6

Part of 2019 China National Olympiad

Problems(1)

China Mathematical Olympiad 2019 Q6

Source: China Chengdu Nov 15, 2018

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.

inequalitiesalgebrageometrytrigonometry