Let \(x_1,x_2,\ldots,x_n\) be reals such that \(x_1+x_2+\cdots+x_n=n\) and \(x_1^2+x_2^2+\cdots +x_n^2=n+1\). What is the maximum of \(x_1x_2+x_2x_3+x_3x_4+\cdots + x_{n-1}x_n+x_nx_1\)?

The best solution was submitted by Lee, Jongwon (이종원, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2018-04.

Alternative solutions were submitted by 이본우 (수리과학과 2017학번, +3), 채지석 (수리과학과 2016학번, +3), 고성훈 (2018학번, +2).