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MathNet 2020 — Math Olympiad Vault — Part 04 Question 84

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 04

Question 84

Let $n$ be a positive integer. There are $2n$ red lines and $n$ blue lines in general position given on the plane. Prove that there are at least $\frac{(n-1)(n-2)}{2}$ regions with a monochromatic perimeter. (An infinite region is also counted as a region with rays and segments forming its perimeter).