IMO 2007 Shortlist C1

Category: Combinatorics

Problem

Let n > 1 be an integer. Find all sequences a1,a2,...,an2+n satisfying the following conditions: (a) ai ∈ {0,1} for all 1 ≤ i ≤ n2

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combinatorics

n; (b) ai+1 + ai+2 + ... + ai+n < ai+n+1 + ai+n+2 + ... + ai+2n for all 0 ≤ i ≤ n2 − n. (Serbia)