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This puzzle is dedicated to Sciborg. Copying the dear gentleperson, some of the 4s are hiding in the corners.

Rules: (Nurikabe section shamelessly stolen from an earlier puzzle by @jafe)

  • Numbered cells are unshaded.
  • Unshaded cells are divided into regions, all of which contain exactly one number. The number indicates how many unshaded cells there are in that region.
  • SPECIAL RULE: the regions will form a tetromino set, with rotation and reflection allowed.
  • Regions of unshaded cells cannot be (orthogonally) adjacent to one another, but they may touch at a corner.
  • All shaded cells must be connected.
  • There are no groups of shaded cells that form a 2 × 2 square anywhere in the grid.

the puzzle - see transcription below

I've included all available tetrominoes as a reference.

A playable version of this puzzle can be found here. The link leads to a puzz.link editor. Note that this editor won't force you to use the tetromino rule, and it has a timer.

The first answer with a fully-explained logical solution path will get the checkmark. I welcome multiple answers, if later ones can show a better-explained or more elegant path.

CSV:

,,,,,,4
,,,,,,
,,,4,,,
,,4,,4,,
,,,,,,
,,,,,,
4,,,,,,
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  • $\begingroup$ Should each tetromino be used exactly once? Also, this seems quite easy even to brute force since the shape is restricted. But good puzzle! $\endgroup$
    – justhalf
    Dec 2 '20 at 4:10
  • $\begingroup$ Yes, each tetromino should be used exactly once, that's what is meant by a "tetromino set". And of course you could brute-force it due to the small size, but you can do that with any small puzzle. The fun is supposed to be finding the elegant solution. $\endgroup$
    – bobble
    Dec 2 '20 at 4:12
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@Bubbler and others solved this before me, but I figured I would share my solve path too, since I love that this puzzle was dedicated to me!

So first, I filled in the obvious squares to give me a starting point:

enter image description here

Then I saw that there were two 2x2 regions that needed to be filled with island, since we can't have any 2x2 oceans. Those were these regions here:

enter image description here

Then I realized those 2x2 regions could only be reached in specific ways - that is, I needed to have the bottom right piece reach downwards, and a piece reaching up to the top left corner. So I knew that I had to place the L and the S pieces in those two spots, although I wasn't sure yet which was which.

I filled in some oceans. And, since I knew the top piece had to reach upwards:

enter image description here enter image description here

From here it was clear to me that the L piece had to go in this spot, since the S-piece wouldn't fit. So now I had placed a tetromino, and I knew the S piece had to go in the other spot in the only orientation that made sense.

enter image description here enter image description here

Now I looked at my grid again. Having placed the L and S, it was clear to me that the top right corner must be the T piece. If it was the O piece, there would be a 2x2 region left unfilled, and there wasn't enough room for it to be the I piece.

So I placed the T:

enter image description here

And from there, the final grid was clear:

enter image description here

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Apparently too late to the game, but anyway here it goes. Hope this one is the intended solving path. (I think the existing two answers have at least some logical leaps.)

Step 1:

Start by marking walls between the crammed fours at the center. Looking at top left and bottom right 2x2 corners, the only cell that can be occupied by a tetromino is the inner cell (R2C2 and R6C6 respectively).

Step 2:

R2C2 must be part of a 4 starting from either R3C4 or R4C3. That piece is an L either way. R6C6 must share the area with R4C5, and it can't be L, so it must be an S.

Step 3:

In order to avoid 2x2 wall at R6-7C4-5, the only way is to place an I horizontally at the bottom. (Placing an L starting from R4C3 to cover R6C4 doesn't work because L must contain R2C2.)

Finally:

Placing L on the left side makes problems, so L should go right and cover R3C4. Then it is straightforward to see that the middle left must be an O and the upper right corner must be a T.

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  • $\begingroup$ This is indeed the intended solve path. The exact reason that placing an L on the left side causes problems is that R5C3 must be unshaded to prevent a 2x2 in R56C34. $\endgroup$
    – bobble
    Dec 2 '20 at 4:56
  • $\begingroup$ Oh yes, that works too. $\endgroup$
    – Bubbler
    Dec 2 '20 at 4:58
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enter image description here

Will provide explanations later...please wait

Logical deductions by picture:

First of all the blue tiles represent some obvious deductions then I saw R2C2 could not be blue... So I tried this hypothetical situation....

enter image description here

But using this there was way no way to complete the grid...

enter image description here

So I saw that it could only be covered by of the tetromino on the top of the image. Then the square at R6C6 can only by covered with the remaining tetromino:

enter image description here

Then the tetromino in the bottom left could only be a straight because the last two remaining cannot be and the middle left tetromino could not be the T tetromino other wise it would block regions of blue from each other so it has to be a square so the top right in a T and with a little bit of a fiddle I solved it. enter image description here

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  • $\begingroup$ It's not clear why your "no way to complete the grid state" is required by your guessed placement of the L. Absolutely no guessing and no "fiddle" should be required; this puzzle is supposed to be solved with purely logical deduction and no case-basing. And finally, please spoiler (and crop) your pictures. $\endgroup$
    – bobble
    Dec 2 '20 at 4:49
  • $\begingroup$ The fiddling was all worked out with logical deductions I am using a phone so it takes ages to upload every single step. $\endgroup$ Dec 2 '20 at 4:53
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    $\begingroup$ Please don't post answers without logical explanations if you're only going to add in logical explanations immediately after. Even if you don't intend for it to come off this way, it appears like you're just posting to "claim a spot" and don't care about answer quality. (We talked about this on meta in the context of "lists of clues" puzzles, but it applies equally to situations like this.) $\endgroup$
    – Deusovi
    Dec 2 '20 at 5:06
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    $\begingroup$ Additionally, screenshots with a bunch of clutter like this are not particularly useful in answers. The extra bits are distracting and make the answer very hard to read -- overpowering the text that contains the actual explanation. It means that the answer will likely not be very useful for any future solvers. $\endgroup$
    – Deusovi
    Dec 2 '20 at 5:08
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    $\begingroup$ Given that you're using an image editor, you could have used "save image" feature within the app, which give much cleaner images than your screenshots here. We're not blind, we're just trying to improve the post quality. $\endgroup$
    – Bubbler
    Dec 2 '20 at 5:26

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