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Squares and Circles is a puzzle in Professor Layton and the Curious Village.

Puzzle

Sylvain brought you this diagram to see if you can help him with it.

Several circles and squares are pictured in the diagram below. How many times larger is the area of the blue square when compared to that of the red square?

Hints

Click a Tab to reveal the Hint.

Do you see the circle that touches the sides of the big blue square?

A smaller square sits inside the circle and touches it. Since the square is smaller than the circle, you can rotate it within the circle.

If you rotate the middle square 45 degrees, its corners will touch the sides of the large blue square.

At the same time, notice that this rotation has made it so that the red square's corners now make contact with the middle square.

Having trouble visualizing the rotation? Try drawing it on your screen.

From the rotation described in the second hint, draw two perpendicular lines from the outer circle through the middle to divide the squares into four quadrants.

Do this and you'll see that the middle square's area is equal to half of the blue square's. Go and try if for yourself.

Solution

Incorrect

Nope!

You don't need to work any high-level math to figure out the answer.

If you've been trying to solve this one with cold hard math, you might want to try a more simple approach.

Correct

That's right!

If you rotate the middle square 45 degrees as shown in the picture above, the answer becomes apparent.

The middle square has half the area of the large blue square, and the little red square has half the area of the middle square. Therefore, the little red square is one- fourth the size of the blue square.

The blue square is four times the size of the red square.

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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