2013 OIM Problems/Problem 6

Problem

A configuration is a finite set $S$ of points in the plane between which there are no three collinear and each point is assigned some color, so if a triangle whose vertices are in $S$ has an angle greater than or equal to $120^{\circ}$, then exactly two of its vertices are the same color.

Find the maximum number of points that a configuration can have.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

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See also

OIM Problems and Solutions