86-71=15, Resulting Numbers: [7, 15] Generated Node #0,1,1: 87:[7, 15] Operation: 86-71=15 Exploring Operation: 7+86=93, Resulting Numbers: [71, 93] Generated Node #0,1,2: 87:[71, 93] Operation: 7+86=93 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 87:[86, 78], Operations: ['78+8=86', '7+71=78'] Exploring Operation: 86-78=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 86*78=6708, Resulting Numbers: [6708] 6708,87 unequal: No Solution Exploring Operation: 86+78=164, Resulting Numbers: [164] 164,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 87:[7, 15], Operations: ['78+8=86', '86-71=15'] Exploring Operation: 7+15=22, Resulting Numbers: [22] 22,87 unequal: No Solution Exploring Operation: 15-7=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 7*15=105, Resulting Numbers: [105] 105,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 87:[71, 93], Operations: ['78+8=86', '7+86=93'] Exploring Operation: 71*93=6603, Resulting Numbers: [6603] 6603,87 unequal: No Solution Exploring Operation: 93-71=22, Resulting Numbers: [22] 22,87 unequal: No Solution Exploring Operation: 71+93=164, Resulting Numbers: [164] 164,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 87:[78, 7, 79], Operations: ['8+71=79'] Exploring Operation: 78+7=85, Resulting Numbers: [79, 85] Generated Node #0,2,0: 87:[79, 85] Operation: 78+7=85 Exploring Operation: 7+79=86, Resulting Numbers: [78, 86] Generated Node #0,2,1: 87:[78, 86] Operation: 7+79=86 Exploring Operation: 79-78=1, Resulting Numbers: [7, 1] Generated Node #0,2,2: 87:[7, 1] Operation: 79-78=1 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 87:[7, 1], Operations: ['8+71=79', '79-78=1'] Exploring Operation: 7*1=7, Resulting Numbers: [7] 7,87 unequal: No Solution Exploring Operation: 7-1=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 7/1=7, Resulting Numbers: [7] 7,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 87:[79, 85], Operations: ['8+71=79', '78+7=85'] Exploring Operation: 79*85=6715, Resulting Numbers: [6715] 6715,87 unequal: No Solution Exploring Operation: 85-79=6, Resulting Numbers: [6] 6,87 unequal: No Solution Exploring Operation: 79+85=164, Resulting Numbers: [164] 164,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 87:[78, 86], Operations: ['8+71=79', '7+79=86'] Exploring Operation: 86-78=8, Resulting Numbers: [8] 8,87 unequal: No Solution Exploring Operation: 78*86=6708, Resulting Numbers: [6708] 6708,87 unequal: No Solution Exploring Operation: 78+86=164, Resulting Numbers: [164] 164,87 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
sum_heuristic
[ 6, 1, 64, 5 ]
75
[ "6*1=6", "64+5=69", "6+69=75" ]
Current State: 75:[6, 1, 64, 5], Operations: [] Exploring Operation: 6*1=6, Resulting Numbers: [64, 5, 6] Generated Node #2: [64, 5, 6] from Operation: 6*1=6 Current State: 75:[64, 5, 6], Operations: ['6*1=6'] Exploring Operation: 64+5=69, Resulting Numbers: [6, 69] Generated Node #3: [6, 69] from Operation: 64+5=69 Current State: 75:[6, 69], Operations: ['6*1=6', '64+5=69'] Exploring Operation: 6+69=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[6, 1, 64, 5], Operations: [] Exploring Operation: 6+64=70, Resulting Numbers: [1, 5, 70] Generated Node #0,0: 75:[1, 5, 70] Operation: 6+64=70 Exploring Operation: 64+5=69, Resulting Numbers: [6, 1, 69] Generated Node #0,1: 75:[6, 1, 69] Operation: 64+5=69 Exploring Operation: 1+64=65, Resulting Numbers: [6, 5, 65] Generated Node #0,2: 75:[6, 5, 65] Operation: 1+64=65 Exploring Operation: 6-1=5, Resulting Numbers: [64, 5, 5] Generated Node #0,3: 75:[64, 5, 5] Operation: 6-1=5 Exploring Operation: 6*1=6, Resulting Numbers: [64, 5, 6] Generated Node #0,4: 75:[64, 5, 6] Operation: 6*1=6 Moving to Node #0,0 Current State: 75:[1, 5, 70], Operations: ['6+64=70'] Exploring Operation: 70/5=14, Resulting Numbers: [1, 14] Generated Node #0,0,0: 75:[1, 14] Operation: 70/5=14 Exploring Operation: 1*5=5, Resulting Numbers: [70, 5] Generated Node #0,0,1: 75:[70, 5] Operation: 1*5=5 Exploring Operation: 5+70=75, Resulting Numbers: [1, 75] Generated Node #0,0,2: 75:[1, 75] Operation: 5+70=75 Exploring Operation: 1+70=71, Resulting Numbers: [5, 71] Generated Node #0,0,3: 75:[5, 71] Operation: 1+70=71 Exploring Operation: 5/1=5, Resulting Numbers: [70, 5] Generated Node #0,0,4: 75:[70, 5] Operation: 5/1=5 Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 75:[1, 75], Operations: ['6+64=70', '5+70=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Moving to Node #0 Current State: 75:[6, 1, 64, 5], Operations: [] Exploring Operation: 6+64=70, Resulting Numbers: [1, 5, 70] Generated Node #0,0: 75:[1, 5, 70] Operation: 6+64=70 Moving to Node #0,0 Current State: 75:[1, 5, 70], Operations: ['6+64=70'] Exploring Operation: 5+70=75, Resulting Numbers: [1, 75] Generated Node #0,0,2: 75:[1, 75] Operation: 5+70=75 Moving to Node #0,0,2 Current State: 75:[1, 75], Operations: ['6+64=70', '5+70=75'] Exploring Operation: 75/1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_5
mult_heuristic
[ 6, 26, 34, 69 ]
21
[ "34-26=8", "6*8=48", "69-48=21" ]
Current State: 21:[6, 26, 34, 69], Operations: [] Exploring Operation: 34-26=8, Resulting Numbers: [6, 69, 8] Generated Node #2: [6, 69, 8] from Operation: 34-26=8 Current State: 21:[6, 69, 8], Operations: ['34-26=8'] Exploring Operation: 6*8=48, Resulting Numbers: [69, 48] Generated Node #3: [69, 48] from Operation: 6*8=48 Current State: 21:[69, 48], Operations: ['34-26=8', '6*8=48'] Exploring Operation: 69-48=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[6, 26, 34, 69], Operations: [] Exploring Operation: 69-34=35, Resulting Numbers: [6, 26, 35] Generated Node #0,0: 21:[6, 26, 35] Operation: 69-34=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 21:[6, 26, 35], Operations: ['69-34=35'] Exploring Operation: 35-26=9, Resulting Numbers: [6, 9] Generated Node #0,0,0: 21:[6, 9] Operation: 35-26=9 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 21:[6, 9], Operations: ['69-34=35', '35-26=9'] Exploring Operation: 9-6=3, Resulting Numbers: [3] 3,21 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 79, 56, 60, 41 ]
78
[ "79-56=23", "60+41=101", "101-23=78" ]
Current State: 78:[79, 56, 60, 41], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [60, 41, 23] Generated Node #2: [60, 41, 23] from Operation: 79-56=23 Current State: 78:[60, 41, 23], Operations: ['79-56=23'] Exploring Operation: 60+41=101, Resulting Numbers: [23, 101] Generated Node #3: [23, 101] from Operation: 60+41=101 Current State: 78:[23, 101], Operations: ['79-56=23', '60+41=101'] Exploring Operation: 101-23=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
4
Current State: 78:[79, 56, 60, 41], Operations: [] Exploring Operation: 60-56=4, Resulting Numbers: [79, 41, 4] Generated Node #0,0: 78:[79, 41, 4] Operation: 60-56=4 Exploring Operation: 79-60=19, Resulting Numbers: [56, 41, 19] Generated Node #0,1: 78:[56, 41, 19] Operation: 79-60=19 Exploring Operation: 60-41=19, Resulting Numbers: [79, 56, 19] Generated Node #0,2: 78:[79, 56, 19] Operation: 60-41=19 Exploring Operation: 79-56=23, Resulting Numbers: [60, 41, 23] Generated Node #0,3: 78:[60, 41, 23] Operation: 79-56=23 Exploring Operation: 56-41=15, Resulting Numbers: [79, 60, 15] Generated Node #0,4: 78:[79, 60, 15] Operation: 56-41=15 Moving to Node #0,0 Current State: 78:[79, 41, 4], Operations: ['60-56=4'] Exploring Operation: 79-41=38, Resulting Numbers: [4, 38] Generated Node #0,0,0: 78:[4, 38] Operation: 79-41=38 Exploring Operation: 79-4=75, Resulting Numbers: [41, 75] Generated Node #0,0,1: 78:[41, 75] Operation: 79-4=75 Exploring Operation: 41-4=37, Resulting Numbers: [79, 37] Generated Node #0,0,2: 78:[79, 37] Operation: 41-4=37 Exploring Operation: 79+4=83, Resulting Numbers: [41, 83] Generated Node #0,0,3: 78:[41, 83] Operation: 79+4=83 Exploring Operation: 41+4=45, Resulting Numbers: [79, 45] Generated Node #0,0,4: 78:[79, 45] Operation: 41+4=45 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 78:[4, 38], Operations: ['60-56=4', '79-41=38'] Exploring Operation: 4*38=152, Resulting Numbers: [152] 152,78 unequal: No Solution Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 4+38=42, Resulting Numbers: [42] 42,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 78:[79, 37], Operations: ['60-56=4', '41-4=37'] Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,78 unequal: No Solution Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 78:[41, 75], Operations: ['60-56=4', '79-4=75'] Exploring Operation: 41*75=3075, Resulting Numbers: [3075] 3075,78 unequal: No Solution Exploring Operation: 75-41=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 41+75=116, Resulting Numbers: [116] 116,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 78:[41, 83], Operations: ['60-56=4', '79+4=83'] Exploring Operation: 83-41=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 41*83=3403, Resulting Numbers: [3403] 3403,78 unequal: No Solution Exploring Operation: 41+83=124, Resulting Numbers: [124] 124,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 78:[79, 45], Operations: ['60-56=4', '41+4=45'] Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,78 unequal: No Solution Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 78:[79, 60, 15], Operations: ['56-41=15'] Exploring Operation: 60+15=75, Resulting Numbers: [79, 75] Generated Node #0,4,0: 78:[79, 75] Operation: 60+15=75 Exploring Operation: 79-60=19, Resulting Numbers: [15, 19] Generated Node #0,4,1: 78:[15, 19] Operation: 79-60=19 Exploring Operation: 79-15=64, Resulting Numbers: [60, 64] Generated Node #0,4,2: 78:[60, 64] Operation: 79-15=64 Exploring Operation: 60/15=4, Resulting Numbers: [79, 4] Generated Node #0,4,3: 78:[79, 4] Operation: 60/15=4 Exploring Operation: 60-15=45, Resulting Numbers: [79, 45] Generated Node #0,4,4: 78:[79, 45] Operation: 60-15=45 Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 78:[79, 4], Operations: ['56-41=15', '60/15=4'] Exploring Operation: 79+4=83, Resulting Numbers: [83] 83,78 unequal: No Solution Exploring Operation: 79*4=316, Resulting Numbers: [316] 316,78 unequal: No Solution Exploring Operation: 79-4=75, Resulting Numbers: [75] 75,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 78:[79, 75], Operations: ['56-41=15', '60+15=75'] Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,78 unequal: No Solution Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,78 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 78:[79, 45], Operations: ['56-41=15', '60-15=45'] Exploring Operation: 79-45=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 79*45=3555, Resulting Numbers: [3555] 3555,78 unequal: No Solution Exploring Operation: 79+45=124, Resulting Numbers: [124] 124,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 78:[15, 19], Operations: ['56-41=15', '79-60=19'] Exploring Operation: 15+19=34, Resulting Numbers: [34] 34,78 unequal: No Solution Exploring Operation: 19-15=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 15*19=285, Resulting Numbers: [285] 285,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 78:[60, 64], Operations: ['56-41=15', '79-15=64'] Exploring Operation: 64-60=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 60+64=124, Resulting Numbers: [124] 124,78 unequal: No Solution Exploring Operation: 60*64=3840, Resulting Numbers: [3840] 3840,78 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: 78:[60, 41, 23], Operations: ['79-56=23'] Exploring Operation: 41-23=18, Resulting Numbers: [60, 18] Generated Node #0,3,0: 78:[60, 18] Operation: 41-23=18 Exploring Operation: 60-23=37, Resulting Numbers: [41, 37] Generated Node #0,3,1: 78:[41, 37] Operation: 60-23=37 Exploring Operation: 60-41=19, Resulting Numbers: [23, 19] Generated Node #0,3,2: 78:[23, 19] Operation: 60-41=19 Exploring Operation: 60+41=101, Resulting Numbers: [23, 101] Generated Node #0,3,3: 78:[23, 101] Operation: 60+41=101 Exploring Operation: 60+23=83, Resulting Numbers: [41, 83] Generated Node #0,3,4: 78:[41, 83] Operation: 60+23=83 Moving to Node #0,2 Current State: 78:[79, 56, 19], Operations: ['60-41=19'] Exploring Operation: 56-19=37, Resulting Numbers: [79, 37] Generated Node #0,2,0: 78:[79, 37] Operation: 56-19=37 Exploring Operation: 79-56=23, Resulting Numbers: [19, 23] Generated Node #0,2,1: 78:[19, 23] Operation: 79-56=23 Exploring Operation: 56+19=75, Resulting Numbers: [79, 75] Generated Node #0,2,2: 78:[79, 75] Operation: 56+19=75 Exploring Operation: 79+19=98, Resulting Numbers: [56, 98] Generated Node #0,2,3: 78:[56, 98] Operation: 79+19=98 Exploring Operation: 79-19=60, Resulting Numbers: [56, 60] Generated Node #0,2,4: 78:[56, 60] Operation: 79-19=60 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 78:[79, 37], Operations: ['60-41=19', '56-19=37'] Exploring Operation: 79+37=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 79-37=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 79*37=2923, Resulting Numbers: [2923] 2923,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 78:[79, 75], Operations: ['60-41=19', '56+19=75'] Exploring Operation: 79+75=154, Resulting Numbers: [154] 154,78 unequal: No Solution Exploring Operation: 79*75=5925, Resulting Numbers: [5925] 5925,78 unequal: No Solution Exploring Operation: 79-75=4, Resulting Numbers: [4] 4,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 78:[19, 23], Operations: ['60-41=19', '79-56=23'] Exploring Operation: 23-19=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 19*23=437, Resulting Numbers: [437] 437,78 unequal: No Solution Exploring Operation: 19+23=42, Resulting Numbers: [42] 42,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 78:[56, 60], Operations: ['60-41=19', '79-19=60'] Exploring Operation: 60-56=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 56+60=116, Resulting Numbers: [116] 116,78 unequal: No Solution Exploring Operation: 56*60=3360, Resulting Numbers: [3360] 3360,78 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 78:[56, 98], Operations: ['60-41=19', '79+19=98'] Exploring Operation: 56+98=154, Resulting Numbers: [154] 154,78 unequal: No Solution Exploring Operation: 98-56=42, Resulting Numbers: [42] 42,78 unequal: No Solution Exploring Operation: 56*98=5488, Resulting Numbers: [5488] 5488,78 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: 78:[56, 41, 19], Operations: ['79-60=19'] Exploring Operation: 41-19=22, Resulting Numbers: [56, 22] Generated Node #0,1,0: 78:[56, 22] Operation: 41-19=22 Exploring Operation: 56+19=75, Resulting Numbers: [41, 75] Generated Node #0,1,1: 78:[41, 75] Operation: 56+19=75 Exploring Operation: 56+41=97, Resulting Numbers: [19, 97] Generated Node #0,1,2: 78:[19, 97] Operation: 56+41=97 Exploring Operation: 56-19=37, Resulting Numbers: [41, 37] Generated Node #0,1,3: 78:[41, 37] Operation: 56-19=37 Exploring Operation: 56-41=15, Resulting Numbers: [19, 15] Generated Node #0,1,4: 78:[19, 15] Operation: 56-41=15 Moving to Node #0,3,1 Current State: 78:[41, 37], Operations: ['79-56=23', '60-23=37'] Exploring Operation: 41-37=4, Resulting Numbers: [4] 4,78 unequal: No Solution Exploring Operation: 41*37=1517, Resulting Numbers: [1517] 1517,78 unequal: No Solution Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,78 equal: Goal Reached Moving to Node #0 Current State: 78:[79, 56, 60, 41], Operations: [] Exploring Operation: 79-56=23, Resulting Numbers: [60, 41, 23] Generated Node #0,3: 78:[60, 41, 23] Operation: 79-56=23 Moving to Node #0,3 Current State: 78:[60, 41, 23], Operations: ['79-56=23'] Exploring Operation: 60-23=37, Resulting Numbers: [41, 37] Generated Node #0,3,1: 78:[41, 37] Operation: 60-23=37 Moving to Node #0,3,1 Current State: 78:[41, 37], Operations: ['79-56=23', '60-23=37'] Exploring Operation: 41+37=78, Resulting Numbers: [78] 78,78 equal: Goal Reached
0.928819
hs_5
sum_heuristic
[ 14, 84, 1, 39 ]
60
[ "14+84=98", "39-1=38", "98-38=60" ]
Current State: 60:[14, 84, 1, 39], Operations: [] Exploring Operation: 14+84=98, Resulting Numbers: [1, 39, 98] Generated Node #2: [1, 39, 98] from Operation: 14+84=98 Current State: 60:[1, 39, 98], Operations: ['14+84=98'] Exploring Operation: 39-1=38, Resulting Numbers: [98, 38] Generated Node #3: [98, 38] from Operation: 39-1=38 Current State: 60:[98, 38], Operations: ['14+84=98', '39-1=38'] Exploring Operation: 98-38=60, Resulting Numbers: [60] 60,60 equal: Goal Reached
4
Current State: 60:[14, 84, 1, 39], Operations: [] Exploring Operation: 84/14=6, Resulting Numbers: [1, 39, 6] Generated Node #0,0: 60:[1, 39, 6] Operation: 84/14=6 Exploring Operation: 84-39=45, Resulting Numbers: [14, 1, 45] Generated Node #0,1: 60:[14, 1, 45] Operation: 84-39=45 Start Sub Search at level 1: Moving to Node #0,0 Current State: 60:[1, 39, 6], Operations: ['84/14=6'] Exploring Operation: 39-1=38, Resulting Numbers: [6, 38] Generated Node #0,0,0: 60:[6, 38] Operation: 39-1=38 Exploring Operation: 39-6=33, Resulting Numbers: [1, 33] Generated Node #0,0,1: 60:[1, 33] Operation: 39-6=33 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 60:[1, 33], Operations: ['84/14=6', '39-6=33'] Exploring Operation: 1*33=33, Resulting Numbers: [33] 33,60 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,60 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 60:[6, 38], Operations: ['84/14=6', '39-1=38'] Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,60 unequal: No Solution Exploring Operation: 6+38=44, Resulting Numbers: [44] 44,60 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: 60:[14, 1, 45], Operations: ['84-39=45'] Exploring Operation: 14+45=59, Resulting Numbers: [1, 59] Generated Node #0,1,0: 60:[1, 59] Operation: 14+45=59 Exploring Operation: 45-14=31, Resulting Numbers: [1, 31] Generated Node #0,1,1: 60:[1, 31] Operation: 45-14=31 Moving to Node #0,1,0 Current State: 60:[1, 59], Operations: ['84-39=45', '14+45=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Moving to Node #0 Current State: 60:[14, 84, 1, 39], Operations: [] Exploring Operation: 84-39=45, Resulting Numbers: [14, 1, 45] Generated Node #0,1: 60:[14, 1, 45] Operation: 84-39=45 Moving to Node #0,1 Current State: 60:[14, 1, 45], Operations: ['84-39=45'] Exploring Operation: 14+45=59, Resulting Numbers: [1, 59] Generated Node #0,1,0: 60:[1, 59] Operation: 14+45=59 Moving to Node #0,1,0 Current State: 60:[1, 59], Operations: ['84-39=45', '14+45=59'] Exploring Operation: 1+59=60, Resulting Numbers: [60] 60,60 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_2
mult_heuristic
[ 7, 27, 99, 91 ]
12
[ "27-7=20", "99-91=8", "20-8=12" ]
Current State: 12:[7, 27, 99, 91], Operations: [] Exploring Operation: 27-7=20, Resulting Numbers: [99, 91, 20] Generated Node #2: [99, 91, 20] from Operation: 27-7=20 Current State: 12:[99, 91, 20], Operations: ['27-7=20'] Exploring Operation: 99-91=8, Resulting Numbers: [20, 8] Generated Node #3: [20, 8] from Operation: 99-91=8 Current State: 12:[20, 8], Operations: ['27-7=20', '99-91=8'] Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,12 equal: Goal Reached
4
Current State: 12:[7, 27, 99, 91], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [7, 27, 8] Generated Node #0,0: 12:[7, 27, 8] Operation: 99-91=8 Exploring Operation: 91/7=13, Resulting Numbers: [27, 99, 13] Generated Node #0,1: 12:[27, 99, 13] Operation: 91/7=13 Start Sub Search at level 1: Moving to Node #0,0 Current State: 12:[7, 27, 8], Operations: ['99-91=8'] Exploring Operation: 27-7=20, Resulting Numbers: [8, 20] Generated Node #0,0,0: 12:[8, 20] Operation: 27-7=20 Exploring Operation: 27-8=19, Resulting Numbers: [7, 19] Generated Node #0,0,1: 12:[7, 19] Operation: 27-8=19 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 12:[7, 19], Operations: ['99-91=8', '27-8=19'] Exploring Operation: 7+19=26, Resulting Numbers: [26] 26,12 unequal: No Solution Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Moving to Node #0 Current State: 12:[7, 27, 99, 91], Operations: [] Exploring Operation: 99-91=8, Resulting Numbers: [7, 27, 8] Generated Node #0,0: 12:[7, 27, 8] Operation: 99-91=8 Moving to Node #0,0 Current State: 12:[7, 27, 8], Operations: ['99-91=8'] Exploring Operation: 27-8=19, Resulting Numbers: [7, 19] Generated Node #0,0,1: 12:[7, 19] Operation: 27-8=19 Moving to Node #0,0,1 Current State: 12:[7, 19], Operations: ['99-91=8', '27-8=19'] Exploring Operation: 19-7=12, Resulting Numbers: [12] 12,12 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.991319
hs_2
mult_heuristic
[ 22, 54, 72, 46 ]
50
[ "22+54=76", "72-46=26", "76-26=50" ]
Current State: 50:[22, 54, 72, 46], Operations: [] Exploring Operation: 22+54=76, Resulting Numbers: [72, 46, 76] Generated Node #2: [72, 46, 76] from Operation: 22+54=76 Current State: 50:[72, 46, 76], Operations: ['22+54=76'] Exploring Operation: 72-46=26, Resulting Numbers: [76, 26] Generated Node #3: [76, 26] from Operation: 72-46=26 Current State: 50:[76, 26], Operations: ['22+54=76', '72-46=26'] Exploring Operation: 76-26=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[22, 54, 72, 46], Operations: [] Exploring Operation: 72-54=18, Resulting Numbers: [22, 46, 18] Generated Node #0,0: 50:[22, 46, 18] Operation: 72-54=18 Exploring Operation: 72-46=26, Resulting Numbers: [22, 54, 26] Generated Node #0,1: 50:[22, 54, 26] Operation: 72-46=26 Exploring Operation: 72-22=50, Resulting Numbers: [54, 46, 50] Generated Node #0,2: 50:[54, 46, 50] Operation: 72-22=50 Start Sub Search at level 1: Moving to Node #0,1 Current State: 50:[22, 54, 26], Operations: ['72-46=26'] Exploring Operation: 54-26=28, Resulting Numbers: [22, 28] Generated Node #0,1,0: 50:[22, 28] Operation: 54-26=28 Exploring Operation: 26-22=4, Resulting Numbers: [54, 4] Generated Node #0,1,1: 50:[54, 4] Operation: 26-22=4 Exploring Operation: 22+26=48, Resulting Numbers: [54, 48] Generated Node #0,1,2: 50:[54, 48] Operation: 22+26=48 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 50:[54, 4], Operations: ['72-46=26', '26-22=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Moving to Node #0 Current State: 50:[22, 54, 72, 46], Operations: [] Exploring Operation: 72-46=26, Resulting Numbers: [22, 54, 26] Generated Node #0,1: 50:[22, 54, 26] Operation: 72-46=26 Moving to Node #0,1 Current State: 50:[22, 54, 26], Operations: ['72-46=26'] Exploring Operation: 26-22=4, Resulting Numbers: [54, 4] Generated Node #0,1,1: 50:[54, 4] Operation: 26-22=4 Moving to Node #0,1,1 Current State: 50:[54, 4], Operations: ['72-46=26', '26-22=4'] Exploring Operation: 54-4=50, Resulting Numbers: [50] 50,50 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.990451
hs_3
sum_heuristic
[ 50, 94, 20, 52 ]
90
[ "50*94=4700", "4700-20=4680", "4680/52=90" ]
Current State: 90:[50, 94, 20, 52], Operations: [] Exploring Operation: 50*94=4700, Resulting Numbers: [20, 52, 4700] Generated Node #2: [20, 52, 4700] from Operation: 50*94=4700 Current State: 90:[20, 52, 4700], Operations: ['50*94=4700'] Exploring Operation: 4700-20=4680, Resulting Numbers: [52, 4680] Generated Node #3: [52, 4680] from Operation: 4700-20=4680 Current State: 90:[52, 4680], Operations: ['50*94=4700', '4700-20=4680'] Exploring Operation: 4680/52=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[50, 94, 20, 52], Operations: [] Exploring Operation: 94-50=44, Resulting Numbers: [20, 52, 44] Generated Node #0,0: 90:[20, 52, 44] Operation: 94-50=44 Exploring Operation: 94-52=42, Resulting Numbers: [50, 20, 42] Generated Node #0,1: 90:[50, 20, 42] Operation: 94-52=42 Exploring Operation: 52-50=2, Resulting Numbers: [94, 20, 2] Generated Node #0,2: 90:[94, 20, 2] Operation: 52-50=2 Exploring Operation: 50-20=30, Resulting Numbers: [94, 52, 30] Generated Node #0,3: 90:[94, 52, 30] Operation: 50-20=30 Exploring Operation: 52-20=32, Resulting Numbers: [50, 94, 32] Generated Node #0,4: 90:[50, 94, 32] Operation: 52-20=32 Start Sub Search at level 1: Moving to Node #0,2 Current State: 90:[94, 20, 2], Operations: ['52-50=2'] Exploring Operation: 20/2=10, Resulting Numbers: [94, 10] Generated Node #0,2,0: 90:[94, 10] Operation: 20/2=10 Exploring Operation: 94/2=47, Resulting Numbers: [20, 47] Generated Node #0,2,1: 90:[20, 47] Operation: 94/2=47 Exploring Operation: 20-2=18, Resulting Numbers: [94, 18] Generated Node #0,2,2: 90:[94, 18] Operation: 20-2=18 Exploring Operation: 94-2=92, Resulting Numbers: [20, 92] Generated Node #0,2,3: 90:[20, 92] Operation: 94-2=92 Exploring Operation: 94+2=96, Resulting Numbers: [20, 96] Generated Node #0,2,4: 90:[20, 96] Operation: 94+2=96 Moving to Node #0,2,0 Current State: 90:[94, 10], Operations: ['52-50=2', '20/2=10'] Exploring Operation: 94-10=84, Resulting Numbers: [84] 84,90 unequal: No Solution Exploring Operation: 94*10=940, Resulting Numbers: [940] 940,90 unequal: No Solution Exploring Operation: 94+10=104, Resulting Numbers: [104] 104,90 unequal: No Solution Moving to Node #0,2,2 Current State: 90:[94, 18], Operations: ['52-50=2', '20-2=18'] Exploring Operation: 94*18=1692, Resulting Numbers: [1692] 1692,90 unequal: No Solution Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 94+18=112, Resulting Numbers: [112] 112,90 unequal: No Solution Moving to Node #0,2,1 Current State: 90:[20, 47], Operations: ['52-50=2', '94/2=47'] Exploring Operation: 20*47=940, Resulting Numbers: [940] 940,90 unequal: No Solution Exploring Operation: 47-20=27, Resulting Numbers: [27] 27,90 unequal: No Solution Exploring Operation: 20+47=67, Resulting Numbers: [67] 67,90 unequal: No Solution Moving to Node #0,2,3 Current State: 90:[20, 92], Operations: ['52-50=2', '94-2=92'] Exploring Operation: 20*92=1840, Resulting Numbers: [1840] 1840,90 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 20+92=112, Resulting Numbers: [112] 112,90 unequal: No Solution Moving to Node #0,2,4 Current State: 90:[20, 96], Operations: ['52-50=2', '94+2=96'] Exploring Operation: 20*96=1920, Resulting Numbers: [1920] 1920,90 unequal: No Solution Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 20+96=116, Resulting Numbers: [116] 116,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 90:[20, 52, 44], Operations: ['94-50=44'] Exploring Operation: 52-44=8, Resulting Numbers: [20, 8] Generated Node #0,0,0: 90:[20, 8] Operation: 52-44=8 Exploring Operation: 20+52=72, Resulting Numbers: [44, 72] Generated Node #0,0,1: 90:[44, 72] Operation: 20+52=72 Exploring Operation: 52+44=96, Resulting Numbers: [20, 96] Generated Node #0,0,2: 90:[20, 96] Operation: 52+44=96 Exploring Operation: 44-20=24, Resulting Numbers: [52, 24] Generated Node #0,0,3: 90:[52, 24] Operation: 44-20=24 Exploring Operation: 52-20=32, Resulting Numbers: [44, 32] Generated Node #0,0,4: 90:[44, 32] Operation: 52-20=32 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 90:[20, 8], Operations: ['94-50=44', '52-44=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 90:[44, 32], Operations: ['94-50=44', '52-20=32'] Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 44*32=1408, Resulting Numbers: [1408] 1408,90 unequal: No Solution Exploring Operation: 44+32=76, Resulting Numbers: [76] 76,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 90:[20, 96], Operations: ['94-50=44', '52+44=96'] Exploring Operation: 20+96=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 96-20=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 20*96=1920, Resulting Numbers: [1920] 1920,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 90:[52, 24], Operations: ['94-50=44', '44-20=24'] Exploring Operation: 52+24=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 52-24=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 52*24=1248, Resulting Numbers: [1248] 1248,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 90:[44, 72], Operations: ['94-50=44', '20+52=72'] Exploring Operation: 44+72=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 72-44=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 44*72=3168, Resulting Numbers: [3168] 3168,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 90:[50, 20, 42], Operations: ['94-52=42'] Exploring Operation: 50-20=30, Resulting Numbers: [42, 30] Generated Node #0,1,0: 90:[42, 30] Operation: 50-20=30 Exploring Operation: 20+42=62, Resulting Numbers: [50, 62] Generated Node #0,1,1: 90:[50, 62] Operation: 20+42=62 Exploring Operation: 50+42=92, Resulting Numbers: [20, 92] Generated Node #0,1,2: 90:[20, 92] Operation: 50+42=92 Exploring Operation: 42-20=22, Resulting Numbers: [50, 22] Generated Node #0,1,3: 90:[50, 22] Operation: 42-20=22 Exploring Operation: 50-42=8, Resulting Numbers: [20, 8] Generated Node #0,1,4: 90:[20, 8] Operation: 50-42=8 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 90:[42, 30], Operations: ['94-52=42', '50-20=30'] Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 42*30=1260, Resulting Numbers: [1260] 1260,90 unequal: No Solution Exploring Operation: 42+30=72, Resulting Numbers: [72] 72,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 90:[20, 8], Operations: ['94-52=42', '50-42=8'] Exploring Operation: 20+8=28, Resulting Numbers: [28] 28,90 unequal: No Solution Exploring Operation: 20*8=160, Resulting Numbers: [160] 160,90 unequal: No Solution Exploring Operation: 20-8=12, Resulting Numbers: [12] 12,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 90:[20, 92], Operations: ['94-52=42', '50+42=92'] Exploring Operation: 20+92=112, Resulting Numbers: [112] 112,90 unequal: No Solution Exploring Operation: 92-20=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 20*92=1840, Resulting Numbers: [1840] 1840,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 90:[50, 22], Operations: ['94-52=42', '42-20=22'] Exploring Operation: 50*22=1100, Resulting Numbers: [1100] 1100,90 unequal: No Solution Exploring Operation: 50+22=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 50-22=28, Resulting Numbers: [28] 28,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 90:[50, 62], Operations: ['94-52=42', '20+42=62'] Exploring Operation: 50*62=3100, Resulting Numbers: [3100] 3100,90 unequal: No Solution Exploring Operation: 50+62=112, Resulting Numbers: [112] 112,90 unequal: No Solution Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 90:[94, 52, 30], Operations: ['50-20=30'] Exploring Operation: 52-30=22, Resulting Numbers: [94, 22] Generated Node #0,3,0: 90:[94, 22] Operation: 52-30=22 Exploring Operation: 52+30=82, Resulting Numbers: [94, 82] Generated Node #0,3,1: 90:[94, 82] Operation: 52+30=82 Exploring Operation: 94-52=42, Resulting Numbers: [30, 42] Generated Node #0,3,2: 90:[30, 42] Operation: 94-52=42 Exploring Operation: 94-30=64, Resulting Numbers: [52, 64] Generated Node #0,3,3: 90:[52, 64] Operation: 94-30=64 Exploring Operation: 94+30=124, Resulting Numbers: [52, 124] Generated Node #0,3,4: 90:[52, 124] Operation: 94+30=124 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 90:[30, 42], Operations: ['50-20=30', '94-52=42'] Exploring Operation: 30*42=1260, Resulting Numbers: [1260] 1260,90 unequal: No Solution Exploring Operation: 30+42=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 42-30=12, Resulting Numbers: [12] 12,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 90:[94, 22], Operations: ['50-20=30', '52-30=22'] Exploring Operation: 94-22=72, Resulting Numbers: [72] 72,90 unequal: No Solution Exploring Operation: 94+22=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 94*22=2068, Resulting Numbers: [2068] 2068,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 90:[94, 82], Operations: ['50-20=30', '52+30=82'] Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,90 unequal: No Solution Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 90:[52, 64], Operations: ['50-20=30', '94-30=64'] Exploring Operation: 52+64=116, Resulting Numbers: [116] 116,90 unequal: No Solution Exploring Operation: 64-52=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 52*64=3328, Resulting Numbers: [3328] 3328,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 90:[52, 124], Operations: ['50-20=30', '94+30=124'] Exploring Operation: 52*124=6448, Resulting Numbers: [6448] 6448,90 unequal: No Solution Exploring Operation: 52+124=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 124-52=72, Resulting Numbers: [72] 72,90 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4 Current State: 90:[50, 94, 32], Operations: ['52-20=32'] Exploring Operation: 94+32=126, Resulting Numbers: [50, 126] Generated Node #0,4,0: 90:[50, 126] Operation: 94+32=126 Exploring Operation: 94-50=44, Resulting Numbers: [32, 44] Generated Node #0,4,1: 90:[32, 44] Operation: 94-50=44 Exploring Operation: 50+32=82, Resulting Numbers: [94, 82] Generated Node #0,4,2: 90:[94, 82] Operation: 50+32=82 Exploring Operation: 50-32=18, Resulting Numbers: [94, 18] Generated Node #0,4,3: 90:[94, 18] Operation: 50-32=18 Exploring Operation: 94-32=62, Resulting Numbers: [50, 62] Generated Node #0,4,4: 90:[50, 62] Operation: 94-32=62 Moving to Node #0,4,1 Current State: 90:[32, 44], Operations: ['52-20=32', '94-50=44'] Exploring Operation: 32*44=1408, Resulting Numbers: [1408] 1408,90 unequal: No Solution Exploring Operation: 32+44=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 44-32=12, Resulting Numbers: [12] 12,90 unequal: No Solution Moving to Node #0,4,3 Current State: 90:[94, 18], Operations: ['52-20=32', '50-32=18'] Exploring Operation: 94+18=112, Resulting Numbers: [112] 112,90 unequal: No Solution Exploring Operation: 94*18=1692, Resulting Numbers: [1692] 1692,90 unequal: No Solution Exploring Operation: 94-18=76, Resulting Numbers: [76] 76,90 unequal: No Solution Moving to Node #0,4,2 Current State: 90:[94, 82], Operations: ['52-20=32', '50+32=82'] Exploring Operation: 94-82=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 94+82=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 94*82=7708, Resulting Numbers: [7708] 7708,90 unequal: No Solution Moving to Node #0,4,4 Current State: 90:[50, 62], Operations: ['52-20=32', '94-32=62'] Exploring Operation: 50*62=3100, Resulting Numbers: [3100] 3100,90 unequal: No Solution Exploring Operation: 62-50=12, Resulting Numbers: [12] 12,90 unequal: No Solution Exploring Operation: 50+62=112, Resulting Numbers: [112] 112,90 unequal: No Solution Moving to Node #0,4,0 Current State: 90:[50, 126], Operations: ['52-20=32', '94+32=126'] Exploring Operation: 126-50=76, Resulting Numbers: [76] 76,90 unequal: No Solution Exploring Operation: 50+126=176, Resulting Numbers: [176] 176,90 unequal: No Solution Exploring Operation: 50*126=6300, Resulting Numbers: [6300] 6300,90 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_5
mult_heuristic
[ 98, 35, 61, 11 ]
83
[ "98+35=133", "61-11=50", "133-50=83" ]
Current State: 83:[98, 35, 61, 11], Operations: [] Exploring Operation: 98+35=133, Resulting Numbers: [61, 11, 133] Generated Node #2: [61, 11, 133] from Operation: 98+35=133 Current State: 83:[61, 11, 133], Operations: ['98+35=133'] Exploring Operation: 61-11=50, Resulting Numbers: [133, 50] Generated Node #3: [133, 50] from Operation: 61-11=50 Current State: 83:[133, 50], Operations: ['98+35=133', '61-11=50'] Exploring Operation: 133-50=83, Resulting Numbers: [83] 83,83 equal: Goal Reached
4
Current State: 83:[98, 35, 61, 11], Operations: [] Exploring Operation: 98-11=87, Resulting Numbers: [35, 61, 87] Generated Node #0,0: 83:[35, 61, 87] Operation: 98-11=87 Start Sub Search at level 1: Moving to Node #0,0 Current State: 83:[35, 61, 87], Operations: ['98-11=87'] Exploring Operation: 35+61=96, Resulting Numbers: [87, 96] Generated Node #0,0,0: 83:[87, 96] Operation: 35+61=96 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 83:[87, 96], Operations: ['98-11=87', '35+61=96'] Exploring Operation: 96-87=9, Resulting Numbers: [9] 9,83 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_1
sum_heuristic
[ 89, 23, 9, 42 ]
79
[ "89+23=112", "42-9=33", "112-33=79" ]
Current State: 79:[89, 23, 9, 42], Operations: [] Exploring Operation: 89+23=112, Resulting Numbers: [9, 42, 112] Generated Node #2: [9, 42, 112] from Operation: 89+23=112 Current State: 79:[9, 42, 112], Operations: ['89+23=112'] Exploring Operation: 42-9=33, Resulting Numbers: [112, 33] Generated Node #3: [112, 33] from Operation: 42-9=33 Current State: 79:[112, 33], Operations: ['89+23=112', '42-9=33'] Exploring Operation: 112-33=79, Resulting Numbers: [79] 79,79 equal: Goal Reached
4
Current State: 79:[89, 23, 9, 42], Operations: [] Exploring Operation: 89-9=80, Resulting Numbers: [23, 42, 80] Generated Node #0,0: 79:[23, 42, 80] Operation: 89-9=80 Moving to Node #0,0 Current State: 79:[23, 42, 80], Operations: ['89-9=80'] Exploring Operation: 23+42=65, Resulting Numbers: [80, 65] Generated Node #0,0,0: 79:[80, 65] Operation: 23+42=65 Moving to Node #0,0,0 Current State: 79:[80, 65], Operations: ['89-9=80', '23+42=65'] Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,79 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 15, 91, 18, 79 ]
90
[ "91-18=73", "79-73=6", "15*6=90" ]
Current State: 90:[15, 91, 18, 79], Operations: [] Exploring Operation: 91-18=73, Resulting Numbers: [15, 79, 73] Generated Node #2: [15, 79, 73] from Operation: 91-18=73 Current State: 90:[15, 79, 73], Operations: ['91-18=73'] Exploring Operation: 79-73=6, Resulting Numbers: [15, 6] Generated Node #3: [15, 6] from Operation: 79-73=6 Current State: 90:[15, 6], Operations: ['91-18=73', '79-73=6'] Exploring Operation: 15*6=90, Resulting Numbers: [90] 90,90 equal: Goal Reached
4
Current State: 90:[15, 91, 18, 79], Operations: [] Exploring Operation: 91-79=12, Resulting Numbers: [15, 18, 12] Generated Node #0,0: 90:[15, 18, 12] Operation: 91-79=12 Exploring Operation: 15+79=94, Resulting Numbers: [91, 18, 94] Generated Node #0,1: 90:[91, 18, 94] Operation: 15+79=94 Moving to Node #0,0 Current State: 90:[15, 18, 12], Operations: ['91-79=12'] Exploring Operation: 15-12=3, Resulting Numbers: [18, 3] Generated Node #0,0,0: 90:[18, 3] Operation: 15-12=3 Exploring Operation: 18+12=30, Resulting Numbers: [15, 30] Generated Node #0,0,1: 90:[15, 30] Operation: 18+12=30 Moving to Node #0,1 Current State: 90:[91, 18, 94], Operations: ['15+79=94'] Exploring Operation: 94-91=3, Resulting Numbers: [18, 3] Generated Node #0,1,0: 90:[18, 3] Operation: 94-91=3 Exploring Operation: 94-18=76, Resulting Numbers: [91, 76] Generated Node #0,1,1: 90:[91, 76] Operation: 94-18=76 Moving to Node #0,0,0 Current State: 90:[18, 3], Operations: ['91-79=12', '15-12=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,90 unequal: No Solution Moving to Node #0,1,0 Current State: 90:[18, 3], Operations: ['15+79=94', '94-91=3'] Exploring Operation: 18/3=6, Resulting Numbers: [6] 6,90 unequal: No Solution Exploring Operation: 18-3=15, Resulting Numbers: [15] 15,90 unequal: No Solution Moving to Node #0,0,1 Current State: 90:[15, 30], Operations: ['91-79=12', '18+12=30'] Exploring Operation: 30-15=15, Resulting Numbers: [15] 15,90 unequal: No Solution Exploring Operation: 15+30=45, Resulting Numbers: [45] 45,90 unequal: No Solution Moving to Node #0,1,1 Current State: 90:[91, 76], Operations: ['15+79=94', '94-18=76'] Exploring Operation: 91+76=167, Resulting Numbers: [167] 167,90 unequal: No Solution Exploring Operation: 91-76=15, Resulting Numbers: [15] 15,90 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 60, 20, 42, 59 ]
14
[ "60/20=3", "59-42=17", "17-3=14" ]
Current State: 14:[60, 20, 42, 59], Operations: [] Exploring Operation: 60/20=3, Resulting Numbers: [42, 59, 3] Generated Node #2: [42, 59, 3] from Operation: 60/20=3 Current State: 14:[42, 59, 3], Operations: ['60/20=3'] Exploring Operation: 59-42=17, Resulting Numbers: [3, 17] Generated Node #3: [3, 17] from Operation: 59-42=17 Current State: 14:[3, 17], Operations: ['60/20=3', '59-42=17'] Exploring Operation: 17-3=14, Resulting Numbers: [14] 14,14 equal: Goal Reached
4
Current State: 14:[60, 20, 42, 59], Operations: [] Exploring Operation: 60-59=1, Resulting Numbers: [20, 42, 1] Generated Node #0,0: 14:[20, 42, 1] Operation: 60-59=1 Moving to Node #0,0 Current State: 14:[20, 42, 1], Operations: ['60-59=1'] Exploring Operation: 42-20=22, Resulting Numbers: [1, 22] Generated Node #0,0,0: 14:[1, 22] Operation: 42-20=22 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 14:[1, 22], Operations: ['60-59=1', '42-20=22'] Exploring Operation: 22-1=21, Resulting Numbers: [21] 21,14 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
[ 91, 79, 83, 18 ]
53
[ "91-79=12", "83-18=65", "65-12=53" ]
Current State: 53:[91, 79, 83, 18], Operations: [] Exploring Operation: 91-79=12, Resulting Numbers: [83, 18, 12] Generated Node #2: [83, 18, 12] from Operation: 91-79=12 Current State: 53:[83, 18, 12], Operations: ['91-79=12'] Exploring Operation: 83-18=65, Resulting Numbers: [12, 65] Generated Node #3: [12, 65] from Operation: 83-18=65 Current State: 53:[12, 65], Operations: ['91-79=12', '83-18=65'] Exploring Operation: 65-12=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
4
Current State: 53:[91, 79, 83, 18], Operations: [] Exploring Operation: 91-18=73, Resulting Numbers: [79, 83, 73] Generated Node #0,0: 53:[79, 83, 73] Operation: 91-18=73 Exploring Operation: 79-18=61, Resulting Numbers: [91, 83, 61] Generated Node #0,1: 53:[91, 83, 61] Operation: 79-18=61 Moving to Node #0,0 Current State: 53:[79, 83, 73], Operations: ['91-18=73'] Exploring Operation: 83-73=10, Resulting Numbers: [79, 10] Generated Node #0,0,0: 53:[79, 10] Operation: 83-73=10 Exploring Operation: 83-79=4, Resulting Numbers: [73, 4] Generated Node #0,0,1: 53:[73, 4] Operation: 83-79=4 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 53:[79, 10], Operations: ['91-18=73', '83-73=10'] Exploring Operation: 79-10=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 79+10=89, Resulting Numbers: [89] 89,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 53:[73, 4], Operations: ['91-18=73', '83-79=4'] Exploring Operation: 73-4=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 73+4=77, Resulting Numbers: [77] 77,53 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 53:[91, 83, 61], Operations: ['79-18=61'] Exploring Operation: 91-83=8, Resulting Numbers: [61, 8] Generated Node #0,1,0: 53:[61, 8] Operation: 91-83=8 Exploring Operation: 91-61=30, Resulting Numbers: [83, 30] Generated Node #0,1,1: 53:[83, 30] Operation: 91-61=30 Moving to Node #0,1,0 Current State: 53:[61, 8], Operations: ['79-18=61', '91-83=8'] Exploring Operation: 61+8=69, Resulting Numbers: [69] 69,53 unequal: No Solution Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,53 equal: Goal Reached Moving to Node #0 Current State: 53:[91, 79, 83, 18], Operations: [] Exploring Operation: 79-18=61, Resulting Numbers: [91, 83, 61] Generated Node #0,1: 53:[91, 83, 61] Operation: 79-18=61 Moving to Node #0,1 Current State: 53:[91, 83, 61], Operations: ['79-18=61'] Exploring Operation: 91-83=8, Resulting Numbers: [61, 8] Generated Node #0,1,0: 53:[61, 8] Operation: 91-83=8 Moving to Node #0,1,0 Current State: 53:[61, 8], Operations: ['79-18=61', '91-83=8'] Exploring Operation: 61-8=53, Resulting Numbers: [53] 53,53 equal: Goal Reached
0.986111
hs_2
mult_heuristic
[ 54, 45, 43, 34 ]
11
[ "54+45=99", "43-34=9", "99/9=11" ]
Current State: 11:[54, 45, 43, 34], Operations: [] Exploring Operation: 54+45=99, Resulting Numbers: [43, 34, 99] Generated Node #2: [43, 34, 99] from Operation: 54+45=99 Current State: 11:[43, 34, 99], Operations: ['54+45=99'] Exploring Operation: 43-34=9, Resulting Numbers: [99, 9] Generated Node #3: [99, 9] from Operation: 43-34=9 Current State: 11:[99, 9], Operations: ['54+45=99', '43-34=9'] Exploring Operation: 99/9=11, Resulting Numbers: [11] 11,11 equal: Goal Reached
4
Current State: 11:[54, 45, 43, 34], Operations: [] Exploring Operation: 54-43=11, Resulting Numbers: [45, 34, 11] Generated Node #0,0: 11:[45, 34, 11] Operation: 54-43=11 Exploring Operation: 54-45=9, Resulting Numbers: [43, 34, 9] Generated Node #0,1: 11:[43, 34, 9] Operation: 54-45=9 Start Sub Search at level 1: Moving to Node #0,0 Current State: 11:[45, 34, 11], Operations: ['54-43=11'] Exploring Operation: 45-34=11, Resulting Numbers: [11, 11] Generated Node #0,0,0: 11:[11, 11] Operation: 45-34=11 Exploring Operation: 45-11=34, Resulting Numbers: [34, 34] Generated Node #0,0,1: 11:[34, 34] Operation: 45-11=34 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 11:[11, 11], Operations: ['54-43=11', '45-34=11'] Exploring Operation: 11/11=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 11+11=22, Resulting Numbers: [22] 22,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 11:[34, 34], Operations: ['54-43=11', '45-11=34'] Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 11:[43, 34, 9], Operations: ['54-45=9'] Exploring Operation: 43-9=34, Resulting Numbers: [34, 34] Generated Node #0,1,0: 11:[34, 34] Operation: 43-9=34 Exploring Operation: 43-34=9, Resulting Numbers: [9, 9] Generated Node #0,1,1: 11:[9, 9] Operation: 43-34=9 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 11:[9, 9], Operations: ['54-45=9', '43-34=9'] Exploring Operation: 9+9=18, Resulting Numbers: [18] 18,11 unequal: No Solution Exploring Operation: 9/9=1, Resulting Numbers: [1] 1,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 11:[34, 34], Operations: ['54-45=9', '43-9=34'] Exploring Operation: 34/34=1, Resulting Numbers: [1] 1,11 unequal: No Solution Exploring Operation: 34-34=0, Resulting Numbers: [0] 0,11 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_2
sum_heuristic
[ 37, 17, 65, 26 ]
59
[ "37-17=20", "65-26=39", "20+39=59" ]
Current State: 59:[37, 17, 65, 26], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [65, 26, 20] Generated Node #2: [65, 26, 20] from Operation: 37-17=20 Current State: 59:[65, 26, 20], Operations: ['37-17=20'] Exploring Operation: 65-26=39, Resulting Numbers: [20, 39] Generated Node #3: [20, 39] from Operation: 65-26=39 Current State: 59:[20, 39], Operations: ['37-17=20', '65-26=39'] Exploring Operation: 20+39=59, Resulting Numbers: [59] 59,59 equal: Goal Reached
4
Current State: 59:[37, 17, 65, 26], Operations: [] Exploring Operation: 37-17=20, Resulting Numbers: [65, 26, 20] Generated Node #0,0: 59:[65, 26, 20] Operation: 37-17=20 Exploring Operation: 37+17=54, Resulting Numbers: [65, 26, 54] Generated Node #0,1: 59:[65, 26, 54] Operation: 37+17=54 Exploring Operation: 37+26=63, Resulting Numbers: [17, 65, 63] Generated Node #0,2: 59:[17, 65, 63] Operation: 37+26=63 Exploring Operation: 17+26=43, Resulting Numbers: [37, 65, 43] Generated Node #0,3: 59:[37, 65, 43] Operation: 17+26=43 Exploring Operation: 65-17=48, Resulting Numbers: [37, 26, 48] Generated Node #0,4: 59:[37, 26, 48] Operation: 65-17=48 Start Sub Search at level 1: Moving to Node #0,1 Current State: 59:[65, 26, 54], Operations: ['37+17=54'] Exploring Operation: 65-26=39, Resulting Numbers: [54, 39] Generated Node #0,1,0: 59:[54, 39] Operation: 65-26=39 Exploring Operation: 26+54=80, Resulting Numbers: [65, 80] Generated Node #0,1,1: 59:[65, 80] Operation: 26+54=80 Exploring Operation: 54-26=28, Resulting Numbers: [65, 28] Generated Node #0,1,2: 59:[65, 28] Operation: 54-26=28 Exploring Operation: 65+26=91, Resulting Numbers: [54, 91] Generated Node #0,1,3: 59:[54, 91] Operation: 65+26=91 Exploring Operation: 65-54=11, Resulting Numbers: [26, 11] Generated Node #0,1,4: 59:[26, 11] Operation: 65-54=11 Moving to Node #0,1,0 Current State: 59:[54, 39], Operations: ['37+17=54', '65-26=39'] Exploring Operation: 54*39=2106, Resulting Numbers: [2106] 2106,59 unequal: No Solution Exploring Operation: 54+39=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 54-39=15, Resulting Numbers: [15] 15,59 unequal: No Solution Moving to Node #0,1,1 Current State: 59:[65, 80], Operations: ['37+17=54', '26+54=80'] Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 65+80=145, Resulting Numbers: [145] 145,59 unequal: No Solution Exploring Operation: 65*80=5200, Resulting Numbers: [5200] 5200,59 unequal: No Solution Moving to Node #0,1,2 Current State: 59:[65, 28], Operations: ['37+17=54', '54-26=28'] Exploring Operation: 65*28=1820, Resulting Numbers: [1820] 1820,59 unequal: No Solution Exploring Operation: 65+28=93, Resulting Numbers: [93] 93,59 unequal: No Solution Exploring Operation: 65-28=37, Resulting Numbers: [37] 37,59 unequal: No Solution Moving to Node #0,1,3 Current State: 59:[54, 91], Operations: ['37+17=54', '65+26=91'] Exploring Operation: 54+91=145, Resulting Numbers: [145] 145,59 unequal: No Solution Exploring Operation: 91-54=37, Resulting Numbers: [37] 37,59 unequal: No Solution Exploring Operation: 54*91=4914, Resulting Numbers: [4914] 4914,59 unequal: No Solution Moving to Node #0,1,4 Current State: 59:[26, 11], Operations: ['37+17=54', '65-54=11'] Exploring Operation: 26*11=286, Resulting Numbers: [286] 286,59 unequal: No Solution Exploring Operation: 26+11=37, Resulting Numbers: [37] 37,59 unequal: No Solution Exploring Operation: 26-11=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 59:[37, 65, 43], Operations: ['17+26=43'] Exploring Operation: 65-43=22, Resulting Numbers: [37, 22] Generated Node #0,3,0: 59:[37, 22] Operation: 65-43=22 Exploring Operation: 43-37=6, Resulting Numbers: [65, 6] Generated Node #0,3,1: 59:[65, 6] Operation: 43-37=6 Exploring Operation: 37+43=80, Resulting Numbers: [65, 80] Generated Node #0,3,2: 59:[65, 80] Operation: 37+43=80 Exploring Operation: 37+65=102, Resulting Numbers: [43, 102] Generated Node #0,3,3: 59:[43, 102] Operation: 37+65=102 Exploring Operation: 65-37=28, Resulting Numbers: [43, 28] Generated Node #0,3,4: 59:[43, 28] Operation: 65-37=28 Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 59:[65, 80], Operations: ['17+26=43', '37+43=80'] Exploring Operation: 65+80=145, Resulting Numbers: [145] 145,59 unequal: No Solution Exploring Operation: 80-65=15, Resulting Numbers: [15] 15,59 unequal: No Solution Exploring Operation: 65*80=5200, Resulting Numbers: [5200] 5200,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 59:[43, 28], Operations: ['17+26=43', '65-37=28'] Exploring Operation: 43+28=71, Resulting Numbers: [71] 71,59 unequal: No Solution Exploring Operation: 43*28=1204, Resulting Numbers: [1204] 1204,59 unequal: No Solution Exploring Operation: 43-28=15, Resulting Numbers: [15] 15,59 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 59:[37, 22], Operations: ['17+26=43', '65-43=22'] Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Moving to Node #0 Current State: 59:[37, 17, 65, 26], Operations: [] Exploring Operation: 17+26=43, Resulting Numbers: [37, 65, 43] Generated Node #0,3: 59:[37, 65, 43] Operation: 17+26=43 Moving to Node #0,3 Current State: 59:[37, 65, 43], Operations: ['17+26=43'] Exploring Operation: 65-43=22, Resulting Numbers: [37, 22] Generated Node #0,3,0: 59:[37, 22] Operation: 65-43=22 Moving to Node #0,3,0 Current State: 59:[37, 22], Operations: ['17+26=43', '65-43=22'] Exploring Operation: 37+22=59, Resulting Numbers: [59] 59,59 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96441
hs_5
mult_heuristic
[ 12, 33, 99, 83 ]
72
[ "33+99=132", "132/12=11", "83-11=72" ]
Current State: 72:[12, 33, 99, 83], Operations: [] Exploring Operation: 33+99=132, Resulting Numbers: [12, 83, 132] Generated Node #2: [12, 83, 132] from Operation: 33+99=132 Current State: 72:[12, 83, 132], Operations: ['33+99=132'] Exploring Operation: 132/12=11, Resulting Numbers: [83, 11] Generated Node #3: [83, 11] from Operation: 132/12=11 Current State: 72:[83, 11], Operations: ['33+99=132', '132/12=11'] Exploring Operation: 83-11=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[12, 33, 99, 83], Operations: [] Exploring Operation: 83-12=71, Resulting Numbers: [33, 99, 71] Generated Node #0,0: 72:[33, 99, 71] Operation: 83-12=71 Exploring Operation: 99-12=87, Resulting Numbers: [33, 83, 87] Generated Node #0,1: 72:[33, 83, 87] Operation: 99-12=87 Exploring Operation: 99/33=3, Resulting Numbers: [12, 83, 3] Generated Node #0,2: 72:[12, 83, 3] Operation: 99/33=3 Exploring Operation: 99-33=66, Resulting Numbers: [12, 83, 66] Generated Node #0,3: 72:[12, 83, 66] Operation: 99-33=66 Exploring Operation: 99-83=16, Resulting Numbers: [12, 33, 16] Generated Node #0,4: 72:[12, 33, 16] Operation: 99-83=16 Start Sub Search at level 1: Moving to Node #0,4 Current State: 72:[12, 33, 16], Operations: ['99-83=16'] Exploring Operation: 33-16=17, Resulting Numbers: [12, 17] Generated Node #0,4,0: 72:[12, 17] Operation: 33-16=17 Exploring Operation: 33-12=21, Resulting Numbers: [16, 21] Generated Node #0,4,1: 72:[16, 21] Operation: 33-12=21 Exploring Operation: 12+33=45, Resulting Numbers: [16, 45] Generated Node #0,4,2: 72:[16, 45] Operation: 12+33=45 Exploring Operation: 16-12=4, Resulting Numbers: [33, 4] Generated Node #0,4,3: 72:[33, 4] Operation: 16-12=4 Exploring Operation: 12+16=28, Resulting Numbers: [33, 28] Generated Node #0,4,4: 72:[33, 28] Operation: 12+16=28 Start Sub Search at level 2: Moving to Node #0,4,0 Current State: 72:[12, 17], Operations: ['99-83=16', '33-16=17'] Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,72 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,3 Current State: 72:[33, 4], Operations: ['99-83=16', '16-12=4'] Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,72 unequal: No Solution Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,1 Current State: 72:[16, 21], Operations: ['99-83=16', '33-12=21'] Exploring Operation: 16*21=336, Resulting Numbers: [336] 336,72 unequal: No Solution Exploring Operation: 16+21=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 21-16=5, Resulting Numbers: [5] 5,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,4 Current State: 72:[33, 28], Operations: ['99-83=16', '12+16=28'] Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 33*28=924, Resulting Numbers: [924] 924,72 unequal: No Solution Exploring Operation: 33+28=61, Resulting Numbers: [61] 61,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,4,2 Current State: 72:[16, 45], Operations: ['99-83=16', '12+33=45'] Exploring Operation: 45-16=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 16*45=720, Resulting Numbers: [720] 720,72 unequal: No Solution Exploring Operation: 16+45=61, Resulting Numbers: [61] 61,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 72:[12, 83, 3], Operations: ['99/33=3'] Exploring Operation: 12*3=36, Resulting Numbers: [83, 36] Generated Node #0,2,0: 72:[83, 36] Operation: 12*3=36 Exploring Operation: 83-12=71, Resulting Numbers: [3, 71] Generated Node #0,2,1: 72:[3, 71] Operation: 83-12=71 Exploring Operation: 12/3=4, Resulting Numbers: [83, 4] Generated Node #0,2,2: 72:[83, 4] Operation: 12/3=4 Exploring Operation: 83-3=80, Resulting Numbers: [12, 80] Generated Node #0,2,3: 72:[12, 80] Operation: 83-3=80 Exploring Operation: 12-3=9, Resulting Numbers: [83, 9] Generated Node #0,2,4: 72:[83, 9] Operation: 12-3=9 Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 72:[3, 71], Operations: ['99/33=3', '83-12=71'] Exploring Operation: 3+71=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 3*71=213, Resulting Numbers: [213] 213,72 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,3 Current State: 72:[12, 80], Operations: ['99/33=3', '83-3=80'] Exploring Operation: 12+80=92, Resulting Numbers: [92] 92,72 unequal: No Solution Exploring Operation: 80-12=68, Resulting Numbers: [68] 68,72 unequal: No Solution Exploring Operation: 12*80=960, Resulting Numbers: [960] 960,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 72:[83, 36], Operations: ['99/33=3', '12*3=36'] Exploring Operation: 83+36=119, Resulting Numbers: [119] 119,72 unequal: No Solution Exploring Operation: 83-36=47, Resulting Numbers: [47] 47,72 unequal: No Solution Exploring Operation: 83*36=2988, Resulting Numbers: [2988] 2988,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 72:[83, 4], Operations: ['99/33=3', '12/3=4'] Exploring Operation: 83+4=87, Resulting Numbers: [87] 87,72 unequal: No Solution Exploring Operation: 83-4=79, Resulting Numbers: [79] 79,72 unequal: No Solution Exploring Operation: 83*4=332, Resulting Numbers: [332] 332,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,4 Current State: 72:[83, 9], Operations: ['99/33=3', '12-3=9'] Exploring Operation: 83*9=747, Resulting Numbers: [747] 747,72 unequal: No Solution Exploring Operation: 83-9=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 83+9=92, Resulting Numbers: [92] 92,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 72:[12, 83, 66], Operations: ['99-33=66'] Exploring Operation: 66-12=54, Resulting Numbers: [83, 54] Generated Node #0,3,0: 72:[83, 54] Operation: 66-12=54 Exploring Operation: 83-12=71, Resulting Numbers: [66, 71] Generated Node #0,3,1: 72:[66, 71] Operation: 83-12=71 Exploring Operation: 12+66=78, Resulting Numbers: [83, 78] Generated Node #0,3,2: 72:[83, 78] Operation: 12+66=78 Exploring Operation: 12+83=95, Resulting Numbers: [66, 95] Generated Node #0,3,3: 72:[66, 95] Operation: 12+83=95 Exploring Operation: 83-66=17, Resulting Numbers: [12, 17] Generated Node #0,3,4: 72:[12, 17] Operation: 83-66=17 Start Sub Search at level 2: Moving to Node #0,3,4 Current State: 72:[12, 17], Operations: ['99-33=66', '83-66=17'] Exploring Operation: 12*17=204, Resulting Numbers: [204] 204,72 unequal: No Solution Exploring Operation: 12+17=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 17-12=5, Resulting Numbers: [5] 5,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 72:[66, 71], Operations: ['99-33=66', '83-12=71'] Exploring Operation: 66+71=137, Resulting Numbers: [137] 137,72 unequal: No Solution Exploring Operation: 71-66=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 66*71=4686, Resulting Numbers: [4686] 4686,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 72:[83, 78], Operations: ['99-33=66', '12+66=78'] Exploring Operation: 83*78=6474, Resulting Numbers: [6474] 6474,72 unequal: No Solution Exploring Operation: 83+78=161, Resulting Numbers: [161] 161,72 unequal: No Solution Exploring Operation: 83-78=5, Resulting Numbers: [5] 5,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 72:[83, 54], Operations: ['99-33=66', '66-12=54'] Exploring Operation: 83*54=4482, Resulting Numbers: [4482] 4482,72 unequal: No Solution Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 83+54=137, Resulting Numbers: [137] 137,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 72:[66, 95], Operations: ['99-33=66', '12+83=95'] Exploring Operation: 66+95=161, Resulting Numbers: [161] 161,72 unequal: No Solution Exploring Operation: 66*95=6270, Resulting Numbers: [6270] 6270,72 unequal: No Solution Exploring Operation: 95-66=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 72:[33, 83, 87], Operations: ['99-12=87'] Exploring Operation: 83-33=50, Resulting Numbers: [87, 50] Generated Node #0,1,0: 72:[87, 50] Operation: 83-33=50 Exploring Operation: 87-33=54, Resulting Numbers: [83, 54] Generated Node #0,1,1: 72:[83, 54] Operation: 87-33=54 Exploring Operation: 33+87=120, Resulting Numbers: [83, 120] Generated Node #0,1,2: 72:[83, 120] Operation: 33+87=120 Exploring Operation: 33+83=116, Resulting Numbers: [87, 116] Generated Node #0,1,3: 72:[87, 116] Operation: 33+83=116 Exploring Operation: 87-83=4, Resulting Numbers: [33, 4] Generated Node #0,1,4: 72:[33, 4] Operation: 87-83=4 Start Sub Search at level 2: Moving to Node #0,1,4 Current State: 72:[33, 4], Operations: ['99-12=87', '87-83=4'] Exploring Operation: 33-4=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 33*4=132, Resulting Numbers: [132] 132,72 unequal: No Solution Exploring Operation: 33+4=37, Resulting Numbers: [37] 37,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 72:[87, 50], Operations: ['99-12=87', '83-33=50'] Exploring Operation: 87-50=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 87*50=4350, Resulting Numbers: [4350] 4350,72 unequal: No Solution Exploring Operation: 87+50=137, Resulting Numbers: [137] 137,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 72:[83, 54], Operations: ['99-12=87', '87-33=54'] Exploring Operation: 83*54=4482, Resulting Numbers: [4482] 4482,72 unequal: No Solution Exploring Operation: 83+54=137, Resulting Numbers: [137] 137,72 unequal: No Solution Exploring Operation: 83-54=29, Resulting Numbers: [29] 29,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,2 Current State: 72:[83, 120], Operations: ['99-12=87', '33+87=120'] Exploring Operation: 83+120=203, Resulting Numbers: [203] 203,72 unequal: No Solution Exploring Operation: 120-83=37, Resulting Numbers: [37] 37,72 unequal: No Solution Exploring Operation: 83*120=9960, Resulting Numbers: [9960] 9960,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,1,3 Current State: 72:[87, 116], Operations: ['99-12=87', '33+83=116'] Exploring Operation: 87+116=203, Resulting Numbers: [203] 203,72 unequal: No Solution Exploring Operation: 116-87=29, Resulting Numbers: [29] 29,72 unequal: No Solution Exploring Operation: 87*116=10092, Resulting Numbers: [10092] 10092,72 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 72:[33, 99, 71], Operations: ['83-12=71'] Exploring Operation: 99/33=3, Resulting Numbers: [71, 3] Generated Node #0,0,0: 72:[71, 3] Operation: 99/33=3 Exploring Operation: 33+71=104, Resulting Numbers: [99, 104] Generated Node #0,0,1: 72:[99, 104] Operation: 33+71=104 Exploring Operation: 99-71=28, Resulting Numbers: [33, 28] Generated Node #0,0,2: 72:[33, 28] Operation: 99-71=28 Exploring Operation: 71-33=38, Resulting Numbers: [99, 38] Generated Node #0,0,3: 72:[99, 38] Operation: 71-33=38 Exploring Operation: 99-33=66, Resulting Numbers: [71, 66] Generated Node #0,0,4: 72:[71, 66] Operation: 99-33=66 Moving to Node #0,0,0 Current State: 72:[71, 3], Operations: ['83-12=71', '99/33=3'] Exploring Operation: 71+3=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 71*3=213, Resulting Numbers: [213] 213,72 unequal: No Solution Exploring Operation: 71-3=68, Resulting Numbers: [68] 68,72 unequal: No Solution Moving to Node #0,0,4 Current State: 72:[71, 66], Operations: ['83-12=71', '99-33=66'] Exploring Operation: 71*66=4686, Resulting Numbers: [4686] 4686,72 unequal: No Solution Exploring Operation: 71+66=137, Resulting Numbers: [137] 137,72 unequal: No Solution Exploring Operation: 71-66=5, Resulting Numbers: [5] 5,72 unequal: No Solution Moving to Node #0,0,2 Current State: 72:[33, 28], Operations: ['83-12=71', '99-71=28'] Exploring Operation: 33*28=924, Resulting Numbers: [924] 924,72 unequal: No Solution Exploring Operation: 33-28=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 33+28=61, Resulting Numbers: [61] 61,72 unequal: No Solution Moving to Node #0,0,3 Current State: 72:[99, 38], Operations: ['83-12=71', '71-33=38'] Exploring Operation: 99+38=137, Resulting Numbers: [137] 137,72 unequal: No Solution Exploring Operation: 99-38=61, Resulting Numbers: [61] 61,72 unequal: No Solution Exploring Operation: 99*38=3762, Resulting Numbers: [3762] 3762,72 unequal: No Solution Moving to Node #0,0,1 Current State: 72:[99, 104], Operations: ['83-12=71', '33+71=104'] Exploring Operation: 99*104=10296, Resulting Numbers: [10296] 10296,72 unequal: No Solution Exploring Operation: 104-99=5, Resulting Numbers: [5] 5,72 unequal: No Solution Exploring Operation: 99+104=203, Resulting Numbers: [203] 203,72 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
[ 84, 13, 6, 75 ]
75
[ "84/6=14", "14-13=1", "75*1=75" ]
Current State: 75:[84, 13, 6, 75], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [13, 75, 14] Generated Node #2: [13, 75, 14] from Operation: 84/6=14 Current State: 75:[13, 75, 14], Operations: ['84/6=14'] Exploring Operation: 14-13=1, Resulting Numbers: [75, 1] Generated Node #3: [75, 1] from Operation: 14-13=1 Current State: 75:[75, 1], Operations: ['84/6=14', '14-13=1'] Exploring Operation: 75*1=75, Resulting Numbers: [75] 75,75 equal: Goal Reached
4
Current State: 75:[84, 13, 6, 75], Operations: [] Exploring Operation: 84/6=14, Resulting Numbers: [13, 75, 14] Generated Node #0,0: 75:[13, 75, 14] Operation: 84/6=14 Moving to Node #0,0 Current State: 75:[13, 75, 14], Operations: ['84/6=14'] Exploring Operation: 13+14=27, Resulting Numbers: [75, 27] Generated Node #0,0,0: 75:[75, 27] Operation: 13+14=27 Moving to Node #0,0,0 Current State: 75:[75, 27], Operations: ['84/6=14', '13+14=27'] Exploring Operation: 75-27=48, Resulting Numbers: [48] 48,75 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 61, 61, 12, 69 ]
58
[ "61/61=1", "69-12=57", "1+57=58" ]
Current State: 58:[61, 61, 12, 69], Operations: [] Exploring Operation: 61/61=1, Resulting Numbers: [12, 69, 1] Generated Node #2: [12, 69, 1] from Operation: 61/61=1 Current State: 58:[12, 69, 1], Operations: ['61/61=1'] Exploring Operation: 69-12=57, Resulting Numbers: [1, 57] Generated Node #3: [1, 57] from Operation: 69-12=57 Current State: 58:[1, 57], Operations: ['61/61=1', '69-12=57'] Exploring Operation: 1+57=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[61, 61, 12, 69], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [61, 12, 8] Generated Node #0,0: 58:[61, 12, 8] Operation: 69-61=8 Exploring Operation: 69-61=8, Resulting Numbers: [61, 12, 8] Generated Node #0,1: 58:[61, 12, 8] Operation: 69-61=8 Exploring Operation: 69-12=57, Resulting Numbers: [61, 61, 57] Generated Node #0,2: 58:[61, 61, 57] Operation: 69-12=57 Exploring Operation: 61/61=1, Resulting Numbers: [12, 69, 1] Generated Node #0,3: 58:[12, 69, 1] Operation: 61/61=1 Moving to Node #0,2 Current State: 58:[61, 61, 57], Operations: ['69-12=57'] Exploring Operation: 61/61=1, Resulting Numbers: [57, 1] Generated Node #0,2,0: 58:[57, 1] Operation: 61/61=1 Exploring Operation: 61-61=0, Resulting Numbers: [57, 0] Generated Node #0,2,1: 58:[57, 0] Operation: 61-61=0 Exploring Operation: 61-57=4, Resulting Numbers: [61, 4] Generated Node #0,2,2: 58:[61, 4] Operation: 61-57=4 Exploring Operation: 61-57=4, Resulting Numbers: [61, 4] Generated Node #0,2,3: 58:[61, 4] Operation: 61-57=4 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 58:[57, 1], Operations: ['69-12=57', '61/61=1'] Exploring Operation: 57*1=57, Resulting Numbers: [57] 57,58 unequal: No Solution Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[61, 61, 12, 69], Operations: [] Exploring Operation: 69-12=57, Resulting Numbers: [61, 61, 57] Generated Node #0,2: 58:[61, 61, 57] Operation: 69-12=57 Moving to Node #0,2 Current State: 58:[61, 61, 57], Operations: ['69-12=57'] Exploring Operation: 61/61=1, Resulting Numbers: [57, 1] Generated Node #0,2,0: 58:[57, 1] Operation: 61/61=1 Moving to Node #0,2,0 Current State: 58:[57, 1], Operations: ['69-12=57', '61/61=1'] Exploring Operation: 57+1=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
sum_heuristic
[ 5, 97, 20, 5 ]
15
[ "5*20=100", "100-97=3", "5*3=15" ]
Current State: 15:[5, 97, 20, 5], Operations: [] Exploring Operation: 5*20=100, Resulting Numbers: [97, 100] Generated Node #2: [97, 100] from Operation: 5*20=100 Current State: 15:[97, 100], Operations: ['5*20=100'] Exploring Operation: 100-97=3, Resulting Numbers: [3] 3,15 equal: Goal Reached Exploring Operation: 5*3=15, Resulting Numbers: [15] 15,15 equal: Goal Reached
4
Current State: 15:[5, 97, 20, 5], Operations: [] Exploring Operation: 97-20=77, Resulting Numbers: [5, 5, 77] Generated Node #0,0: 15:[5, 5, 77] Operation: 97-20=77 Exploring Operation: 97-5=92, Resulting Numbers: [20, 5, 92] Generated Node #0,1: 15:[20, 5, 92] Operation: 97-5=92 Exploring Operation: 20-5=15, Resulting Numbers: [97, 5, 15] Generated Node #0,2: 15:[97, 5, 15] Operation: 20-5=15 Moving to Node #0,0 Current State: 15:[5, 5, 77], Operations: ['97-20=77'] Exploring Operation: 5/5=1, Resulting Numbers: [77, 1] Generated Node #0,0,0: 15:[77, 1] Operation: 5/5=1 Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,1: 15:[5, 72] Operation: 77-5=72 Exploring Operation: 77-5=72, Resulting Numbers: [5, 72] Generated Node #0,0,2: 15:[5, 72] Operation: 77-5=72 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 15:[5, 72], Operations: ['97-20=77', '77-5=72'] Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 15:[5, 72], Operations: ['97-20=77', '77-5=72'] Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,15 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 15:[77, 1], Operations: ['97-20=77', '5/5=1'] Exploring Operation: 77/1=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 77-1=76, Resulting Numbers: [76] 76,15 unequal: No Solution Exploring Operation: 77*1=77, Resulting Numbers: [77] 77,15 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: 15:[20, 5, 92], Operations: ['97-5=92'] Exploring Operation: 20-5=15, Resulting Numbers: [92, 15] Generated Node #0,1,0: 15:[92, 15] Operation: 20-5=15 Exploring Operation: 92-20=72, Resulting Numbers: [5, 72] Generated Node #0,1,1: 15:[5, 72] Operation: 92-20=72 Exploring Operation: 92-5=87, Resulting Numbers: [20, 87] Generated Node #0,1,2: 15:[20, 87] Operation: 92-5=87 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 15:[5, 72], Operations: ['97-5=92', '92-20=72'] Exploring Operation: 5*72=360, Resulting Numbers: [360] 360,15 unequal: No Solution Exploring Operation: 5+72=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 72-5=67, Resulting Numbers: [67] 67,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 15:[92, 15], Operations: ['97-5=92', '20-5=15'] Exploring Operation: 92+15=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 92*15=1380, Resulting Numbers: [1380] 1380,15 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,15 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 15:[20, 87], Operations: ['97-5=92', '92-5=87'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,15 unequal: No Solution Exploring Operation: 20*87=1740, Resulting Numbers: [1740] 1740,15 unequal: No Solution Exploring Operation: 20+87=107, Resulting Numbers: [107] 107,15 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: 15:[97, 5, 15], Operations: ['20-5=15'] Exploring Operation: 97-5=92, Resulting Numbers: [15, 92] Generated Node #0,2,0: 15:[15, 92] Operation: 97-5=92 Exploring Operation: 97-15=82, Resulting Numbers: [5, 82] Generated Node #0,2,1: 15:[5, 82] Operation: 97-15=82 Exploring Operation: 15/5=3, Resulting Numbers: [97, 3] Generated Node #0,2,2: 15:[97, 3] Operation: 15/5=3 Moving to Node #0,2,1 Current State: 15:[5, 82], Operations: ['20-5=15', '97-15=82'] Exploring Operation: 5*82=410, Resulting Numbers: [410] 410,15 unequal: No Solution Exploring Operation: 82-5=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 5+82=87, Resulting Numbers: [87] 87,15 unequal: No Solution Moving to Node #0,2,0 Current State: 15:[15, 92], Operations: ['20-5=15', '97-5=92'] Exploring Operation: 15+92=107, Resulting Numbers: [107] 107,15 unequal: No Solution Exploring Operation: 92-15=77, Resulting Numbers: [77] 77,15 unequal: No Solution Exploring Operation: 15*92=1380, Resulting Numbers: [1380] 1380,15 unequal: No Solution Moving to Node #0,2,2 Current State: 15:[97, 3], Operations: ['20-5=15', '15/5=3'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,15 unequal: No Solution Exploring Operation: 97+3=100, Resulting Numbers: [100] 100,15 unequal: No Solution Exploring Operation: 97*3=291, Resulting Numbers: [291] 291,15 unequal: No Solution No solution found.
0
hs_3
sum_heuristic
[ 45, 79, 48, 14 ]
68
[ "79-45=34", "48-14=34", "34+34=68" ]
Current State: 68:[45, 79, 48, 14], Operations: [] Exploring Operation: 79-45=34, Resulting Numbers: [48, 14, 34] Generated Node #2: [48, 14, 34] from Operation: 79-45=34 Current State: 68:[48, 14, 34], Operations: ['79-45=34'] Exploring Operation: 48-14=34, Resulting Numbers: [34, 34] Generated Node #3: [34, 34] from Operation: 48-14=34 Current State: 68:[34, 34], Operations: ['79-45=34', '48-14=34'] Exploring Operation: 34+34=68, Resulting Numbers: [68] 68,68 equal: Goal Reached
4
Current State: 68:[45, 79, 48, 14], Operations: [] Exploring Operation: 79-45=34, Resulting Numbers: [48, 14, 34] Generated Node #0,0: 68:[48, 14, 34] Operation: 79-45=34 Exploring Operation: 48-45=3, Resulting Numbers: [79, 14, 3] Generated Node #0,1: 68:[79, 14, 3] Operation: 48-45=3 Exploring Operation: 79-48=31, Resulting Numbers: [45, 14, 31] Generated Node #0,2: 68:[45, 14, 31] Operation: 79-48=31 Exploring Operation: 48-14=34, Resulting Numbers: [45, 79, 34] Generated Node #0,3: 68:[45, 79, 34] Operation: 48-14=34 Start Sub Search at level 1: Moving to Node #0,1 Current State: 68:[79, 14, 3], Operations: ['48-45=3'] Exploring Operation: 79+3=82, Resulting Numbers: [14, 82] Generated Node #0,1,0: 68:[14, 82] Operation: 79+3=82 Exploring Operation: 14+3=17, Resulting Numbers: [79, 17] Generated Node #0,1,1: 68:[79, 17] Operation: 14+3=17 Exploring Operation: 79-14=65, Resulting Numbers: [3, 65] Generated Node #0,1,2: 68:[3, 65] Operation: 79-14=65 Exploring Operation: 79-3=76, Resulting Numbers: [14, 76] Generated Node #0,1,3: 68:[14, 76] Operation: 79-3=76 Moving to Node #0,1,2 Current State: 68:[3, 65], Operations: ['48-45=3', '79-14=65'] Exploring Operation: 65-3=62, Resulting Numbers: [62] 62,68 unequal: No Solution Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Moving to Node #0 Current State: 68:[45, 79, 48, 14], Operations: [] Exploring Operation: 48-45=3, Resulting Numbers: [79, 14, 3] Generated Node #0,1: 68:[79, 14, 3] Operation: 48-45=3 Moving to Node #0,1 Current State: 68:[79, 14, 3], Operations: ['48-45=3'] Exploring Operation: 79-14=65, Resulting Numbers: [3, 65] Generated Node #0,1,2: 68:[3, 65] Operation: 79-14=65 Moving to Node #0,1,2 Current State: 68:[3, 65], Operations: ['48-45=3', '79-14=65'] Exploring Operation: 3+65=68, Resulting Numbers: [68] 68,68 equal: Goal Reached Exit Sub Search at level 1
0.987847
hs_4
mult_heuristic
[ 51, 97, 1, 8 ]
37
[ "97-51=46", "1+8=9", "46-9=37" ]
Current State: 37:[51, 97, 1, 8], Operations: [] Exploring Operation: 97-51=46, Resulting Numbers: [1, 8, 46] Generated Node #2: [1, 8, 46] from Operation: 97-51=46 Current State: 37:[1, 8, 46], Operations: ['97-51=46'] Exploring Operation: 1+8=9, Resulting Numbers: [46, 9] Generated Node #3: [46, 9] from Operation: 1+8=9 Current State: 37:[46, 9], Operations: ['97-51=46', '1+8=9'] Exploring Operation: 46-9=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[51, 97, 1, 8], Operations: [] Exploring Operation: 51-1=50, Resulting Numbers: [97, 8, 50] Generated Node #0,0: 37:[97, 8, 50] Operation: 51-1=50 Exploring Operation: 97-1=96, Resulting Numbers: [51, 8, 96] Generated Node #0,1: 37:[51, 8, 96] Operation: 97-1=96 Exploring Operation: 97-51=46, Resulting Numbers: [1, 8, 46] Generated Node #0,2: 37:[1, 8, 46] Operation: 97-51=46 Exploring Operation: 51-8=43, Resulting Numbers: [97, 1, 43] Generated Node #0,3: 37:[97, 1, 43] Operation: 51-8=43 Moving to Node #0,2 Current State: 37:[1, 8, 46], Operations: ['97-51=46'] Exploring Operation: 46-1=45, Resulting Numbers: [8, 45] Generated Node #0,2,0: 37:[8, 45] Operation: 46-1=45 Exploring Operation: 1*8=8, Resulting Numbers: [46, 8] Generated Node #0,2,1: 37:[46, 8] Operation: 1*8=8 Exploring Operation: 1+8=9, Resulting Numbers: [46, 9] Generated Node #0,2,2: 37:[46, 9] Operation: 1+8=9 Exploring Operation: 46-8=38, Resulting Numbers: [1, 38] Generated Node #0,2,3: 37:[1, 38] Operation: 46-8=38 Moving to Node #0,1 Current State: 37:[51, 8, 96], Operations: ['97-1=96'] Exploring Operation: 51-8=43, Resulting Numbers: [96, 43] Generated Node #0,1,0: 37:[96, 43] Operation: 51-8=43 Exploring Operation: 96-8=88, Resulting Numbers: [51, 88] Generated Node #0,1,1: 37:[51, 88] Operation: 96-8=88 Exploring Operation: 96/8=12, Resulting Numbers: [51, 12] Generated Node #0,1,2: 37:[51, 12] Operation: 96/8=12 Exploring Operation: 96-51=45, Resulting Numbers: [8, 45] Generated Node #0,1,3: 37:[8, 45] Operation: 96-51=45 Moving to Node #0,0 Current State: 37:[97, 8, 50], Operations: ['51-1=50'] Exploring Operation: 97-8=89, Resulting Numbers: [50, 89] Generated Node #0,0,0: 37:[50, 89] Operation: 97-8=89 Exploring Operation: 97-50=47, Resulting Numbers: [8, 47] Generated Node #0,0,1: 37:[8, 47] Operation: 97-50=47 Exploring Operation: 50-8=42, Resulting Numbers: [97, 42] Generated Node #0,0,2: 37:[97, 42] Operation: 50-8=42 Exploring Operation: 97+8=105, Resulting Numbers: [50, 105] Generated Node #0,0,3: 37:[50, 105] Operation: 97+8=105 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 37:[8, 47], Operations: ['51-1=50', '97-50=47'] Exploring Operation: 8+47=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 47-8=39, Resulting Numbers: [39] 39,37 unequal: No Solution Exploring Operation: 8*47=376, Resulting Numbers: [376] 376,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 37:[50, 89], Operations: ['51-1=50', '97-8=89'] Exploring Operation: 50+89=139, Resulting Numbers: [139] 139,37 unequal: No Solution Exploring Operation: 50*89=4450, Resulting Numbers: [4450] 4450,37 unequal: No Solution Exploring Operation: 89-50=39, Resulting Numbers: [39] 39,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 37:[97, 42], Operations: ['51-1=50', '50-8=42'] Exploring Operation: 97-42=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 97+42=139, Resulting Numbers: [139] 139,37 unequal: No Solution Exploring Operation: 97*42=4074, Resulting Numbers: [4074] 4074,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 37:[50, 105], Operations: ['51-1=50', '97+8=105'] Exploring Operation: 105-50=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 50+105=155, Resulting Numbers: [155] 155,37 unequal: No Solution Exploring Operation: 50*105=5250, Resulting Numbers: [5250] 5250,37 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: 37:[97, 1, 43], Operations: ['51-8=43'] Exploring Operation: 97-1=96, Resulting Numbers: [43, 96] Generated Node #0,3,0: 37:[43, 96] Operation: 97-1=96 Exploring Operation: 97*1=97, Resulting Numbers: [43, 97] Generated Node #0,3,1: 37:[43, 97] Operation: 97*1=97 Exploring Operation: 97-43=54, Resulting Numbers: [1, 54] Generated Node #0,3,2: 37:[1, 54] Operation: 97-43=54 Exploring Operation: 43-1=42, Resulting Numbers: [97, 42] Generated Node #0,3,3: 37:[97, 42] Operation: 43-1=42 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 37:[1, 54], Operations: ['51-8=43', '97-43=54'] Exploring Operation: 54-1=53, Resulting Numbers: [53] 53,37 unequal: No Solution Exploring Operation: 1+54=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 54/1=54, Resulting Numbers: [54] 54,37 unequal: No Solution Exploring Operation: 1*54=54, Resulting Numbers: [54] 54,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 37:[43, 96], Operations: ['51-8=43', '97-1=96'] Exploring Operation: 43*96=4128, Resulting Numbers: [4128] 4128,37 unequal: No Solution Exploring Operation: 43+96=139, Resulting Numbers: [139] 139,37 unequal: No Solution Exploring Operation: 96-43=53, Resulting Numbers: [53] 53,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 37:[97, 42], Operations: ['51-8=43', '43-1=42'] Exploring Operation: 97-42=55, Resulting Numbers: [55] 55,37 unequal: No Solution Exploring Operation: 97+42=139, Resulting Numbers: [139] 139,37 unequal: No Solution Exploring Operation: 97*42=4074, Resulting Numbers: [4074] 4074,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 37:[43, 97], Operations: ['51-8=43', '97*1=97'] Exploring Operation: 43+97=140, Resulting Numbers: [140] 140,37 unequal: No Solution Exploring Operation: 43*97=4171, Resulting Numbers: [4171] 4171,37 unequal: No Solution Exploring Operation: 97-43=54, Resulting Numbers: [54] 54,37 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,2,0 Current State: 37:[8, 45], Operations: ['97-51=46', '46-1=45'] Exploring Operation: 8*45=360, Resulting Numbers: [360] 360,37 unequal: No Solution Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[51, 97, 1, 8], Operations: [] Exploring Operation: 97-51=46, Resulting Numbers: [1, 8, 46] Generated Node #0,2: 37:[1, 8, 46] Operation: 97-51=46 Moving to Node #0,2 Current State: 37:[1, 8, 46], Operations: ['97-51=46'] Exploring Operation: 46-1=45, Resulting Numbers: [8, 45] Generated Node #0,2,0: 37:[8, 45] Operation: 46-1=45 Moving to Node #0,2,0 Current State: 37:[8, 45], Operations: ['97-51=46', '46-1=45'] Exploring Operation: 45-8=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
0.955729
hs_4
sum_heuristic
[ 75, 44, 44, 20 ]
96
[ "75+20=95", "44/44=1", "95+1=96" ]
Current State: 96:[75, 44, 44, 20], Operations: [] Exploring Operation: 75+20=95, Resulting Numbers: [44, 44, 95] Generated Node #2: [44, 44, 95] from Operation: 75+20=95 Current State: 96:[44, 44, 95], Operations: ['75+20=95'] Exploring Operation: 44/44=1, Resulting Numbers: [95, 1] Generated Node #3: [95, 1] from Operation: 44/44=1 Current State: 96:[95, 1], Operations: ['75+20=95', '44/44=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[75, 44, 44, 20], Operations: [] Exploring Operation: 75-44=31, Resulting Numbers: [44, 20, 31] Generated Node #0,0: 96:[44, 20, 31] Operation: 75-44=31 Exploring Operation: 75-44=31, Resulting Numbers: [44, 20, 31] Generated Node #0,1: 96:[44, 20, 31] Operation: 75-44=31 Exploring Operation: 75+20=95, Resulting Numbers: [44, 44, 95] Generated Node #0,2: 96:[44, 44, 95] Operation: 75+20=95 Start Sub Search at level 1: Moving to Node #0,0 Current State: 96:[44, 20, 31], Operations: ['75-44=31'] Exploring Operation: 44-31=13, Resulting Numbers: [20, 13] Generated Node #0,0,0: 96:[20, 13] Operation: 44-31=13 Exploring Operation: 44-20=24, Resulting Numbers: [31, 24] Generated Node #0,0,1: 96:[31, 24] Operation: 44-20=24 Exploring Operation: 31-20=11, Resulting Numbers: [44, 11] Generated Node #0,0,2: 96:[44, 11] Operation: 31-20=11 Moving to Node #0,0,1 Current State: 96:[31, 24], Operations: ['75-44=31', '44-20=24'] Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,96 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,96 unequal: No Solution Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[20, 13], Operations: ['75-44=31', '44-31=13'] Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,96 unequal: No Solution Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[44, 11], Operations: ['75-44=31', '31-20=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,96 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,96 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 Current State: 96:[44, 20, 31], Operations: ['75-44=31'] Exploring Operation: 31-20=11, Resulting Numbers: [44, 11] Generated Node #0,1,0: 96:[44, 11] Operation: 31-20=11 Exploring Operation: 44-20=24, Resulting Numbers: [31, 24] Generated Node #0,1,1: 96:[31, 24] Operation: 44-20=24 Exploring Operation: 44-31=13, Resulting Numbers: [20, 13] Generated Node #0,1,2: 96:[20, 13] Operation: 44-31=13 Start Sub Search at level 2: Moving to Node #0,1,1 Current State: 96:[31, 24], Operations: ['75-44=31', '44-20=24'] Exploring Operation: 31+24=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 31*24=744, Resulting Numbers: [744] 744,96 unequal: No Solution Exploring Operation: 31-24=7, Resulting Numbers: [7] 7,96 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 #0,1,0 Current State: 96:[44, 11], Operations: ['75-44=31', '31-20=11'] Exploring Operation: 44+11=55, Resulting Numbers: [55] 55,96 unequal: No Solution Exploring Operation: 44-11=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 44/11=4, Resulting Numbers: [4] 4,96 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 #0,1,2 Current State: 96:[20, 13], Operations: ['75-44=31', '44-31=13'] Exploring Operation: 20+13=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 20-13=7, Resulting Numbers: [7] 7,96 unequal: No Solution Exploring Operation: 20*13=260, Resulting Numbers: [260] 260,96 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 96:[44, 44, 95], Operations: ['75+20=95'] Exploring Operation: 44/44=1, Resulting Numbers: [95, 1] Generated Node #0,2,0: 96:[95, 1] Operation: 44/44=1 Exploring Operation: 44-44=0, Resulting Numbers: [95, 0] Generated Node #0,2,1: 96:[95, 0] Operation: 44-44=0 Exploring Operation: 95-44=51, Resulting Numbers: [44, 51] Generated Node #0,2,2: 96:[44, 51] Operation: 95-44=51 Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 96:[95, 1], Operations: ['75+20=95', '44/44=1'] Exploring Operation: 95/1=95, Resulting Numbers: [95] 95,96 unequal: No Solution Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Moving to Node #0 Current State: 96:[75, 44, 44, 20], Operations: [] Exploring Operation: 75+20=95, Resulting Numbers: [44, 44, 95] Generated Node #0,2: 96:[44, 44, 95] Operation: 75+20=95 Moving to Node #0,2 Current State: 96:[44, 44, 95], Operations: ['75+20=95'] Exploring Operation: 44/44=1, Resulting Numbers: [95, 1] Generated Node #0,2,0: 96:[95, 1] Operation: 44/44=1 Moving to Node #0,2,0 Current State: 96:[95, 1], Operations: ['75+20=95', '44/44=1'] Exploring Operation: 95+1=96, Resulting Numbers: [96] 96,96 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.96875
hs_3
sum_heuristic
[ 74, 70, 7, 39 ]
36
[ "74-70=4", "39-7=32", "4+32=36" ]
Current State: 36:[74, 70, 7, 39], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [7, 39, 4] Generated Node #2: [7, 39, 4] from Operation: 74-70=4 Current State: 36:[7, 39, 4], Operations: ['74-70=4'] Exploring Operation: 39-7=32, Resulting Numbers: [4, 32] Generated Node #3: [4, 32] from Operation: 39-7=32 Current State: 36:[4, 32], Operations: ['74-70=4', '39-7=32'] Exploring Operation: 4+32=36, Resulting Numbers: [36] 36,36 equal: Goal Reached
4
Current State: 36:[74, 70, 7, 39], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [7, 39, 4] Generated Node #0,0: 36:[7, 39, 4] Operation: 74-70=4 Exploring Operation: 70/7=10, Resulting Numbers: [74, 39, 10] Generated Node #0,1: 36:[74, 39, 10] Operation: 70/7=10 Exploring Operation: 70-39=31, Resulting Numbers: [74, 7, 31] Generated Node #0,2: 36:[74, 7, 31] Operation: 70-39=31 Exploring Operation: 74-39=35, Resulting Numbers: [70, 7, 35] Generated Node #0,3: 36:[70, 7, 35] Operation: 74-39=35 Start Sub Search at level 1: Moving to Node #0,0 Current State: 36:[7, 39, 4], Operations: ['74-70=4'] Exploring Operation: 7+4=11, Resulting Numbers: [39, 11] Generated Node #0,0,0: 36:[39, 11] Operation: 7+4=11 Exploring Operation: 39-7=32, Resulting Numbers: [4, 32] Generated Node #0,0,1: 36:[4, 32] Operation: 39-7=32 Exploring Operation: 7-4=3, Resulting Numbers: [39, 3] Generated Node #0,0,2: 36:[39, 3] Operation: 7-4=3 Exploring Operation: 39-4=35, Resulting Numbers: [7, 35] Generated Node #0,0,3: 36:[7, 35] Operation: 39-4=35 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 36:[7, 35], Operations: ['74-70=4', '39-4=35'] Exploring Operation: 7+35=42, Resulting Numbers: [42] 42,36 unequal: No Solution Exploring Operation: 35/7=5, Resulting Numbers: [5] 5,36 unequal: No Solution Exploring Operation: 7*35=245, Resulting Numbers: [245] 245,36 unequal: No Solution Exploring Operation: 35-7=28, Resulting Numbers: [28] 28,36 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:[39, 3], Operations: ['74-70=4', '7-4=3'] Exploring Operation: 39*3=117, Resulting Numbers: [117] 117,36 unequal: No Solution Exploring Operation: 39/3=13, Resulting Numbers: [13] 13,36 unequal: No Solution Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Moving to Node #0 Current State: 36:[74, 70, 7, 39], Operations: [] Exploring Operation: 74-70=4, Resulting Numbers: [7, 39, 4] Generated Node #0,0: 36:[7, 39, 4] Operation: 74-70=4 Moving to Node #0,0 Current State: 36:[7, 39, 4], Operations: ['74-70=4'] Exploring Operation: 7-4=3, Resulting Numbers: [39, 3] Generated Node #0,0,2: 36:[39, 3] Operation: 7-4=3 Moving to Node #0,0,2 Current State: 36:[39, 3], Operations: ['74-70=4', '7-4=3'] Exploring Operation: 39-3=36, Resulting Numbers: [36] 36,36 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.983507
hs_4
sum_heuristic
[ 2, 88, 99, 91 ]
99
[ "2+88=90", "91-90=1", "99*1=99" ]
Current State: 99:[2, 88, 99, 91], Operations: [] Exploring Operation: 2+88=90, Resulting Numbers: [99, 91, 90] Generated Node #2: [99, 91, 90] from Operation: 2+88=90 Current State: 99:[99, 91, 90], Operations: ['2+88=90'] Exploring Operation: 91-90=1, Resulting Numbers: [99, 1] Generated Node #3: [99, 1] from Operation: 91-90=1 Current State: 99:[99, 1], Operations: ['2+88=90', '91-90=1'] Exploring Operation: 99*1=99, Resulting Numbers: [99] 99,99 equal: Goal Reached
4
Current State: 99:[2, 88, 99, 91], Operations: [] Exploring Operation: 99-88=11, Resulting Numbers: [2, 91, 11] Generated Node #0,0: 99:[2, 91, 11] Operation: 99-88=11 Exploring Operation: 91-88=3, Resulting Numbers: [2, 99, 3] Generated Node #0,1: 99:[2, 99, 3] Operation: 91-88=3 Exploring Operation: 99-91=8, Resulting Numbers: [2, 88, 8] Generated Node #0,2: 99:[2, 88, 8] Operation: 99-91=8 Start Sub Search at level 1: Moving to Node #0,1 Current State: 99:[2, 99, 3], Operations: ['91-88=3'] Exploring Operation: 2+99=101, Resulting Numbers: [3, 101] Generated Node #0,1,0: 99:[3, 101] Operation: 2+99=101 Exploring Operation: 99/3=33, Resulting Numbers: [2, 33] Generated Node #0,1,1: 99:[2, 33] Operation: 99/3=33 Exploring Operation: 99-2=97, Resulting Numbers: [3, 97] Generated Node #0,1,2: 99:[3, 97] Operation: 99-2=97 Moving to Node #0,1,1 Current State: 99:[2, 33], Operations: ['91-88=3', '99/3=33'] Exploring Operation: 2*33=66, Resulting Numbers: [66] 66,99 unequal: No Solution Exploring Operation: 2+33=35, Resulting Numbers: [35] 35,99 unequal: No Solution Exploring Operation: 33-2=31, Resulting Numbers: [31] 31,99 unequal: No Solution Moving to Node #0,1,0 Current State: 99:[3, 101], Operations: ['91-88=3', '2+99=101'] Exploring Operation: 3+101=104, Resulting Numbers: [104] 104,99 unequal: No Solution Exploring Operation: 3*101=303, Resulting Numbers: [303] 303,99 unequal: No Solution Exploring Operation: 101-3=98, Resulting Numbers: [98] 98,99 unequal: No Solution Moving to Node #0,1,2 Current State: 99:[3, 97], Operations: ['91-88=3', '99-2=97'] Exploring Operation: 97-3=94, Resulting Numbers: [94] 94,99 unequal: No Solution Exploring Operation: 3+97=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 3*97=291, Resulting Numbers: [291] 291,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 99:[2, 91, 11], Operations: ['99-88=11'] Exploring Operation: 11-2=9, Resulting Numbers: [91, 9] Generated Node #0,0,0: 99:[91, 9] Operation: 11-2=9 Exploring Operation: 2+91=93, Resulting Numbers: [11, 93] Generated Node #0,0,1: 99:[11, 93] Operation: 2+91=93 Exploring Operation: 91+11=102, Resulting Numbers: [2, 102] Generated Node #0,0,2: 99:[2, 102] Operation: 91+11=102 Moving to Node #0,0,2 Current State: 99:[2, 102], Operations: ['99-88=11', '91+11=102'] Exploring Operation: 2+102=104, Resulting Numbers: [104] 104,99 unequal: No Solution Exploring Operation: 102-2=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 102/2=51, Resulting Numbers: [51] 51,99 unequal: No Solution Moving to Node #0,0,1 Current State: 99:[11, 93], Operations: ['99-88=11', '2+91=93'] Exploring Operation: 11+93=104, Resulting Numbers: [104] 104,99 unequal: No Solution Exploring Operation: 93-11=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 11*93=1023, Resulting Numbers: [1023] 1023,99 unequal: No Solution Moving to Node #0,0,0 Current State: 99:[91, 9], Operations: ['99-88=11', '11-2=9'] Exploring Operation: 91-9=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 91+9=100, Resulting Numbers: [100] 100,99 unequal: No Solution Exploring Operation: 91*9=819, Resulting Numbers: [819] 819,99 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 99:[2, 88, 8], Operations: ['99-91=8'] Exploring Operation: 2+88=90, Resulting Numbers: [8, 90] Generated Node #0,2,0: 99:[8, 90] Operation: 2+88=90 Exploring Operation: 88+8=96, Resulting Numbers: [2, 96] Generated Node #0,2,1: 99:[2, 96] Operation: 88+8=96 Exploring Operation: 88/8=11, Resulting Numbers: [2, 11] Generated Node #0,2,2: 99:[2, 11] Operation: 88/8=11 Start Sub Search at level 2: Moving to Node #0,2,2 Current State: 99:[2, 11], Operations: ['99-91=8', '88/8=11'] Exploring Operation: 2+11=13, Resulting Numbers: [13] 13,99 unequal: No Solution Exploring Operation: 2*11=22, Resulting Numbers: [22] 22,99 unequal: No Solution Exploring Operation: 11-2=9, Resulting Numbers: [9] 9,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,1 Current State: 99:[2, 96], Operations: ['99-91=8', '88+8=96'] Exploring Operation: 96/2=48, Resulting Numbers: [48] 48,99 unequal: No Solution Exploring Operation: 2+96=98, Resulting Numbers: [98] 98,99 unequal: No Solution Exploring Operation: 96-2=94, Resulting Numbers: [94] 94,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,2,0 Current State: 99:[8, 90], Operations: ['99-91=8', '2+88=90'] Exploring Operation: 90-8=82, Resulting Numbers: [82] 82,99 unequal: No Solution Exploring Operation: 8*90=720, Resulting Numbers: [720] 720,99 unequal: No Solution Exploring Operation: 8+90=98, Resulting Numbers: [98] 98,99 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_3
mult_heuristic
[ 77, 54, 67, 61 ]
29
[ "77-54=23", "67-61=6", "23+6=29" ]
Current State: 29:[77, 54, 67, 61], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [67, 61, 23] Generated Node #2: [67, 61, 23] from Operation: 77-54=23 Current State: 29:[67, 61, 23], Operations: ['77-54=23'] Exploring Operation: 67-61=6, Resulting Numbers: [23, 6] Generated Node #3: [23, 6] from Operation: 67-61=6 Current State: 29:[23, 6], Operations: ['77-54=23', '67-61=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[77, 54, 67, 61], Operations: [] Exploring Operation: 77-67=10, Resulting Numbers: [54, 61, 10] Generated Node #0,0: 29:[54, 61, 10] Operation: 77-67=10 Exploring Operation: 77-54=23, Resulting Numbers: [67, 61, 23] Generated Node #0,1: 29:[67, 61, 23] Operation: 77-54=23 Start Sub Search at level 1: Moving to Node #0,0 Current State: 29:[54, 61, 10], Operations: ['77-67=10'] Exploring Operation: 61-54=7, Resulting Numbers: [10, 7] Generated Node #0,0,0: 29:[10, 7] Operation: 61-54=7 Exploring Operation: 54-10=44, Resulting Numbers: [61, 44] Generated Node #0,0,1: 29:[61, 44] Operation: 54-10=44 Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 29:[10, 7], Operations: ['77-67=10', '61-54=7'] Exploring Operation: 10+7=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 10-7=3, Resulting Numbers: [3] 3,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 29:[61, 44], Operations: ['77-67=10', '54-10=44'] Exploring Operation: 61-44=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 61+44=105, Resulting Numbers: [105] 105,29 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1 Current State: 29:[67, 61, 23], Operations: ['77-54=23'] Exploring Operation: 67-23=44, Resulting Numbers: [61, 44] Generated Node #0,1,0: 29:[61, 44] Operation: 67-23=44 Exploring Operation: 67-61=6, Resulting Numbers: [23, 6] Generated Node #0,1,1: 29:[23, 6] Operation: 67-61=6 Moving to Node #0,1,1 Current State: 29:[23, 6], Operations: ['77-54=23', '67-61=6'] Exploring Operation: 23-6=17, Resulting Numbers: [17] 17,29 unequal: No Solution Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[77, 54, 67, 61], Operations: [] Exploring Operation: 77-54=23, Resulting Numbers: [67, 61, 23] Generated Node #0,1: 29:[67, 61, 23] Operation: 77-54=23 Moving to Node #0,1 Current State: 29:[67, 61, 23], Operations: ['77-54=23'] Exploring Operation: 67-61=6, Resulting Numbers: [23, 6] Generated Node #0,1,1: 29:[23, 6] Operation: 67-61=6 Moving to Node #0,1,1 Current State: 29:[23, 6], Operations: ['77-54=23', '67-61=6'] Exploring Operation: 23+6=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.986111
hs_2
mult_heuristic
[ 32, 89, 5, 2 ]
19
[ "89-32=57", "5-2=3", "57/3=19" ]
Current State: 19:[32, 89, 5, 2], Operations: [] Exploring Operation: 89-32=57, Resulting Numbers: [5, 2, 57] Generated Node #2: [5, 2, 57] from Operation: 89-32=57 Current State: 19:[5, 2, 57], Operations: ['89-32=57'] Exploring Operation: 5-2=3, Resulting Numbers: [57, 3] Generated Node #3: [57, 3] from Operation: 5-2=3 Current State: 19:[57, 3], Operations: ['89-32=57', '5-2=3'] Exploring Operation: 57/3=19, Resulting Numbers: [19] 19,19 equal: Goal Reached
4
Current State: 19:[32, 89, 5, 2], Operations: [] Exploring Operation: 89-32=57, Resulting Numbers: [5, 2, 57] Generated Node #0,0: 19:[5, 2, 57] Operation: 89-32=57 Start Sub Search at level 1: Moving to Node #0,0 Current State: 19:[5, 2, 57], Operations: ['89-32=57'] Exploring Operation: 5*2=10, Resulting Numbers: [57, 10] Generated Node #0,0,0: 19:[57, 10] Operation: 5*2=10 Moving to Node #0,0,0 Current State: 19:[57, 10], Operations: ['89-32=57', '5*2=10'] Exploring Operation: 57-10=47, Resulting Numbers: [47] 47,19 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
[ 10, 24, 15, 35 ]
95
[ "35-24=11", "10*11=110", "110-15=95" ]
Current State: 95:[10, 24, 15, 35], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [10, 15, 11] Generated Node #2: [10, 15, 11] from Operation: 35-24=11 Current State: 95:[10, 15, 11], Operations: ['35-24=11'] Exploring Operation: 10*11=110, Resulting Numbers: [15, 110] Generated Node #3: [15, 110] from Operation: 10*11=110 Current State: 95:[15, 110], Operations: ['35-24=11', '10*11=110'] Exploring Operation: 110-15=95, Resulting Numbers: [95] 95,95 equal: Goal Reached
4
Current State: 95:[10, 24, 15, 35], Operations: [] Exploring Operation: 35-15=20, Resulting Numbers: [10, 24, 20] Generated Node #0,0: 95:[10, 24, 20] Operation: 35-15=20 Moving to Node #0,0 Current State: 95:[10, 24, 20], Operations: ['35-15=20'] Exploring Operation: 24-10=14, Resulting Numbers: [20, 14] Generated Node #0,0,0: 95:[20, 14] Operation: 24-10=14 Moving to Node #0,0,0 Current State: 95:[20, 14], Operations: ['35-15=20', '24-10=14'] Exploring Operation: 20-14=6, Resulting Numbers: [6] 6,95 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 55, 53, 49, 72 ]
41
[ "55-49=6", "72/6=12", "53-12=41" ]
Current State: 41:[55, 53, 49, 72], Operations: [] Exploring Operation: 55-49=6, Resulting Numbers: [53, 72, 6] Generated Node #2: [53, 72, 6] from Operation: 55-49=6 Current State: 41:[53, 72, 6], Operations: ['55-49=6'] Exploring Operation: 72/6=12, Resulting Numbers: [53, 12] Generated Node #3: [53, 12] from Operation: 72/6=12 Current State: 41:[53, 12], Operations: ['55-49=6', '72/6=12'] Exploring Operation: 53-12=41, Resulting Numbers: [41] 41,41 equal: Goal Reached
4
Current State: 41:[55, 53, 49, 72], Operations: [] Exploring Operation: 55-53=2, Resulting Numbers: [49, 72, 2] Generated Node #0,0: 41:[49, 72, 2] Operation: 55-53=2 Exploring Operation: 72-55=17, Resulting Numbers: [53, 49, 17] Generated Node #0,1: 41:[53, 49, 17] Operation: 72-55=17 Exploring Operation: 72-49=23, Resulting Numbers: [55, 53, 23] Generated Node #0,2: 41:[55, 53, 23] Operation: 72-49=23 Exploring Operation: 72-53=19, Resulting Numbers: [55, 49, 19] Generated Node #0,3: 41:[55, 49, 19] Operation: 72-53=19 Start Sub Search at level 1: Moving to Node #0,1 Current State: 41:[53, 49, 17], Operations: ['72-55=17'] Exploring Operation: 53+17=70, Resulting Numbers: [49, 70] Generated Node #0,1,0: 41:[49, 70] Operation: 53+17=70 Exploring Operation: 49+17=66, Resulting Numbers: [53, 66] Generated Node #0,1,1: 41:[53, 66] Operation: 49+17=66 Exploring Operation: 49-17=32, Resulting Numbers: [53, 32] Generated Node #0,1,2: 41:[53, 32] Operation: 49-17=32 Exploring Operation: 53-17=36, Resulting Numbers: [49, 36] Generated Node #0,1,3: 41:[49, 36] Operation: 53-17=36 Moving to Node #0,1,3 Current State: 41:[49, 36], Operations: ['72-55=17', '53-17=36'] Exploring Operation: 49+36=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,41 unequal: No Solution Exploring Operation: 49*36=1764, Resulting Numbers: [1764] 1764,41 unequal: No Solution Moving to Node #0,1,2 Current State: 41:[53, 32], Operations: ['72-55=17', '49-17=32'] Exploring Operation: 53+32=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 53*32=1696, Resulting Numbers: [1696] 1696,41 unequal: No Solution Moving to Node #0,1,1 Current State: 41:[53, 66], Operations: ['72-55=17', '49+17=66'] Exploring Operation: 53+66=119, Resulting Numbers: [119] 119,41 unequal: No Solution Exploring Operation: 53*66=3498, Resulting Numbers: [3498] 3498,41 unequal: No Solution Exploring Operation: 66-53=13, Resulting Numbers: [13] 13,41 unequal: No Solution Moving to Node #0,1,0 Current State: 41:[49, 70], Operations: ['72-55=17', '53+17=70'] Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,41 unequal: No Solution Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2 Current State: 41:[55, 53, 23], Operations: ['72-49=23'] Exploring Operation: 55-23=32, Resulting Numbers: [53, 32] Generated Node #0,2,0: 41:[53, 32] Operation: 55-23=32 Exploring Operation: 53-23=30, Resulting Numbers: [55, 30] Generated Node #0,2,1: 41:[55, 30] Operation: 53-23=30 Exploring Operation: 53+23=76, Resulting Numbers: [55, 76] Generated Node #0,2,2: 41:[55, 76] Operation: 53+23=76 Exploring Operation: 55+23=78, Resulting Numbers: [53, 78] Generated Node #0,2,3: 41:[53, 78] Operation: 55+23=78 Moving to Node #0,2,0 Current State: 41:[53, 32], Operations: ['72-49=23', '55-23=32'] Exploring Operation: 53-32=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 53+32=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 53*32=1696, Resulting Numbers: [1696] 1696,41 unequal: No Solution Moving to Node #0,2,1 Current State: 41:[55, 30], Operations: ['72-49=23', '53-23=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,41 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,41 unequal: No Solution Moving to Node #0,2,3 Current State: 41:[53, 78], Operations: ['72-49=23', '55+23=78'] Exploring Operation: 53*78=4134, Resulting Numbers: [4134] 4134,41 unequal: No Solution Exploring Operation: 53+78=131, Resulting Numbers: [131] 131,41 unequal: No Solution Exploring Operation: 78-53=25, Resulting Numbers: [25] 25,41 unequal: No Solution Moving to Node #0,2,2 Current State: 41:[55, 76], Operations: ['72-49=23', '53+23=76'] Exploring Operation: 55+76=131, Resulting Numbers: [131] 131,41 unequal: No Solution Exploring Operation: 55*76=4180, Resulting Numbers: [4180] 4180,41 unequal: No Solution Exploring Operation: 76-55=21, Resulting Numbers: [21] 21,41 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 41:[55, 49, 19], Operations: ['72-53=19'] Exploring Operation: 49+19=68, Resulting Numbers: [55, 68] Generated Node #0,3,0: 41:[55, 68] Operation: 49+19=68 Exploring Operation: 55-19=36, Resulting Numbers: [49, 36] Generated Node #0,3,1: 41:[49, 36] Operation: 55-19=36 Exploring Operation: 55+19=74, Resulting Numbers: [49, 74] Generated Node #0,3,2: 41:[49, 74] Operation: 55+19=74 Exploring Operation: 49-19=30, Resulting Numbers: [55, 30] Generated Node #0,3,3: 41:[55, 30] Operation: 49-19=30 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 41:[49, 36], Operations: ['72-53=19', '55-19=36'] Exploring Operation: 49*36=1764, Resulting Numbers: [1764] 1764,41 unequal: No Solution Exploring Operation: 49+36=85, Resulting Numbers: [85] 85,41 unequal: No Solution Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,3 Current State: 41:[55, 30], Operations: ['72-53=19', '49-19=30'] Exploring Operation: 55*30=1650, Resulting Numbers: [1650] 1650,41 unequal: No Solution Exploring Operation: 55-30=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 55+30=85, Resulting Numbers: [85] 85,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,0 Current State: 41:[55, 68], Operations: ['72-53=19', '49+19=68'] Exploring Operation: 55*68=3740, Resulting Numbers: [3740] 3740,41 unequal: No Solution Exploring Operation: 55+68=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 68-55=13, Resulting Numbers: [13] 13,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,3,2 Current State: 41:[49, 74], Operations: ['72-53=19', '55+19=74'] Exploring Operation: 74-49=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 49+74=123, Resulting Numbers: [123] 123,41 unequal: No Solution Exploring Operation: 49*74=3626, Resulting Numbers: [3626] 3626,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0 Current State: 41:[49, 72, 2], Operations: ['55-53=2'] Exploring Operation: 49-2=47, Resulting Numbers: [72, 47] Generated Node #0,0,0: 41:[72, 47] Operation: 49-2=47 Exploring Operation: 72-2=70, Resulting Numbers: [49, 70] Generated Node #0,0,1: 41:[49, 70] Operation: 72-2=70 Exploring Operation: 49+2=51, Resulting Numbers: [72, 51] Generated Node #0,0,2: 41:[72, 51] Operation: 49+2=51 Exploring Operation: 72/2=36, Resulting Numbers: [49, 36] Generated Node #0,0,3: 41:[49, 36] Operation: 72/2=36 Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 41:[49, 36], Operations: ['55-53=2', '72/2=36'] Exploring Operation: 49-36=13, Resulting Numbers: [13] 13,41 unequal: No Solution Exploring Operation: 49*36=1764, Resulting Numbers: [1764] 1764,41 unequal: No Solution Exploring Operation: 49+36=85, Resulting Numbers: [85] 85,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 41:[72, 47], Operations: ['55-53=2', '49-2=47'] Exploring Operation: 72+47=119, Resulting Numbers: [119] 119,41 unequal: No Solution Exploring Operation: 72-47=25, Resulting Numbers: [25] 25,41 unequal: No Solution Exploring Operation: 72*47=3384, Resulting Numbers: [3384] 3384,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 41:[49, 70], Operations: ['55-53=2', '72-2=70'] Exploring Operation: 70-49=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 49+70=119, Resulting Numbers: [119] 119,41 unequal: No Solution Exploring Operation: 49*70=3430, Resulting Numbers: [3430] 3430,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 41:[72, 51], Operations: ['55-53=2', '49+2=51'] Exploring Operation: 72*51=3672, Resulting Numbers: [3672] 3672,41 unequal: No Solution Exploring Operation: 72-51=21, Resulting Numbers: [21] 21,41 unequal: No Solution Exploring Operation: 72+51=123, Resulting Numbers: [123] 123,41 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 79, 43, 5, 23 ]
65
[ "79-43=36", "36-23=13", "5*13=65" ]
Current State: 65:[79, 43, 5, 23], Operations: [] Exploring Operation: 79-43=36, Resulting Numbers: [5, 23, 36] Generated Node #2: [5, 23, 36] from Operation: 79-43=36 Current State: 65:[5, 23, 36], Operations: ['79-43=36'] Exploring Operation: 36-23=13, Resulting Numbers: [5, 13] Generated Node #3: [5, 13] from Operation: 36-23=13 Current State: 65:[5, 13], Operations: ['79-43=36', '36-23=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[79, 43, 5, 23], Operations: [] Exploring Operation: 43-23=20, Resulting Numbers: [79, 5, 20] Generated Node #0,0: 65:[79, 5, 20] Operation: 43-23=20 Exploring Operation: 43+23=66, Resulting Numbers: [79, 5, 66] Generated Node #0,1: 65:[79, 5, 66] Operation: 43+23=66 Start Sub Search at level 1: Moving to Node #0,1 Current State: 65:[79, 5, 66], Operations: ['43+23=66'] Exploring Operation: 79-66=13, Resulting Numbers: [5, 13] Generated Node #0,1,0: 65:[5, 13] Operation: 79-66=13 Exploring Operation: 79-5=74, Resulting Numbers: [66, 74] Generated Node #0,1,1: 65:[66, 74] Operation: 79-5=74 Start Sub Search at level 2: Moving to Node #0,1,0 Current State: 65:[5, 13], Operations: ['43+23=66', '79-66=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Moving to Node #0 Current State: 65:[79, 43, 5, 23], Operations: [] Exploring Operation: 43+23=66, Resulting Numbers: [79, 5, 66] Generated Node #0,1: 65:[79, 5, 66] Operation: 43+23=66 Moving to Node #0,1 Current State: 65:[79, 5, 66], Operations: ['43+23=66'] Exploring Operation: 79-66=13, Resulting Numbers: [5, 13] Generated Node #0,1,0: 65:[5, 13] Operation: 79-66=13 Moving to Node #0,1,0 Current State: 65:[5, 13], Operations: ['43+23=66', '79-66=13'] Exploring Operation: 5*13=65, Resulting Numbers: [65] 65,65 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.992188
hs_2
mult_heuristic
[ 16, 32, 35, 69 ]
88
[ "32-16=16", "35+69=104", "104-16=88" ]
Current State: 88:[16, 32, 35, 69], Operations: [] Exploring Operation: 32-16=16, Resulting Numbers: [35, 69, 16] Generated Node #2: [35, 69, 16] from Operation: 32-16=16 Current State: 88:[35, 69, 16], Operations: ['32-16=16'] Exploring Operation: 35+69=104, Resulting Numbers: [16, 104] Generated Node #3: [16, 104] from Operation: 35+69=104 Current State: 88:[16, 104], Operations: ['32-16=16', '35+69=104'] Exploring Operation: 104-16=88, Resulting Numbers: [88] 88,88 equal: Goal Reached
4
Current State: 88:[16, 32, 35, 69], Operations: [] Exploring Operation: 69-35=34, Resulting Numbers: [16, 32, 34] Generated Node #0,0: 88:[16, 32, 34] Operation: 69-35=34 Exploring Operation: 35-32=3, Resulting Numbers: [16, 69, 3] Generated Node #0,1: 88:[16, 69, 3] Operation: 35-32=3 Exploring Operation: 69-32=37, Resulting Numbers: [16, 35, 37] Generated Node #0,2: 88:[16, 35, 37] Operation: 69-32=37 Exploring Operation: 16+69=85, Resulting Numbers: [32, 35, 85] Generated Node #0,3: 88:[32, 35, 85] Operation: 16+69=85 Start Sub Search at level 1: Moving to Node #0,2 Current State: 88:[16, 35, 37], Operations: ['69-32=37'] Exploring Operation: 16+35=51, Resulting Numbers: [37, 51] Generated Node #0,2,0: 88:[37, 51] Operation: 16+35=51 Exploring Operation: 37-35=2, Resulting Numbers: [16, 2] Generated Node #0,2,1: 88:[16, 2] Operation: 37-35=2 Exploring Operation: 35-16=19, Resulting Numbers: [37, 19] Generated Node #0,2,2: 88:[37, 19] Operation: 35-16=19 Exploring Operation: 37-16=21, Resulting Numbers: [35, 21] Generated Node #0,2,3: 88:[35, 21] Operation: 37-16=21 Moving to Node #0,2,1 Current State: 88:[16, 2], Operations: ['69-32=37', '37-35=2'] Exploring Operation: 16+2=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 16*2=32, Resulting Numbers: [32] 32,88 unequal: No Solution Exploring Operation: 16/2=8, Resulting Numbers: [8] 8,88 unequal: No Solution Exploring Operation: 16-2=14, Resulting Numbers: [14] 14,88 unequal: No Solution Moving to Node #0,2,3 Current State: 88:[35, 21], Operations: ['69-32=37', '37-16=21'] Exploring Operation: 35+21=56, Resulting Numbers: [56] 56,88 unequal: No Solution Exploring Operation: 35-21=14, Resulting Numbers: [14] 14,88 unequal: No Solution Exploring Operation: 35*21=735, Resulting Numbers: [735] 735,88 unequal: No Solution Moving to Node #0,2,2 Current State: 88:[37, 19], Operations: ['69-32=37', '35-16=19'] Exploring Operation: 37-19=18, Resulting Numbers: [18] 18,88 unequal: No Solution Exploring Operation: 37*19=703, Resulting Numbers: [703] 703,88 unequal: No Solution Exploring Operation: 37+19=56, Resulting Numbers: [56] 56,88 unequal: No Solution Moving to Node #0,2,0 Current State: 88:[37, 51], Operations: ['69-32=37', '16+35=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Moving to Node #0 Current State: 88:[16, 32, 35, 69], Operations: [] Exploring Operation: 69-32=37, Resulting Numbers: [16, 35, 37] Generated Node #0,2: 88:[16, 35, 37] Operation: 69-32=37 Moving to Node #0,2 Current State: 88:[16, 35, 37], Operations: ['69-32=37'] Exploring Operation: 16+35=51, Resulting Numbers: [37, 51] Generated Node #0,2,0: 88:[37, 51] Operation: 16+35=51 Moving to Node #0,2,0 Current State: 88:[37, 51], Operations: ['69-32=37', '16+35=51'] Exploring Operation: 37+51=88, Resulting Numbers: [88] 88,88 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_4
mult_heuristic
[ 96, 90, 51, 19 ]
87
[ "51-19=32", "96/32=3", "90-3=87" ]
Current State: 87:[96, 90, 51, 19], Operations: [] Exploring Operation: 51-19=32, Resulting Numbers: [96, 90, 32] Generated Node #2: [96, 90, 32] from Operation: 51-19=32 Current State: 87:[96, 90, 32], Operations: ['51-19=32'] Exploring Operation: 96/32=3, Resulting Numbers: [90, 3] Generated Node #3: [90, 3] from Operation: 96/32=3 Current State: 87:[90, 3], Operations: ['51-19=32', '96/32=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached
4
Current State: 87:[96, 90, 51, 19], Operations: [] Exploring Operation: 96-51=45, Resulting Numbers: [90, 19, 45] Generated Node #0,0: 87:[90, 19, 45] Operation: 96-51=45 Exploring Operation: 51-19=32, Resulting Numbers: [96, 90, 32] Generated Node #0,1: 87:[96, 90, 32] Operation: 51-19=32 Exploring Operation: 90-51=39, Resulting Numbers: [96, 19, 39] Generated Node #0,2: 87:[96, 19, 39] Operation: 90-51=39 Start Sub Search at level 1: Moving to Node #0,1 Current State: 87:[96, 90, 32], Operations: ['51-19=32'] Exploring Operation: 96/32=3, Resulting Numbers: [90, 3] Generated Node #0,1,0: 87:[90, 3] Operation: 96/32=3 Exploring Operation: 96-32=64, Resulting Numbers: [90, 64] Generated Node #0,1,1: 87:[90, 64] Operation: 96-32=64 Exploring Operation: 96-90=6, Resulting Numbers: [32, 6] Generated Node #0,1,2: 87:[32, 6] Operation: 96-90=6 Moving to Node #0,1,0 Current State: 87:[90, 3], Operations: ['51-19=32', '96/32=3'] Exploring Operation: 90+3=93, Resulting Numbers: [93] 93,87 unequal: No Solution Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Moving to Node #0 Current State: 87:[96, 90, 51, 19], Operations: [] Exploring Operation: 51-19=32, Resulting Numbers: [96, 90, 32] Generated Node #0,1: 87:[96, 90, 32] Operation: 51-19=32 Moving to Node #0,1 Current State: 87:[96, 90, 32], Operations: ['51-19=32'] Exploring Operation: 96/32=3, Resulting Numbers: [90, 3] Generated Node #0,1,0: 87:[90, 3] Operation: 96/32=3 Moving to Node #0,1,0 Current State: 87:[90, 3], Operations: ['51-19=32', '96/32=3'] Exploring Operation: 90-3=87, Resulting Numbers: [87] 87,87 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_3
mult_heuristic
[ 96, 96, 14, 97 ]
84
[ "96/96=1", "97-14=83", "1+83=84" ]
Current State: 84:[96, 96, 14, 97], Operations: [] Exploring Operation: 96/96=1, Resulting Numbers: [14, 97, 1] Generated Node #2: [14, 97, 1] from Operation: 96/96=1 Current State: 84:[14, 97, 1], Operations: ['96/96=1'] Exploring Operation: 97-14=83, Resulting Numbers: [1, 83] Generated Node #3: [1, 83] from Operation: 97-14=83 Current State: 84:[1, 83], Operations: ['96/96=1', '97-14=83'] Exploring Operation: 1+83=84, Resulting Numbers: [84] 84,84 equal: Goal Reached
4
Current State: 84:[96, 96, 14, 97], Operations: [] Exploring Operation: 97-96=1, Resulting Numbers: [96, 14, 1] Generated Node #0,0: 84:[96, 14, 1] Operation: 97-96=1 Moving to Node #0,0 Current State: 84:[96, 14, 1], Operations: ['97-96=1'] Exploring Operation: 96-14=82, Resulting Numbers: [1, 82] Generated Node #0,0,0: 84:[1, 82] Operation: 96-14=82 Moving to Node #0,0,0 Current State: 84:[1, 82], Operations: ['97-96=1', '96-14=82'] Exploring Operation: 1+82=83, Resulting Numbers: [83] 83,84 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 5, 38, 41, 40 ]
31
[ "40-38=2", "5*2=10", "41-10=31" ]
Current State: 31:[5, 38, 41, 40], Operations: [] Exploring Operation: 40-38=2, Resulting Numbers: [5, 41, 2] Generated Node #2: [5, 41, 2] from Operation: 40-38=2 Current State: 31:[5, 41, 2], Operations: ['40-38=2'] Exploring Operation: 5*2=10, Resulting Numbers: [41, 10] Generated Node #3: [41, 10] from Operation: 5*2=10 Current State: 31:[41, 10], Operations: ['40-38=2', '5*2=10'] Exploring Operation: 41-10=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[5, 38, 41, 40], Operations: [] Exploring Operation: 5+38=43, Resulting Numbers: [41, 40, 43] Generated Node #0,0: 31:[41, 40, 43] Operation: 5+38=43 Exploring Operation: 41-5=36, Resulting Numbers: [38, 40, 36] Generated Node #0,1: 31:[38, 40, 36] Operation: 41-5=36 Exploring Operation: 40-5=35, Resulting Numbers: [38, 41, 35] Generated Node #0,2: 31:[38, 41, 35] Operation: 40-5=35 Exploring Operation: 38-5=33, Resulting Numbers: [41, 40, 33] Generated Node #0,3: 31:[41, 40, 33] Operation: 38-5=33 Moving to Node #0,1 Current State: 31:[38, 40, 36], Operations: ['41-5=36'] Exploring Operation: 38-36=2, Resulting Numbers: [40, 2] Generated Node #0,1,0: 31:[40, 2] Operation: 38-36=2 Exploring Operation: 40-38=2, Resulting Numbers: [36, 2] Generated Node #0,1,1: 31:[36, 2] Operation: 40-38=2 Exploring Operation: 40-36=4, Resulting Numbers: [38, 4] Generated Node #0,1,2: 31:[38, 4] Operation: 40-36=4 Exploring Operation: 38+40=78, Resulting Numbers: [36, 78] Generated Node #0,1,3: 31:[36, 78] Operation: 38+40=78 Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 31:[36, 2], Operations: ['41-5=36', '40-38=2'] Exploring Operation: 36-2=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 36+2=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 36/2=18, Resulting Numbers: [18] 18,31 unequal: No Solution Exploring Operation: 36*2=72, Resulting Numbers: [72] 72,31 unequal: No Solution No 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: 31:[38, 4], Operations: ['41-5=36', '40-36=4'] Exploring Operation: 38-4=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 38+4=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 38*4=152, Resulting Numbers: [152] 152,31 unequal: No Solution No 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: 31:[40, 2], Operations: ['41-5=36', '38-36=2'] Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,31 unequal: No Solution No 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: 31:[36, 78], Operations: ['41-5=36', '38+40=78'] Exploring Operation: 78-36=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 36+78=114, Resulting Numbers: [114] 114,31 unequal: No Solution Exploring Operation: 36*78=2808, Resulting Numbers: [2808] 2808,31 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: 31:[41, 40, 33], Operations: ['38-5=33'] Exploring Operation: 41+40=81, Resulting Numbers: [33, 81] Generated Node #0,3,0: 31:[33, 81] Operation: 41+40=81 Exploring Operation: 40-33=7, Resulting Numbers: [41, 7] Generated Node #0,3,1: 31:[41, 7] Operation: 40-33=7 Exploring Operation: 41-33=8, Resulting Numbers: [40, 8] Generated Node #0,3,2: 31:[40, 8] Operation: 41-33=8 Exploring Operation: 41-40=1, Resulting Numbers: [33, 1] Generated Node #0,3,3: 31:[33, 1] Operation: 41-40=1 Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 31:[40, 8], Operations: ['38-5=33', '41-33=8'] Exploring Operation: 40*8=320, Resulting Numbers: [320] 320,31 unequal: No Solution Exploring Operation: 40/8=5, Resulting Numbers: [5] 5,31 unequal: No Solution Exploring Operation: 40+8=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 40-8=32, Resulting Numbers: [32] 32,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 31:[33, 1], Operations: ['38-5=33', '41-40=1'] Exploring Operation: 33+1=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 33/1=33, Resulting Numbers: [33] 33,31 unequal: No Solution Exploring Operation: 33-1=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 33*1=33, Resulting Numbers: [33] 33,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 31:[41, 7], Operations: ['38-5=33', '40-33=7'] Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,31 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,31 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 31:[33, 81], Operations: ['38-5=33', '41+40=81'] Exploring Operation: 33+81=114, Resulting Numbers: [114] 114,31 unequal: No Solution Exploring Operation: 81-33=48, Resulting Numbers: [48] 48,31 unequal: No Solution Exploring Operation: 33*81=2673, Resulting Numbers: [2673] 2673,31 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: 31:[38, 41, 35], Operations: ['40-5=35'] Exploring Operation: 38+41=79, Resulting Numbers: [35, 79] Generated Node #0,2,0: 31:[35, 79] Operation: 38+41=79 Exploring Operation: 41-35=6, Resulting Numbers: [38, 6] Generated Node #0,2,1: 31:[38, 6] Operation: 41-35=6 Exploring Operation: 41-38=3, Resulting Numbers: [35, 3] Generated Node #0,2,2: 31:[35, 3] Operation: 41-38=3 Exploring Operation: 38-35=3, Resulting Numbers: [41, 3] Generated Node #0,2,3: 31:[41, 3] Operation: 38-35=3 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 31:[38, 6], Operations: ['40-5=35', '41-35=6'] Exploring Operation: 38*6=228, Resulting Numbers: [228] 228,31 unequal: No Solution Exploring Operation: 38-6=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 38+6=44, Resulting Numbers: [44] 44,31 unequal: No Solution No 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: 31:[35, 3], Operations: ['40-5=35', '41-38=3'] Exploring Operation: 35-3=32, Resulting Numbers: [32] 32,31 unequal: No Solution Exploring Operation: 35+3=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 35*3=105, Resulting Numbers: [105] 105,31 unequal: No Solution No 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: 31:[41, 3], Operations: ['40-5=35', '38-35=3'] Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,31 unequal: No Solution No 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: 31:[35, 79], Operations: ['40-5=35', '38+41=79'] Exploring Operation: 35*79=2765, Resulting Numbers: [2765] 2765,31 unequal: No Solution Exploring Operation: 35+79=114, Resulting Numbers: [114] 114,31 unequal: No Solution Exploring Operation: 79-35=44, Resulting Numbers: [44] 44,31 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: 31:[41, 40, 43], Operations: ['5+38=43'] Exploring Operation: 43-40=3, Resulting Numbers: [41, 3] Generated Node #0,0,0: 31:[41, 3] Operation: 43-40=3 Exploring Operation: 41+40=81, Resulting Numbers: [43, 81] Generated Node #0,0,1: 31:[43, 81] Operation: 41+40=81 Exploring Operation: 43-41=2, Resulting Numbers: [40, 2] Generated Node #0,0,2: 31:[40, 2] Operation: 43-41=2 Exploring Operation: 41-40=1, Resulting Numbers: [43, 1] Generated Node #0,0,3: 31:[43, 1] Operation: 41-40=1 Moving to Node #0,0,0 Current State: 31:[41, 3], Operations: ['5+38=43', '43-40=3'] Exploring Operation: 41*3=123, Resulting Numbers: [123] 123,31 unequal: No Solution Exploring Operation: 41+3=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 41-3=38, Resulting Numbers: [38] 38,31 unequal: No Solution Moving to Node #0,0,2 Current State: 31:[40, 2], Operations: ['5+38=43', '43-41=2'] Exploring Operation: 40*2=80, Resulting Numbers: [80] 80,31 unequal: No Solution Exploring Operation: 40/2=20, Resulting Numbers: [20] 20,31 unequal: No Solution Exploring Operation: 40-2=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 40+2=42, Resulting Numbers: [42] 42,31 unequal: No Solution Moving to Node #0,0,3 Current State: 31:[43, 1], Operations: ['5+38=43', '41-40=1'] Exploring Operation: 43/1=43, Resulting Numbers: [43] 43,31 unequal: No Solution Exploring Operation: 43+1=44, Resulting Numbers: [44] 44,31 unequal: No Solution Exploring Operation: 43-1=42, Resulting Numbers: [42] 42,31 unequal: No Solution Exploring Operation: 43*1=43, Resulting Numbers: [43] 43,31 unequal: No Solution Moving to Node #0,0,1 Current State: 31:[43, 81], Operations: ['5+38=43', '41+40=81'] Exploring Operation: 81-43=38, Resulting Numbers: [38] 38,31 unequal: No Solution Exploring Operation: 43+81=124, Resulting Numbers: [124] 124,31 unequal: No Solution Exploring Operation: 43*81=3483, Resulting Numbers: [3483] 3483,31 unequal: No Solution No solution found.
0
hs_4
mult_heuristic
[ 15, 66, 33, 63 ]
50
[ "63-15=48", "66/33=2", "48+2=50" ]
Current State: 50:[15, 66, 33, 63], Operations: [] Exploring Operation: 63-15=48, Resulting Numbers: [66, 33, 48] Generated Node #2: [66, 33, 48] from Operation: 63-15=48 Current State: 50:[66, 33, 48], Operations: ['63-15=48'] Exploring Operation: 66/33=2, Resulting Numbers: [48, 2] Generated Node #3: [48, 2] from Operation: 66/33=2 Current State: 50:[48, 2], Operations: ['63-15=48', '66/33=2'] Exploring Operation: 48+2=50, Resulting Numbers: [50] 50,50 equal: Goal Reached
4
Current State: 50:[15, 66, 33, 63], Operations: [] Exploring Operation: 66-63=3, Resulting Numbers: [15, 33, 3] Generated Node #0,0: 50:[15, 33, 3] Operation: 66-63=3 Moving to Node #0,0 Current State: 50:[15, 33, 3], Operations: ['66-63=3'] Exploring Operation: 15+33=48, Resulting Numbers: [3, 48] Generated Node #0,0,0: 50:[3, 48] Operation: 15+33=48 Moving to Node #0,0,0 Current State: 50:[3, 48], Operations: ['66-63=3', '15+33=48'] Exploring Operation: 3+48=51, Resulting Numbers: [51] 51,50 unequal: No Solution No solution found.
0
hs_1
sum_heuristic
[ 47, 59, 15, 51 ]
40
[ "47+59=106", "15+51=66", "106-66=40" ]
Current State: 40:[47, 59, 15, 51], Operations: [] Exploring Operation: 47+59=106, Resulting Numbers: [15, 51, 106] Generated Node #2: [15, 51, 106] from Operation: 47+59=106 Current State: 40:[15, 51, 106], Operations: ['47+59=106'] Exploring Operation: 15+51=66, Resulting Numbers: [106, 66] Generated Node #3: [106, 66] from Operation: 15+51=66 Current State: 40:[106, 66], Operations: ['47+59=106', '15+51=66'] Exploring Operation: 106-66=40, Resulting Numbers: [40] 40,40 equal: Goal Reached
4
Current State: 40:[47, 59, 15, 51], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [47, 15, 8] Generated Node #0,0: 40:[47, 15, 8] Operation: 59-51=8 Exploring Operation: 59-47=12, Resulting Numbers: [15, 51, 12] Generated Node #0,1: 40:[15, 51, 12] Operation: 59-47=12 Exploring Operation: 51-47=4, Resulting Numbers: [59, 15, 4] Generated Node #0,2: 40:[59, 15, 4] Operation: 51-47=4 Exploring Operation: 59-15=44, Resulting Numbers: [47, 51, 44] Generated Node #0,3: 40:[47, 51, 44] Operation: 59-15=44 Exploring Operation: 51-15=36, Resulting Numbers: [47, 59, 36] Generated Node #0,4: 40:[47, 59, 36] Operation: 51-15=36 Start Sub Search at level 1: Moving to Node #0,0 Current State: 40:[47, 15, 8], Operations: ['59-51=8'] Exploring Operation: 15-8=7, Resulting Numbers: [47, 7] Generated Node #0,0,0: 40:[47, 7] Operation: 15-8=7 Exploring Operation: 47-15=32, Resulting Numbers: [8, 32] Generated Node #0,0,1: 40:[8, 32] Operation: 47-15=32 Exploring Operation: 47-8=39, Resulting Numbers: [15, 39] Generated Node #0,0,2: 40:[15, 39] Operation: 47-8=39 Exploring Operation: 47+8=55, Resulting Numbers: [15, 55] Generated Node #0,0,3: 40:[15, 55] Operation: 47+8=55 Exploring Operation: 15+8=23, Resulting Numbers: [47, 23] Generated Node #0,0,4: 40:[47, 23] Operation: 15+8=23 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 40:[15, 39], Operations: ['59-51=8', '47-8=39'] Exploring Operation: 39-15=24, Resulting Numbers: [24] 24,40 unequal: No Solution Exploring Operation: 15*39=585, Resulting Numbers: [585] 585,40 unequal: No Solution Exploring Operation: 15+39=54, Resulting Numbers: [54] 54,40 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:[47, 7], Operations: ['59-51=8', '15-8=7'] Exploring Operation: 47+7=54, Resulting Numbers: [54] 54,40 unequal: No Solution Exploring Operation: 47*7=329, Resulting Numbers: [329] 329,40 unequal: No Solution Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Moving to Node #0 Current State: 40:[47, 59, 15, 51], Operations: [] Exploring Operation: 59-51=8, Resulting Numbers: [47, 15, 8] Generated Node #0,0: 40:[47, 15, 8] Operation: 59-51=8 Moving to Node #0,0 Current State: 40:[47, 15, 8], Operations: ['59-51=8'] Exploring Operation: 15-8=7, Resulting Numbers: [47, 7] Generated Node #0,0,0: 40:[47, 7] Operation: 15-8=7 Moving to Node #0,0,0 Current State: 40:[47, 7], Operations: ['59-51=8', '15-8=7'] Exploring Operation: 47-7=40, Resulting Numbers: [40] 40,40 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.982639
hs_5
mult_heuristic
[ 87, 23, 41, 44 ]
18
[ "44-41=3", "23*3=69", "87-69=18" ]
Current State: 18:[87, 23, 41, 44], Operations: [] Exploring Operation: 44-41=3, Resulting Numbers: [87, 23, 3] Generated Node #2: [87, 23, 3] from Operation: 44-41=3 Current State: 18:[87, 23, 3], Operations: ['44-41=3'] Exploring Operation: 23*3=69, Resulting Numbers: [87, 69] Generated Node #3: [87, 69] from Operation: 23*3=69 Current State: 18:[87, 69], Operations: ['44-41=3', '23*3=69'] Exploring Operation: 87-69=18, Resulting Numbers: [18] 18,18 equal: Goal Reached
4
Current State: 18:[87, 23, 41, 44], Operations: [] Exploring Operation: 87-44=43, Resulting Numbers: [23, 41, 43] Generated Node #0,0: 18:[23, 41, 43] Operation: 87-44=43 Exploring Operation: 87-23=64, Resulting Numbers: [41, 44, 64] Generated Node #0,1: 18:[41, 44, 64] Operation: 87-23=64 Exploring Operation: 44-41=3, Resulting Numbers: [87, 23, 3] Generated Node #0,2: 18:[87, 23, 3] Operation: 44-41=3 Exploring Operation: 87-41=46, Resulting Numbers: [23, 44, 46] Generated Node #0,3: 18:[23, 44, 46] Operation: 87-41=46 Moving to Node #0,0 Current State: 18:[23, 41, 43], Operations: ['87-44=43'] Exploring Operation: 23+41=64, Resulting Numbers: [43, 64] Generated Node #0,0,0: 18:[43, 64] Operation: 23+41=64 Exploring Operation: 43-23=20, Resulting Numbers: [41, 20] Generated Node #0,0,1: 18:[41, 20] Operation: 43-23=20 Exploring Operation: 41-23=18, Resulting Numbers: [43, 18] Generated Node #0,0,2: 18:[43, 18] Operation: 41-23=18 Exploring Operation: 43-41=2, Resulting Numbers: [23, 2] Generated Node #0,0,3: 18:[23, 2] Operation: 43-41=2 Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 18:[23, 2], Operations: ['87-44=43', '43-41=2'] Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 18:[41, 20], Operations: ['87-44=43', '43-23=20'] Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,18 unequal: No Solution Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 18:[43, 18], Operations: ['87-44=43', '41-23=18'] Exploring Operation: 43-18=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 43*18=774, Resulting Numbers: [774] 774,18 unequal: No Solution Exploring Operation: 43+18=61, Resulting Numbers: [61] 61,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 18:[43, 64], Operations: ['87-44=43', '23+41=64'] Exploring Operation: 43*64=2752, Resulting Numbers: [2752] 2752,18 unequal: No Solution Exploring Operation: 64-43=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 43+64=107, Resulting Numbers: [107] 107,18 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: 18:[23, 44, 46], Operations: ['87-41=46'] Exploring Operation: 46/23=2, Resulting Numbers: [44, 2] Generated Node #0,3,0: 18:[44, 2] Operation: 46/23=2 Exploring Operation: 44-23=21, Resulting Numbers: [46, 21] Generated Node #0,3,1: 18:[46, 21] Operation: 44-23=21 Exploring Operation: 46-23=23, Resulting Numbers: [44, 23] Generated Node #0,3,2: 18:[44, 23] Operation: 46-23=23 Exploring Operation: 46-44=2, Resulting Numbers: [23, 2] Generated Node #0,3,3: 18:[23, 2] Operation: 46-44=2 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 18:[23, 2], Operations: ['87-41=46', '46-44=2'] Exploring Operation: 23+2=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 23*2=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 23-2=21, Resulting Numbers: [21] 21,18 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 #0,3,0 Current State: 18:[44, 2], Operations: ['87-41=46', '46/23=2'] Exploring Operation: 44+2=46, Resulting Numbers: [46] 46,18 unequal: No Solution Exploring Operation: 44*2=88, Resulting Numbers: [88] 88,18 unequal: No Solution Exploring Operation: 44-2=42, Resulting Numbers: [42] 42,18 unequal: No Solution Exploring Operation: 44/2=22, Resulting Numbers: [22] 22,18 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 #0,3,1 Current State: 18:[46, 21], Operations: ['87-41=46', '44-23=21'] Exploring Operation: 46-21=25, Resulting Numbers: [25] 25,18 unequal: No Solution Exploring Operation: 46+21=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 46*21=966, Resulting Numbers: [966] 966,18 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 #0,3,2 Current State: 18:[44, 23], Operations: ['87-41=46', '46-23=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,18 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: 18:[87, 23, 3], Operations: ['44-41=3'] Exploring Operation: 87/3=29, Resulting Numbers: [23, 29] Generated Node #0,2,0: 18:[23, 29] Operation: 87/3=29 Exploring Operation: 87-23=64, Resulting Numbers: [3, 64] Generated Node #0,2,1: 18:[3, 64] Operation: 87-23=64 Exploring Operation: 87-3=84, Resulting Numbers: [23, 84] Generated Node #0,2,2: 18:[23, 84] Operation: 87-3=84 Exploring Operation: 23-3=20, Resulting Numbers: [87, 20] Generated Node #0,2,3: 18:[87, 20] Operation: 23-3=20 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 18:[23, 29], Operations: ['44-41=3', '87/3=29'] Exploring Operation: 29-23=6, Resulting Numbers: [6] 6,18 unequal: No Solution Exploring Operation: 23+29=52, Resulting Numbers: [52] 52,18 unequal: No Solution Exploring Operation: 23*29=667, Resulting Numbers: [667] 667,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 18:[3, 64], Operations: ['44-41=3', '87-23=64'] Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,18 unequal: No Solution Exploring Operation: 3+64=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 3*64=192, Resulting Numbers: [192] 192,18 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:[23, 84], Operations: ['44-41=3', '87-3=84'] Exploring Operation: 23*84=1932, Resulting Numbers: [1932] 1932,18 unequal: No Solution Exploring Operation: 23+84=107, Resulting Numbers: [107] 107,18 unequal: No Solution Exploring Operation: 84-23=61, Resulting Numbers: [61] 61,18 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 #0,2,3 Current State: 18:[87, 20], Operations: ['44-41=3', '23-3=20'] Exploring Operation: 87-20=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 87+20=107, Resulting Numbers: [107] 107,18 unequal: No Solution Exploring Operation: 87*20=1740, Resulting Numbers: [1740] 1740,18 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: 18:[41, 44, 64], Operations: ['87-23=64'] Exploring Operation: 64-41=23, Resulting Numbers: [44, 23] Generated Node #0,1,0: 18:[44, 23] Operation: 64-41=23 Exploring Operation: 44-41=3, Resulting Numbers: [64, 3] Generated Node #0,1,1: 18:[64, 3] Operation: 44-41=3 Exploring Operation: 41+44=85, Resulting Numbers: [64, 85] Generated Node #0,1,2: 18:[64, 85] Operation: 41+44=85 Exploring Operation: 64-44=20, Resulting Numbers: [41, 20] Generated Node #0,1,3: 18:[41, 20] Operation: 64-44=20 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 18:[41, 20], Operations: ['87-23=64', '64-44=20'] Exploring Operation: 41-20=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 41*20=820, Resulting Numbers: [820] 820,18 unequal: No Solution Exploring Operation: 41+20=61, Resulting Numbers: [61] 61,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 18:[44, 23], Operations: ['87-23=64', '64-41=23'] Exploring Operation: 44+23=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 44*23=1012, Resulting Numbers: [1012] 1012,18 unequal: No Solution Exploring Operation: 44-23=21, Resulting Numbers: [21] 21,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 18:[64, 3], Operations: ['87-23=64', '44-41=3'] Exploring Operation: 64+3=67, Resulting Numbers: [67] 67,18 unequal: No Solution Exploring Operation: 64*3=192, Resulting Numbers: [192] 192,18 unequal: No Solution Exploring Operation: 64-3=61, Resulting Numbers: [61] 61,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 18:[64, 85], Operations: ['87-23=64', '41+44=85'] Exploring Operation: 64*85=5440, Resulting Numbers: [5440] 5440,18 unequal: No Solution Exploring Operation: 85-64=21, Resulting Numbers: [21] 21,18 unequal: No Solution Exploring Operation: 64+85=149, Resulting Numbers: [149] 149,18 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_4
sum_heuristic
[ 4, 24, 1, 32 ]
65
[ "4*24=96", "32-1=31", "96-31=65" ]
Current State: 65:[4, 24, 1, 32], Operations: [] Exploring Operation: 4*24=96, Resulting Numbers: [1, 32, 96] Generated Node #2: [1, 32, 96] from Operation: 4*24=96 Current State: 65:[1, 32, 96], Operations: ['4*24=96'] Exploring Operation: 32-1=31, Resulting Numbers: [96, 31] Generated Node #3: [96, 31] from Operation: 32-1=31 Current State: 65:[96, 31], Operations: ['4*24=96', '32-1=31'] Exploring Operation: 96-31=65, Resulting Numbers: [65] 65,65 equal: Goal Reached
4
Current State: 65:[4, 24, 1, 32], Operations: [] Exploring Operation: 32/4=8, Resulting Numbers: [24, 1, 8] Generated Node #0,0: 65:[24, 1, 8] Operation: 32/4=8 Exploring Operation: 32-24=8, Resulting Numbers: [4, 1, 8] Generated Node #0,1: 65:[4, 1, 8] Operation: 32-24=8 Exploring Operation: 24+32=56, Resulting Numbers: [4, 1, 56] Generated Node #0,2: 65:[4, 1, 56] Operation: 24+32=56 Exploring Operation: 24/4=6, Resulting Numbers: [1, 32, 6] Generated Node #0,3: 65:[1, 32, 6] Operation: 24/4=6 Moving to Node #0,1 Current State: 65:[4, 1, 8], Operations: ['32-24=8'] Exploring Operation: 4+1=5, Resulting Numbers: [8, 5] Generated Node #0,1,0: 65:[8, 5] Operation: 4+1=5 Exploring Operation: 4*1=4, Resulting Numbers: [8, 4] Generated Node #0,1,1: 65:[8, 4] Operation: 4*1=4 Exploring Operation: 4/1=4, Resulting Numbers: [8, 4] Generated Node #0,1,2: 65:[8, 4] Operation: 4/1=4 Exploring Operation: 8-1=7, Resulting Numbers: [4, 7] Generated Node #0,1,3: 65:[4, 7] Operation: 8-1=7 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 65:[8, 5], Operations: ['32-24=8', '4+1=5'] Exploring Operation: 8-5=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 8+5=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 8*5=40, Resulting Numbers: [40] 40,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 65:[4, 7], Operations: ['32-24=8', '8-1=7'] Exploring Operation: 7-4=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 4*7=28, Resulting Numbers: [28] 28,65 unequal: No Solution Exploring Operation: 4+7=11, Resulting Numbers: [11] 11,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 65:[8, 4], Operations: ['32-24=8', '4*1=4'] Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,65 unequal: No Solution Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 65:[8, 4], Operations: ['32-24=8', '4/1=4'] Exploring Operation: 8+4=12, Resulting Numbers: [12] 12,65 unequal: No Solution Exploring Operation: 8*4=32, Resulting Numbers: [32] 32,65 unequal: No Solution Exploring Operation: 8/4=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 8-4=4, Resulting Numbers: [4] 4,65 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: 65:[4, 1, 56], Operations: ['24+32=56'] Exploring Operation: 56/4=14, Resulting Numbers: [1, 14] Generated Node #0,2,0: 65:[1, 14] Operation: 56/4=14 Exploring Operation: 4+1=5, Resulting Numbers: [56, 5] Generated Node #0,2,1: 65:[56, 5] Operation: 4+1=5 Exploring Operation: 1+56=57, Resulting Numbers: [4, 57] Generated Node #0,2,2: 65:[4, 57] Operation: 1+56=57 Exploring Operation: 4+56=60, Resulting Numbers: [1, 60] Generated Node #0,2,3: 65:[1, 60] Operation: 4+56=60 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 65:[1, 14], Operations: ['24+32=56', '56/4=14'] Exploring Operation: 14/1=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 14-1=13, Resulting Numbers: [13] 13,65 unequal: No Solution Exploring Operation: 1*14=14, Resulting Numbers: [14] 14,65 unequal: No Solution Exploring Operation: 1+14=15, Resulting Numbers: [15] 15,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 65:[56, 5], Operations: ['24+32=56', '4+1=5'] Exploring Operation: 56*5=280, Resulting Numbers: [280] 280,65 unequal: No Solution Exploring Operation: 56-5=51, Resulting Numbers: [51] 51,65 unequal: No Solution Exploring Operation: 56+5=61, Resulting Numbers: [61] 61,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 65:[4, 57], Operations: ['24+32=56', '1+56=57'] Exploring Operation: 4*57=228, Resulting Numbers: [228] 228,65 unequal: No Solution Exploring Operation: 4+57=61, Resulting Numbers: [61] 61,65 unequal: No Solution Exploring Operation: 57-4=53, Resulting Numbers: [53] 53,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 65:[1, 60], Operations: ['24+32=56', '4+56=60'] Exploring Operation: 60/1=60, Resulting Numbers: [60] 60,65 unequal: No Solution Exploring Operation: 60-1=59, Resulting Numbers: [59] 59,65 unequal: No Solution Exploring Operation: 1+60=61, Resulting Numbers: [61] 61,65 unequal: No Solution Exploring Operation: 1*60=60, Resulting Numbers: [60] 60,65 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: 65:[24, 1, 8], Operations: ['32/4=8'] Exploring Operation: 24/8=3, Resulting Numbers: [1, 3] Generated Node #0,0,0: 65:[1, 3] Operation: 24/8=3 Exploring Operation: 24-8=16, Resulting Numbers: [1, 16] Generated Node #0,0,1: 65:[1, 16] Operation: 24-8=16 Exploring Operation: 8-1=7, Resulting Numbers: [24, 7] Generated Node #0,0,2: 65:[24, 7] Operation: 8-1=7 Exploring Operation: 24-1=23, Resulting Numbers: [8, 23] Generated Node #0,0,3: 65:[8, 23] Operation: 24-1=23 Moving to Node #0,3 Current State: 65:[1, 32, 6], Operations: ['24/4=6'] Exploring Operation: 32-6=26, Resulting Numbers: [1, 26] Generated Node #0,3,0: 65:[1, 26] Operation: 32-6=26 Exploring Operation: 32-1=31, Resulting Numbers: [6, 31] Generated Node #0,3,1: 65:[6, 31] Operation: 32-1=31 Exploring Operation: 1*32=32, Resulting Numbers: [6, 32] Generated Node #0,3,2: 65:[6, 32] Operation: 1*32=32 Exploring Operation: 6-1=5, Resulting Numbers: [32, 5] Generated Node #0,3,3: 65:[32, 5] Operation: 6-1=5 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 65:[1, 26], Operations: ['24/4=6', '32-6=26'] Exploring Operation: 26/1=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 26-1=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 1+26=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 1*26=26, Resulting Numbers: [26] 26,65 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 #0,3,1 Current State: 65:[6, 31], Operations: ['24/4=6', '32-1=31'] Exploring Operation: 6+31=37, Resulting Numbers: [37] 37,65 unequal: No Solution Exploring Operation: 31-6=25, Resulting Numbers: [25] 25,65 unequal: No Solution Exploring Operation: 6*31=186, Resulting Numbers: [186] 186,65 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 #0,3,3 Current State: 65:[32, 5], Operations: ['24/4=6', '6-1=5'] Exploring Operation: 32*5=160, Resulting Numbers: [160] 160,65 unequal: No Solution Exploring Operation: 32-5=27, Resulting Numbers: [27] 27,65 unequal: No Solution Exploring Operation: 32+5=37, Resulting Numbers: [37] 37,65 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 #0,3,2 Current State: 65:[6, 32], Operations: ['24/4=6', '1*32=32'] Exploring Operation: 32-6=26, Resulting Numbers: [26] 26,65 unequal: No Solution Exploring Operation: 6+32=38, Resulting Numbers: [38] 38,65 unequal: No Solution Exploring Operation: 6*32=192, Resulting Numbers: [192] 192,65 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,0 Current State: 65:[1, 3], Operations: ['32/4=8', '24/8=3'] Exploring Operation: 3/1=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 3-1=2, Resulting Numbers: [2] 2,65 unequal: No Solution Exploring Operation: 1*3=3, Resulting Numbers: [3] 3,65 unequal: No Solution Exploring Operation: 1+3=4, Resulting Numbers: [4] 4,65 unequal: No Solution Moving to Node #0,0,1 Current State: 65:[1, 16], Operations: ['32/4=8', '24-8=16'] Exploring Operation: 16/1=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 16-1=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 1*16=16, Resulting Numbers: [16] 16,65 unequal: No Solution Exploring Operation: 1+16=17, Resulting Numbers: [17] 17,65 unequal: No Solution Moving to Node #0,0,3 Current State: 65:[8, 23], Operations: ['32/4=8', '24-1=23'] Exploring Operation: 8+23=31, Resulting Numbers: [31] 31,65 unequal: No Solution Exploring Operation: 23-8=15, Resulting Numbers: [15] 15,65 unequal: No Solution Exploring Operation: 8*23=184, Resulting Numbers: [184] 184,65 unequal: No Solution Moving to Node #0,0,2 Current State: 65:[24, 7], Operations: ['32/4=8', '8-1=7'] Exploring Operation: 24+7=31, Resulting Numbers: [31] 31,65 unequal: No Solution Exploring Operation: 24*7=168, Resulting Numbers: [168] 168,65 unequal: No Solution Exploring Operation: 24-7=17, Resulting Numbers: [17] 17,65 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 19, 31, 75, 20 ]
30
[ "19+31=50", "75*20=1500", "1500/50=30" ]
Current State: 30:[19, 31, 75, 20], Operations: [] Exploring Operation: 19+31=50, Resulting Numbers: [75, 20, 50] Generated Node #2: [75, 20, 50] from Operation: 19+31=50 Current State: 30:[75, 20, 50], Operations: ['19+31=50'] Exploring Operation: 75*20=1500, Resulting Numbers: [50, 1500] Generated Node #3: [50, 1500] from Operation: 75*20=1500 Current State: 30:[50, 1500], Operations: ['19+31=50', '75*20=1500'] Exploring Operation: 1500/50=30, Resulting Numbers: [30] 30,30 equal: Goal Reached
4
Current State: 30:[19, 31, 75, 20], Operations: [] Exploring Operation: 75-20=55, Resulting Numbers: [19, 31, 55] Generated Node #0,0: 30:[19, 31, 55] Operation: 75-20=55 Exploring Operation: 75-19=56, Resulting Numbers: [31, 20, 56] Generated Node #0,1: 30:[31, 20, 56] Operation: 75-19=56 Exploring Operation: 75-31=44, Resulting Numbers: [19, 20, 44] Generated Node #0,2: 30:[19, 20, 44] Operation: 75-31=44 Exploring Operation: 20-19=1, Resulting Numbers: [31, 75, 1] Generated Node #0,3: 30:[31, 75, 1] Operation: 20-19=1 Moving to Node #0,2 Current State: 30:[19, 20, 44], Operations: ['75-31=44'] Exploring Operation: 44-20=24, Resulting Numbers: [19, 24] Generated Node #0,2,0: 30:[19, 24] Operation: 44-20=24 Exploring Operation: 44-19=25, Resulting Numbers: [20, 25] Generated Node #0,2,1: 30:[20, 25] Operation: 44-19=25 Exploring Operation: 20-19=1, Resulting Numbers: [44, 1] Generated Node #0,2,2: 30:[44, 1] Operation: 20-19=1 Exploring Operation: 19+20=39, Resulting Numbers: [44, 39] Generated Node #0,2,3: 30:[44, 39] Operation: 19+20=39 Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 30:[19, 24], Operations: ['75-31=44', '44-20=24'] Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,30 unequal: No Solution Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 30:[20, 25], Operations: ['75-31=44', '44-19=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 30:[44, 1], Operations: ['75-31=44', '20-19=1'] Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,30 unequal: No Solution Exploring Operation: 44+1=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 44*1=44, Resulting Numbers: [44] 44,30 unequal: No Solution Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 30:[44, 39], Operations: ['75-31=44', '19+20=39'] Exploring Operation: 44*39=1716, Resulting Numbers: [1716] 1716,30 unequal: No Solution Exploring Operation: 44-39=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 44+39=83, Resulting Numbers: [83] 83,30 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: 30:[19, 31, 55], Operations: ['75-20=55'] Exploring Operation: 55-31=24, Resulting Numbers: [19, 24] Generated Node #0,0,0: 30:[19, 24] Operation: 55-31=24 Exploring Operation: 19+31=50, Resulting Numbers: [55, 50] Generated Node #0,0,1: 30:[55, 50] Operation: 19+31=50 Exploring Operation: 31-19=12, Resulting Numbers: [55, 12] Generated Node #0,0,2: 30:[55, 12] Operation: 31-19=12 Exploring Operation: 55-19=36, Resulting Numbers: [31, 36] Generated Node #0,0,3: 30:[31, 36] Operation: 55-19=36 Moving to Node #0,1 Current State: 30:[31, 20, 56], Operations: ['75-19=56'] Exploring Operation: 31-20=11, Resulting Numbers: [56, 11] Generated Node #0,1,0: 30:[56, 11] Operation: 31-20=11 Exploring Operation: 31+20=51, Resulting Numbers: [56, 51] Generated Node #0,1,1: 30:[56, 51] Operation: 31+20=51 Exploring Operation: 56-31=25, Resulting Numbers: [20, 25] Generated Node #0,1,2: 30:[20, 25] Operation: 56-31=25 Exploring Operation: 56-20=36, Resulting Numbers: [31, 36] Generated Node #0,1,3: 30:[31, 36] Operation: 56-20=36 Start Sub Search at level 1: Moving to Node #0,1,3 Current State: 30:[31, 36], Operations: ['75-19=56', '56-20=36'] Exploring Operation: 31+36=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 31*36=1116, Resulting Numbers: [1116] 1116,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 30:[20, 25], Operations: ['75-19=56', '56-31=25'] Exploring Operation: 20+25=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 25-20=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 20*25=500, Resulting Numbers: [500] 500,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 30:[56, 11], Operations: ['75-19=56', '31-20=11'] Exploring Operation: 56-11=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 56+11=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 56*11=616, Resulting Numbers: [616] 616,30 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 30:[56, 51], Operations: ['75-19=56', '31+20=51'] Exploring Operation: 56+51=107, Resulting Numbers: [107] 107,30 unequal: No Solution Exploring Operation: 56-51=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 56*51=2856, Resulting Numbers: [2856] 2856,30 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: 30:[31, 75, 1], Operations: ['20-19=1'] Exploring Operation: 31*1=31, Resulting Numbers: [75, 31] Generated Node #0,3,0: 30:[75, 31] Operation: 31*1=31 Exploring Operation: 31-1=30, Resulting Numbers: [75, 30] Generated Node #0,3,1: 30:[75, 30] Operation: 31-1=30 Exploring Operation: 75-1=74, Resulting Numbers: [31, 74] Generated Node #0,3,2: 30:[31, 74] Operation: 75-1=74 Exploring Operation: 75-31=44, Resulting Numbers: [1, 44] Generated Node #0,3,3: 30:[1, 44] Operation: 75-31=44 Moving to Node #0,0,3 Current State: 30:[31, 36], Operations: ['75-20=55', '55-19=36'] Exploring Operation: 31+36=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 36-31=5, Resulting Numbers: [5] 5,30 unequal: No Solution Exploring Operation: 31*36=1116, Resulting Numbers: [1116] 1116,30 unequal: No Solution Moving to Node #0,0,0 Current State: 30:[19, 24], Operations: ['75-20=55', '55-31=24'] Exploring Operation: 19*24=456, Resulting Numbers: [456] 456,30 unequal: No Solution Exploring Operation: 19+24=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 24-19=5, Resulting Numbers: [5] 5,30 unequal: No Solution Moving to Node #0,3,3 Current State: 30:[1, 44], Operations: ['20-19=1', '75-31=44'] Exploring Operation: 44-1=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 1*44=44, Resulting Numbers: [44] 44,30 unequal: No Solution Exploring Operation: 1+44=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 44/1=44, Resulting Numbers: [44] 44,30 unequal: No Solution Moving to Node #0,0,2 Current State: 30:[55, 12], Operations: ['75-20=55', '31-19=12'] Exploring Operation: 55+12=67, Resulting Numbers: [67] 67,30 unequal: No Solution Exploring Operation: 55-12=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 55*12=660, Resulting Numbers: [660] 660,30 unequal: No Solution Moving to Node #0,3,1 Current State: 30:[75, 30], Operations: ['20-19=1', '31-1=30'] Exploring Operation: 75-30=45, Resulting Numbers: [45] 45,30 unequal: No Solution Exploring Operation: 75*30=2250, Resulting Numbers: [2250] 2250,30 unequal: No Solution Exploring Operation: 75+30=105, Resulting Numbers: [105] 105,30 unequal: No Solution Moving to Node #0,0,1 Current State: 30:[55, 50], Operations: ['75-20=55', '19+31=50'] Exploring Operation: 55*50=2750, Resulting Numbers: [2750] 2750,30 unequal: No Solution Exploring Operation: 55+50=105, Resulting Numbers: [105] 105,30 unequal: No Solution Exploring Operation: 55-50=5, Resulting Numbers: [5] 5,30 unequal: No Solution Moving to Node #0,3,2 Current State: 30:[31, 74], Operations: ['20-19=1', '75-1=74'] Exploring Operation: 31*74=2294, Resulting Numbers: [2294] 2294,30 unequal: No Solution Exploring Operation: 74-31=43, Resulting Numbers: [43] 43,30 unequal: No Solution Exploring Operation: 31+74=105, Resulting Numbers: [105] 105,30 unequal: No Solution Moving to Node #0,3,0 Current State: 30:[75, 31], Operations: ['20-19=1', '31*1=31'] Exploring Operation: 75+31=106, Resulting Numbers: [106] 106,30 unequal: No Solution Exploring Operation: 75*31=2325, Resulting Numbers: [2325] 2325,30 unequal: No Solution Exploring Operation: 75-31=44, Resulting Numbers: [44] 44,30 unequal: No Solution No solution found.
0
hs_4
sum_heuristic
[ 20, 81, 45, 54 ]
23
[ "81+54=135", "135/45=3", "20+3=23" ]
Current State: 23:[20, 81, 45, 54], Operations: [] Exploring Operation: 81+54=135, Resulting Numbers: [20, 45, 135] Generated Node #2: [20, 45, 135] from Operation: 81+54=135 Current State: 23:[20, 45, 135], Operations: ['81+54=135'] Exploring Operation: 135/45=3, Resulting Numbers: [20, 3] Generated Node #3: [20, 3] from Operation: 135/45=3 Current State: 23:[20, 3], Operations: ['81+54=135', '135/45=3'] Exploring Operation: 20+3=23, Resulting Numbers: [23] 23,23 equal: Goal Reached
4
Current State: 23:[20, 81, 45, 54], Operations: [] Exploring Operation: 81-54=27, Resulting Numbers: [20, 45, 27] Generated Node #0,0: 23:[20, 45, 27] Operation: 81-54=27 Start Sub Search at level 1: Moving to Node #0,0 Current State: 23:[20, 45, 27], Operations: ['81-54=27'] Exploring Operation: 45-20=25, Resulting Numbers: [27, 25] Generated Node #0,0,0: 23:[27, 25] Operation: 45-20=25 Moving to Node #0,0,0 Current State: 23:[27, 25], Operations: ['81-54=27', '45-20=25'] Exploring Operation: 27-25=2, Resulting Numbers: [2] 2,23 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search No solution found.
0
hs_1
sum_heuristic
[ 35, 41, 57, 52 ]
39
[ "35+41=76", "57*52=2964", "2964/76=39" ]
Current State: 39:[35, 41, 57, 52], Operations: [] Exploring Operation: 35+41=76, Resulting Numbers: [57, 52, 76] Generated Node #2: [57, 52, 76] from Operation: 35+41=76 Current State: 39:[57, 52, 76], Operations: ['35+41=76'] Exploring Operation: 57*52=2964, Resulting Numbers: [76, 2964] Generated Node #3: [76, 2964] from Operation: 57*52=2964 Current State: 39:[76, 2964], Operations: ['35+41=76', '57*52=2964'] Exploring Operation: 2964/76=39, Resulting Numbers: [39] 39,39 equal: Goal Reached
4
Current State: 39:[35, 41, 57, 52], Operations: [] Exploring Operation: 52-41=11, Resulting Numbers: [35, 57, 11] Generated Node #0,0: 39:[35, 57, 11] Operation: 52-41=11 Exploring Operation: 57-41=16, Resulting Numbers: [35, 52, 16] Generated Node #0,1: 39:[35, 52, 16] Operation: 57-41=16 Exploring Operation: 57-52=5, Resulting Numbers: [35, 41, 5] Generated Node #0,2: 39:[35, 41, 5] Operation: 57-52=5 Exploring Operation: 57-35=22, Resulting Numbers: [41, 52, 22] Generated Node #0,3: 39:[41, 52, 22] Operation: 57-35=22 Exploring Operation: 52-35=17, Resulting Numbers: [41, 57, 17] Generated Node #0,4: 39:[41, 57, 17] Operation: 52-35=17 Moving to Node #0,2 Current State: 39:[35, 41, 5], Operations: ['57-52=5'] Exploring Operation: 35-5=30, Resulting Numbers: [41, 30] Generated Node #0,2,0: 39:[41, 30] Operation: 35-5=30 Exploring Operation: 41-5=36, Resulting Numbers: [35, 36] Generated Node #0,2,1: 39:[35, 36] Operation: 41-5=36 Exploring Operation: 41-35=6, Resulting Numbers: [5, 6] Generated Node #0,2,2: 39:[5, 6] Operation: 41-35=6 Exploring Operation: 35/5=7, Resulting Numbers: [41, 7] Generated Node #0,2,3: 39:[41, 7] Operation: 35/5=7 Exploring Operation: 35+5=40, Resulting Numbers: [41, 40] Generated Node #0,2,4: 39:[41, 40] Operation: 35+5=40 Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 39:[41, 40], Operations: ['57-52=5', '35+5=40'] Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 39:[5, 6], Operations: ['57-52=5', '41-35=6'] Exploring Operation: 5+6=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 5*6=30, Resulting Numbers: [30] 30,39 unequal: No Solution Exploring Operation: 6-5=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 39:[41, 7], Operations: ['57-52=5', '35/5=7'] Exploring Operation: 41-7=34, Resulting Numbers: [34] 34,39 unequal: No Solution Exploring Operation: 41+7=48, Resulting Numbers: [48] 48,39 unequal: No Solution Exploring Operation: 41*7=287, Resulting Numbers: [287] 287,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 39:[35, 36], Operations: ['57-52=5', '41-5=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,39 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 39:[41, 30], Operations: ['57-52=5', '35-5=30'] Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,39 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: 39:[35, 52, 16], Operations: ['57-41=16'] Exploring Operation: 35+16=51, Resulting Numbers: [52, 51] Generated Node #0,1,0: 39:[52, 51] Operation: 35+16=51 Exploring Operation: 52+16=68, Resulting Numbers: [35, 68] Generated Node #0,1,1: 39:[35, 68] Operation: 52+16=68 Exploring Operation: 35-16=19, Resulting Numbers: [52, 19] Generated Node #0,1,2: 39:[52, 19] Operation: 35-16=19 Exploring Operation: 52-35=17, Resulting Numbers: [16, 17] Generated Node #0,1,3: 39:[16, 17] Operation: 52-35=17 Exploring Operation: 52-16=36, Resulting Numbers: [35, 36] Generated Node #0,1,4: 39:[35, 36] Operation: 52-16=36 Moving to Node #0,0 Current State: 39:[35, 57, 11], Operations: ['52-41=11'] Exploring Operation: 57-35=22, Resulting Numbers: [11, 22] Generated Node #0,0,0: 39:[11, 22] Operation: 57-35=22 Exploring Operation: 57-11=46, Resulting Numbers: [35, 46] Generated Node #0,0,1: 39:[35, 46] Operation: 57-11=46 Exploring Operation: 57+11=68, Resulting Numbers: [35, 68] Generated Node #0,0,2: 39:[35, 68] Operation: 57+11=68 Exploring Operation: 35-11=24, Resulting Numbers: [57, 24] Generated Node #0,0,3: 39:[57, 24] Operation: 35-11=24 Exploring Operation: 35+11=46, Resulting Numbers: [57, 46] Generated Node #0,0,4: 39:[57, 46] Operation: 35+11=46 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 39:[11, 22], Operations: ['52-41=11', '57-35=22'] Exploring Operation: 11*22=242, Resulting Numbers: [242] 242,39 unequal: No Solution Exploring Operation: 11+22=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 39:[35, 46], Operations: ['52-41=11', '57-11=46'] Exploring Operation: 46-35=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 35+46=81, Resulting Numbers: [81] 81,39 unequal: No Solution Exploring Operation: 35*46=1610, Resulting Numbers: [1610] 1610,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,4 Current State: 39:[57, 46], Operations: ['52-41=11', '35+11=46'] Exploring Operation: 57*46=2622, Resulting Numbers: [2622] 2622,39 unequal: No Solution Exploring Operation: 57+46=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 57-46=11, Resulting Numbers: [11] 11,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,3 Current State: 39:[57, 24], Operations: ['52-41=11', '35-11=24'] Exploring Operation: 57*24=1368, Resulting Numbers: [1368] 1368,39 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,2 Current State: 39:[35, 68], Operations: ['52-41=11', '57+11=68'] Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 35*68=2380, Resulting Numbers: [2380] 2380,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,3 Current State: 39:[41, 52, 22], Operations: ['57-35=22'] Exploring Operation: 52-41=11, Resulting Numbers: [22, 11] Generated Node #0,3,0: 39:[22, 11] Operation: 52-41=11 Exploring Operation: 41+22=63, Resulting Numbers: [52, 63] Generated Node #0,3,1: 39:[52, 63] Operation: 41+22=63 Exploring Operation: 41-22=19, Resulting Numbers: [52, 19] Generated Node #0,3,2: 39:[52, 19] Operation: 41-22=19 Exploring Operation: 52-22=30, Resulting Numbers: [41, 30] Generated Node #0,3,3: 39:[41, 30] Operation: 52-22=30 Exploring Operation: 52+22=74, Resulting Numbers: [41, 74] Generated Node #0,3,4: 39:[41, 74] Operation: 52+22=74 Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 39:[22, 11], Operations: ['57-35=22', '52-41=11'] Exploring Operation: 22/11=2, Resulting Numbers: [2] 2,39 unequal: No Solution Exploring Operation: 22-11=11, Resulting Numbers: [11] 11,39 unequal: No Solution Exploring Operation: 22*11=242, Resulting Numbers: [242] 242,39 unequal: No Solution Exploring Operation: 22+11=33, Resulting Numbers: [33] 33,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 39:[41, 30], Operations: ['57-35=22', '52-22=30'] Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,39 unequal: No Solution Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 39:[52, 19], Operations: ['57-35=22', '41-22=19'] Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,39 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 39:[52, 63], Operations: ['57-35=22', '41+22=63'] Exploring Operation: 52*63=3276, Resulting Numbers: [3276] 3276,39 unequal: No Solution Exploring Operation: 52+63=115, Resulting Numbers: [115] 115,39 unequal: No Solution Exploring Operation: 63-52=11, Resulting Numbers: [11] 11,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 39:[41, 74], Operations: ['57-35=22', '52+22=74'] Exploring Operation: 41+74=115, Resulting Numbers: [115] 115,39 unequal: No Solution Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 41*74=3034, Resulting Numbers: [3034] 3034,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,4 Current State: 39:[41, 57, 17], Operations: ['52-35=17'] Exploring Operation: 57+17=74, Resulting Numbers: [41, 74] Generated Node #0,4,0: 39:[41, 74] Operation: 57+17=74 Exploring Operation: 41-17=24, Resulting Numbers: [57, 24] Generated Node #0,4,1: 39:[57, 24] Operation: 41-17=24 Exploring Operation: 57-41=16, Resulting Numbers: [17, 16] Generated Node #0,4,2: 39:[17, 16] Operation: 57-41=16 Exploring Operation: 41+17=58, Resulting Numbers: [57, 58] Generated Node #0,4,3: 39:[57, 58] Operation: 41+17=58 Exploring Operation: 57-17=40, Resulting Numbers: [41, 40] Generated Node #0,4,4: 39:[41, 40] Operation: 57-17=40 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 39:[41, 40], Operations: ['52-35=17', '57-17=40'] Exploring Operation: 41*40=1640, Resulting Numbers: [1640] 1640,39 unequal: No Solution Exploring Operation: 41-40=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 41+40=81, Resulting Numbers: [81] 81,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 39:[17, 16], Operations: ['52-35=17', '57-41=16'] Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 17+16=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 17*16=272, Resulting Numbers: [272] 272,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 39:[57, 24], Operations: ['52-35=17', '41-17=24'] Exploring Operation: 57*24=1368, Resulting Numbers: [1368] 1368,39 unequal: No Solution Exploring Operation: 57-24=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 57+24=81, Resulting Numbers: [81] 81,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 39:[41, 74], Operations: ['52-35=17', '57+17=74'] Exploring Operation: 74-41=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 41*74=3034, Resulting Numbers: [3034] 3034,39 unequal: No Solution Exploring Operation: 41+74=115, Resulting Numbers: [115] 115,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 39:[57, 58], Operations: ['52-35=17', '41+17=58'] Exploring Operation: 58-57=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 57*58=3306, Resulting Numbers: [3306] 3306,39 unequal: No Solution Exploring Operation: 57+58=115, Resulting Numbers: [115] 115,39 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1,3 Current State: 39:[16, 17], Operations: ['57-41=16', '52-35=17'] Exploring Operation: 16+17=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 16*17=272, Resulting Numbers: [272] 272,39 unequal: No Solution Exploring Operation: 17-16=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,1,4 Current State: 39:[35, 36], Operations: ['57-41=16', '52-16=36'] Exploring Operation: 35+36=71, Resulting Numbers: [71] 71,39 unequal: No Solution Exploring Operation: 36-35=1, Resulting Numbers: [1] 1,39 unequal: No Solution Exploring Operation: 35*36=1260, Resulting Numbers: [1260] 1260,39 unequal: No Solution Moving to Node #0,1,2 Current State: 39:[52, 19], Operations: ['57-41=16', '35-16=19'] Exploring Operation: 52*19=988, Resulting Numbers: [988] 988,39 unequal: No Solution Exploring Operation: 52-19=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 52+19=71, Resulting Numbers: [71] 71,39 unequal: No Solution Moving to Node #0,1,0 Current State: 39:[52, 51], Operations: ['57-41=16', '35+16=51'] Exploring Operation: 52*51=2652, Resulting Numbers: [2652] 2652,39 unequal: No Solution Exploring Operation: 52+51=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 52-51=1, Resulting Numbers: [1] 1,39 unequal: No Solution Moving to Node #0,1,1 Current State: 39:[35, 68], Operations: ['57-41=16', '52+16=68'] Exploring Operation: 35+68=103, Resulting Numbers: [103] 103,39 unequal: No Solution Exploring Operation: 68-35=33, Resulting Numbers: [33] 33,39 unequal: No Solution Exploring Operation: 35*68=2380, Resulting Numbers: [2380] 2380,39 unequal: No Solution No solution found.
0
hs_5
sum_heuristic
[ 58, 56, 2, 73 ]
86
[ "73-58=15", "2*15=30", "56+30=86" ]
Current State: 86:[58, 56, 2, 73], Operations: [] Exploring Operation: 73-58=15, Resulting Numbers: [56, 2, 15] Generated Node #2: [56, 2, 15] from Operation: 73-58=15 Current State: 86:[56, 2, 15], Operations: ['73-58=15'] Exploring Operation: 2*15=30, Resulting Numbers: [56, 30] Generated Node #3: [56, 30] from Operation: 2*15=30 Current State: 86:[56, 30], Operations: ['73-58=15', '2*15=30'] Exploring Operation: 56+30=86, Resulting Numbers: [86] 86,86 equal: Goal Reached
4
Current State: 86:[58, 56, 2, 73], Operations: [] Exploring Operation: 73-58=15, Resulting Numbers: [56, 2, 15] Generated Node #0,0: 86:[56, 2, 15] Operation: 73-58=15 Exploring Operation: 58-56=2, Resulting Numbers: [2, 73, 2] Generated Node #0,1: 86:[2, 73, 2] Operation: 58-56=2 Moving to Node #0,1 Current State: 86:[2, 73, 2], Operations: ['58-56=2'] Exploring Operation: 73+2=75, Resulting Numbers: [2, 75] Generated Node #0,1,0: 86:[2, 75] Operation: 73+2=75 Exploring Operation: 2+73=75, Resulting Numbers: [2, 75] Generated Node #0,1,1: 86:[2, 75] Operation: 2+73=75 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 86:[2, 75], Operations: ['58-56=2', '73+2=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,86 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,86 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 86:[2, 75], Operations: ['58-56=2', '2+73=75'] Exploring Operation: 75-2=73, Resulting Numbers: [73] 73,86 unequal: No Solution Exploring Operation: 2+75=77, Resulting Numbers: [77] 77,86 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: 86:[56, 2, 15], Operations: ['73-58=15'] Exploring Operation: 56+15=71, Resulting Numbers: [2, 71] Generated Node #0,0,0: 86:[2, 71] Operation: 56+15=71 Exploring Operation: 56-15=41, Resulting Numbers: [2, 41] Generated Node #0,0,1: 86:[2, 41] Operation: 56-15=41 Moving to Node #0,0,1 Current State: 86:[2, 41], Operations: ['73-58=15', '56-15=41'] Exploring Operation: 2*41=82, Resulting Numbers: [82] 82,86 unequal: No Solution Exploring Operation: 2+41=43, Resulting Numbers: [43] 43,86 unequal: No Solution Moving to Node #0,0,0 Current State: 86:[2, 71], Operations: ['73-58=15', '56+15=71'] Exploring Operation: 2+71=73, Resulting Numbers: [73] 73,86 unequal: No Solution Exploring Operation: 71-2=69, Resulting Numbers: [69] 69,86 unequal: No Solution No solution found.
0
hs_2
sum_heuristic
[ 28, 47, 54, 23 ]
35
[ "28-23=5", "54-47=7", "5*7=35" ]
Current State: 35:[28, 47, 54, 23], Operations: [] Exploring Operation: 28-23=5, Resulting Numbers: [47, 54, 5] Generated Node #2: [47, 54, 5] from Operation: 28-23=5 Current State: 35:[47, 54, 5], Operations: ['28-23=5'] Exploring Operation: 54-47=7, Resulting Numbers: [5, 7] Generated Node #3: [5, 7] from Operation: 54-47=7 Current State: 35:[5, 7], Operations: ['28-23=5', '54-47=7'] Exploring Operation: 5*7=35, Resulting Numbers: [35] 35,35 equal: Goal Reached
4
Current State: 35:[28, 47, 54, 23], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [28, 23, 7] Generated Node #0,0: 35:[28, 23, 7] Operation: 54-47=7 Moving to Node #0,0 Current State: 35:[28, 23, 7], Operations: ['54-47=7'] Exploring Operation: 28-23=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 28-23=5 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['54-47=7', '28-23=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Moving to Node #0 Current State: 35:[28, 47, 54, 23], Operations: [] Exploring Operation: 54-47=7, Resulting Numbers: [28, 23, 7] Generated Node #0,0: 35:[28, 23, 7] Operation: 54-47=7 Moving to Node #0,0 Current State: 35:[28, 23, 7], Operations: ['54-47=7'] Exploring Operation: 28-23=5, Resulting Numbers: [7, 5] Generated Node #0,0,0: 35:[7, 5] Operation: 28-23=5 Moving to Node #0,0,0 Current State: 35:[7, 5], Operations: ['54-47=7', '28-23=5'] Exploring Operation: 7*5=35, Resulting Numbers: [35] 35,35 equal: Goal Reached Exit Sub Search at level 1
0.993924
hs_1
mult_heuristic
[ 71, 13, 88, 41 ]
37
[ "71+13=84", "88-41=47", "84-47=37" ]
Current State: 37:[71, 13, 88, 41], Operations: [] Exploring Operation: 71+13=84, Resulting Numbers: [88, 41, 84] Generated Node #2: [88, 41, 84] from Operation: 71+13=84 Current State: 37:[88, 41, 84], Operations: ['71+13=84'] Exploring Operation: 88-41=47, Resulting Numbers: [84, 47] Generated Node #3: [84, 47] from Operation: 88-41=47 Current State: 37:[84, 47], Operations: ['71+13=84', '88-41=47'] Exploring Operation: 84-47=37, Resulting Numbers: [37] 37,37 equal: Goal Reached
4
Current State: 37:[71, 13, 88, 41], Operations: [] Exploring Operation: 71-13=58, Resulting Numbers: [88, 41, 58] Generated Node #0,0: 37:[88, 41, 58] Operation: 71-13=58 Exploring Operation: 88-13=75, Resulting Numbers: [71, 41, 75] Generated Node #0,1: 37:[71, 41, 75] Operation: 88-13=75 Exploring Operation: 88-41=47, Resulting Numbers: [71, 13, 47] Generated Node #0,2: 37:[71, 13, 47] Operation: 88-41=47 Exploring Operation: 88-71=17, Resulting Numbers: [13, 41, 17] Generated Node #0,3: 37:[13, 41, 17] Operation: 88-71=17 Exploring Operation: 71-41=30, Resulting Numbers: [13, 88, 30] Generated Node #0,4: 37:[13, 88, 30] Operation: 71-41=30 Start Sub Search at level 1: Moving to Node #0,3 Current State: 37:[13, 41, 17], Operations: ['88-71=17'] Exploring Operation: 41-17=24, Resulting Numbers: [13, 24] Generated Node #0,3,0: 37:[13, 24] Operation: 41-17=24 Exploring Operation: 13+41=54, Resulting Numbers: [17, 54] Generated Node #0,3,1: 37:[17, 54] Operation: 13+41=54 Exploring Operation: 13+17=30, Resulting Numbers: [41, 30] Generated Node #0,3,2: 37:[41, 30] Operation: 13+17=30 Exploring Operation: 17-13=4, Resulting Numbers: [41, 4] Generated Node #0,3,3: 37:[41, 4] Operation: 17-13=4 Exploring Operation: 41-13=28, Resulting Numbers: [17, 28] Generated Node #0,3,4: 37:[17, 28] Operation: 41-13=28 Moving to Node #0,3,2 Current State: 37:[41, 30], Operations: ['88-71=17', '13+17=30'] Exploring Operation: 41*30=1230, Resulting Numbers: [1230] 1230,37 unequal: No Solution Exploring Operation: 41-30=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 41+30=71, Resulting Numbers: [71] 71,37 unequal: No Solution Moving to Node #0,3,4 Current State: 37:[17, 28], Operations: ['88-71=17', '41-13=28'] Exploring Operation: 17*28=476, Resulting Numbers: [476] 476,37 unequal: No Solution Exploring Operation: 17+28=45, Resulting Numbers: [45] 45,37 unequal: No Solution Exploring Operation: 28-17=11, Resulting Numbers: [11] 11,37 unequal: No Solution Moving to Node #0,3,0 Current State: 37:[13, 24], Operations: ['88-71=17', '41-17=24'] Exploring Operation: 24-13=11, Resulting Numbers: [11] 11,37 unequal: No Solution Exploring Operation: 13*24=312, Resulting Numbers: [312] 312,37 unequal: No Solution Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Moving to Node #0 Current State: 37:[71, 13, 88, 41], Operations: [] Exploring Operation: 88-71=17, Resulting Numbers: [13, 41, 17] Generated Node #0,3: 37:[13, 41, 17] Operation: 88-71=17 Moving to Node #0,3 Current State: 37:[13, 41, 17], Operations: ['88-71=17'] Exploring Operation: 41-17=24, Resulting Numbers: [13, 24] Generated Node #0,3,0: 37:[13, 24] Operation: 41-17=24 Moving to Node #0,3,0 Current State: 37:[13, 24], Operations: ['88-71=17', '41-17=24'] Exploring Operation: 13+24=37, Resulting Numbers: [37] 37,37 equal: Goal Reached Exit Sub Search at level 1
0.980035
hs_5
sum_heuristic
[ 50, 25, 28, 78 ]
31
[ "50+25=75", "28+78=106", "106-75=31" ]
Current State: 31:[50, 25, 28, 78], Operations: [] Exploring Operation: 50+25=75, Resulting Numbers: [28, 78, 75] Generated Node #2: [28, 78, 75] from Operation: 50+25=75 Current State: 31:[28, 78, 75], Operations: ['50+25=75'] Exploring Operation: 28+78=106, Resulting Numbers: [75, 106] Generated Node #3: [75, 106] from Operation: 28+78=106 Current State: 31:[75, 106], Operations: ['50+25=75', '28+78=106'] Exploring Operation: 106-75=31, Resulting Numbers: [31] 31,31 equal: Goal Reached
4
Current State: 31:[50, 25, 28, 78], Operations: [] Exploring Operation: 78-50=28, Resulting Numbers: [25, 28, 28] Generated Node #0,0: 31:[25, 28, 28] Operation: 78-50=28 Moving to Node #0,0 Current State: 31:[25, 28, 28], Operations: ['78-50=28'] Exploring Operation: 25+28=53, Resulting Numbers: [28, 53] Generated Node #0,0,0: 31:[28, 53] Operation: 25+28=53 Moving to Node #0,0,0 Current State: 31:[28, 53], Operations: ['78-50=28', '25+28=53'] Exploring Operation: 53-28=25, Resulting Numbers: [25] 25,31 unequal: No Solution No solution found.
0
hs_1
mult_heuristic
[ 38, 84, 75, 4 ]
58
[ "75-38=37", "84/4=21", "37+21=58" ]
Current State: 58:[38, 84, 75, 4], Operations: [] Exploring Operation: 75-38=37, Resulting Numbers: [84, 4, 37] Generated Node #2: [84, 4, 37] from Operation: 75-38=37 Current State: 58:[84, 4, 37], Operations: ['75-38=37'] Exploring Operation: 84/4=21, Resulting Numbers: [37, 21] Generated Node #3: [37, 21] from Operation: 84/4=21 Current State: 58:[37, 21], Operations: ['75-38=37', '84/4=21'] Exploring Operation: 37+21=58, Resulting Numbers: [58] 58,58 equal: Goal Reached
4
Current State: 58:[38, 84, 75, 4], Operations: [] Exploring Operation: 84-38=46, Resulting Numbers: [75, 4, 46] Generated Node #0,0: 58:[75, 4, 46] Operation: 84-38=46 Exploring Operation: 38-4=34, Resulting Numbers: [84, 75, 34] Generated Node #0,1: 58:[84, 75, 34] Operation: 38-4=34 Exploring Operation: 84-75=9, Resulting Numbers: [38, 4, 9] Generated Node #0,2: 58:[38, 4, 9] Operation: 84-75=9 Exploring Operation: 84/4=21, Resulting Numbers: [38, 75, 21] Generated Node #0,3: 58:[38, 75, 21] Operation: 84/4=21 Exploring Operation: 75-38=37, Resulting Numbers: [84, 4, 37] Generated Node #0,4: 58:[84, 4, 37] Operation: 75-38=37 Start Sub Search at level 1: Moving to Node #0,2 Current State: 58:[38, 4, 9], Operations: ['84-75=9'] Exploring Operation: 4*9=36, Resulting Numbers: [38, 36] Generated Node #0,2,0: 58:[38, 36] Operation: 4*9=36 Exploring Operation: 38-4=34, Resulting Numbers: [9, 34] Generated Node #0,2,1: 58:[9, 34] Operation: 38-4=34 Exploring Operation: 38+9=47, Resulting Numbers: [4, 47] Generated Node #0,2,2: 58:[4, 47] Operation: 38+9=47 Exploring Operation: 38-9=29, Resulting Numbers: [4, 29] Generated Node #0,2,3: 58:[4, 29] Operation: 38-9=29 Exploring Operation: 9-4=5, Resulting Numbers: [38, 5] Generated Node #0,2,4: 58:[38, 5] Operation: 9-4=5 Moving to Node #0,2,3 Current State: 58:[4, 29], Operations: ['84-75=9', '38-9=29'] Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,58 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,58 unequal: No Solution Moving to Node #0,2,4 Current State: 58:[38, 5], Operations: ['84-75=9', '9-4=5'] Exploring Operation: 38*5=190, Resulting Numbers: [190] 190,58 unequal: No Solution Exploring Operation: 38-5=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 38+5=43, Resulting Numbers: [43] 43,58 unequal: No Solution Moving to Node #0,2,1 Current State: 58:[9, 34], Operations: ['84-75=9', '38-4=34'] Exploring Operation: 34-9=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 9*34=306, Resulting Numbers: [306] 306,58 unequal: No Solution Exploring Operation: 9+34=43, Resulting Numbers: [43] 43,58 unequal: No Solution Moving to Node #0,2,2 Current State: 58:[4, 47], Operations: ['84-75=9', '38+9=47'] Exploring Operation: 4+47=51, Resulting Numbers: [51] 51,58 unequal: No Solution Exploring Operation: 47-4=43, Resulting Numbers: [43] 43,58 unequal: No Solution Exploring Operation: 4*47=188, Resulting Numbers: [188] 188,58 unequal: No Solution Moving to Node #0,2,0 Current State: 58:[38, 36], Operations: ['84-75=9', '4*9=36'] Exploring Operation: 38+36=74, Resulting Numbers: [74] 74,58 unequal: No Solution Exploring Operation: 38*36=1368, Resulting Numbers: [1368] 1368,58 unequal: No Solution Exploring Operation: 38-36=2, Resulting Numbers: [2] 2,58 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 Current State: 58:[75, 4, 46], Operations: ['84-38=46'] Exploring Operation: 4+46=50, Resulting Numbers: [75, 50] Generated Node #0,0,0: 58:[75, 50] Operation: 4+46=50 Exploring Operation: 75-4=71, Resulting Numbers: [46, 71] Generated Node #0,0,1: 58:[46, 71] Operation: 75-4=71 Exploring Operation: 75-46=29, Resulting Numbers: [4, 29] Generated Node #0,0,2: 58:[4, 29] Operation: 75-46=29 Exploring Operation: 75+4=79, Resulting Numbers: [46, 79] Generated Node #0,0,3: 58:[46, 79] Operation: 75+4=79 Exploring Operation: 46-4=42, Resulting Numbers: [75, 42] Generated Node #0,0,4: 58:[75, 42] Operation: 46-4=42 Start Sub Search at level 2: Moving to Node #0,0,2 Current State: 58:[4, 29], Operations: ['84-38=46', '75-46=29'] Exploring Operation: 4*29=116, Resulting Numbers: [116] 116,58 unequal: No Solution Exploring Operation: 4+29=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 29-4=25, Resulting Numbers: [25] 25,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,0 Current State: 58:[75, 50], Operations: ['84-38=46', '4+46=50'] Exploring Operation: 75*50=3750, Resulting Numbers: [3750] 3750,58 unequal: No Solution Exploring Operation: 75-50=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 75+50=125, Resulting Numbers: [125] 125,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 58:[46, 71], Operations: ['84-38=46', '75-4=71'] Exploring Operation: 46*71=3266, Resulting Numbers: [3266] 3266,58 unequal: No Solution Exploring Operation: 71-46=25, Resulting Numbers: [25] 25,58 unequal: No Solution Exploring Operation: 46+71=117, Resulting Numbers: [117] 117,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,4 Current State: 58:[75, 42], Operations: ['84-38=46', '46-4=42'] Exploring Operation: 75*42=3150, Resulting Numbers: [3150] 3150,58 unequal: No Solution Exploring Operation: 75-42=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 75+42=117, Resulting Numbers: [117] 117,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search Start Sub Search at level 2: Moving to Node #0,0,3 Current State: 58:[46, 79], Operations: ['84-38=46', '75+4=79'] Exploring Operation: 79-46=33, Resulting Numbers: [33] 33,58 unequal: No Solution Exploring Operation: 46+79=125, Resulting Numbers: [125] 125,58 unequal: No Solution Exploring Operation: 46*79=3634, Resulting Numbers: [3634] 3634,58 unequal: No Solution No solution found. Exit Sub Search at level 2 No solution found in sub search No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3 Current State: 58:[38, 75, 21], Operations: ['84/4=21'] Exploring Operation: 75-21=54, Resulting Numbers: [38, 54] Generated Node #0,3,0: 58:[38, 54] Operation: 75-21=54 Exploring Operation: 38+21=59, Resulting Numbers: [75, 59] Generated Node #0,3,1: 58:[75, 59] Operation: 38+21=59 Exploring Operation: 75+21=96, Resulting Numbers: [38, 96] Generated Node #0,3,2: 58:[38, 96] Operation: 75+21=96 Exploring Operation: 75-38=37, Resulting Numbers: [21, 37] Generated Node #0,3,3: 58:[21, 37] Operation: 75-38=37 Exploring Operation: 38-21=17, Resulting Numbers: [75, 17] Generated Node #0,3,4: 58:[75, 17] Operation: 38-21=17 Moving to Node #0,3,0 Current State: 58:[38, 54], Operations: ['84/4=21', '75-21=54'] Exploring Operation: 38*54=2052, Resulting Numbers: [2052] 2052,58 unequal: No Solution Exploring Operation: 54-38=16, Resulting Numbers: [16] 16,58 unequal: No Solution Exploring Operation: 38+54=92, Resulting Numbers: [92] 92,58 unequal: No Solution Moving to Node #0,3,3 Current State: 58:[21, 37], Operations: ['84/4=21', '75-38=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Moving to Node #0 Current State: 58:[38, 84, 75, 4], Operations: [] Exploring Operation: 84/4=21, Resulting Numbers: [38, 75, 21] Generated Node #0,3: 58:[38, 75, 21] Operation: 84/4=21 Moving to Node #0,3 Current State: 58:[38, 75, 21], Operations: ['84/4=21'] Exploring Operation: 75-38=37, Resulting Numbers: [21, 37] Generated Node #0,3,3: 58:[21, 37] Operation: 75-38=37 Moving to Node #0,3,3 Current State: 58:[21, 37], Operations: ['84/4=21', '75-38=37'] Exploring Operation: 21+37=58, Resulting Numbers: [58] 58,58 equal: Goal Reached Exit Sub Search at level 1
0.949653
hs_5
mult_heuristic
[ 59, 32, 58, 55 ]
66
[ "59-55=4", "32/4=8", "58+8=66" ]
Current State: 66:[59, 32, 58, 55], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [32, 58, 4] Generated Node #2: [32, 58, 4] from Operation: 59-55=4 Current State: 66:[32, 58, 4], Operations: ['59-55=4'] Exploring Operation: 32/4=8, Resulting Numbers: [58, 8] Generated Node #3: [58, 8] from Operation: 32/4=8 Current State: 66:[58, 8], Operations: ['59-55=4', '32/4=8'] Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached
4
Current State: 66:[59, 32, 58, 55], Operations: [] Exploring Operation: 58-55=3, Resulting Numbers: [59, 32, 3] Generated Node #0,0: 66:[59, 32, 3] Operation: 58-55=3 Exploring Operation: 59-58=1, Resulting Numbers: [32, 55, 1] Generated Node #0,1: 66:[32, 55, 1] Operation: 59-58=1 Exploring Operation: 55-32=23, Resulting Numbers: [59, 58, 23] Generated Node #0,2: 66:[59, 58, 23] Operation: 55-32=23 Exploring Operation: 59-55=4, Resulting Numbers: [32, 58, 4] Generated Node #0,3: 66:[32, 58, 4] Operation: 59-55=4 Start Sub Search at level 1: Moving to Node #0,0 Current State: 66:[59, 32, 3], Operations: ['58-55=3'] Exploring Operation: 32+3=35, Resulting Numbers: [59, 35] Generated Node #0,0,0: 66:[59, 35] Operation: 32+3=35 Exploring Operation: 59+3=62, Resulting Numbers: [32, 62] Generated Node #0,0,1: 66:[32, 62] Operation: 59+3=62 Exploring Operation: 59-32=27, Resulting Numbers: [3, 27] Generated Node #0,0,2: 66:[3, 27] Operation: 59-32=27 Exploring Operation: 59-3=56, Resulting Numbers: [32, 56] Generated Node #0,0,3: 66:[32, 56] Operation: 59-3=56 Start Sub Search at level 2: Moving to Node #0,0,1 Current State: 66:[32, 62], Operations: ['58-55=3', '59+3=62'] Exploring Operation: 32*62=1984, Resulting Numbers: [1984] 1984,66 unequal: No Solution Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,66 unequal: No Solution Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,66 unequal: No Solution No 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: 66:[3, 27], Operations: ['58-55=3', '59-32=27'] Exploring Operation: 27/3=9, Resulting Numbers: [9] 9,66 unequal: No Solution Exploring Operation: 3+27=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 3*27=81, Resulting Numbers: [81] 81,66 unequal: No Solution Exploring Operation: 27-3=24, Resulting Numbers: [24] 24,66 unequal: No Solution No 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: 66:[59, 35], Operations: ['58-55=3', '32+3=35'] Exploring Operation: 59-35=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 59+35=94, Resulting Numbers: [94] 94,66 unequal: No Solution Exploring Operation: 59*35=2065, Resulting Numbers: [2065] 2065,66 unequal: No Solution No 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: 66:[32, 56], Operations: ['58-55=3', '59-3=56'] Exploring Operation: 32+56=88, Resulting Numbers: [88] 88,66 unequal: No Solution Exploring Operation: 56-32=24, Resulting Numbers: [24] 24,66 unequal: No Solution Exploring Operation: 32*56=1792, Resulting Numbers: [1792] 1792,66 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: 66:[32, 58, 4], Operations: ['59-55=4'] Exploring Operation: 32+4=36, Resulting Numbers: [58, 36] Generated Node #0,3,0: 66:[58, 36] Operation: 32+4=36 Exploring Operation: 58+4=62, Resulting Numbers: [32, 62] Generated Node #0,3,1: 66:[32, 62] Operation: 58+4=62 Exploring Operation: 32/4=8, Resulting Numbers: [58, 8] Generated Node #0,3,2: 66:[58, 8] Operation: 32/4=8 Exploring Operation: 58-32=26, Resulting Numbers: [4, 26] Generated Node #0,3,3: 66:[4, 26] Operation: 58-32=26 Start Sub Search at level 2: Moving to Node #0,3,1 Current State: 66:[32, 62], Operations: ['59-55=4', '58+4=62'] Exploring Operation: 62-32=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 32+62=94, Resulting Numbers: [94] 94,66 unequal: No Solution Exploring Operation: 32*62=1984, Resulting Numbers: [1984] 1984,66 unequal: No Solution No 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: 66:[4, 26], Operations: ['59-55=4', '58-32=26'] Exploring Operation: 4+26=30, Resulting Numbers: [30] 30,66 unequal: No Solution Exploring Operation: 26-4=22, Resulting Numbers: [22] 22,66 unequal: No Solution Exploring Operation: 4*26=104, Resulting Numbers: [104] 104,66 unequal: No Solution No 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: 66:[58, 8], Operations: ['59-55=4', '32/4=8'] Exploring Operation: 58-8=50, Resulting Numbers: [50] 50,66 unequal: No Solution Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Moving to Node #0 Current State: 66:[59, 32, 58, 55], Operations: [] Exploring Operation: 59-55=4, Resulting Numbers: [32, 58, 4] Generated Node #0,3: 66:[32, 58, 4] Operation: 59-55=4 Moving to Node #0,3 Current State: 66:[32, 58, 4], Operations: ['59-55=4'] Exploring Operation: 32/4=8, Resulting Numbers: [58, 8] Generated Node #0,3,2: 66:[58, 8] Operation: 32/4=8 Moving to Node #0,3,2 Current State: 66:[58, 8], Operations: ['59-55=4', '32/4=8'] Exploring Operation: 58+8=66, Resulting Numbers: [66] 66,66 equal: Goal Reached Exit Sub Search at level 2 Exit Sub Search at level 1
0.967882
hs_4
sum_heuristic
[ 69, 42, 61, 2 ]
13
[ "69-61=8", "42/2=21", "21-8=13" ]
Current State: 13:[69, 42, 61, 2], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [42, 2, 8] Generated Node #2: [42, 2, 8] from Operation: 69-61=8 Current State: 13:[42, 2, 8], Operations: ['69-61=8'] Exploring Operation: 42/2=21, Resulting Numbers: [8, 21] Generated Node #3: [8, 21] from Operation: 42/2=21 Current State: 13:[8, 21], Operations: ['69-61=8', '42/2=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
4
Current State: 13:[69, 42, 61, 2], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [42, 2, 8] Generated Node #0,0: 13:[42, 2, 8] Operation: 69-61=8 Exploring Operation: 42/2=21, Resulting Numbers: [69, 61, 21] Generated Node #0,1: 13:[69, 61, 21] Operation: 42/2=21 Exploring Operation: 69-42=27, Resulting Numbers: [61, 2, 27] Generated Node #0,2: 13:[61, 2, 27] Operation: 69-42=27 Exploring Operation: 61-42=19, Resulting Numbers: [69, 2, 19] Generated Node #0,3: 13:[69, 2, 19] Operation: 61-42=19 Exploring Operation: 69-2=67, Resulting Numbers: [42, 61, 67] Generated Node #0,4: 13:[42, 61, 67] Operation: 69-2=67 Moving to Node #0,0 Current State: 13:[42, 2, 8], Operations: ['69-61=8'] Exploring Operation: 42-8=34, Resulting Numbers: [2, 34] Generated Node #0,0,0: 13:[2, 34] Operation: 42-8=34 Exploring Operation: 42-2=40, Resulting Numbers: [8, 40] Generated Node #0,0,1: 13:[8, 40] Operation: 42-2=40 Exploring Operation: 2*8=16, Resulting Numbers: [42, 16] Generated Node #0,0,2: 13:[42, 16] Operation: 2*8=16 Exploring Operation: 2+8=10, Resulting Numbers: [42, 10] Generated Node #0,0,3: 13:[42, 10] Operation: 2+8=10 Exploring Operation: 42/2=21, Resulting Numbers: [8, 21] Generated Node #0,0,4: 13:[8, 21] Operation: 42/2=21 Moving to Node #0,3 Current State: 13:[69, 2, 19], Operations: ['61-42=19'] Exploring Operation: 2+19=21, Resulting Numbers: [69, 21] Generated Node #0,3,0: 13:[69, 21] Operation: 2+19=21 Exploring Operation: 69+2=71, Resulting Numbers: [19, 71] Generated Node #0,3,1: 13:[19, 71] Operation: 69+2=71 Exploring Operation: 69-2=67, Resulting Numbers: [19, 67] Generated Node #0,3,2: 13:[19, 67] Operation: 69-2=67 Exploring Operation: 19-2=17, Resulting Numbers: [69, 17] Generated Node #0,3,3: 13:[69, 17] Operation: 19-2=17 Exploring Operation: 69-19=50, Resulting Numbers: [2, 50] Generated Node #0,3,4: 13:[2, 50] Operation: 69-19=50 Start Sub Search at level 1: Moving to Node #0,3,4 Current State: 13:[2, 50], Operations: ['61-42=19', '69-19=50'] Exploring Operation: 2*50=100, Resulting Numbers: [100] 100,13 unequal: No Solution Exploring Operation: 50-2=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 2+50=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 50/2=25, Resulting Numbers: [25] 25,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 13:[19, 67], Operations: ['61-42=19', '69-2=67'] Exploring Operation: 19*67=1273, Resulting Numbers: [1273] 1273,13 unequal: No Solution Exploring Operation: 19+67=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 13:[69, 17], Operations: ['61-42=19', '19-2=17'] Exploring Operation: 69-17=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 69*17=1173, Resulting Numbers: [1173] 1173,13 unequal: No Solution Exploring Operation: 69+17=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 13:[69, 21], Operations: ['61-42=19', '2+19=21'] Exploring Operation: 69+21=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 69-21=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 69*21=1449, Resulting Numbers: [1449] 1449,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,1 Current State: 13:[19, 71], Operations: ['61-42=19', '69+2=71'] Exploring Operation: 71-19=52, Resulting Numbers: [52] 52,13 unequal: No Solution Exploring Operation: 19*71=1349, Resulting Numbers: [1349] 1349,13 unequal: No Solution Exploring Operation: 19+71=90, Resulting Numbers: [90] 90,13 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: 13:[61, 2, 27], Operations: ['69-42=27'] Exploring Operation: 61-2=59, Resulting Numbers: [27, 59] Generated Node #0,2,0: 13:[27, 59] Operation: 61-2=59 Exploring Operation: 61-27=34, Resulting Numbers: [2, 34] Generated Node #0,2,1: 13:[2, 34] Operation: 61-27=34 Exploring Operation: 27-2=25, Resulting Numbers: [61, 25] Generated Node #0,2,2: 13:[61, 25] Operation: 27-2=25 Exploring Operation: 2+27=29, Resulting Numbers: [61, 29] Generated Node #0,2,3: 13:[61, 29] Operation: 2+27=29 Exploring Operation: 61+2=63, Resulting Numbers: [27, 63] Generated Node #0,2,4: 13:[27, 63] Operation: 61+2=63 Start Sub Search at level 1: Moving to Node #0,2,1 Current State: 13:[2, 34], Operations: ['69-42=27', '61-27=34'] Exploring Operation: 2*34=68, Resulting Numbers: [68] 68,13 unequal: No Solution Exploring Operation: 34/2=17, Resulting Numbers: [17] 17,13 unequal: No Solution Exploring Operation: 2+34=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 34-2=32, Resulting Numbers: [32] 32,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,0 Current State: 13:[27, 59], Operations: ['69-42=27', '61-2=59'] Exploring Operation: 59-27=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 27+59=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 27*59=1593, Resulting Numbers: [1593] 1593,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,2 Current State: 13:[61, 25], Operations: ['69-42=27', '27-2=25'] Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,13 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,3 Current State: 13:[61, 29], Operations: ['69-42=27', '2+27=29'] Exploring Operation: 61+29=90, Resulting Numbers: [90] 90,13 unequal: No Solution Exploring Operation: 61-29=32, Resulting Numbers: [32] 32,13 unequal: No Solution Exploring Operation: 61*29=1769, Resulting Numbers: [1769] 1769,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,2,4 Current State: 13:[27, 63], Operations: ['69-42=27', '61+2=63'] Exploring Operation: 27*63=1701, Resulting Numbers: [1701] 1701,13 unequal: No Solution Exploring Operation: 63-27=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 27+63=90, Resulting Numbers: [90] 90,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,1 Current State: 13:[69, 61, 21], Operations: ['42/2=21'] Exploring Operation: 69+21=90, Resulting Numbers: [61, 90] Generated Node #0,1,0: 13:[61, 90] Operation: 69+21=90 Exploring Operation: 61-21=40, Resulting Numbers: [69, 40] Generated Node #0,1,1: 13:[69, 40] Operation: 61-21=40 Exploring Operation: 69-61=8, Resulting Numbers: [21, 8] Generated Node #0,1,2: 13:[21, 8] Operation: 69-61=8 Exploring Operation: 69-21=48, Resulting Numbers: [61, 48] Generated Node #0,1,3: 13:[61, 48] Operation: 69-21=48 Exploring Operation: 69+61=130, Resulting Numbers: [21, 130] Generated Node #0,1,4: 13:[21, 130] Operation: 69+61=130 Moving to Node #0,4 Current State: 13:[42, 61, 67], Operations: ['69-2=67'] Exploring Operation: 42+67=109, Resulting Numbers: [61, 109] Generated Node #0,4,0: 13:[61, 109] Operation: 42+67=109 Exploring Operation: 67-42=25, Resulting Numbers: [61, 25] Generated Node #0,4,1: 13:[61, 25] Operation: 67-42=25 Exploring Operation: 61-42=19, Resulting Numbers: [67, 19] Generated Node #0,4,2: 13:[67, 19] Operation: 61-42=19 Exploring Operation: 42+61=103, Resulting Numbers: [67, 103] Generated Node #0,4,3: 13:[67, 103] Operation: 42+61=103 Exploring Operation: 67-61=6, Resulting Numbers: [42, 6] Generated Node #0,4,4: 13:[42, 6] Operation: 67-61=6 Start Sub Search at level 1: Moving to Node #0,4,4 Current State: 13:[42, 6], Operations: ['69-2=67', '67-61=6'] Exploring Operation: 42/6=7, Resulting Numbers: [7] 7,13 unequal: No Solution Exploring Operation: 42*6=252, Resulting Numbers: [252] 252,13 unequal: No Solution Exploring Operation: 42+6=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 42-6=36, Resulting Numbers: [36] 36,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,1 Current State: 13:[61, 25], Operations: ['69-2=67', '67-42=25'] Exploring Operation: 61+25=86, Resulting Numbers: [86] 86,13 unequal: No Solution Exploring Operation: 61*25=1525, Resulting Numbers: [1525] 1525,13 unequal: No Solution Exploring Operation: 61-25=36, Resulting Numbers: [36] 36,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,2 Current State: 13:[67, 19], Operations: ['69-2=67', '61-42=19'] Exploring Operation: 67*19=1273, Resulting Numbers: [1273] 1273,13 unequal: No Solution Exploring Operation: 67-19=48, Resulting Numbers: [48] 48,13 unequal: No Solution Exploring Operation: 67+19=86, Resulting Numbers: [86] 86,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,0 Current State: 13:[61, 109], Operations: ['69-2=67', '42+67=109'] Exploring Operation: 61+109=170, Resulting Numbers: [170] 170,13 unequal: No Solution Exploring Operation: 61*109=6649, Resulting Numbers: [6649] 6649,13 unequal: No Solution Exploring Operation: 109-61=48, Resulting Numbers: [48] 48,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,4,3 Current State: 13:[67, 103], Operations: ['69-2=67', '42+61=103'] Exploring Operation: 103-67=36, Resulting Numbers: [36] 36,13 unequal: No Solution Exploring Operation: 67*103=6901, Resulting Numbers: [6901] 6901,13 unequal: No Solution Exploring Operation: 67+103=170, Resulting Numbers: [170] 170,13 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Moving to Node #0,0,4 Current State: 13:[8, 21], Operations: ['69-61=8', '42/2=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached Moving to Node #0 Current State: 13:[69, 42, 61, 2], Operations: [] Exploring Operation: 69-61=8, Resulting Numbers: [42, 2, 8] Generated Node #0,0: 13:[42, 2, 8] Operation: 69-61=8 Moving to Node #0,0 Current State: 13:[42, 2, 8], Operations: ['69-61=8'] Exploring Operation: 42/2=21, Resulting Numbers: [8, 21] Generated Node #0,0,4: 13:[8, 21] Operation: 42/2=21 Moving to Node #0,0,4 Current State: 13:[8, 21], Operations: ['69-61=8', '42/2=21'] Exploring Operation: 21-8=13, Resulting Numbers: [13] 13,13 equal: Goal Reached
0.927951
hs_5
sum_heuristic
[ 80, 24, 45, 72 ]
29
[ "80-24=56", "72-45=27", "56-27=29" ]
Current State: 29:[80, 24, 45, 72], Operations: [] Exploring Operation: 80-24=56, Resulting Numbers: [45, 72, 56] Generated Node #2: [45, 72, 56] from Operation: 80-24=56 Current State: 29:[45, 72, 56], Operations: ['80-24=56'] Exploring Operation: 72-45=27, Resulting Numbers: [56, 27] Generated Node #3: [56, 27] from Operation: 72-45=27 Current State: 29:[56, 27], Operations: ['80-24=56', '72-45=27'] Exploring Operation: 56-27=29, Resulting Numbers: [29] 29,29 equal: Goal Reached
4
Current State: 29:[80, 24, 45, 72], Operations: [] Exploring Operation: 80-24=56, Resulting Numbers: [45, 72, 56] Generated Node #0,0: 29:[45, 72, 56] Operation: 80-24=56 Exploring Operation: 80-45=35, Resulting Numbers: [24, 72, 35] Generated Node #0,1: 29:[24, 72, 35] Operation: 80-45=35 Exploring Operation: 72-24=48, Resulting Numbers: [80, 45, 48] Generated Node #0,2: 29:[80, 45, 48] Operation: 72-24=48 Exploring Operation: 80-72=8, Resulting Numbers: [24, 45, 8] Generated Node #0,3: 29:[24, 45, 8] Operation: 80-72=8 Exploring Operation: 72-45=27, Resulting Numbers: [80, 24, 27] Generated Node #0,4: 29:[80, 24, 27] Operation: 72-45=27 Moving to Node #0,3 Current State: 29:[24, 45, 8], Operations: ['80-72=8'] Exploring Operation: 45-24=21, Resulting Numbers: [8, 21] Generated Node #0,3,0: 29:[8, 21] Operation: 45-24=21 Exploring Operation: 45+8=53, Resulting Numbers: [24, 53] Generated Node #0,3,1: 29:[24, 53] Operation: 45+8=53 Exploring Operation: 24+8=32, Resulting Numbers: [45, 32] Generated Node #0,3,2: 29:[45, 32] Operation: 24+8=32 Exploring Operation: 45-8=37, Resulting Numbers: [24, 37] Generated Node #0,3,3: 29:[24, 37] Operation: 45-8=37 Exploring Operation: 24-8=16, Resulting Numbers: [45, 16] Generated Node #0,3,4: 29:[45, 16] Operation: 24-8=16 Start Sub Search at level 1: Moving to Node #0,3,3 Current State: 29:[24, 37], Operations: ['80-72=8', '45-8=37'] Exploring Operation: 37-24=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 24*37=888, Resulting Numbers: [888] 888,29 unequal: No Solution Exploring Operation: 24+37=61, Resulting Numbers: [61] 61,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,2 Current State: 29:[45, 32], Operations: ['80-72=8', '24+8=32'] Exploring Operation: 45-32=13, Resulting Numbers: [13] 13,29 unequal: No Solution Exploring Operation: 45+32=77, Resulting Numbers: [77] 77,29 unequal: No Solution Exploring Operation: 45*32=1440, Resulting Numbers: [1440] 1440,29 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,3,0 Current State: 29:[8, 21], Operations: ['80-72=8', '45-24=21'] Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Moving to Node #0 Current State: 29:[80, 24, 45, 72], Operations: [] Exploring Operation: 80-72=8, Resulting Numbers: [24, 45, 8] Generated Node #0,3: 29:[24, 45, 8] Operation: 80-72=8 Moving to Node #0,3 Current State: 29:[24, 45, 8], Operations: ['80-72=8'] Exploring Operation: 45-24=21, Resulting Numbers: [8, 21] Generated Node #0,3,0: 29:[8, 21] Operation: 45-24=21 Moving to Node #0,3,0 Current State: 29:[8, 21], Operations: ['80-72=8', '45-24=21'] Exploring Operation: 8+21=29, Resulting Numbers: [29] 29,29 equal: Goal Reached Exit Sub Search at level 1
0.981771
hs_5
sum_heuristic
[ 17, 73, 32, 48 ]
72
[ "73-17=56", "48-32=16", "56+16=72" ]
Current State: 72:[17, 73, 32, 48], Operations: [] Exploring Operation: 73-17=56, Resulting Numbers: [32, 48, 56] Generated Node #2: [32, 48, 56] from Operation: 73-17=56 Current State: 72:[32, 48, 56], Operations: ['73-17=56'] Exploring Operation: 48-32=16, Resulting Numbers: [56, 16] Generated Node #3: [56, 16] from Operation: 48-32=16 Current State: 72:[56, 16], Operations: ['73-17=56', '48-32=16'] Exploring Operation: 56+16=72, Resulting Numbers: [72] 72,72 equal: Goal Reached
4
Current State: 72:[17, 73, 32, 48], Operations: [] Exploring Operation: 48-32=16, Resulting Numbers: [17, 73, 16] Generated Node #0,0: 72:[17, 73, 16] Operation: 48-32=16 Exploring Operation: 73-48=25, Resulting Numbers: [17, 32, 25] Generated Node #0,1: 72:[17, 32, 25] Operation: 73-48=25 Exploring Operation: 32+48=80, Resulting Numbers: [17, 73, 80] Generated Node #0,2: 72:[17, 73, 80] Operation: 32+48=80 Exploring Operation: 48-17=31, Resulting Numbers: [73, 32, 31] Generated Node #0,3: 72:[73, 32, 31] Operation: 48-17=31 Moving to Node #0,0 Current State: 72:[17, 73, 16], Operations: ['48-32=16'] Exploring Operation: 17+16=33, Resulting Numbers: [73, 33] Generated Node #0,0,0: 72:[73, 33] Operation: 17+16=33 Exploring Operation: 17-16=1, Resulting Numbers: [73, 1] Generated Node #0,0,1: 72:[73, 1] Operation: 17-16=1 Exploring Operation: 73-17=56, Resulting Numbers: [16, 56] Generated Node #0,0,2: 72:[16, 56] Operation: 73-17=56 Exploring Operation: 73-16=57, Resulting Numbers: [17, 57] Generated Node #0,0,3: 72:[17, 57] Operation: 73-16=57 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 72:[73, 1], Operations: ['48-32=16', '17-16=1'] Exploring Operation: 73+1=74, Resulting Numbers: [74] 74,72 unequal: No Solution Exploring Operation: 73/1=73, Resulting Numbers: [73] 73,72 unequal: No Solution Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Moving to Node #0 Current State: 72:[17, 73, 32, 48], Operations: [] Exploring Operation: 48-32=16, Resulting Numbers: [17, 73, 16] Generated Node #0,0: 72:[17, 73, 16] Operation: 48-32=16 Moving to Node #0,0 Current State: 72:[17, 73, 16], Operations: ['48-32=16'] Exploring Operation: 17-16=1, Resulting Numbers: [73, 1] Generated Node #0,0,1: 72:[73, 1] Operation: 17-16=1 Moving to Node #0,0,1 Current State: 72:[73, 1], Operations: ['48-32=16', '17-16=1'] Exploring Operation: 73-1=72, Resulting Numbers: [72] 72,72 equal: Goal Reached Exit Sub Search at level 1
0.986979
hs_4
sum_heuristic
[ 20, 41, 14, 14 ]
21
[ "41-20=21", "14-14=0", "21+0=21" ]
Current State: 21:[20, 41, 14, 14], Operations: [] Exploring Operation: 41-20=21, Resulting Numbers: [14, 14, 21] Generated Node #2: [14, 14, 21] from Operation: 41-20=21 Current State: 21:[14, 14, 21], Operations: ['41-20=21'] Exploring Operation: 14-14=0, Resulting Numbers: [21, 0] Generated Node #3: [21, 0] from Operation: 14-14=0 Current State: 21:[21, 0], Operations: ['41-20=21', '14-14=0'] Exploring Operation: 21+0=21, Resulting Numbers: [21] 21,21 equal: Goal Reached
4
Current State: 21:[20, 41, 14, 14], Operations: [] Exploring Operation: 41-20=21, Resulting Numbers: [14, 14, 21] Generated Node #0,0: 21:[14, 14, 21] Operation: 41-20=21 Exploring Operation: 41-14=27, Resulting Numbers: [20, 14, 27] Generated Node #0,1: 21:[20, 14, 27] Operation: 41-14=27 Moving to Node #0,0 Current State: 21:[14, 14, 21], Operations: ['41-20=21'] Exploring Operation: 14-14=0, Resulting Numbers: [21, 0] Generated Node #0,0,0: 21:[21, 0] Operation: 14-14=0 Exploring Operation: 14/14=1, Resulting Numbers: [21, 1] Generated Node #0,0,1: 21:[21, 1] Operation: 14/14=1 Moving to Node #0,1 Current State: 21:[20, 14, 27], Operations: ['41-14=27'] Exploring Operation: 27-20=7, Resulting Numbers: [14, 7] Generated Node #0,1,0: 21:[14, 7] Operation: 27-20=7 Exploring Operation: 20-14=6, Resulting Numbers: [27, 6] Generated Node #0,1,1: 21:[27, 6] Operation: 20-14=6 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 21:[14, 7], Operations: ['41-14=27', '27-20=7'] Exploring Operation: 14-7=7, Resulting Numbers: [7] 7,21 unequal: No Solution Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Moving to Node #0 Current State: 21:[20, 41, 14, 14], Operations: [] Exploring Operation: 41-14=27, Resulting Numbers: [20, 14, 27] Generated Node #0,1: 21:[20, 14, 27] Operation: 41-14=27 Moving to Node #0,1 Current State: 21:[20, 14, 27], Operations: ['41-14=27'] Exploring Operation: 27-20=7, Resulting Numbers: [14, 7] Generated Node #0,1,0: 21:[14, 7] Operation: 27-20=7 Moving to Node #0,1,0 Current State: 21:[14, 7], Operations: ['41-14=27', '27-20=7'] Exploring Operation: 14+7=21, Resulting Numbers: [21] 21,21 equal: Goal Reached Exit Sub Search at level 1
0.989583
hs_2
mult_heuristic
[ 18, 80, 73, 58 ]
96
[ "18*80=1440", "73-58=15", "1440/15=96" ]
Current State: 96:[18, 80, 73, 58], Operations: [] Exploring Operation: 18*80=1440, Resulting Numbers: [73, 58, 1440] Generated Node #2: [73, 58, 1440] from Operation: 18*80=1440 Current State: 96:[73, 58, 1440], Operations: ['18*80=1440'] Exploring Operation: 73-58=15, Resulting Numbers: [1440, 15] Generated Node #3: [1440, 15] from Operation: 73-58=15 Current State: 96:[1440, 15], Operations: ['18*80=1440', '73-58=15'] Exploring Operation: 1440/15=96, Resulting Numbers: [96] 96,96 equal: Goal Reached
4
Current State: 96:[18, 80, 73, 58], Operations: [] Exploring Operation: 80-58=22, Resulting Numbers: [18, 73, 22] Generated Node #0,0: 96:[18, 73, 22] Operation: 80-58=22 Exploring Operation: 73-58=15, Resulting Numbers: [18, 80, 15] Generated Node #0,1: 96:[18, 80, 15] Operation: 73-58=15 Exploring Operation: 80-73=7, Resulting Numbers: [18, 58, 7] Generated Node #0,2: 96:[18, 58, 7] Operation: 80-73=7 Moving to Node #0,2 Current State: 96:[18, 58, 7], Operations: ['80-73=7'] Exploring Operation: 58-7=51, Resulting Numbers: [18, 51] Generated Node #0,2,0: 96:[18, 51] Operation: 58-7=51 Exploring Operation: 58-18=40, Resulting Numbers: [7, 40] Generated Node #0,2,1: 96:[7, 40] Operation: 58-18=40 Exploring Operation: 18+7=25, Resulting Numbers: [58, 25] Generated Node #0,2,2: 96:[58, 25] Operation: 18+7=25 Moving to Node #0,1 Current State: 96:[18, 80, 15], Operations: ['73-58=15'] Exploring Operation: 80-18=62, Resulting Numbers: [15, 62] Generated Node #0,1,0: 96:[15, 62] Operation: 80-18=62 Exploring Operation: 80+15=95, Resulting Numbers: [18, 95] Generated Node #0,1,1: 96:[18, 95] Operation: 80+15=95 Exploring Operation: 18+80=98, Resulting Numbers: [15, 98] Generated Node #0,1,2: 96:[15, 98] Operation: 18+80=98 Moving to Node #0,0 Current State: 96:[18, 73, 22], Operations: ['80-58=22'] Exploring Operation: 73+22=95, Resulting Numbers: [18, 95] Generated Node #0,0,0: 96:[18, 95] Operation: 73+22=95 Exploring Operation: 73-22=51, Resulting Numbers: [18, 51] Generated Node #0,0,1: 96:[18, 51] Operation: 73-22=51 Exploring Operation: 18+73=91, Resulting Numbers: [22, 91] Generated Node #0,0,2: 96:[22, 91] Operation: 18+73=91 Moving to Node #0,1,1 Current State: 96:[18, 95], Operations: ['73-58=15', '80+15=95'] Exploring Operation: 18+95=113, Resulting Numbers: [113] 113,96 unequal: No Solution Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,96 unequal: No Solution Exploring Operation: 18*95=1710, Resulting Numbers: [1710] 1710,96 unequal: No Solution Moving to Node #0,0,0 Current State: 96:[18, 95], Operations: ['80-58=22', '73+22=95'] Exploring Operation: 18+95=113, Resulting Numbers: [113] 113,96 unequal: No Solution Exploring Operation: 18*95=1710, Resulting Numbers: [1710] 1710,96 unequal: No Solution Exploring Operation: 95-18=77, Resulting Numbers: [77] 77,96 unequal: No Solution Moving to Node #0,1,2 Current State: 96:[15, 98], Operations: ['73-58=15', '18+80=98'] Exploring Operation: 15+98=113, Resulting Numbers: [113] 113,96 unequal: No Solution Exploring Operation: 15*98=1470, Resulting Numbers: [1470] 1470,96 unequal: No Solution Exploring Operation: 98-15=83, Resulting Numbers: [83] 83,96 unequal: No Solution Moving to Node #0,2,0 Current State: 96:[18, 51], Operations: ['80-73=7', '58-7=51'] Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,96 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 18*51=918, Resulting Numbers: [918] 918,96 unequal: No Solution Moving to Node #0,0,1 Current State: 96:[18, 51], Operations: ['80-58=22', '73-22=51'] Exploring Operation: 18*51=918, Resulting Numbers: [918] 918,96 unequal: No Solution Exploring Operation: 18+51=69, Resulting Numbers: [69] 69,96 unequal: No Solution Exploring Operation: 51-18=33, Resulting Numbers: [33] 33,96 unequal: No Solution Moving to Node #0,0,2 Current State: 96:[22, 91], Operations: ['80-58=22', '18+73=91'] Exploring Operation: 22+91=113, Resulting Numbers: [113] 113,96 unequal: No Solution Exploring Operation: 91-22=69, Resulting Numbers: [69] 69,96 unequal: No Solution Exploring Operation: 22*91=2002, Resulting Numbers: [2002] 2002,96 unequal: No Solution Moving to Node #0,2,1 Current State: 96:[7, 40], Operations: ['80-73=7', '58-18=40'] Exploring Operation: 7+40=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 40-7=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 7*40=280, Resulting Numbers: [280] 280,96 unequal: No Solution Moving to Node #0,2,2 Current State: 96:[58, 25], Operations: ['80-73=7', '18+7=25'] Exploring Operation: 58-25=33, Resulting Numbers: [33] 33,96 unequal: No Solution Exploring Operation: 58+25=83, Resulting Numbers: [83] 83,96 unequal: No Solution Exploring Operation: 58*25=1450, Resulting Numbers: [1450] 1450,96 unequal: No Solution Moving to Node #0,1,0 Current State: 96:[15, 62], Operations: ['73-58=15', '80-18=62'] Exploring Operation: 62-15=47, Resulting Numbers: [47] 47,96 unequal: No Solution Exploring Operation: 15+62=77, Resulting Numbers: [77] 77,96 unequal: No Solution Exploring Operation: 15*62=930, Resulting Numbers: [930] 930,96 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 88, 53, 34, 55 ]
61
[ "88+34=122", "55-53=2", "122/2=61" ]
Current State: 61:[88, 53, 34, 55], Operations: [] Exploring Operation: 88+34=122, Resulting Numbers: [53, 55, 122] Generated Node #2: [53, 55, 122] from Operation: 88+34=122 Current State: 61:[53, 55, 122], Operations: ['88+34=122'] Exploring Operation: 55-53=2, Resulting Numbers: [122, 2] Generated Node #3: [122, 2] from Operation: 55-53=2 Current State: 61:[122, 2], Operations: ['88+34=122', '55-53=2'] Exploring Operation: 122/2=61, Resulting Numbers: [61] 61,61 equal: Goal Reached
4
Current State: 61:[88, 53, 34, 55], Operations: [] Exploring Operation: 88-34=54, Resulting Numbers: [53, 55, 54] Generated Node #0,0: 61:[53, 55, 54] Operation: 88-34=54 Exploring Operation: 88-53=35, Resulting Numbers: [34, 55, 35] Generated Node #0,1: 61:[34, 55, 35] Operation: 88-53=35 Exploring Operation: 53+34=87, Resulting Numbers: [88, 55, 87] Generated Node #0,2: 61:[88, 55, 87] Operation: 53+34=87 Moving to Node #0,0 Current State: 61:[53, 55, 54], Operations: ['88-34=54'] Exploring Operation: 55+54=109, Resulting Numbers: [53, 109] Generated Node #0,0,0: 61:[53, 109] Operation: 55+54=109 Exploring Operation: 53+54=107, Resulting Numbers: [55, 107] Generated Node #0,0,1: 61:[55, 107] Operation: 53+54=107 Exploring Operation: 53+55=108, Resulting Numbers: [54, 108] Generated Node #0,0,2: 61:[54, 108] Operation: 53+55=108 Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 61:[55, 107], Operations: ['88-34=54', '53+54=107'] Exploring Operation: 55*107=5885, Resulting Numbers: [5885] 5885,61 unequal: No Solution Exploring Operation: 107-55=52, Resulting Numbers: [52] 52,61 unequal: No Solution Exploring Operation: 55+107=162, Resulting Numbers: [162] 162,61 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 #0,0,2 Current State: 61:[54, 108], Operations: ['88-34=54', '53+55=108'] Exploring Operation: 108/54=2, Resulting Numbers: [2] 2,61 unequal: No Solution Exploring Operation: 108-54=54, Resulting Numbers: [54] 54,61 unequal: No Solution Exploring Operation: 54+108=162, Resulting Numbers: [162] 162,61 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 #0,0,0 Current State: 61:[53, 109], Operations: ['88-34=54', '55+54=109'] Exploring Operation: 53+109=162, Resulting Numbers: [162] 162,61 unequal: No Solution Exploring Operation: 53*109=5777, Resulting Numbers: [5777] 5777,61 unequal: No Solution Exploring Operation: 109-53=56, Resulting Numbers: [56] 56,61 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: 61:[34, 55, 35], Operations: ['88-53=35'] Exploring Operation: 34+55=89, Resulting Numbers: [35, 89] Generated Node #0,1,0: 61:[35, 89] Operation: 34+55=89 Exploring Operation: 55+35=90, Resulting Numbers: [34, 90] Generated Node #0,1,1: 61:[34, 90] Operation: 55+35=90 Exploring Operation: 34+35=69, Resulting Numbers: [55, 69] Generated Node #0,1,2: 61:[55, 69] Operation: 34+35=69 Start Sub Search at level 1: Moving to Node #0,1,2 Current State: 61:[55, 69], Operations: ['88-53=35', '34+35=69'] Exploring Operation: 55+69=124, Resulting Numbers: [124] 124,61 unequal: No Solution Exploring Operation: 55*69=3795, Resulting Numbers: [3795] 3795,61 unequal: No Solution Exploring Operation: 69-55=14, Resulting Numbers: [14] 14,61 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 #0,1,0 Current State: 61:[35, 89], Operations: ['88-53=35', '34+55=89'] Exploring Operation: 35*89=3115, Resulting Numbers: [3115] 3115,61 unequal: No Solution Exploring Operation: 89-35=54, Resulting Numbers: [54] 54,61 unequal: No Solution Exploring Operation: 35+89=124, Resulting Numbers: [124] 124,61 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 #0,1,1 Current State: 61:[34, 90], Operations: ['88-53=35', '55+35=90'] Exploring Operation: 90-34=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 34+90=124, Resulting Numbers: [124] 124,61 unequal: No Solution Exploring Operation: 34*90=3060, Resulting Numbers: [3060] 3060,61 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: 61:[88, 55, 87], Operations: ['53+34=87'] Exploring Operation: 87-55=32, Resulting Numbers: [88, 32] Generated Node #0,2,0: 61:[88, 32] Operation: 87-55=32 Exploring Operation: 88-87=1, Resulting Numbers: [55, 1] Generated Node #0,2,1: 61:[55, 1] Operation: 88-87=1 Exploring Operation: 88-55=33, Resulting Numbers: [87, 33] Generated Node #0,2,2: 61:[87, 33] Operation: 88-55=33 Moving to Node #0,2,2 Current State: 61:[87, 33], Operations: ['53+34=87', '88-55=33'] Exploring Operation: 87-33=54, Resulting Numbers: [54] 54,61 unequal: No Solution Exploring Operation: 87+33=120, Resulting Numbers: [120] 120,61 unequal: No Solution Exploring Operation: 87*33=2871, Resulting Numbers: [2871] 2871,61 unequal: No Solution Moving to Node #0,2,0 Current State: 61:[88, 32], Operations: ['53+34=87', '87-55=32'] Exploring Operation: 88+32=120, Resulting Numbers: [120] 120,61 unequal: No Solution Exploring Operation: 88-32=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 88*32=2816, Resulting Numbers: [2816] 2816,61 unequal: No Solution Moving to Node #0,2,1 Current State: 61:[55, 1], Operations: ['53+34=87', '88-87=1'] Exploring Operation: 55+1=56, Resulting Numbers: [56] 56,61 unequal: No Solution Exploring Operation: 55*1=55, Resulting Numbers: [55] 55,61 unequal: No Solution Exploring Operation: 55/1=55, Resulting Numbers: [55] 55,61 unequal: No Solution No solution found.
0
hs_3
mult_heuristic
[ 35, 87, 7, 24 ]
10
[ "35-24=11", "7*11=77", "87-77=10" ]
Current State: 10:[35, 87, 7, 24], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [87, 7, 11] Generated Node #2: [87, 7, 11] from Operation: 35-24=11 Current State: 10:[87, 7, 11], Operations: ['35-24=11'] Exploring Operation: 7*11=77, Resulting Numbers: [87, 77] Generated Node #3: [87, 77] from Operation: 7*11=77 Current State: 10:[87, 77], Operations: ['35-24=11', '7*11=77'] Exploring Operation: 87-77=10, Resulting Numbers: [10] 10,10 equal: Goal Reached
4
Current State: 10:[35, 87, 7, 24], Operations: [] Exploring Operation: 35-24=11, Resulting Numbers: [87, 7, 11] Generated Node #0,0: 10:[87, 7, 11] Operation: 35-24=11 Exploring Operation: 87-35=52, Resulting Numbers: [7, 24, 52] Generated Node #0,1: 10:[7, 24, 52] Operation: 87-35=52 Moving to Node #0,1 Current State: 10:[7, 24, 52], Operations: ['87-35=52'] Exploring Operation: 52-24=28, Resulting Numbers: [7, 28] Generated Node #0,1,0: 10:[7, 28] Operation: 52-24=28 Exploring Operation: 24-7=17, Resulting Numbers: [52, 17] Generated Node #0,1,1: 10:[52, 17] Operation: 24-7=17 Start Sub Search at level 1: Moving to Node #0,1,0 Current State: 10:[7, 28], Operations: ['87-35=52', '52-24=28'] Exploring Operation: 28/7=4, Resulting Numbers: [4] 4,10 unequal: No Solution Exploring Operation: 28-7=21, Resulting Numbers: [21] 21,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,1,1 Current State: 10:[52, 17], Operations: ['87-35=52', '24-7=17'] Exploring Operation: 52-17=35, Resulting Numbers: [35] 35,10 unequal: No Solution Exploring Operation: 52+17=69, Resulting Numbers: [69] 69,10 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: 10:[87, 7, 11], Operations: ['35-24=11'] Exploring Operation: 87-11=76, Resulting Numbers: [7, 76] Generated Node #0,0,0: 10:[7, 76] Operation: 87-11=76 Exploring Operation: 87-7=80, Resulting Numbers: [11, 80] Generated Node #0,0,1: 10:[11, 80] Operation: 87-7=80 Start Sub Search at level 1: Moving to Node #0,0,0 Current State: 10:[7, 76], Operations: ['35-24=11', '87-11=76'] Exploring Operation: 76-7=69, Resulting Numbers: [69] 69,10 unequal: No Solution Exploring Operation: 7+76=83, Resulting Numbers: [83] 83,10 unequal: No Solution No solution found. Exit Sub Search at level 1 No solution found in sub search Start Sub Search at level 1: Moving to Node #0,0,1 Current State: 10:[11, 80], Operations: ['35-24=11', '87-7=80'] Exploring Operation: 11+80=91, Resulting Numbers: [91] 91,10 unequal: No Solution Exploring Operation: 80-11=69, Resulting Numbers: [69] 69,10 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