Problem

Source: 2024 FKMO P5

Tags: inequalities



A positive integer $n (\ge 4)$ is given. Let $a_1, a_2, \cdots ,a_n$ be $n$ pairwise distinct positive integers where $a_i \le n$ for all $1 \le i \le n$. Determine the maximum value of $$\sum_{i=1}^{n}{|a_i - a_{i+1} + a_{i+2} - a_{i+3}|}$$where all indices are modulo $n$