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MathNet 2015-part-02 — 191 problems (EN–VI) Question 180

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 180

2015 pairwise distinct lines are drawn in the plane. Suppose that they delimit fewer than 8000 regions (the regions may be unbounded). Show that the number of regions is equal to 2016, 4030, 6042 or 6043, and give an example of a configuration in each case.