Question 4
An infinite sequence of integers, $a_0,a_1,a_2,\ldots$, with $a_0\gt 0$, has the property that for every $n\ge0$, $a_{n+1}=a_n-b_n$, where $b_n$ is the number having the same sign as $a_n$ but having the digits written in reverse order. For example, if $a_0=1210$, then $a_1=1089$ and $a_2=-8712$, etc. Find the smallest value of $a_0$ so that $a_n\ne0$ for all $n\ge1$.