DK-GEORGMOHR 2014 Problem 5

Let $x_0, x_1, . . . , x_{2014}$ be a sequence of real numbers, which for all $i < j$ satisfy $x_i + x_j \le 2j$ . Determine the largest possible value of the sum $x_0 + x_1 + · · · + x_{2014}$ .

Dataset text AI-MO AoPS. Quoted with source.

Official text: Georg Mohr Contest 2014 official paper, page 1.

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