Question 185
An infinite sequence of integers, $a_0, a_1, a_2, \dots$, with $a_0 \gt 0$, has the property that for any $n \ge 0$, $a_{n+1} = a_n - b_n$, where $b_n$ is the number having the same sign as $a_n$, but having the digits written in the reverse order. For example if $a_0 = 1210$, $a_1 = 1089$ and $a_2 = -8712$, etc. Find the smallest value of $a_0$ so that $a_n \ne 0$ for all $n \ge 1$.