. In the decimal writing of $A$, the digits appear in (strictly) increasing order from left to right. What is the sum of the digits of $9 A$?
. Let $A=\overline{a_{1} a_{2} \cdots a_{k}}$ be the decimal representation of $A$. By performing the subtraction

$$
\begin{aligned}
& \begin{array}{cccccc}
a_{1} & a_{2} & a_{3} & \cdots & a_{k} & 0
\end{array} \\
& \begin{array}{llllll}
- & a_{1} & a_{2} & \cdots & a_{k-1} & a_{k} \\
\hline
\end{array}
\end{aligned}
$$

we find that the digits of $9 A=10 A-A$ are $a_{1}, a_{2}-a_{1}, a_{3}-a_{2}, \ldots, a_{k-1}-a_{k-2}, a_{k}-a_{k-1}-1,10-a_{k}$. Their sum is $10-1=9$.