MathDB

2009

points have been marked on a circle. Lucía colors them with

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different colors of her choice. Then Ivan can join three points of the same color, thus forming monochrome triangles. Triangles cannot have points in common; not even vertices in common. Ivan's goal is to draw as many monochrome triangles as possible. Lucía's objective is to prevent Iván's task as much as possible through a good choice of colouring. How many monochrome triangles will Ivan get if they both do their homework to the best of their ability?

Problem Statement