MathDB

vertices of a rectangle between colored latticial points

Source: Romanian IMO Team Selection Test TST 1996, problem 10

September 27, 2005

geometryrectanglecombinatorics proposedcombinatorics

Problem Statement

Let

n

and

r

be positive integers and

A

be a set of lattice points in the plane such that any open disc of radius

r

contains a point of

A

. Show that for any coloring of the points of

A

n

colors there exists four points of the same color which are the vertices of a rectangle.