Anti-Coprime Yin-Yang
(Published on 17. September 2026, 22:22 by juggler)
Thanks to sirxemic for generously helping with computer solver support.
Latin Square: Place the digits 1-9 in each cell of the grid such that no digit repeats in any row or column.
XV: Digits separated by an X must sum to 10. Digits separated by a V must sum to 5.
Yin-Yang / Sightlines: Choose two colors with which to color each cell in the grid such that all cells of either color are orthogonally connected to each other, and no 2x2 area may be entirely one color. A digit in a cage indicates how many cells of the same color are seen in all orthogonal directions, including itself. Cells of the other color block vision.
Coprime/Anti-Coprime Neighbors: Within the area defined by one of the colors, orthogonally neighboring digits must be coprime, i.e. their largest common factor must be 1. Within the area defined by the other color, orthogonally neighboring digits cannot be coprime.
Solution code: Column 6
Comments
on 26. September 2026, 21:42 by PatternSpren
If there was an option of giving higher than very nice score then I would have. Sightlines/Yin-Yang is becoming one of my favourite variants of all time. Special mention to Blobz for making it happen for me at least.
This is my first latin sq puzzle. I absolutely loved it, this combination of Yin-Yang / Sightlines and Coprime/Anti-Coprime Neighbors is beautiful.
When it comes to solving it, I struggled a bit in the beginning but once I had the shading done right, it was mostly a smooth sailing for me. 3*
Thanks again.
on 19. September 2026, 00:56 by emoney1374
Great puzzle with a fun ruleset!
on 18. September 2026, 16:50 by Franjo
Thank you very much for creating and sharing this beautiful mathpuzzle. Perfect setting - as usual.
on 18. September 2026, 16:03 by Saltensity
What a nice puzzle! Once you figure out the implications, the puzzle becomes close to smooth, thank you for making this! :)
on 18. September 2026, 00:30 by palletpusher
Brilliant puzzle, Michael! Very challenging break-in, but went increasingly smoothly as I got a feel for the constraint and the yin-yang shading went in.
I did have to restart twice early on due to getting myself into impossible shading configurations. I think I might have benefited from a clarification like "adjacent digits across shading boundaries are unrestricted by coprimality", or specifying "_Strictly_ within the area defined..." in the existing text.
I love the types of maths you bring to your constructions. Your Rubik's Cube sudoku from a few years back is probably my favourite of all time. This puzzle is delightful; thank you.
