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Shrinking square

By David, 5 August 2021 Brainteaser

Difficulty: Fun

Alex has a square of paper, but it’s a bit too big. To make it smaller, they found the middle of each side, and then ruled lines between them. Then they cut off the four corners along the lines, leaving a square in the middle.

Is there more paper in the small square, or in the bits that got cut off?

Scroll down or click for a hint, or the answer!

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Brainteaser hint

This brainteaser is a lot easier if you try drawing it!

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Brainteaser answer

The square and the scraps are exactly the same size! To see why, imagine that Alex folded along the lines instead of cutting. The flaps will all meet in the centre, fully covering the little square with no gaps and no overlaps. That means the area of the flaps and the area of the small square must be the same.

Cross on a square of paper with dotted cut lines between the points of the cross.

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