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2018 Geometry #9

Source:

February 12, 2018
geometry

Problem Statement

Po picks 100100 points P1,P2,⋯ ,P100P_1,P_2,\cdots, P_{100} on a circle independently and uniformly at random. He then draws the line segments connecting P1P2,P2P3,…,P100P1.P_1P_2,P_2P_3,\ldots,P_{100}P_1. Find the expected number of regions that have all sides bounded by straight lines.
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