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8x8 Sudoku variant - Help required please

Posted: Wed 09 Dec, 2020 10:20 am
by Caprakan
Hi all. I'm looking to create an 8x8 Sudoku-esque puzzle for a Dungeons & Dragons game but I'm really struggling.

The criteria are as follows:
1 - Each number (1-8) can only appear in each row or column once (easy peasy - I can find solutions online for that!)
2 (and this is the bit I'm stuck on) - If I were to highlight the number for each row (starting with 1 at the bottom, then 2, etc.) in that row, there must not be two highlighted numbers in the same column (and ideally not form a regular pattern). Diagonals are fine.

Does anyone know if this is even possible or how I could go about producing such a puzzle?

Many thanks!

Re: 8x8 Sudoku variant - Help required please

Posted: Wed 09 Dec, 2020 2:45 pm
by david mcneill
This is certainly possible. It is not at all a difficult constraint to satisfy. I have found a solution in under 5 minutes.

Re: 8x8 Sudoku variant - Help required please

Posted: Wed 09 Dec, 2020 3:11 pm
by Caprakan
I was sure it would be possible but simply couldn't get my head around it.

Any chance you could provide the solution, please?

Thank you! :D

Re: 8x8 Sudoku variant - Help required please

Posted: Wed 23 Dec, 2020 6:56 am
by Caprakan
Unfortunately, I am still unable to find a solution to this problem, despite it being a straightforward proposition for some.

If anyone could provide a solution, I would be most grateful.

Many thanks, and Season's Greetings to one and all.

Re: 8x8 Sudoku variant - Help required please

Posted: Wed 23 Dec, 2020 10:14 am
by detuned
So the first point sounds like a Latin square (just rows and columns) rather than sudoku (which would also gave regions.

Since writing down 12345678 down the top left bottom right diagonal works fine, start with a blank grid, add in that diagonal, and then fill out the rest of the grid using sudoku rules. You will need to make a few arbitrary choices as there are many different ways to proceed from here.

In this case the 8 highlighted cells will just be the diagonal. If you want to make that slightly less regular, try permuting the columns of the finished grid. (If you do have regions, then you need to be careful here)

Re: 8x8 Sudoku variant - Help required please

Posted: Wed 23 Dec, 2020 11:55 am
by Caprakan
Thanks!