Assume that \( x \in \mathbb{R}^n \) with at least \( k \) non-zero entries \( ( k> 0 ) \). Let
\[
A = \{ y \in \{-1, 1\}^n : y \cdot x = 0 \}.
\]
Prove that \( |A| \leq k^{-1/2} 2^n \).

The best solution was submitted by Chae, Jiseok (채지석, 수리과학과 2016학번). Congratulations!

Here is his solution of problem 2018-13.

An alternative solution was submitted by 이대석 (수리과학과 2017학번, +3). Two incorrect solutions were received.