Question 31
Let $x_1$ and $x_2$ be positive integers. $n$ are given infinite arithmetic progressions of non-negative integers such that among any $x$ consecutive non-negative integers there is at least one that belongs to any of the $n$ progressions. Let $d_1, d_2, \ldots, d_n$ be the differences of the progressions and $d = \min\{d_1, d_2, \ldots, d_n\}$. What is the maximum possible value of $d$?