\section*{Problem 1 - V01001}

The digit sum of a two-digit number is 9. If you multiply the number by 5 and subtract 9 from the product, you get a two-digit number with the same digits in reverse order. What is the two-digit number?
}

We denote the two-digit number with \(a\). Due to the second condition, that \(5 a-9<100\) must hold, \(a<22\) must be true. Therefore, the candidate we are looking for is 18, since

\[
5 \cdot 18-9=90-9=81
\]

satisfies the second condition and 18 has a digit sum of 9.