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.
qiuyanzhe