425*. A two-digit number was divided by a number written with the same digits but in reverse order, and the quotient and remainder were equal. Find all such two-digit numbers.
$\triangle$ Let the desired number be denoted by $\overline{x y}$. Then

$$
10 x+y=(10 y+x) r+r, \quad 10 x+y=(10 y+x+1) r
$$

where $r-$ is the remainder (and the quotient at the same time). Obviously, $1 \leqslant r < 10$. But this is impossible.

Answer: 52.