2019 CMO 第 4 题

The point $P_1, P_2,\cdots ,P_{2018}$ is placed inside or on the boundary of a given regular pentagon. Find all placement methods are made so that $$S=\sum_{1\leq i<j\leq 2018}|P_iP_j| ^2$$ takes the maximum value.

点 $P_1, P_2,\cdots ,P_{2018}$ 放置在给定正五边形的内部或边界上。查找所有放置方法均满足 $$S=\sum_{1\leq i<j\leq 2018}|P_iP_j| ^2$$ 取最大值。