Olympiad Combinatorics Problems | Solutions

When stuck, ask: “What’s the smallest/biggest/largest/minimal possible …?” 5. Graph Theory Modeling: Turn the Problem into Vertices & Edges Many combinatorial problems—about friendships, tournaments, networks, or matchings—are secretly graph problems.

But here’s the secret:

At a party, some people shake hands. Prove that the number of people who shake an odd number of hands is even. Olympiad Combinatorics Problems Solutions

When a problem says "prove there exist two such that…", think pigeonhole. 2. Invariants & Monovariants: Finding the Unchanging Invariants are properties that never change under allowed operations. Monovariants are quantities that always increase or decrease (but never go back). Olympiad Combinatorics Problems Solutions