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China Northern Mathematical Olympiad 2017, Problem 8

Source: China Northern Mathematical Olympiad 2017

July 29, 2017
inequalities

Problem Statement

Let n>1n>1 be an integer, and let x1,x2,...,xnx_1, x_2, ..., x_n be real numbers satisfying x1,x2,...,xn∈[0,n]x_1, x_2, ..., x_n \in [0,n] with x1x2...xn=(n−x1)(n−x2)...(n−xn)x_1x_2...x_n = (n-x_1)(n-x_2)...(n-x_n). Find the maximum value of y=x1+x2+...+xny = x_1 + x_2 + ... + x_n.
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