For a set \( A \subset \mathbb{R} \), let \( f(A) \) be the size of the largest set \( B \subset A \) such that \( (B+B) \cap B = \emptyset \). For a positive integer \( n \), let \( f(n) = \min_{0 \notin A, |A|=n} f(A) \). Prove that \( f(n) \geq n/3 \).

The best solution was submitted by Kook, Yun Bum (국윤범, 수리과학과 2015학번). Congratulations!

Here is his solution of problem 2016-7.

Alternative solutions were submitted by 이종원 (수리과학과 2014학번, +3), 장기정 (수리과학과 2014학번, +3).