All-Russian Olympiad Problem 4

Given a circle and \(2006\) points lying on this circle. Albatross colors these \(2006\) points in \(17\) colors. After that, Frankinfueter joins some of the points by chords such that the endpoints of each chord have the same color and two different chords have no common points (not even a common endpoint). Hereby, Frankinfueter intends to draw as many chords as possible, while Albatross is trying to hinder him as much as he can. What is the maximal number of chords Frankinfueter will always be able to draw?This problem is part of this set.

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