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CSMO 2017 Grade 10 Problem 4

Source: CSMO 2017 Grade 10 Problem 4

August 6, 2017
algebramaximum value

Problem Statement

Let a1,a2,…,a2017a_1,a_2,\dots,a_{2017} be reals satisfied a1=a2017a_1=a_{2017}, ∣ai+ai+2−2ai+1∣≤1|a_i+a_{i+2}-2a_{i+1}|\le 1 for all i=1,2,…,2015i=1,2,\dots,2015. Find the maximum value of max⁡1≤i<j≤2017∣ai−aj∣\max_{1\le i<j\le 2017}|a_i-a_j|.
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