2. In 1986, Janez will be as many years old as the sum of the digits of the year he was born. How old will Janez be in 1986?
Solution. Janez was born in the year $1900+10 x+y$. According to the condition of the problem

$$
1986-(1900+10 x+y)=1+9+x+y \text{, i.e., } 11 x+2 y=76
$$

In the set of natural numbers, the last equation has a unique solution $x=y, y=5$. Therefore, Janez was born in 1965 and in 1986 he will be 21 years old.