Friends in the Fog
(Published on 13. April 2025, 06:52 by pdyxs)
This is a follow-up to Whispers in the Mist, where fog clearance has a clear and defined meaning.
Rules
Sudoku: Fill the grid with the digits 1-9, so that each digit occurs exactly once in every row, every column and every 3x3 box.
Nurikabe: Divide the grid into a number of islands — orthogonally-connected groups of cells. Every island contains a single circled cell; the digit in the circle indicates the number of cells making up the island.
The islands are surrounded by a waterway — a single orthogonally-connected group of cells. Digits on islands can repeat if otherwise allowed.
All caged cells are waterway cells; the digit in a caged cell indicates how many waterway cells are seen orthogonally from that position, including itself (island cells block vision). The waterway cannot form any 2x2 areas.
Nurikabe fog: The grid is covered in fog. A correct digit entered into a waterway cell will clear fog from that cell, and from any waterway cells which are adjacent (either orthogonally or diagonally). The fog on island cells will never be cleared.
Friendly Islands: A cell is “friendly” if it has a value identical to its row-, column- or box-number (e.g. r2c3 can be a 1, 2 or 3). All friendly cells in the grid must be on islands, and all circled cells are friendly.
Kropki: Digits connected by a white dot are consecutive.
More Experimental Fog puzzles:
- The grid of forking paths
- Recounting the counting
- A murder most fogged
- Cartography
- Whispers in the mist
- Some Things Fogn
- Recounting the Rooms
- Sunny, with a chance of fog
For more puzzles, follow me on Bluesky at @pdyxs.bsky.social
Solution code: The digits in all caged cells, from top to bottom and left to right, starting with the first row.
Comments
on 7. May 2025, 13:55 by QuiltyAsCharged
I love the way fog is used creatively as part of the solving process. Brilliant puzzle!
on 1. May 2025, 01:03 by pdyxs
Hey Frank, thanks so much for your comments. I'm sorry to hear that the rules caused you so much trouble. It's generally pretty hard to predict every way that a ruleset could be misinterpreted, so I tend to look for wordings from other puzzles that have been widely used. I probably didn't pick the best source in this case, though what I might look to do in future is actually link to an example (which tends to clarify things much better than anything else).
Yeah, I agree that the difficulty for puzzles is pretty all over the place - something can be 'easy' if you know a certain trick, but basically inscrutable otherwise. It probably doesn't help you that i made this just after CTC published a nurikabe sudoku puzzle pack, meaning that the rules and tricks of the format are probably more widely known.
on 25. April 2025, 00:40 by Frank Puzzles
This was a lovely puzzle, but there are a couple of things I want to talk about.
It would be greatly appreciated in the future if a complete version of the nurikabe rules were explicitly stated. I haven't done many nurikabe puzzles, so I didn't know that islands cannot be orthogonally connected to DIFFERENT islands, and so was stuck for around half an hour trying to understand how to break-in this puzzle.
Also, even with knowledge of that ruleset, IMO, this is nowhere near an "easy" puzzle, as it requires a lot of thought of where you can place certain digits because of the friendship ruleset which is not trivial. Now, this is not on the setter at all, but IMO, people shouldn't assume a facile knowledge of nurikabe puzzles when grading the difficulty of puzzles.
It could be that the vast majority of people on LMD are familiar with the puzzle type and the tricks involved in it, and that I'm just barking up the wrong tree. If so, I'd love to know that too.
My video for this won't come up until May 15th, as I've added a whole backload of solves to my channel, but please let me know if you're interested in seeing my solve of this puzzle (along with my frustrations :D).
on 18. April 2025, 12:35 by JoBerlin
I really liked this combination of Nurikabe and friendly cells!
on 15. April 2025, 00:17 by pdyxs
Thanks for the lovely comment TheNineElements! I'm glad you enjoyed it! And yeah, the negative constraint ended up being pretty forcing - I originally wanted this to use the fog clearance a lot more, but the friends were just too powerful!
In terms of the 2x2, I'm generally pretty hesitant add rules that say what the rules aren't, as it adds extra length to the rules which tends to be confusing in and of itself (especially since others will have different solving histories and therefore different assumptions). In this case, the island rules are completely standard nurikabe rules, and so I err on the side of only saying what the rules are.
I did add a clarification that digits can repeat on islands since that's a common pattern in combining nurikabe with sudoku and I'm deviating from that norm.
on 13. April 2025, 09:28 by TheNineElements
Solve Time: 68:07
I rated this 3/5 difficulty
Great puzzle! I found the logic to be quite tricky, but once I fully understood what the rules were everything came together nicely.
I spent FAR too long (probably 30 minutes) with extremely stalled progress in the early midgame because I had failed to realize that there was a negative constraint on the 'friendly' values (I.e., water cells cannot be "friendly"). Of course this is obvious in hindsight, but got very stuck early on with zero clue how to proceed - contributing to my longer solve time.
Either way, once I realized that, I began making quicker progress and the rest of the solve went smoothly. That rule was very interesting and led to some really nice logic.
Thanks for sharing!
Edit:
I might suggest adding a clarifying note in the rules about whether or not islands are permitted to form 2*2 regions.
The rules explicitly state that 2*2 regions of water cells are illegal - but does not state the same about island cells (which does imply we can't assume that the same restriction applies).
As it currently reads (in a vacuum), I think it is fair to assume that islands are permitted to form 2*2 regions. However, other similar rulesets (like yin/yang) would suggest that 2*2 islands are illegal.
Since this confusion/ambiguity may arise depending on the solver's knowledge of the ruleset (and how carefully they read the rules) I think it would be worth specifying just to avoid any potential issues/confusion.
This really shouldn't be a big deal, but just something I noticed.
