Let \( A, B, C \) be \( N \times N \) Hermitian matrices with \( C = A+B \). Let \( \alpha_1 \geq \dots \geq \alpha_N \), \( \beta_1 \geq \dots \geq \beta_N \), \( \gamma_1 \geq \dots \geq \gamma_N \) be the eigenvalues of \( A, B, C \), respectively. For any \( 1 \leq k \leq N \), prove that
\[ \gamma_1 + \gamma_2 + \dots + \gamma_k \leq (\alpha_1 + \alpha_2 + \dots + \alpha_k) + (\beta_1 + \beta_2 + \dots + \beta_k) \]

The best solution was submitted by Sounggun Wee (위성군, 수리과학과 2015학번). Congratulations!

Here is his solution of problem 2017-01.

Alternative solutions were submitted by 강한필 (2016학번, +3), 김태균 (수리과학과 2016학번, +3), 배형진 (마포고 3학년, +3), 오동우 (수리과학과 2015학번, +3), 이시우 (포항공대 수학과 2013학번, +3), 이정환 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3), 조태혁 (수리과학과 2014학번, +3), 최대범 (수리과학과 2016학번, +3), 최인혁 (물리학과 2015학번, +3), Huy Tung Nguyen (2016학번, +3), 곽상훈 (수리과학과 2013학번, +3), 이본우 (2017학번, +3), 이태영 (수리과학과 2013학번, +2).