## 16. How many of you were there, children?

If you had asked me such a question, I would have answered you only that my mother dreamed of having no fewer than 19 children, but she did not manage to fulfill her dream; however, I had three times as many sisters as cousins, and brothers - half as many as sisters. How many children did my mother have?
16. From the conditions of the problem, it follows that the number of my sisters is divisible by both 3 and 2. Therefore, it is divisible by 6. Hence, the total number of children is

$$
[(\text { number divisible by } 6) \cdot(1+1 / 2)]+1
$$

(the last 1 corresponds to myself). This number must be strictly less than 19, so it inevitably equals 6.

Therefore, I had 6 sisters and 3 brothers, and my mother had a total of 10 children.