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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:

The 16 by 9 rectangle is cut as shown.

16 by 9 rectangle cut into pieces

If the pieces are rearranged to form a square, what is the perimeter of the square?


If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.