Logic Masters Deutschland e.V.

Queens on 11x11 Torus

(Eingestellt am 1. September 2020, 11:11 Uhr von SudokuExplorer)

Some people wanted a larger anti-queen toroidal sudoku after I created my Queens on 7x7 Torus sudoku. So here it is! (There are two Penpa links depending on your preference).

If you had a go at the bonus puzzles at the bottom of my 7x7 sudoku, you would have realised that no 8x8, 9x9 or 10x10 toroidal sudoku can have the anti-queen constraint. There is a purely logical path which may use some slightly unusual logic. (I did add a few extra givens to avoid any trial and error).
Normal sudoku rules apply (each row, column and region contains the numbers 0 to 10). We will use the roman numeral X to represent 10.

We also have the toroidal constraint.
On a torus, when you walk along a row you end up back to the start of that row. Whilst if you climb up a column, you end up back to the bottom of that column. To visualise the regions in this sudoku, you may have to walk/climb through the thick grey lines at the "edges" of the sudoku. The thick black lines are the edges of the regions.

Moreover, every digit has the anti-queen constraint. This constraint is toroidal, meaning that you can move diagonally across from one side to the other side of the sudoku. For example, the 2 in the 1st row is a queen's move away from the 9 in the 10th row.

You can try this on
Penpa-Edit. Have fun on this larger torus!

With a checkerboard coloured grid, you can try here on Penpa-Edit.
(Note that, apart from the two main diagonals, the diagonal changes colour when you move diagonally across from one side to the other side of the sudoku).

Hint:
The toroidal diagonals contain each of the numbers 0 to 10, because of the toroidal anti-queen constraint. This provides extra regions.

Hint 2:
A standard trick is to find two regions that have digits A in exactly two rows/columns, then that would imply that there are no more As elsewhere on those rows/columns. A similar trick may be needed but for diagonals instead of rows/columns.

Lösungscode: Enter the first column (top to bottom) followed by the bottom row (left to right) (using the roman numeral X in place of the number 10, 22 characters in total).

Zuletzt geändert am 31. Juli 2021, 20:33 Uhr

Gelöst von zorant, glum_hippo, panthchesh, polar, NikolaZ, ManuH, clover, Semax, dm_litv, TimE, Storm, Bobby, Dina, Vebby, zrbakhtiar, starelev5
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Kommentare

am 31. Juli 2021, 20:33 Uhr von SudokuExplorer
Fixed labels/tags

am 12. Dezember 2020, 17:27 Uhr von SudokuExplorer
@Dina + @Storm: Thanks for giving it a go and for your feedback. It seems like I overestimated its difficulty, but I'm glad you enjoyed it :-)

am 12. Dezember 2020, 05:48 Uhr von Dina
The size seemed daunting at first, but it turned out to be quite easy and very fun!

am 12. Dezember 2020, 01:05 Uhr von Storm
@SudokuExplorer: Fun puzzle!

@dm_litv: Thanks for the interesting link :-)

Zuletzt geändert am 8. Oktober 2020, 23:52 Uhr

am 8. Oktober 2020, 23:49 Uhr von SudokuExplorer
@dm_litv Wow! Thanks for the link. I just had a brief look at some of the results and conjectures, and they look very interesting. I'm not too surprised that a Hungarian mathematician noticed this property. Thanks again :-)

am 8. Oktober 2020, 22:48 Uhr von dm_litv
This fact (N must be coprime with 6) was first noticed and proven by György Pólya in 1918. The proof using the sum of the values ​​and the squares of the permutation values ​​is the simplest and clearest.
A good overview of the current state of the art in placement of queens problem (not just on a toroidal board) can be found here
https://www.sciencedirect.com/science/article/pii/S0012365X07010394

am 21. September 2020, 19:18 Uhr von SudokuExplorer
Added toroidal tag (it seems to have magically disappeared)

am 18. September 2020, 01:56 Uhr von SudokuExplorer
Adjusted image of sudoku

Zuletzt geändert am 18. September 2020, 01:53 Uhr

am 6. September 2020, 19:53 Uhr von SudokuExplorer
Added two hints about anti-queen constraint

am 5. September 2020, 11:09 Uhr von SudokuExplorer
If anyone does try this puzzle, do tell me what you like or dislike about the solving experience. This will help greatly if I decide to set a 13x13 puzzle.

am 2. September 2020, 16:59 Uhr von SudokuExplorer
@panthchesh Your wish was my command! I'm glad you had fun :-)

am 2. September 2020, 03:51 Uhr von panthchesh
That was very interesting! Thanks for the puzzle! :D

am 1. September 2020, 18:13 Uhr von SudokuExplorer
Added a link with a checkerboard colouring to visually aid you during the solve.

Schwierigkeit:2
Bewertung:81 %
Gelöst:16 mal
Beobachtet:7 mal
ID:000446

Variantenkombination Online-Solving-Tool Groß Kantenverklebung

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