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Pythagorean Triples

How many right-angled triangles are there with sides that are all integers less than 100 units?

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A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area?

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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Rectangle Dissection

Age 11 to 14 Short Challenge Level:

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.