Olympiad: Combinatorics Problems Solutions

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.

But here’s the secret:

In a tournament (every pair of players plays one game, no ties), prove there is a ranking such that each player beats the next player in the ranking. 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. When a problem involves moves or transformations, look