## 8. Devetke

If we sum 199 mutually distinct natural numbers whose digits are all 9, and the largest of them has 199 digits, we get the number $n$. Determine the sum of the digits of the number $n$.

Result: $\quad 207$
Solution. Note that

$$
\begin{aligned}
n & =9+99+999+\ldots+999 \ldots 99 \\
& =(10-1)+(100-1)+(1000-1)+\cdots+(10000 \ldots 0-1) \\
& =(10+100+1000+\cdots+\underbrace{10000 \ldots 0}_{200 \text { digits }})-199 \\
& =\underbrace{1111 \ldots 11110}_{200 \text { digits }}-199=\underbrace{1111 \ldots 10911}_{200 \text { digits }}
\end{aligned}
$$