Minimum number of clues for X-windoku?

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Minimum number of clues for X-windoku?

Postby m_b_metcalf » Mon Aug 30, 2021 9:58 am

We know that the minimum number of clues for standard sudoku is 17. By adding the additional constraints of X, the number has been reduced to at least 12. Adding the additional constraints of windows should reduce it even further. Below is an X-windoku with only 11 clues. Can anyone go lower?

Regards,

Mike

Code: Select all
+---+-----------+---+-----------+---+
| . | .   .   . | 6 | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| . | 5   .   . | . | .   .   . | 1 |
+---+-----------+---+-----------+---+
| . | .   .   9 | . | .   .   . | 7 |
+---+-----------+---+-----------+---+
| 9 | 2   .   . | . | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | . | .   8   . | . |
|   |           |   |           |   |
| . | 7   3   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   6   . | . | .   .   . | . |
+---+-----------+---+-----------+---+

....6.......................5......1...9....792.............8...73........6......   X-windoku, 11 clues, very hard.
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Re: Minimum number of clues for X-windoku?

Postby 1to9only » Mon Aug 30, 2021 1:12 pm

This was generated sometime last year, when adding variants to Sudoku/Sukaku Explainer.
Code: Select all
..4........2...8......1..7..............3.....5....2.........9....3.............. X-Windoku, 10 clues, ED=9.2/1.5/1.5

This is the only 10-clues X-Windoku in my files. There are a number of 11-clues.
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Re: Minimum number of clues for X-windoku?

Postby Mathimagics » Mon Aug 30, 2021 1:29 pm

Hi Mike,

For SudokuWX (Windoku + X) I reported 9-clue puzzles back in 2018, see here.

Example:
Code: Select all
.......8.....7...........5....3......6............4.2..................17........


Many 9-clue puzzles were found, but no 8-clue cases, as far as I can recall.

Cheers
MM
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Re: Minimum number of clues for X-windoku?

Postby m_b_metcalf » Mon Aug 30, 2021 1:51 pm

Mathimagics wrote:For SudokuWX (Windoku + X) I reported 9-clue puzzles back in 2018, see here.
Oh, thanks. That's four pages back and I didn't look that far.

Regards,

Mike
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