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a set of M points on a circle, with only one colored red

Source: 2001 Moldova JBMO TST p1

February 20, 2021
Coloringpointscombinatorial geometrycombinatorics

Problem Statement

On a circle we consider a set MM consisting of nn (n≥3n \ge 3) points, of which only one is colored red. Determine of which polygons inscribed in a circle having the vertices in the set MM are more: those that contain the red dot or those that do not contain those points? How many more are there than others?
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