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Maximum Separating Lines Point Set

2175ExpertCombinatoricsGeometry

54. matematično tekmovanje srednješolcev Slovenije

Let $n$ be a natural number. In the plane there are $2n+2$ points, no three of which are collinear. A line in the plane is called a separator if it contains two of the given points and has exactly $n$ points on each side. Determine the maximum number $m$ such that there are always at least $m$ separators in the plane.
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