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IMC 2011 Day 1 Problem 5

Let $n$ be a positive integer and let $V$ be a $(2n-1)$-dimensional vector space over the field with two elements. Prove that for arbitrary vectors $v_1,v_2,...,v_{4n-1} \in V$, there exists a sequence $1 \leq i_1 <...< i_{2n} \leq 4n-1$ of indices such that $v_{i_1}+...+v_{i_{2n}}=0$.