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?

Comment for:
"Take any two points that are of different colors; let's say that they are blue and orange."
I do not think that it is supposed in the problem that you can actually chose 2 points of different colors... what about 3 points of the same color?
So, if you just chose randomly 2 points and it will happen to have the same color -->> what is your solution then?

Posted by aln on 2003-09-20 23:12:44