Olympiad Combinatorics Problems Solutions 【LATEST — 2026】

Pick one person, say Alex. Among the other 5, either at least 3 are friends with Alex or at least 3 are strangers to Alex. By focusing on that group of 3, you apply the pigeonhole principle again to force a monochromatic triangle in the friendship graph.

Take a classic problem like “Prove that in any set of 10 integers, there exist two whose difference is divisible by 9.” Apply the pigeonhole principle. You’ve just taken the first step into a larger world. Olympiad Combinatorics Problems Solutions

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

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. Take a classic problem like “Prove that in