Remainders and Cycles
Use repeating patterns and remainders to replace large calculations with small ones.
4 problemsMATHS4U · OLYMPIAD MATHEMATICS
Foundation · Years 6–8 Olympiad Problems
Number patterns, geometry and the first steps in mathematical proof.
106 problems · Hints and worked solutions
LATEST PRACTICE
Number Theory
A 12-problem lesson, from a warm-up to a complete proof.
Number Theory
Divisibility and Prime Factors
Factor integers, track prime exponents and organise possible divisors.
5 problemsDigits and Place Value
Combine place value, digit sums and divisibility tests in number puzzles.
15 problemsGCD and Coprimality
Reason with common divisors, prime factors and pairwise coprime sets.
1 problemInteger Equations
Find every integer solution using factorisation, substitutions and bounds.
4 problemsAlgebra
Sequences and Recurrences
Translate a progression or recurrence into a formula you can reason with.
2 problemsAlgebraic Reasoning and Bounds
Use simple equations, comparisons and inequalities to justify an answer.
3 problemsAge Problems
Translate family relationships and changing ages into equations.
13 problemsGeometry
Visual Geometry
Read diagrams, compare areas and reason about geometric constructions.
48 problemsLogic and Combinatorics
Logic and Proof
Use examples, counterexamples and precise logical implications.
5 problemsInvariants and Parity
Identify properties that a sequence of moves cannot change.
5 problemsThe Pigeonhole Principle
Choose useful categories and prove that a match is unavoidable.
5 problemsGames and Strategies
Find a strategy that answers every legal move of an opponent.
5 problemsNo matching topic. Try a shorter search.
Lesson lists and worksheets
Use a prepared sequence when teaching or practising a complete lesson.
Number Theory — Foundation12 problemsExamples and logical conclusions5 problemsWhat cannot change?5 problemsA match is unavoidable5 problemsA strategy that always works5 problemsAge problems — Year 613 problemsDigits and decimal notation — Years 8-913 problemsVisual geometry — Years 6-724 problemsVisual geometry — Years 8-924 problems
Previous weekly lists
The original club lists are still available in their original order.