Swiss Mathematical Olympiad Archive

SMO Archive

First Round

Algebra

Arithmetic

Variables and Equations

Real Numbers

Rational Numbers

Algebraic Manipulations

Order of Operations

Combinatorics

Simple Counting

Counterexamples

Constructions

Case Distinctions

Tilings

Dates and Times

Geometry

Points, Lines and Circles

Polygons

Simple 3D Objects

Angles in Degrees

Areas and Perimeters

Distances

Spacial Reasoning

Reflection and Rotation

Number Theory

Integer Numbers

Digits of an Integer

Perfect Powers

Simple Factoring

Parity

Divisors and Multiples

Prime Numbers

Second Round

Combinatorics

Divide and Conquer

Fundamental Selction Processes

Inclusion-Exclusion Principle

Pigeonhole Principle

Geometry

Angles in Triangles

Angles in Circles

Cyclic Quadrilaterals

Number Theory

Divisibility

GCD and LCM

Estimations

Induction

Final Round

Algebra

Inequalities

QM-AM-GM-HM

Cauchy Schwarz

Functional Equations

Variable Substitutions

Injectivity and Surjectivity

Equating Terms

Discrete Domains

Sequences

Change of Variables

Periodicity

Telescoping Sums

Recurrence Relations

Combinatorics

Double Counting

Invariants and Monovariants

Extremal Principle

Colouring Arguments

Combinatorial Games

Geometry

Similar Triangles

Power of a Point

Working Backwards

Trigonometry

Ceva and Menelaus

Number Theory

Modular Arithmetic

Euler-Fermat

Chinese Remainder Theorem

Orders

P-adic Valuations

Selection

Algebra

Inequalities

Jensen

General Mean

Hölder

Ordered Sequences

Chebyshev

Functional Equations

Cauchy Equation

Functional Substitution

Fixed Points

Monotonicity

Polynomials

Vieta

Complex Numbers

Irreducibility

Symmetric Plynomials

Combinatorics

Graph Theory

Combinatorial Geometry

Probabilistic Method

Geometry

Pascal and Brianchon

Symmedians

Inversions

Cross-Ratio

Number Theory

Generators

Pell's Equation

Pythagorean Triples

Cyclotomic Polynomials

Lifting the Exponent