Suppose you have an infinite plane, and each point on the plane has been arbitrarily painted one of two colors.

Prove that there exists an equilateral triangle whose vertices are all the same color.

What is the fewest number of points needed to prove this?

This problem is the motivation for Ramsay numbers.5 is the smallest such Ramsay number.

Posted by B M on 2003-09-29 04:46:38