2011 IMO Shortlist C2

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

假设 1000 名学生站成一圈。证明存在一个整数 $k$，$100 \leq k \leq 300$，使得在这个圆圈中存在一个连续的 $2 k$ 学生组，其中前半部分包含与后半部分相同数量的女孩。