Question 10
Let $m$ be a positive integer of $1000$ digits, with the property that all of its digits are non-zero. For a positive integer $n$, consider $\left\lfloor \frac{m}{n} \right\rfloor$, where we define for any real number $r$, $\lfloor r \rfloor$ to be the largest integer less than or equal to $r$. Determine the largest possible number of digits which are $0$ for $\left\lfloor \frac{m}{n} \right\rfloor$, where $1 \le n \le m$.