Suppose that P is a finite set of points in the plane colored by red or blue. Show that if no straight line contains all points of P, then there exists a straight line L with at least two points of P on L such that all points on \(P\cap L\) have the same color.

The best solution was submitted by Haewon Yoon (윤혜원), 수리과학과 2004학번. Congratulations!