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My friend Thetis and I cons— wait, where's Thetis? Hmm, that's funny... she was here a minute ago....

Wait, a note!... Oh dear, it seems things have taken a turn from bad to worse; Thetis is not only missing but she's been abducted! Thetis is asking us to help find her, but to prevent her hijackers from making it off with the perfect crime, she left clues to her whereabouts (How she got this information by her kidnappers, I have no idea).

Thetis usually likes Tapa Puzzles1, but this doesn't look like a typical Tapa...

Zed's second Thetis grid

No, wait! This isn't a Tapa Puzzle... i–it's a Kurotto Puzzle; perhaps Thetis doesn't want her captors to know it was her leaving breadcrumbs! Hmm... it doesn't look quite right, though... What are these random dots scattered about? Oh, another note... It says these dots are called "pearls — both black and white for all shades of beauty"... hmm, more like casting your pearls before swine.

The note says that if we can solve the puzzle, her location would be "magically revealed". Let me try first... huh? I–It all looks Greek to me; it's just garbled-up nonsense... ugh, I guess this puzzle is Thetis' swan song, huh?


I got nowhere with this note, so perhaps you might have better luck than me... We need to find Thetis quickly; who knows what her captors are planning to do with her?

To solve the puzzle, you need to discover the hidden message in the Kurotto Puzzle that reveals where Thetis is being held.

For those of you who never heard of a Kurotto Puzzle, here is a summary of the rules provided by the Grandmaster's "Art of Puzzles" archive:

  • You shade in the cells of the grid so each number represents the total count of shaded cells in orthogonal polyominoes (i.e., groups of connected cells that shares an edge in any of the Cardinal directions).
  • You cannot shade in numbered cells; these are hints.
  • Cells with a "?" are wildcards; they can share an edge with any natural number (i.e., integer greater than zero) of cells.

As well, there are some special rules that are included in this version of the Kurotto Puzzle:

  • Shaded cells cannot form a 2×2 square, or 'pool,' anywhere in the grid.
  • "Pearls" can be treated as wildcards
    • However, the ratio between the total number of cells for white 'pearls' and the number for 'black' pearls is 19:4.

1I want apologize to anyone who tried solving my first "Thetis" puzzle, especially @Deusovi; I rushed to make a puzzle that turned out to be unsolvable despite my best efforts to make a unique solution (not only that, the end solution was rather dull and contrived). Hopefully this second version of this puzzle — with a new solution and a new strategy — is much more entertaining and concise.

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Partial answer: logic solved, stuck on extraction

First, some easy deductions can be made:

enter image description here

Next,

the 14 in the top row needs another group of 7 to satisfy it; this group cannot be the one on the left (which must be a 7 due to the "18" clue), so it must be on the right. The same logic can be used on the topmost 14 in the second-to-last column. enter image description here

For another step,

we need a 17, a 13, and an 8 in the upper left region. There is only one way to fit all of these regions in.
Similarly, there is only one way to fit a 17 in the bottom left without hitting the 11.
enter image description here

And to finish the puzzle,

there's only one way to fit the 16 into the bottom right.
enter image description here

Now,

I'm not sure how to get an extraction. It seems clear that we need to ignore every fourth row and column to get a bunch of shapes:
enter image description here
But it's not clear how to interpret these. I've tried a number of variations of the pigpen cipher (using "no dot", "white dot", and "black dot" as three pigpen grids). I've also noticed that the question marks are suspiciously placed as well: both in a place where a dot would be. None of these approaches have worked for me yet.

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    $\begingroup$ Some feedback on the logic: It is very overclued. I would say that maybe 15-20 of these numbers are necessary at most - the rest could easily be question-marked, just because you use so many clues. And I'd say at least a third of these numbers could be removed entirely, if not more: because of how tightly packed these shapes are, and the fact that shapes can't collide, a bunch of clues could've been left out entirely without affecting the logic. (Also, the pearl restriction was completely unnecessary -- I would recommend just removing extra rules like that entirely.) $\endgroup$ – Deusovi May 1 at 23:22
  • $\begingroup$ Very good progress so far, but it feels like I've inadvertently insulted your intelligence by making this puzzle, @Deusovi. For myself, it took a while to solve, even if I probably made the grid puzzle too easy, but that's because I wanted to make sure I didn't make the same mistake as last time and I wasn't sure what would be needed to solve the puzzle (it also shows how inexperienced I am with Kurotto or Tapa and the likes; deduction puzzles aren't my forte). The challenge, then, is the second half, isn't it? $\endgroup$ – Omicron Zed May 2 at 16:17

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