Problem

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Tags: combinatorial geometry, combinatorics, geometry



$3n$ lines are drawn on the plane ($n > 1$), such that no two of them are parallel and no three of them are concurrent. Prove that, if $2n$ of the lines are coloured red and the other $n$ lines blue, there are at least two regions of the plane such that all of their borders are red. Note: for each region, all of its borders are contained in the original set of lines, and no line passes through the region.