MathDB

Suppose that to every point of the plane a colour, either red or blue, is associated.
(a) Show that if there is no equilateral triangle with all vertices of the same colour then there must exist three points

A,B

and

C

of the same colour such that

B

is the midpoint of

AC

.
(b) Show that there must be an equilateral triangle with all vertices of the same colour.

Problem Statement