olymmath

RU-ALLRUSSIAN 1985 Problem 12

    n lines are drawn in the plane. Some of the resulting regions are colored black, no pair of painted regions have a boundary line in common (but they may have a common vertex). Show that at most (n2+n)/3(\mathrm{n}^2 +\mathrm{n}) / 3 regions are black.

    Dataset text NuminaMath olympiads. Quoted with source.

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