IMO · International Mathematical Olympiad
Maths olympiad practice.
Short-answer contest rounds up to full IMO-style proofs.
TierTopic
Feeder round
Two powers and their last digit
Walking on a city grid
Power sums of the roots of a quadratic
Centres of a 7-24-25 triangle
National final
Three positive numbers with sum 3
How many 3s divide 2^n + 1?
Fifty-one numbers from one to a hundred
A difference-of-squares functional equation
International
The arc midpoint and Euler's inequality
When is n times a power of two, plus one, a square?
Monotone runs hidden in a list
Shifting inside a functional equation
Tier
QuestionsTime
One clock for the whole drill. Answers and explanations come at the end, like a real paper.