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?
I have four rectangular pieces of thin hardboard whose dimensions (in cm) are 55 x 85, 65 x 75, 65 x 85, 90 x 105. Without bending the hardboard, how many of these can I get through an open rectangular window measuring 60 cm x 80 cm?
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.