# Zed's Mystery: Thetis… Vanished into Thin Air!

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 also 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...

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" for whatever reason... 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 also be treated as wildcards.

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.

HINTS:

I could've added the tag to help out, but how do I know you're not one of Thetis' captors in disguise?!

Edward Brumgnach and Dan Brown would be disappointed.

Maybe you shouldn't take me so literally — transliterally, perhaps?

Oh, how could I have missed this! There's a tape recording on the back of one Thetis' notes! Perhaps she got one of her captors' voices on tape? Here, I'll play it for you...

1: Brothers, I think this is a perfect spot t– Wait, where's the key?2: You lost the key?!1: No, I gave it to Stan. He should have it, right?3: I thought you left it unlocked?2: You mean all this time the door was left open?!1: Relax, brothers, relax...I have a trick.(A pause)2: You're doing it wrong!3: Yeah, you have it backwards!2: No, upside-down, you dolt!1: Stop breathing on me!3: (whispered) So much for being sincere.1: Oh, hush up, Stan.(Another pause, then a door creaking)4: Ah, welcome brothers! What took you so long?3: See? What did I tell you? Unlocked!2: Boy, if it wasn't for our treaty, you'd be mud!1: Quiet now, fools! She's waking up!
Wha— Who the heck are these people?

Partial answer: logic solved, stuck on extraction

First, some easy deductions can be made:

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.

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.

And to finish the puzzle,

there's only one way to fit the 16 into the bottom right.

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:

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.

• 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.) – Deusovi May 1 '20 at 23:22
• 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? – Omicron Zed May 2 '20 at 16:17
• I think the fact that there was Greek writing on the note should refer to some kind of Greek cipher, then try to convert the picture into writing and decode it with the Greek cipher? Or, the location may be in Greece? It's just because the name Thetis sounds like a Greek name... I could be wrong though. Nice puzzle by the way, +1 to question and answer. – user71418 Sep 24 '20 at 8:56
• Also, I found that one of the people in the hint writes computer programming books. – user71418 Sep 24 '20 at 9:05
• I think this is almost certainly referring to a Magic Square, and more specifically, possibly Durer's Magic Square. I spent a long time trying to map both Greek and Roman letters onto both a 4x4 and a 5x5 square, but haven't come up with any real sorts of phrases. – kristinalustig Oct 1 '20 at 21:01