IMO Shortlist 2015 problem A3


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Let n be a fixed positive integer. Find the maximum possible value of \sum_{1 \le r < s \le 2n} (s-r-n)x_rx_s,where -1 \le x_i \le 1 for all i = 1, \cdots , 2n.

(Austria)

Source: https://www.imo-official.org/problems/IMO2015SL.pdf