Problem #PRU-58084

Problems Geometry Plane geometry Circles Circle, sector, segment, etc Methods Pigeonhole principle Pigeonhole principle (angles and lengths) Pigeonhole principle (finite number of poits, lines etc.)
 12–13  4.0

Problem

There are 25 points on a plane, and among any three of them there can be found two points with a distance between them of less than 1. Prove that there is a circle of radius 1 containing at least 13 of these points.