Hi, colleagues!
I've done additional filtering out patterns, not having valid puzzles, appling 40 maximal one-crossing-free patterns (see thread
Investigation of one-crossing-free patterns) to the 199147-patterns list (file "sym18patterns_n-e_filtered4.zip"), based on original 294313-patterns
eleven's list of possible 18-clue vertically symmetric patterns. I got 100728 patterns which potentially can have valid puzzles. Therefore, number of search space for 18-clue vertically symmetric patterns was reduced twice.
- Code: Select all
18-clue possible symmetric distributions (eleven's list + filtering)
N Distribution Patterns
--------------------------
1 000022338 9
2 000022446 32
3 000033336 80
4 000111339 3
5 000111447 16
6 000111555 13
7 000112338 9
8 000112446 72
9 000112455 26
10 000113337 30
11 000113346 81
12 000113355 42
13 000113445 80
14 000114444 56
15 000122229 7
16 000122337 130
17 000122445 200
18 000133335 240
19 000222228 14
20 000222237 46
21 000222246 95
22 000222255 60
23 000222336 402
24 000222444 128
25 000223335 430
26 000223344 259
27 000233334 126
28 001111338 6
29 001111446 60
30 001111455 31
31 001112337 60
32 001112445 200
33 001113336 144
34 001113345 189
35 001113444 164
36 001122228 23
37 001122336 529
38 001122444 316
39 001123335 228
40 001123344 147
41 001133334 338
42 001222227 104
43 001222236 230
44 001222245 272
45 001222335 872
46 001223334 698
47 002222226 217
48 002222235 328
49 002222244 156
50 002222334 556
51 011111229 4
52 011111337 88
53 011111445 80
54 011112228 26
55 011112237 94
56 011112246 206
57 011112255 133
58 011112336 414
59 011112444 415
60 011113335 780
61 011113344 905
62 011122227 172
63 011122335 1218
64 011122344 505
65 011133333 703
66 011222226 672
67 011222235 1251
68 011222244 1093
69 011222334 3579 observed: 1
70 011223333 2604
71 012222225 443
72 012222333 1907
73 022222224 1168 observed: 2
74 022222233 1808 observed: 1
75 111111228 30
76 111111336 354
77 111111444 202
78 111112227 402
79 111112236 1032
80 111112245 1623
81 111112335 2316
82 111112344 911
83 111113334 4059
84 111122226 1844
85 111122235 3477
86 111122244 3105
87 111122334 8179 observed: 5
88 111123333 4194 observed: 1
89 111222225 4347
90 111222234 7458 observed: 4
91 111222333 7963 observed: 32
92 112222224 5872 observed: 4
93 112222233 10455 observed: 35
94 122222223 3145 observed: 24
95 222222222 938 observed: 12
Total number of distributions : 95
Total number of patterns : 100728
Total number of observed patterns: 121
Clues in pattern's central column
0 3145
2 53452
4 41007
6 3124
8 0
Zipped file can be loaded
here.
It turns out, 18-clue vertically symmetric valid patterns containing 8 clues in the central column (c5) are impossible.
Serg
[Edited. I've added pattern #117 discovered by
Afmob on the 6-th of August, 2013. Pattern has distribution 112222233.]
[Edited. I've added pattern #118 discovered by
Afmob on the 3-rd of December, 2013. Pattern has distribution 112222224.]
[Edited. I've added pattern #119 discovered by
Afmob on the 11-n of December, 2013. Pattern has distribution 111122334.]
[Edited. I've added pattern #120 discovered by
Afmob on the 11-n of December, 2013. Pattern has distribution 111222234.]
[Edited. I've added pattern #121 discovered by
Afmob on the 12 of December, 2013. Pattern has distribution 111222234.]
