Problem

Source: Iran second round 2011

Tags: geometry, analytic geometry, combinatorics proposed, combinatorics



We have a line and 1390 points around it such that the distance of each point to the line is less than 1 centimeters and the distance between any two points is more than 2 centimeters. prove that there are two points such that their distance is at least 10 meters (1000 centimeters).