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.