Question 60
(SWE 3) Find the natural number $n$ with the following properties:
(1) Let $S=\{p_1,p_2,\ldots\}$ be an arbitrary finite set of points in the plane, and $r_j$ the distance from $P_j$ to the origin $O$. We assign to each $P_j$ the closed disk $D_j$ with center $P_j$ and radius $r_j$. Then some $n$ of these disks contain all points of $S$.
(2) $n$ is the smallest integer with the above property.
(1) Let $S=\{p_1,p_2,\ldots\}$ be an arbitrary finite set of points in the plane, and $r_j$ the distance from $P_j$ to the origin $O$. We assign to each $P_j$ the closed disk $D_j$ with center $P_j$ and radius $r_j$. Then some $n$ of these disks contain all points of $S$.
(2) $n$ is the smallest integer with the above property.