IMO 2021 Shortlist C5
Let n and k be two integers with n ą k ě 1. There are 2n 1 students standing in a circle. Each student S has 2k neighbou...
Category: Combinatorics
Problem
Let n and k be two integers with n ą k ě 1. There are 2n 1 students standing in a circle. Each student S has 2k neighbours— namely, the k students closest to S on the right, and the k students closest to S on the left. Suppose that n 1 of the students are girls, and the other n are boys. Prove that there is
a girl with at least k girls among her neighbours.