Problem 2. Find any solution to the puzzle

$$
A \cdot B + A + B = \overline{A B}
$$

$A$ and $B$ are two different digits; the notation $\overline{A B}$ represents a two-digit number (i.e., $A \neq 0$) formed by the digits $A$ and $B$. Write the number $\overline{A B}$ as your answer.
Answer: Accept any of the following answers: $19,29,39,49,59,69,79,89$.

Solution. Let's prove that $B=9$.

$$
\begin{gathered}
A \cdot B + A + B = \overline{A B} \\
A \cdot B + A = \overline{A 0} \\
(B + 1) \cdot A = \overline{A 0} \\
B + 1 = 10 \\
B = 9
\end{gathered}
$$

In this case, any $A$, not equal to 0 and 9, is suitable for us.