MathDB
4n points on circle, alternately colored yellow and blue, colored segments

Source: 1989 Swedish Mathematical Competition p6

March 28, 2021
combinatorial geometrycombinatoricsColoring

Problem Statement

On a circle 4n4n points are chosen (n1n \ge 1). The points are alternately colored yellow and blue. The yellow points are divided into nn pairs and the points in each pair are connected with a yellow line segment. In the same manner the blue points are divided into nn pairs and the points in each pair are connected with a blue segment. Assume that no three of the segments pass through a single point. Show that there are at least nn intersection points of blue and yellow segments.