Let n be a positive integer. Consider 2n distinct lines on the plane, no two of which are parallel. Of the 2n lines, n are colored blue, the other n are colored red. Let B be the set of all points on the plane that lie on at least one blue line, and R the set of all points on the plane that lie on at least one red line. Prove that there exists a circle that intersects B in exactly 2n−1 points, and also intersects R in exactly 2n−1 points.Proposed by Pakawut Jiradilok and Warut Suksompong, Thailand combinatorial geometryAPMO