Problem

Source: JBMO TST 3 2017 P2

Tags: inequalities



Given $x_1,x_2,...,x_n$ real numbers, prove that there exists a real number $y$, such that, $$\{y-x_1\}+\{y-x_2\}+...+\{y-x_n\} \leq \frac{n-1}{2}$$