The New Sudoku Players' Forum

[m_b_metcalf]

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

[urhegyi]

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

[m_b_metcalf]

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).

[urhegyi]

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.

Code: Select all

13.....9246.....35...4.5.................................5.6...57.....4681.....79

[m_b_metcalf]

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

[Hajime]

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.

[urhegyi]

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?

[m_b_metcalf]

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

[urhegyi]

A few fiendish examples for your windows open concept:

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.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.


A few diabolical examples:

Code: Select all

.53..829.........5........68.........................81........5.........927..65.
.53..829.........5........68.........................84........5.........927..65.
.53..824.........5........68.........................81........5.........427..65.
.53..824.........5........68.........................89........5.........427..65.


And a very extreme one:

Code: Select all

.39..524.........8........93.........................57........9.........281..79.


[m_b_metcalf]

@ urhegyi :Your impressive list of very hard, up 11.8, x-windokus led me to find a small bug in my code. When corrected, I tested it by producing the hardest yet (I think) open window:

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+---+-----------+---+-----------+---+
| . | .   .   6 | . | 5   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | 2 | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | 6 | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   7 | . | .   .   1 | . |
+---+-----------+---+-----------+---+
| . | .   .   . | 4 | .   .   . | . |
|   |           |   |           |   |
| 7 | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | 2 |
+---+-----------+---+-----------+---+
| . | .   8   1 | . | .   .   9 | . |
+---+-----------+---+-----------+---+   12 clues, x-windoku, open windows

...6.5.......2.................6.......7...1.....4....7................2..81...9.  ED=10.0/5.7/2.9

I stand to be corrected.

Regards,

Mike

[urhegyi]

Very nice,
I got a different rating with a new 4 jan 2022 version of SE.
If anyone can explain if there has been changes in the rating-algorithm?
Mike:

Code: Select all

...6.5.......2.................6.......7...1.....4....7................2..81...9.  ED=10.0/5.7/2.9 Windoku-X

latest SE:

Code: Select all

...6.5.......2.................6.......7...1.....4....7................2..81...9. ED=10.0/7.7/2.6 Windoku-X

[urhegyi]

A few updates:

Code: Select all

...2.5.......9.................4.......7...6.....8....1................2..35...1. ED=10.7/1.2/1.2
...2.5.......7.................4.......7...6.....8....3................2..65...1. ED=10.7/1.2/1.2
...3.5.......9.................4.......7...6.....8....1................2..95...1. ED=10.2/1.2/1.2
...2.5.......9.................4.......7...6.....3....8................2..95...1. ED=10.1/1.2/1.2
...7.5.......4.................2.......6...9.....8....6................7..42...3. ED=10.1/10.1/2.8
...7.5.......4.................1.......6...1.....8....6................3..42...7. ED=10.1/10.1/2.8
...7.5.......4.................6.......1...8.....8....6................7..42...3. ED=10.1/10.1/2.8
...2.5.......7.................4.......7...6.....6....4................2..93...1. ED=10.1/10.1/2.8
...8.5.......7.................4.......7...6.....9....8................2..63...1. ED=10.1/10.1/2.6

[1to9only]

If anyone can explain if there has been changes in the rating-algorithm?

SudokuMonster's: ED=10.0/5.7/2.9
1to9only's: ED=10.0/7.7/2.6

[m_b_metcalf]

Returning to this topic with a vastly improved program, I now have an open window with only 10 clues (close to the minimum of 9):

Code: Select all

+---+-----------+---+-----------+---+
| 1 | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | 8 | .   .   . | . |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | 3 |
|   |           |   |           |   |
| . | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| 7 | .   .   5 | . | .   9   4 | . |
+---+-----------+---+-----------+---+
| . | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| 5 | .   .   . | . | .   .   . | . |
|   |           |   |           |   |
| 2 | .   .   . | . | .   .   . | . |
+---+-----------+---+-----------+---+
| . | .   .   . | 3 | .   .   . | . |
+---+-----------+---+-----------+---+

1............8............3.........7..5..94..........5........2............3....  10 clues, ED=5.7/1.5/1.5

Mike

[urhegyi]

Mike Metcalf's windows-open windoku-x:
1............8............3.........7..5..94..........5........2............3.... 10 clues, ED=5.7/1.5/1.5
Or one more found(Rated 5.7 with SE version 1.18.1):
9............3............2.........4..7..86..........7........1............2....
It seems my program has found a simply morph of yours.
Classical SE 7.8.