Question 165
Given $x_1, x_2, \dots, x_n$ real numbers, prove that there exists a real number $y$ such that
$$
\{y - x_1\} + \{y - x_2\} + \dots + \{y - x_n\} \le \frac{n-1}{2}.
$$
$$
\{y - x_1\} + \{y - x_2\} + \dots + \{y - x_n\} \le \frac{n-1}{2}.
$$