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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Hallway Borders

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

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Lying and Cheating

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Rectangle Dissection

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

12 by 12 square

The square's perimeter is $12\times 4 = 48$

You could also look at the area of the rectangle. This is $16 \times 9 = 144$. This must be the same as the square, so the square must have side lengths of $12$. Therefore its perimeter is $12 \times 4 = 48$.


This problem is taken from the UKMT Mathematical Challenges.