Question 78
Let $a_1, a_2, \dots, a_n$, and $b_1, b_2, \dots, b_n$, $2n$ real numbers. Prove that there exists an integer $k$ with $1 \le k \le n$, such that
$$
\sum_{i=1}^{n} |a_i - a_k| \le \sum_{i=1}^{n} |b_i - a_k|.
$$
$$
\sum_{i=1}^{n} |a_i - a_k| \le \sum_{i=1}^{n} |b_i - a_k|.
$$