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Find all possible values of

Source: Balkan MO ShortList 2009 A1

April 6, 2020

Problem Statement

Let N∈NN \in \mathbb{N} and xk∈[−1,1]x_k \in [-1,1], 1≤k≤N1 \le k \le N such that ∑k=1Nxk=s\sum_{k=1}^N x_k =s. Find all possible values of ∑k=1N∣xk∣\sum_{k=1}^N |x_k|
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