MathDB

Distance between points

Source: Canada 2003

March 5, 2006

pigeonhole principlecombinatorics unsolvedcombinatorics

Problem Statement

Let

S

be a set of

n

points in the plane such that any two points of

S

are at least

1

unit apart. Prove there is a subset

T

S

with at least

\frac{n}{7}

points such that any two points of

T

are at least

\sqrt{3}

units apart.