Home > Olympiad > IMC 2011 Day 1 Problem 5

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.

 

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