PSE Advent Calendar 2022 (Day 6): Christmas and Squares

Question

<sub>This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2022. The accepted answer to this question will be awarded a bounty worth 50 reputation.

< Previous DoorNext Door ></sub>

---

Today's door leads to a signature "easy" puzzle by Anonymus25! I know, some of my recent puzzles haven't performed well (and by recent, I mean many months ago), but I'm back and ready to try again! As I said before, this puzzle is "easy", but only if you truly understand this genre's deductions. It's a Circles and Squares!

Rules: Shade some cells such that all shaded cells form one single orthogonally connected area, and no 2x2 anywhere in the grid may be fully shaded (as in Nurikabe). All unshaded areas must form squares. Black circles are shaded, white circles are unshaded.

Some good example puzzles include this one by Athin and this one by me.

Here's a Penpa link to solve online.

P.S. The green, red, and brown are purely for aesthetics.

Answer 1

Before we continue any further,

Green: Unshaded on this move
Blue: Shaded on this move
Grey: Shaded
Orange: Unshaded

Firstly, the most basic deductions:

Then, we know these squares must be the case: This is because the bottom middle square must be the same (3 by 3), while the left bottom corner square is quickly resolved. That resolves the squares around it as well. At the top, more shaded squares are resolved due to the white squares stopping bigger squares from emerging.

Because of the 2 x 2 square rule, these squares are made:

Further deductions are then made:

Simple small deductions are made here, still relatively easy:

But stupid me, I made a mistake in the bottom left corner. Fixing it now: The bottom right is also solved, as a 3 by 3 square cannot be made.

Then, most of the top right is solved:

Finally, we get the middle resolved: This is because Both white circles there, none of them could have been a 2 x 2 square without causing contradiction to the black squares.

Using the 2 x 2 shaded square rule on R4 C4: , we get a lot of deductions

Almost sense the end... , all those white circles all must be 1 x 1's.

The white circle must be a 2 x 2 square due to the 2 x 2 shading rule...

DONE! VOILA!