Question 13
Let $X = \overline{a1b9}$ and $Y = \overline{51ab}$ be two positive integers, where $a$ and $b$ are digits. It is known that $X$ is a multiple of a two-digit positive number $n$ and $Y$ is the next multiple of that number $n$. Find the number $n$ and the digits $a$ and $b$. Justify why there are no other possibilities.