X---V*Parity Quads
(Published on 18. April 2025, 05:47 by NurglesGift)
Normal sudoku rules apply.
Digits must increase from the bulb of the thermometers.
Orthogonally adjacent cells can not sum to 5 or 10.
Two lines of the same length and same color are connected X lines.
Counting from the bulb, the first cell of each connected X line sum to 10. the second cell of each line sum to 10 etc.
The small white circles with a number indicates how many even or odd digits is in the 4 surrounding cells.
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Feel free to recommend this puzzle to anyone.
Feel free to take special rules for your own puzzle.
Feel free to give feedback.
Bless you!
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Example
Solution code: give the digits of column 5 (top to bottom)
Comments
on 19. January 2026, 03:39 by itsid
would you mind and stop using that faint grey; especially the bulb is always invisible and can only be revealed with some trickery (background colouring).. and most of the time it's still only very faint
Love the puzzle... tricked me hard until I realized that "that sentence" you alays put in the connected X-lines isn't there I was already 45mins in or something and had to restart ... doubting an accident.
on 28. September 2025, 10:42 by NurglesGift
edit example
on 20. April 2025, 13:42 by Bionic Cheese
Great stuff , one of my favourites of your puzzles.
on 18. April 2025, 19:12 by yusuf17
Great puzzle; almost 2 hours.
Had to restart several times.
Even after finding out what the trick was, I kept forgetting about it and so I kept making mistakes.
on 18. April 2025, 18:07 by Swarley
I now feel very silly for missing something so obvious, thank you!
(if my comments are considered a spoiler for the puzzle, please feel free to remove them)
on 18. April 2025, 15:25 by AnebodaSlatorp
Brilliant, thank you! I didn’t see your first comment about the 5 and had a bad moment at the beginning before going back and reading the rules again. I think the rules are fine, I wondered at first how I was going to disambiguate the grey lines with length 2 but I loved the way the colouring works to show the way forward. I think it’s brilliant that you switched the rules around, I enjoyed falling into the trap and then climbing out of it again. I love your puzzles and look out for them every week, thank you so much.
on 18. April 2025, 13:05 by Mikemerin
I understand the rules and the trick of it makes some fun logic to figure out.
If there’s a clarification needed, similar to your other recent puzzle, maybe after the rules are given say something like:
The grey lines are two separate sets. The solver must determine which lines in each set make up the individual X pairs.
And/or in the example image an extra set there showing it.
Though personally I’m good with the rules as is - I like the idea of figuring out the nuances and having the setting itself explain the trick especially when it’s set well like you usually do. That being said I understand the other viewpoint that would lead to the hints above.
on 18. April 2025, 08:12 by NurglesGift
Im busy and can't do anything now. But if you understand the 4-cell grey line... the puzzle will show you what to do with the 3-cell grey line
on 18. April 2025, 07:13 by Donald X.
It's just, in a typical puzzle, for thermos or arrows or whatever, a grey line with a bulb in the middle would actually be two 2-cell lines. In fact if you had two 2-cell lines meeting at the bulb, it would look exactly like that. But that breaks this puzzle, so that's not what you meant. But that's what it would normally be; so, it's confusing.
on 18. April 2025, 06:19 by NurglesGift
Counting from the bulb. they work the same way. The 4cell grey line you can count as a 2cell line + a 3cell line if you wish. the 3cell grey line you have to figure out :)
on 18. April 2025, 06:11 by Donald X.
The rules don't explain the two gray lines that have a bulb in the middle.
on 13. April 2025, 10:45 by NurglesGift
Note that the rule "5 can never be on a line" is gone on this one.....
