X-windoku, windows closed, windows open

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X-windoku, windows closed, windows open

Postby m_b_metcalf » Sun Aug 29, 2021 9:52 am

I wanted to see how difficult it is to make an an x-windoku with the clues either all in the widows or all in the frames. It wasn't too difficult:
Code: Select all
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   1 | . | 2   .   . | . |
|   |           |   |           |   |
| . | .   .   4 | . | 5   .   6 | . |
|   |           |   |           |   |
| . | .   7   . | . | .   .   8 | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | 2   .   . | . | .   3   . | . |
|   |           |   |           |   |
| . | 4   .   5 | . | 6   .   . | . |
|   |           |   |           |   |
| . | .   .   8 | . | 9   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+

............1.2......4.5.6...7....8...........2....3...4.5.6......8.9............

(X)Windows closed, very hard, rotationally symmetric (not quite minimal), 14 clues.

Code: Select all
+---+-----------+---+-----------+---+
| . | 3   5   . | . | 8   4   9 | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | 5 |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | 8 |
|   |           |   |           |   |
| 6 | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | 4 |
|   |           |   |           |   |
| 2 | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| 5 | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | 1   6   2 | . | .   5   7 | . |
+---+-----------+---+-----------+---+


.35..849.........5........86.........................42........5.........162..57.

(X)Windows open, hard, rotationally symmetric (not minimal), 16 clues.


Regards,

Mike
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m_b_metcalf
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Re: X-windoku, windows closed, windows open

Postby urhegyi » Mon Aug 30, 2021 8:13 am

Very nice ones. They both rated 9.5 by sudokuexplainer. But do you also have a less difficult one I can try on paper?
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Re: X-windoku, windows closed, windows open

Postby m_b_metcalf » Mon Aug 30, 2021 8:41 am

urhegyi wrote:Very nice ones. They both rated 9.5 by sudokuexplainer. But do you also have a less difficult one I can try on paper?

No sooner said than done:

Code: Select all
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   1 | . | .   7   3 | . |
|   |           |   |           |   |
| . | 9   .   4 | . | 5   .   6 | . |
|   |           |   |           |   |
| . | .   7   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   3   . | . |
|   |           |   |           |   |
| . | 4   .   5 | . | 6   .   1 | . |
|   |           |   |           |   |
| . | .   3   . | . | 9   2   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+


............1..73..9.4.5.6...7.....................3...4.5.6.1...3..92...........

(X)Windows closed, fairly easy, not minimal(removing further clues makes it very hard).
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Re: X-windoku, windows closed, windows open

Postby urhegyi » Mon Aug 30, 2021 7:29 pm

Here a self-designed human solvable example based on your solution grid.
I think it solves with as hardest step an xy-wing SE 4.2.
Image
Code: Select all
13.....9246.....35...4.5.................................5.6...57.....4681.....79
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Re: X-windoku, windows closed, windows open

Postby m_b_metcalf » Tue Aug 31, 2021 7:19 am

urhegyi wrote:Here a self-designed human solvable example based on your solution grid.

If you look closely at the values of the givens, maybe something will strike you.

Regards,

Mike
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Re: X-windoku, windows closed, windows open

Postby Hajime » Tue Aug 31, 2021 8:36 am

In SiSeSuSo in the pattern tab page you can create these kind of puzzles. A desired pattern must be supplied by you and also WX for WindokuX. Then let 100 solutions be generated in a file to be rated by SudokuExplainer.
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Re: X-windoku, windows closed, windows open

Postby urhegyi » Tue Aug 31, 2021 9:58 am

m_b_metcalf wrote:
urhegyi wrote:Here a self-designed human solvable example based on your solution grid.

If you look closely at the values of the givens, maybe something will strike you.

Regards,

Mike

Thank you for mentioning it but I already found there is the Gurth's symmetrical placement with the normal mappings(R5C5=5).
My last step was an xy-wing that led to solution with singles.
Or do you mean the Phistomel Ring can also be used as an alternative because of the 16 givens at the corners must also be in a ring around box5?
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Re: X-windoku, windows closed, windows open

Postby m_b_metcalf » Tue Aug 31, 2021 11:03 am

urhegyi wrote:Thank you for mentioning it but I already found there is the Gurth's symmetrical placement with the normal mappings(R5C5=5).

Yes, I meant the symmetry of values of the givens.

Mike
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Re: X-windoku, windows closed, windows open

Postby urhegyi » Tue Aug 31, 2021 5:23 pm

A few solvable by hand examples for your windows open concept:
Code: Select all
.83..296.........1........32.........................53........9.........214..57.
.83..296.........1........32.........................53........6.........412..75.
.83..296.........1........32.........................53........9.........217..54.
.83..296.........1........32.........................53........6.........712..45.
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