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circle is divided into n equal arcs by n points, color points in 2 colors

Source: 1998 Estonia National Olympiad Final Round grade 11 p5

March 11, 2020
circlespointsColoringcombinatoricscombinatorial geometry

Problem Statement

A circle is divided into nn equal arcs by nn points. Assume that, no matter how we color the nn points in two colors, there always exists an axis of symmetry of the set of points such that any two of the nn points which are symmetric with respect to that axis have the same color. Find all possible values of nn.
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