Uneven Terrain (Parity Cave Sudoku)
(Published on 29. January 2022, 20:15 by Nordy)
After many months of incubation, I finally figured out a way to make this puzzle work. Hope you enjoy!
Rules:
Normal Sudoku: Place the digits 1 to 9 in every row, column, and 3x3 box.
Odd Cave and Even Walls: In short, all of the odd digits belong to a cave, and all of the even digits belong to the walls. No 2x2 region is completely filled with cave cells or wall cells. In long:
- Some cells must be shaded so that all shaded cells (the walls) are orthogonally connected to the edge of the grid and all unshaded cells (the cave) form an orthogonally connected area.
- Cave cells must contain odd digits.
- Wall cells must contain even digits.
- No 2x2 region may be completely filled with cave cells or completely filled with wall cells.
Parity Sum Cages: Within each cage, the sum of odd digits equals the sum of even digits, and digits must not repeat.
For visual reference, here is a 9x9 example of a 1-cell wide cave (unshaded cells) with 1-cell wide walls (shaded cells). Note that this example would not satisfy the odd/even restrictions in this puzzle, and as a short exercise, I recommend confirming that.
And here is the puzzle. You can solve online:
Solution code: Row 9 then Column 9
Comments
on 10. February 2024, 23:58 by yttrio
Fantastic puzzle, it was quite amazing how the rule set lent itself to being solvable at all! I definitely struggled near the beginning, but once my shading got going it was much smoother sailing.
on 15. August 2023, 17:43 by quantumquark1
It took 3 hours over 2 days but I finally beat it, thanks for the amazing puzzle!
on 12. June 2023, 04:40 by damasosos92
I cannot believe this puzzle exists. That's fantastic. The rules interact in a simple but always intriguing way. I found myself stuck for long minutes every time, and solving it live was a real blast.
It's a lovely and looong ride around beautiful discovery. Very recommended, that's really insane. I had to discover every property of the cages in the grid, and the puzzle stays always fair. Difficult, but fair. Thank you Nordy, I loved it.
on 26. July 2022, 00:46 by Nordy
Updated rules text for clarification
on 10. July 2022, 19:17 by Nordy
Puzzle title upgrade
on 5. July 2022, 13:48 by filuta
Very tough, but I really liked how the rulesets interacted. Great puzzle!
on 18. June 2022, 04:32 by Nordy
Updated difficulty estimate
on 8. April 2022, 23:23 by DiMono
This was a wild ride. 4/5 difficulty might be underselling it a bit. Fantastic puzzle!
on 8. April 2022, 19:18 by Qodec
Wow, incredible!
on 17. March 2022, 22:25 by Nordy
@henrypijames: I’ve been using bold in all my future rule sets! Thanks for the feedback :)
@Phistomefel: I’m not sure whether to say sorry, congratulations on finally solving, or both :P I agree that there are some obscure steps. I went with 4 stars because, if you know where to look, the logic is tricky but not extreme. Still learning how much value to ascribe to the “if you know where to look” part though…
@Dandelo: I appreciate your geometric wisdom!! I like the idea of calling it “coral” - fits very well visually. I’ll keep that in mind for next time :)
on 17. March 2022, 18:27 by Dandelo
Very nice puzzle.
There are both types of caves, with anti-2x2-rule and without. For a while German authors usually used it, but others didn't. Now it is usually not used anymore.
The shape now usually is called coral instead of cave. Corals always use the anti-2x2-rule. And since there are neither cave clues nor coral clues, maybe coral would be more suitable. But it's the author's choice and esp. here you'll find some anti-2x2-caves.
on 17. March 2022, 16:05 by Phistomefel
Oh my god, I cannot begin to tell you how difficult this was for me. This puzzle hit every single weak spot of my solving abilities. The deductions were always at the point I least expected them. Having said that, I really enjoyed the ride and some of the logical steps in there were just exquisit. Thank you, Nordy! :)
on 1. February 2022, 13:32 by henrypijames
Again suffered needlessly for hours until I went back and re-read the rules to realize I'd totally missed the anti-2×2 rule. So typical of me!
Though in hindsight, it was rather remarkable that I managed to solve about 2/3 of the puzzle without applying that rule.
--Ha, and to think I tried to over mention that rule to avoid this exact situation... :P perhaps I shouldn't have overlooked a tactical use of bolding. Hopefully the next person who attempts this puzzle will read your comment first!
<<<
Is the anti-2×2 rule a regular part of cave puzzles? If so, it's just my ignorance of pencil puzzles; but if not, it'd be better to list that rule separately, instead of as a sub-point of the parity cave. And yes, I'm a big proponent to strategic use of *bold* words in rules.
on 29. January 2022, 22:36 by Tilberg
Oh boy, what a ride.
