DE-BUNDESWETTBEWERB 2012 Problem 5

Round 2

given a positive integer $n$ . the set $\{ 1,2,..,2n \}$ is partitioned into $a_1<a_2<...<a_n$ and $b_1>b_2>...>b_n$ . find the value of : $\sum_{i=1}^{n}|a_i - b_i|$

Dataset text AI-MO AoPS. Quoted with source.

Official text: Bundeswettbewerb Mathematik 2012 official paper, page 1.

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