2. Find the smallest natural number $n>1$ with the following property: there exists a set $M$ of $n$ points in the plane such that every line $AB (A, B \in M)$ is parallel to some other line $CD (C, D \in M)$.
Solution. It is obvious that $n \neq 2,3$. Similarly, there does not exist a set $M$ of four points in the plane with the desired property, because in any quadrilateral, the diagonal is not parallel to the other diagonal, nor to any side.

The set $M$ consisting of the vertices of a regular pentagon has the desired property. Therefore, $n=5$.