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MathNet 2018-part-04 — 181 problems (EN–VI) Question 112

Math Olympiad Vault · MathNet 2018-part-04 — 181 problems (EN–VI)

Question 112

Let $n$ be a positive integer and fix $2n$ distinct points on a circumference. Split these points into $n$ pairs and join the points in each pair by an arrow (i.e., an oriented line segment). The resulting configuration is good if no two arrows cross, and there are no arrows $\overrightarrow{AB}$ and $\overrightarrow{CD}$ such that $ABCD$ is a convex quadrangle oriented clockwise. Determine the number of good configurations.