Hi,
Blue!
Thank you for confirmation of my results.
blue wrote:Hi
Serg,
It looks like you forgot to include one.
(I'm sure you have it).
- Code: Select all
+-------+-------+-------+
| . . . | . . . | . . x |
| . . . | . . . | . . x |
| . . x | x x x | x x x |
+-------+-------+-------+
| . . x | x x x | x x x |
| . . x | x x x | x x x |
| x x x | x x x | x x x |
+-------+-------+-------+
| . . . | x x x | x x x |
| . . . | x x x | x x x |
| . . . | x x x | x x x |
+-------+-------+-------+
It isn't a subset of one of the others is it ?
(It isn't maximal).
I missed this pattern. Patterns P101, P103, P105 and P107 were produced "artificially", by hand, from already published 4 maximal patterns which were proven by you not to have valid puzzles, so I can be wrong. But remaining patterns were produced by true exhaustive search (and cross-checks), so I am sure there are no other patterns not having valid puzzles with empty B7 box and filled boxes B5, B6, B8 and B9. Maybe it would be better to publish true maximal patterns only, because at the end of this investigation maximal patterns only will participate final list of patterns not having valid puzzles with free crossing. Nevertheless, thank you for correction (I'll edit my previous post).
I checked remaining 15 published pattern for maximality. It turns out, patterns P102, P104, P108-P116, P118-P119 (totally 13 patterns) are really maximal, but patterns P106 and P117 are not maximal. Both patterns can be extended futher to maximal patterns
- Code: Select all
+-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . .|. . .|
|. . .|. . .|. . x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |. . x|. . .|. . .|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+
So, only published below 13 patterns with empty B7 box are really maximal.
- Code: Select all
Maximal patterns with empty B7 box:
P102 P104 P108
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . x| |. . .|. . x|. . x|
|. . x|. . .|. . .| |. . .|. . .|. . x| |. . x|. . .|. . .|
|x x x|x x x|x x x| |x x x|x x x|x x x| |. x .|. . .|. . .|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |x x x|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |x x x|x x x|x x x| |x . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
P109 P110 P111
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . x|x x x| |. . .|. . .|. x x|
|. . .|. . x|. . x| |. . .|. . x|x x x| |. . .|. . .|. x x|
|. x x|. . .|. . .| |. . x|. . x|x x x| |. . x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|x x x|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
P112 P113 P114
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . x| |. . .|. . x|. . x| |. . .|. x x|. x x|
|. . .|x x x|x x x| |. . .|. . x|. . x| |. . .|. x x|. x x|
|. . x|. . .|. . x| |. . x|x x x|x x x| |. . x|. x x|. x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. x .|x x x|x x x| |. x .|x x x|x x x| |. x .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
P115 P116 P118
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|. . .|. . .| |. . .|. . .|. . .| |. . .|. . x|. . x|
|. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . x|. . x|
|. . x|. . x|. . .| |. . x|. . x|. . .| |. . x|. . x|. . x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . x|x x x|x x x| |. . .|x x x|x x x| |x x x|x x x|x x x|
|. x .|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
|. . .|x x x|x x x| |. . .|x x x|x x x| |. . .|x x x|x x x|
+-----+-----+-----+ +-----+-----+-----+ +-----+-----+-----+
P119
+-----+-----+-----+
|. . .|. . .|. . .|
|. . .|x x x|x x x|
|. . x|. . .|. . .|
+-----+-----+-----+
|. . .|x x x|x x x|
|x x x|x x x|x x x|
|x x x|x x x|x x x|
+-----+-----+-----+
|. . .|x x x|x x x|
|. . .|x x x|x x x|
|. . .|x x x|x x x|
+-----+-----+-----+
Serg