IMO 2011 Shortlist C2

Suppose that 1000 students are standing in a circle. Prove that there exists an integer k with 100 ≤ k ≤ 300 such that i...

IMO 2011 Shortlist C2

Category: Combinatorics

Problem

Suppose that 1000 students are standing in a circle. Prove that there exists an integer k with 100 ≤ k ≤ 300 such that in this circle there exists a contiguous group of 2k students, for which the first half contains the same number of girls as the second half.