Let \(V_1,V_2,\ldots\) be countably many \(k\)-dimensional subspaces of \(\mathbb{R}^n\). Prove that there exists an \((n-k)\)-dimensional subspace \(W\) of \(\mathbb{R}^n\) such that \(\dim V_i\cap W=0\) for all \(i\).

The best solution was submitted by Shin, Joonhyung (신준형, 수리과학과 2015학번). Congratulations!

Here is his solution of problem 2016-20.

Alternative solutions were submitted by 김태균 (2016학번, +3), 국윤범 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3, alternative solution). One incorrect solution was submitted.