11. In which two-digit number is the doubled sum of the digits equal to their product?
11. Solution. Let \(a\) be the tens digit and \(b\) be the units digit of a two-digit number. Clearly, \(a=\{1 ; 2 ; \ldots ; 9\}, b=\{0 ; 1 ; 2 ; \ldots ; 9\}\). According to the problem, \(2(a+b)=a b\), therefore,

\[
b=\frac{2}{a-2} \text { and } a \neq 2
\]

By checking the values of \(a\), we find that \(b\) can be 3, 4, and 6. Thus, the required numbers are: \(63, 44, 36\).