12 vertices fo regular 12-gon
Source: V May Olympiad (Olimpiada de Mayo) 1999 L2 P5
September 17, 2022
combinatoricscombinatorial geometry
Problem Statement
There are points that are vertices of a regular polygon with sides. Rafael must draw segments that have their two ends at two of the points drawn. He is allowed to have each point be an endpoint of more than one segment and for the segments to intersect, but he is prohibited from drawing three segments that are the three sides of a triangle in which each vertex is one of the starting points. Find the maximum number of segments Rafael can draw and justify why he cannot draw a greater number of segments.