Prompted by coloin, I have (among other things) been looking at the "Max Clue Count" problem for SudokuP.
We are of course, referring to clue counts for minimal puzzles, ie: puzzles in which the removal of any single clue results in multiple solutions.
After looking at dobrichev's & blue's (et al) posts on the equivalent problem in regular Sudoku, I looked at various grids that were most likely to have high-clue puzzles, and quickly found exemplars for 30-clues, then 31 etc until it began to get quite hard to go beyond 33 clues.
I then focused on the MC grid (Grid #866802 in the CF catalog) as being the "most likely candidate" of all, and pretty quickly found this 36-clue set:
- Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| 4 5 6 | . . . | . . . |
| 7 8 9 | . . . | 4 5 6 |
+-------+-------+-------+
| . 3 . | . 6 . | . 9 . |
| 5 . 4 | . 9 . | . 3 . |
| 8 . 7 | . 3 . | 5 . 4 |
+-------+-------+-------+
| 3 1 . | 6 4 . | 9 7 . |
| . . 5 | 9 7 . | 3 1 . |
| . . 8 | 3 1 . | . . 5 |
+-------+-------+-------+
I am continuing the search on this grid, using what is basically a DFS search based on {+2, -1} and {+3, -2} morphing, starting with puzzles of size 30 or more found by a random search process.
