Problem

Source: 2021 Saudi Arabia JBMO TST 1.4

Tags: combinatorics



Let F is the set of all sequences {(a1,a2,...,a2020)} with ai{1,1} for all i=1,2,...,2020. Prove that there exists a set S, such that SF, |S|=2020 and for any (a1,a2,...,a2020)F there exists (b1,b2,...,b2020)S, such that 2020i=1aibi=0.