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China Mathematical Olympiad 2019 Q6

Source: China Chengdu Nov 15, 2018

November 15, 2018
inequalitiesalgebrageometrytrigonometry

Problem Statement

The point P1,P2,⋯ ,P2018P_1, P_2,\cdots ,P_{2018} is placed inside or on the boundary of a given regular pentagon. Find all placement methods are made so that S=∑1≤i<j≤2018∣PiPj∣2S=\sum_{1\leq i<j\leq 2018}|P_iP_j| ^2takes the maximum value.
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