Question 22
Let $n$ be a positive integer and $a_1, a_2, \dots, a_{2n}$ be $2n$ distinct integers. Given that the equation
$$
|x - a_1| |x - a_2| \dots |x - a_{2n}| = (n!)^2
$$
has an integer solution $x = m$, find $m$ in terms of $a_1, \dots, a_{2n}$.
$$
|x - a_1| |x - a_2| \dots |x - a_{2n}| = (n!)^2
$$
has an integer solution $x = m$, find $m$ in terms of $a_1, \dots, a_{2n}$.