Olympiad Combinatorics Problems Solutions Apr 2026

Count the total number of handshakes (sum of all handshake counts divided by 2). The sum of degrees is even. The sum of even degrees is even, so the sum of odd degrees must also be even. Hence, an even number of people have odd degree.

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

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. Count the total number of handshakes (sum of

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. Hence, an even number of people have odd degree