Let A be a finite set of complex numbers. Prove that there exists a subset B of A such that \[ \bigl\lvert\sum_{z\in B} z\bigr\lvert \ge \frac{ 1}{\pi}\sum_{z\in A} \lvert z\rvert.\]

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is Solution of Problem 2012-12.

Two incorrect solutions were submitted (M.J.L., W.S.J.).