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Minimum possible number of elements in set

Source: China TST 2011 - Quiz 1 - D3 - P2

May 19, 2011
combinatorics proposedcombinatorics

Problem Statement

For a given integer n≥2n\ge 2, let a0,a1,…,ana_0,a_1,\ldots ,a_n be integers satisfying 0=a0<a1<…<an=2n−10=a_0<a_1<\ldots <a_n=2n-1. Find the smallest possible number of elements in the set {ai+aj∣0≤i≤j≤n}\{ a_i+a_j \mid 0\le i \le j \le n \}.
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