# 2010-20 Monochromatic line

Let X be a finite set of points on the plane such that each point in X is colored with red or blue and there is no line having all points in X. Prove that there is a line L having at least two points of X such that all points in L∩X have the same color.

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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.
P는 평면 상에 점들의 집합으로, 각 점은 파랑색 혹은 빨간색으로 칠해져있다. 모든 P의 점을 포함하는 직선이 없다면, P의 두 점이상을 포함하는 직선 중에 $$P\cap L$$의 모든 점이 같은 색이 되도록 하는 직선이 있음을 보여라.