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?

(In reply to re(2): 5-point proof by DJ)

The problem states what is the fewest number of points needed to prove an equilateral triangle with the same color on all the points exists. I'm not saying you can rearrange the colors any way you want but if someone told you they had five points arranged in the fashion that bryan had and that they were going to randomly select one of two colors for each point you can't prove that one of those triangles meets the condition. That is all I am trying to say.

Posted by Kelsey on 2003-08-26 20:59:23