2023 SSMO Relay Round 4 Problems/Problem 2

Problem

Let $T=$ TNYWR. Let $n = \left\lfloor\sqrt{N}\right\rfloor.$ Suppose that $N$ points are chosen on the sides of a triangle with area 1 such that there is at least one point on each side. Let $m$ be the area of the polygon formed by connecting the $N$ points in counterclockwise order. Find the expected value of $\frac{30}{1-m}$ (Note that $\left\{x\right\} = x - \lfloor x \rfloor$ )

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2023 SSMO Relay Round 4 Problems/Problem 2

Problem

Solution