Let
\[
Q_n=\{0,1\}^n
\]
be the \(n\)-dimensional discrete cube, viewed as a graph in which two vertices are adjacent if they differ in exactly one coordinate.

For a subset \(A\subseteq Q_n\), let \(\partial_e A\) denote the set of edges with one endpoint in \(A\) and the other in \(Q_n\setminus A\).

Prove that for every \(A\subseteq Q_n\),
\[
|\partial_e A|\ge |A|\bigl(n-\log_2|A|\bigr).
\]

The best solution was submitted by 김지원 (전산학부 24학번, +4). Congratulations!

Here is the best solution of problem 2026-07.

Other solutions were submitted by 김은성 (서울대 수리과학부, +3), 신민규 (수리과학과 24학번, +3), 장현준 (서울과학고 3학년, +3), 정서윤 (수리과학과 23학번, +3), 최완수 (서울대 물리천문학부, +3).