A finite set of points in the plane, not all collinear. Prove there exists a line passing through exactly two of the points.

When a problem involves moves or transformations, look for what doesn’t change modulo 2, modulo 3, or some clever coloring. 3. Double Counting: Two Ways to Tell the Same Story One of the most elegant weapons in the Olympiad arsenal. Count the same set of objects in two different ways to derive an identity.

Let’s break down the most common types of Olympiad combinatorics problems and the strategies to solve them. The principle is deceptively simple: If you put (n) items into (m) boxes and (n > m), at least one box contains two items.

A knight starts on a standard chessboard. Is it possible to visit every square exactly once and return to the start (a closed tour)?

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Olympiad Combinatorics Problems Solutions May 2026

A finite set of points in the plane, not all collinear. Prove there exists a line passing through exactly two of the points.

When a problem involves moves or transformations, look for what doesn’t change modulo 2, modulo 3, or some clever coloring. 3. Double Counting: Two Ways to Tell the Same Story One of the most elegant weapons in the Olympiad arsenal. Count the same set of objects in two different ways to derive an identity. Olympiad Combinatorics Problems Solutions

Let’s break down the most common types of Olympiad combinatorics problems and the strategies to solve them. The principle is deceptively simple: If you put (n) items into (m) boxes and (n > m), at least one box contains two items. A finite set of points in the plane, not all collinear

A knight starts on a standard chessboard. Is it possible to visit every square exactly once and return to the start (a closed tour)? Let’s break down the most common types of