3. In 2018, Pavel will be as many years old as the sum of the digits of the year he was born. How old is Pavel?
Solution. If Pavel was born in the 20th century, then according to the condition of the problem, we get the following equation:

$$
\begin{aligned}
& 2018-\overline{19 a b}=1+9+a+b \\
& 2018-1900-10 a-b=10+a+b \\
& 11 a+2 b=108
\end{aligned}
$$

This equation has no solution such that $a$ and $b$ are single-digit numbers. If, however, Pavel was born in the 21st century, then we have the equation:

$$
\begin{aligned}
& 2018-\overline{20 a b}=2+0+a+b \\
& 2018-2000-10 a-b=2+a+b \\
& 11 a+2 b=16
\end{aligned}
$$

The last equation has a unique solution such that $a$ and $b$ are single-digit numbers, which is $a=0, b=8$, meaning that Pavel was born in 2008 and is 10 years old.