Question 69
For any natural number $n$, denote by $N(n)$ the number of digits of $n$ and by $S(n)$ the sum of digits of $n$. (Assume that numbers do not start with zero.)
Which digits can occur in a natural number $n$ if $\frac{n}{S(n)} \lt \frac{m}{S(m)}$ for all other $m$ such that $N(m) = N(n)$?
Which digits can occur in a natural number $n$ if $\frac{n}{S(n)} \lt \frac{m}{S(m)}$ for all other $m$ such that $N(m) = N(n)$?