[ Rebus $]$

Authors: Mitagin A.Yu., Klypets V.A.

The code of the lock is a two-digit number. Buratino forgot the code, but remembers that the sum of the digits of this number, added to their product, equals the number itself. Write down all possible code options so that Buratino can open the lock faster.
Let the first digit of the code be $x$, and the second digit be $y$. Then the number itself can be written as $10x + y$, and the condition of the problem can be expressed by the equation $(x + y) + x \cdot y = 10x + y$. Therefore, $x \cdot y = 9x$.

Since the code is a two-digit number, $x$ is not equal to 0, so $y = 9$. In this case, $x$ can be any number except 0. Check

## Answer

$19, 29, 39, 49, 59, 69, 79, 89, 99$.