CV086 - Squares and Circles

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Squares and Circles
086T.gif
086B.gif
Puzzle Number 086
Puzzle Name Squares and Circles
Picarats Given 30 Picarats
Type Write Answer
Location Sewer Dead End
Previous Puzzle CV085 - Weekend Getaway (US)
CV085 - Train Speed (UK)
Next Puzzle CV087 - Ferris Wheel Riddle

This is the eighty-sixth puzzle that appears in Professor Layton and the Curious Village. To access this puzzle, you must talk to Sylvain. In order to solve this puzzle, you must determine how much larger the blue square is than the red square.

Contents

[edit] Hints

Hint One
    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.

Hint Two
    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.

Hint Three
    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 it for yourself.


[edit] Messages

[edit] When Failed

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.

[edit] When Completed

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.

[edit] Solution

086ST.gif

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

[edit] Progress

3335 Picarats and 157 Hint Coins.



Last edited by Squiggle on 1 January 2016 at 04:51
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