On and Off
(Published on 7. July 2026, 15:36 by Kaktuslav)
Rules: Normal sudoku rules apply.
4-modular diagonal–vertical path: Draw a single path through the centres of cells. The path may not branch, cross itself, or visit any cell more than once. Segments of the path alternate between diagonal segments, joining two cells that touch at a corner, and vertical segments, joining two vertically adjacent cells. Any four consecutive cells along the path contain digits with four different remainders when divided by 4.
Squares and circles: Every square lies on the path; every circle lies off the path. If a square contains digit N, then digit N occurs exactly N times on the path. If a circle contains digit N, then digit N occurs exactly N times in cells not on the path.
Solution code: Digits OFF the path in column 6 (top to bottom, no spaces)
Comments
on 11. July 2026, 16:47 by Qodec
Masterpiece!
on 11. July 2026, 15:44 by highonlife
Wow.. That was hard. Took me a long time.
the idea is brilliant though.
on 10. July 2026, 22:01 by Agent
Awesome, very clever idea!
on 10. July 2026, 19:39 by MixedMathialArts
Impressive
on 10. July 2026, 16:17 by kasperd
The logic to solve this one is marvellous once you see it.
The difficulty was a bit hard to judge. If you spot the right logic early on it's 3 stars of difficulty. But if you miss that logic it may well be 5 stars.
on 9. July 2026, 20:37 by Exigus
Stunning idea and execution. I was also stuck for a while but mainly because I was trying to find a loop and not just a path.
on 9. July 2026, 12:37 by amirs
What a brilliant puzzle. I spent over an hour staring at an empty grid trying to figure out how this could possibly be solved. Once I finally got the break in, it only took a few minutes to draw the path and a few more to fill in the entire grid.
on 9. July 2026, 08:49 by Kaktuslav
Thanks for the very kind comments and suggestions so far! Added an extra clarification: each segment now explicitly joins two cells (which was already implied by the original wording).
on 9. July 2026, 00:59 by sorryimLate
Thank you QuiltyAsCharged for the clarification. I think it should be added to the rules that a segment joins two cells. Otherwise a great puzzle!
on 8. July 2026, 23:27 by eladv
Whow, what a truly beautiful puzzle! CtC should do this, I'm very curious how Simon will approach it.
I agree with all the above. This is a puzzle that really benefits from sitting and thinking about what's really going on. I wish I listened to them: in reality, I fumbled around for 30 mintues discovering almost nothing, wondering "how the hell can this solve", and then I went to bed, and then the next morning I looked at it again, and gave it some thought, and it all clicked in place. Absolutely beautiful logic.
on 8. July 2026, 23:05 by Fool on Hill
I would echo emoney1374's comment. This is a puzzle with an "aha!" moment built in. As I said in my previous comment, it is ingenious and unexpected - but once you have seen it, it is not complicated or difficult. And for such a thing it is pretty impossible to give any hints or nudges - just to encourage people to keep thinking, because the experience of finding what Kaktuslav has hidden here will live with me for some time.
on 8. July 2026, 21:17 by QuiltyAsCharged
Note that a "segment" of the path connects exactly two cells! I thought a segment could be a straight line joining more than two cells, so I was stuck for a long while.
Once I realized that, the rest came together nicely. There are fascinating properties that emerge from these rules
on 8. July 2026, 17:31 by emoney1374
I think this puzzle is very hard, but also feel like it should be easy. Took a long time to wrap my head around the constraints but then everything fell into place and the puzzle finished. Like finding an elegant theory in nature, Kaktuslav set this puzzle ingeniously, and then allowed us to see the beauty that was waiting to be found. Perfect puzzle.
on 7. July 2026, 21:20 by Fool on Hill
Superb. Once I had the right thought, it fell into place and everything clicked nicely. Ingenious and unexpected and very clean and precise.
