Modular Fog
(Published on 13. May 2025, 07:53 by kyuquu)
This is my first attempt at creating a fog puzzle. Please enjoy, and feel free to leave feedback!
RULES:
Normal sudoku rules apply.
Dynamic Fog: The grid is covered in fog, which will gradually clear as correct digits are placed. No guessing is required.
Modular Lines: Any three adjacent digits along a teal line have different residues modulo 3.
(Note: Lines cannot branch and always travel between the centers of adjacent cells. Two distinct lines cannot visit the same cell.)
Partial Kropki: Digits separated by a white kropki dot are consecutive. Digits separated by a black kropki dot are in a 1:2 ratio. Not all possible kropki dots are given.
Killer Cages: Digits in a cage do not repeat and sum to the value in the top left corner.
XV Pairs: Digits separated by a V sum to 5. Digits separated by an X sum to 10.
Solution code: Row 9 (left to right)
Comments
on 26. August 2025, 13:38 by jjianggg
I think it's "at least 3 diff", right?
on 22. June 2025, 11:25 by kyuquu
Added clarification about the modular lines (sorry about that!)
on 8. June 2025, 22:49 by Flinty
It's only a 1 star for solvers that are happy go lucky making assumptions, it's definitely not a 1 star to solve logically.
on 2. June 2025, 15:09 by m_and_m_toastie
Very fun, and perfect 1 star difficulty (even if I kept making mistakes).
Thank you @xrrx for sharing the modulo 3 combinations
on 17. May 2025, 01:21 by GreenieColonThree
me likey
on 14. May 2025, 18:01 by Slumped_5
Great puzzle! Very intricate logic for a 1* puzzle, but enjoyable nonetheless!
on 14. May 2025, 16:37 by Friedhelm
Well done!
on 13. May 2025, 22:27 by JoeyJoeJoe
I did not need to assume there was one modular line to solve this puzzle
on 13. May 2025, 21:41 by Ganbatte
Thank you @xrrx for defining the modulo 3 rule.
on 13. May 2025, 18:53 by Martina
@VitP I had to make that assumption as well.
on 13. May 2025, 18:29 by fishsaltyak
Solvable without additional rules.
Fun puzzle, thanks!
on 13. May 2025, 18:20 by kyuquu
Added dynamic fog to the rules (oops!)
on 13. May 2025, 16:04 by thoughtbyte
Very fun puzzle, thanks!
on 13. May 2025, 15:05 by Myfyr MJ
Very nice fun puzzle.
on 13. May 2025, 14:29 by xocolatl
@VitP, I solved it without assuming anything that wasn't specifically mentioned in the rules.
on 13. May 2025, 14:25 by PinkNickels
Very enjoyable solve! It wasn't super hard, but it was well designed and aesthetically pleasing. Well done!
on 13. May 2025, 13:04 by Gowgon
Nice puzzle. Smooth solve with rules as is.
on 13. May 2025, 12:32 by zonny
Puzzle solves very smoothly without any need to change rules.
on 13. May 2025, 12:06 by VitP
do you mean for there to be ONE modular line, having SIMPLE geometry?
because that is NOT what the rules say, and without that assumption, the puzzle appears to be insoluble.
@VitP I suppose it wouldn't hurt to mention that the line can only travel in a straight line orthogonally or diagonally, but the puzzle is indeed solvable with this in mind, even if you allow that there could be multiple lines.
- kyu
on 13. May 2025, 09:19 by xrrx
Just for the others in case they dont know: residuals of modulo 3 are these combinations 147, 258, 369
