Oil, Water, Paths
(Published on 21. April 2025, 16:00 by Blobz)
Image generated with Hotpot AI Art Generator
Normal sudoku rules apply.
Digits in cages do not repeat and must sum to the small clue, if given.
Each cage is either full of "oil" (even digits), full of "water" (odd digits), or a mix of both. In all cases, each "row" within a cage is of just one type (oil or water). Oil floats on water, so even digits will always be in rows above odd digits in mixed cages.
A path consisting of the digits 1 to 9, in order, crosses from left to right across the grid with each digit in its corresponding column (1 in column 1, 2 in column 2, etc.) The cells along the path are connected orthogonally or diagonally. A similar path crosses the grid from top to bottom, starting with a 1 in row 1, then a 2 in row 2, ending with a 9 in row 9. Again, cells along the path are connected orthogonally or diagonally.
Each path oscillates inside/outside cages, such that all of one path's oil cells (but not water cells) are in cages, and all the other path's water cells (but not oil cells) are in cages. It is permissible for a path to exit and re-enter the same cage.
The two paths (which do not share cells) must be determined by the solver.
Have fun, leave a comment if you enjoy the puzzle!
Solution code: Row 6
Comments
yesterday, 16:11 by bboom
Really enjoyed this one. It had me staring blankly at the grid for a fair bit until some doodling make things click for me, and from there on it was a fun smooth solve without being too easy.
on 28. April 2025, 01:58 by firespire
Not came across an idea like this before. Very satisfying to find the path.
on 24. April 2025, 13:58 by LehanLehan
Such a beautiful combination, thank you very much for the puzzle.
on 22. April 2025, 12:02 by Franjo
I thought the path rules were a bit too complicated. Well, I was totally wrong, and it was a pleasure to find the way through. Thank you very much for creating and sharing this lovely puzzle.
on 21. April 2025, 22:35 by kdkirby
Yay, more oil and water! Loved it, thank you!
on 21. April 2025, 19:42 by teff
very nice, love the series
on 21. April 2025, 19:05 by tryote
remarkably satisfying
