IMO 1969 LL SWE60

Origin: SWE

Problem

Find the natural number n with the following properties: (1) Let S = {p1, p2, . . . } be an arbitrary finite set of points in the plane, and rj the distance from Pj to the origin O. We assign to each Pj the closed disk Dj with center Pj and radius rj. Then some n of these disks contain all points of S. (2) n is the smallest integer with the above property.