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 points are chosen (). The points are alternately colored yellow and blue. The yellow points are divided into pairs and the points in each pair are connected with a yellow line segment. In the same manner the blue points are divided into 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 intersection points of blue and yellow segments.