1. The members of the mathematics section in a school agreed that during the New Year's holiday, each of them would write one greeting card to each of the other members. A total of 342 greeting cards were written. How many members were there in the mathematics section of this school?
Solution. Let the section have $n$ members. Each member sent $n-1$ postcards, which means that together they sent $n(n-1)$ postcards. We have

$$
n(n-1)=342, \text { i.e. } n(n-1)=2 \cdot 2 \cdot 3 \cdot 19=19 \cdot 18
$$

from which we find $n=19$. Therefore, the section had 19 members.