3 colors for 49 maps on a circle
Source: 1962 Leningrad Math Olympiad - Grade 7.5* asterisk problem
September 1, 2024
geometrycombinatoricscombinatorial geometry
Problem Statement
The circle is divided into areas so that no three areas touch at one point. The resulting “map” is colored in three colors so that no two adjacent areas have the same color. The border of two areas is considered to be colored in both colors. Prove that on the circle there are two diametrically opposite points, colored in one color.