Drawn to more than 11 points
Source: Baltic Way 2002
November 13, 2010
combinatorics proposedcombinatorics
Problem Statement
Let be a positive integer. Consider points in the plane such that no three of them are collinear and no two of the distances between them are equal. One by one, we connect each point to the two points nearest to it by line segments (if there are already other line segments drawn to this point, we do not erase these). Prove that there is no point from which line segments will be drawn to more than points.