## Task 12/78

When asked how old he is, someone answers that in the year $x^{2}$ he was exactly $x$ years old. In which year was he born?
Let the birth year be $a$. Then, assuming that the age is at least 1 year and at most 120 years, it is certainly true that

$$
1858 < a + x = x^2 < 1978 \quad \text{so} \quad 43.1 \ldots = \sqrt{1858} < x < \sqrt{1978} = 44.7 \ldots
$$

From this, it immediately follows that $x = 44, x^2 = 1936, a = x^2 - x = 1892$.