How many right-angled triangles are there with sides that are all
integers less than 100 units?
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?
Which is a better fit, a square peg in a round hole or a round peg
in a square hole?
Semicircles are drawn on the sides of a rectangle ABCD as shown
in the diagram. A circle passing through points ABCD carves out
four crescent-shaped regions (coloured yellow and green in the
Prove that the sum of the areas of the four crescents is equal
in area to the rectangle ABCD.