Competition problem — Combinatorics

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Combinatorics Difficulty 6.8 National olympiad Prove it Belarus

$n$ points are marked on a plane. Each pair of these points is connected with a segment. Each segment is painted one of four different colors.
Find the largest possible value of $n$ such that one can paint the segments so that for any four points there are four segments (connecting these four points) of four different colors.

Solution

Answer: the largest possible value of $n$ is $9$ .

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