62nd International Mathematical Olympiad / IMO 2021 / - Problem 2 - 21 July 2021

Problem 2. Show that the inequality

$\sum_{i = 1}^{n} \sum_{j = 1}^{n} \sqrt{| x_{i} - x_{j} |} \leq \sum_{i = 1}^{n} \sum_{j = 1}^{n} \sqrt{| x_{i} + x_{j} |}$

holds for all real numbers x₁, . . . , x_n.

proposed by Calvin Deng, Canada