Mega Circles And Squares

Question

Since recently Athin showed Circles And Squares, a genre which I invented and am very proud of, I thought "Hey, why not give another one!" But this time, I'm sharing one that I made for both the Puzzler's Club and CTC Discord.

Even though the size might terrify you, it should be approachable, as well as some bits of logic which weren't present in Athin's puzzle. Should be a fun solve!

Rules:

1. Shade some cells such that all shaded cells form one orthogonally connected area.
2. Black circles are shaded and white circles are unshaded.
3. Unshaded area must form squares.
4. No 2x2 can be fully shaded.

Penpa link: https://tinyurl.com/79j8crjx

Answer 1

Solution:

For this explanation:

• Blue = shaded
• Green = unshaded
• Yellow = shaded on this move
• Red = unshaded on this move

On the top row, rows of consecutive white circles must be nxn squares



And must have walls around them:



Likewise for the bottom row:

Certain cells must be unshaded because of the 2x2 rule

And the ones in the center of the top row force a 2x2 square

Likewise, another square is forced

A major breakthrough! These groups must be 3x3 squares because otherwise the squares marked pink would be shaded and disconnected. They cannot be any larger. They must have walls around them.

Some minor deductions help us sort out the area below that

The chunk in the bottom left must remain connected to the rest.

The chunk in the bottom right must connect to the rest, but there are tight restraints on where it can go...

This allows us to fill out the rest of that corner.

A few more deductions...

This square has to be a 2x2.

A few more deductions...

This cell must be shaded to break up the squares to either side.

Which opens up a bunch of stuff.

This square is at least a 2x2.

Because of the pink cell, the two nearby green cells cannot be connected into a 3x3.

This cell can't be connected to the cell to the bottom right, it must be on its own.

Which forces the states of these two.

This group can't be any larger than 2x2 because of the pink cell.

Which forces some more deductions...

Another simple deduction.


The red cell must be empty because otherwise there would be a 2x2 shaded square. It forces the neighbouring square to be 2x2.

Some more simple deductions solve that chunk.

The red cells must be empty because of the 2x2 shaded rule, and can't be connected because of the pink squares.

Certain squares must be filled in.

There are four possibilities for the central two white circles:




But only the last is legal.

These two red cells must form a 2x2 square:

Finishing the square:

A few more deductions and we're done!

Final solution:

Feel free to fix the formatting, spoilers are a pain.