1. The age of a person this year (1984) is equal to the sum of the digits of their birth year. How old is the person?
Solution. The person is at most $9+9+9+9=36$ years old, which means they were born in the $X X$-th century, i.e., the first two digits of their birth year are 1 and 9. Let $x$ be the digit of the tens, and $y$ the digit of the units of the birth year; According to the condition of the problem, we have $1+9+x+y=1984-(1000+900+10 x+y)$, i.e., $11 x+2 y=74$. Since $0 \leq x, y \leq 9$, from the equation we get $x=6, y=4$, that is, the person was born in 1964 and is now $1+9+6+4=20$ years old.