## Task 35/79

Last year, my age was the cross sum of my birth year. How old was I?
The largest cross sum of a year since the turn of the era is $1+8+9+9=27$. Therefore, I was at most 27 years old in the previous year 1979 and thus was born no earlier than 1952.

Let $1900+10 a+b$ with $a, b \in N, 0 \leq a, b \leq 9$ be my birth year. Then the following holds for my age:

$$
1979-(1900+10 a+b)=1+9+a+b \quad \text{so} \quad 11 a+2 b=69
$$

This Diophantine equation is easily solvable:

$$
a=6+\frac{3-2 b}{11}
$$

from which $b=7, a=5$ immediately follows (it is $3-2 b \equiv 0 \bmod 11$, so $2 b \equiv 3 \bmod 11$; due to $0 \leq b \leq 9$, only $b=7$ is possible).

Thus, I was born in the year 1957 and was $1+9+5+7=22$ years old in 1979. As the solution shows, the result is unique.