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?
By Pythagoras Theorem, the diagonal of the window is 100 cm, which exceeds the length or breadth of all the sheets. So the first three pieces can go through the window either way and the 90 x 105 cm piece can also go through the window, provided the 90 cm edge goes first.
This problem is taken from the UKMT Mathematical Challenges.