IMO 1977 SL 13

Let B be a set of k sequences each having n terms equal to 1 or

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IMO 1977 SL 13

Origin: POL

Problem

Let B be a set of k sequences each having n terms equal to 1 or −1. The product of two such sequences (a1, a2, . . . , an) and (b1, b2, . . . , bn) is defined as (a1b1, a2b2, . . . , anbn). Prove that there exists a sequence (c1, c2, . . . , cn) such that the intersection of B and the set containing all sequences from B multiplied by (c1, c2, . . . , cn) contains at most k2/2n sequences.