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MathNet 2025-part-02 — 186 problems (EN–VI) Question 151

Math Olympiad Vault · MathNet 2025-part-02 — 186 problems (EN–VI)

Question 151

On the perimeter of a unit circle, 12 points are chosen uniformly and independently at random. Estimate the expected value of the area of the convex 12-gon formed by these points.

Submit a positive number $E$ written in decimal. If the correct answer is $A$, you will receive round $\left(20e^{-15|E - A|}\right)$ points.