Minimum givens on Latin Squares, and r+c+d conjecture

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Re: Minimum givens on Latin Squares, and r+c+d conjecture

Postby Mathimagics » Thu Sep 06, 2018 3:41 am

.
OK, on closer inspection of my 5000 20-clue puzzles it appears that they are indeed all morphs of the same puzzle.

Intriguing ... 8-)
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Re: Minimum givens on Latin Squares, and r+c+d conjecture

Postby qiuyanzhe » Sun Sep 09, 2018 3:44 pm

Something more:
In Latin Squares, rows, columns and digits are equal, so the problem with d=0 is equivalent with c=0 or r=0.

Here we could consider only the r by c grid and (r+c-2) digits, with footprints(given subsets for each row/column), because there is always a way to fill the "given part" of the grid(unless there is hidden single in the initial grid, where the grid could shrink).
Code: Select all
     |1245  1346  2456  1235 
-----+-----------------------
1236 |12    136   26    123
1345 |145   134   45    135
1246 |124   146   246   12
3456 |45    346   456   35
For 3*any it is proved by my own distinction theory, and for further cases we don't have idea currently.
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