Question 66
Let $n$ be a positive integer and let $x_1, x_2, \dots, x_n$ and $y_1, y_2, \dots, y_n$ be real numbers. Prove that there exists a number $i$, $i = 1, 2, \dots, n$, such that
$$
\sum_{j=1}^{n} |x_i - x_j| \le \sum_{j=1}^{n} |x_i - y_j|.
$$
$$
\sum_{j=1}^{n} |x_i - x_j| \le \sum_{j=1}^{n} |x_i - y_j|.
$$