## 10. Anniversary

"Do you remember Leonitina's fortieth birthday? It was December 28, $19 \ldots$ Since then, Leonitina has aged. I noticed that half of her age equals twice the sum of its digits."

Please fill in the missing digits in the date of Leonitina's fortieth birthday.
10. So, Leontina's age is equal to four times the sum of its digits. Therefore, she is less than 100 years old (and not less than 10 years old). Let $d$ be the number of tens, and $u$ be the number of units in the notation of her age. Then

$$
10 d+u=4(d+u)
$$

from which

$$
2 d=u \text {. } \quad \text {. }
$$

Thus, the number of units is twice the number of tens, which corresponds to ages of 12, 24, 36, and 48 years. Since Leontina is over forty years old, on December 28, 1978, she was exactly 48 years old. Therefore, she celebrated her fortieth birthday on December 28, 1970.