### Outside Nurikabe by Tapio Saarinen

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Theme: Clue Symmetry and Logic.

Author/Opus: This is the 2nd puzzle from guest contributor Tapio Saarinen (including an earlier Sunday Surprise co-authored with Thomas Snyder).

Rules: In this variation of Nurikabe, the island clues are now given outside the grid. These numbers must be placed in the first white island cell encountered in the corresponding direction. Each number represents a distinct island, with a total of 10 islands in this puzzle.

Answer String: Enter the length in cells of each of the black segments (the unnumbered, connected “ocean”) from left to right for the marked rows, starting at the top. Separate each row’s entry from the next with a comma.

Time Standards (highlight to view): Grandmaster = 5:45, Master = 8:30, Expert = 17:00

Solution: PDF; a solution video is available here.

Note: Follow this link for classic Nurikabe puzzles on this website and this link for other variations on Nurikabe puzzles. If you are new to this puzzle type, here are our easiest Nurikabe puzzles to get started on.

• Nikolai says:

A pretty difficult puzzle, to me at least. The opening was very neat and tidy, but after that I had to do a lot of educated guesswork as well as some metalogic; took me about the expert time altogether. I enjoyed it a great deal, though; it’s a very cool execution of a very cool idea. Thanks 🙂

• Para says:

I think it’s probably not that difficult anymore after having done a few more. It took a while to understand the logic for me on how the different islands interact. But once I got that down, it turned into a quick filling exercise.

• Nikolai says:

Does this mean that there are more of these out there? I haven’t seen any, and I’d like to.

• Para says:

I don’t know. I just meant, when solving this I noticed a few things that would make it easier to do the next one as I don’t have to find them out again.

• Aaron Chan says:

It’s a tough puzzle. I ended up guessing the whole lower left and beyond. Intuition basically says somehow that corner needs to be filled, and there aren’t many ways to do it.

• chaotic_iak says:

Before solving: Why do I feel like I’ve solved this? Testsolved this or something, at least.

…oh wait, not exactly. Close enough.

• To my knowledge this is a new variant, I haven’t seen any before. Then again, I wouldn’t be surprised if someone else had come up with the idea as well.

Rot13’d thoughts on the puzzle:

Lrf, gur chmmyr vf fbeg bs na bar gevpx cbal, yrnavat urnivyl ba ertvbaf orvat fdhrrmrq orgjrra ertvbayrff ebjf. Nf vg’f n (cerfhznoyl) arj inevnag V’z fher gung’f abg nyy gurer vf gb gur chmmyr glcr. V xabj V’yy or gelvat gb znxr fbzr zber.

Gur vagraqrq fbyivat cngu tbrf obggbz evtug, gbc yrsg, gbc evtug, obggbz yrsg. Gur obggbz evtug pbeare vf zrnag nf n fbeg bs vagebqhpgvba gb gur ybtvp, nsgre juvpu gur bgure oernx-va va gur hccre yrsg pbeare fubhyq or rnfvre.

Gur chmmyr qbrf erdhver n yvggyr ovshepngvba, juvpu cebonoyl pnhfrf gur “uneq ohg vaghvgvir” srry.

• chaotic_iak says:

05:07, although that simply finds one solution; after the easier quadrants, I just happened to stumble on a solution, which after checked turns out to be correct. So…

I’m still figuring out a logical solution here. I have a rough logical solution, but that’s rough, with unpolished stuff, like “that 3 at the bottom right has the island somewhere bottom left, and the 8/7/7 combo needs to fill in somewhere in the middle…” Nice idea, somewhat unfortunate execution.

• I guess the boundary between logical and exploring a bifurcation is always fuzzy – depends on your spatial imagination. Similarly sometimes logical deductions get rolled up into correct compound intuitions.

That said – yes, I also found this puzzle to be far more on the explore/intuition side than average, which always makes me wonder if I missed something more incrementally smart.

Quite possibly not. Patreons get some talkthroughs as rewards. This week Thomas Snyder explained his solution path for this very puzzle, and although he manages to make the fuzzy boundary clearer, there are several “and you can kind of see that there’s no room” points and acknowledgement that the deductions are much less atomic than usual.

Still enjoyed the puzzle lots. Thanks Tapio!

• drsudoku says:

I’ve written about that boundary before and my standard is described like this: “could I have solved the puzzle in ink?” This is a cute way of asking are the necessary explorations quick enough to uncover contradictions that solvers can do them in their head. My definition is an extension to all puzzles of what is called a Nishio in Sudoku, where if the unusual contradiction is simple enough to find, then Tetsuya Nishio is still comfortable publishing it.

This Outside Nurikabe is a little closer to or just across the boundary than usual. But to highlight a different kind of idea and a different constructor I felt it was a good choice. Tapio’s style often requires more exploration that other authors. This is in part because his ideas are often new, so you don’t know enough solving heuristics, and also that the puzzles are just hard in general.

• Francis says:

I found this one more of an impressive construction and less of a fun solve. It was definitely interesting, though, and I didn’t think the trial-and-error parts were necessarily a flaw just because they took me a while to work through; they were all reasonably self-contained even though the progress made after each one was incremental until I’d chfurq gur “cbvag orsber juvpu gur 5 ertvba pna’g ortva” sne rabhtu gb gur evtug gb svanyyl sbepr gur cynprzrag bs gur 1 ertvba.

• Tricia says:

It’s funny that the discussion here has already gone in the direction of whether the puzzle can be solved in ink, because I was just stopping by to mention that after this puzzle, I wish I owned stock in an eraser company.

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