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MathNet 2026 — Part 04 Question 65

Math Olympiad Vault · MathNet 2026 — Part 04

Question 65

Let $x_{1}, \ldots, x_{n}$ of any reals be. Show that $$
\sum_{i=1}^{n} \sum_{j=1}^{n}\left|x_{i}+x_{j}\right| \geqslant n \sum_{i=1}^{n}\left|x_{i}\right| .
$$