Monthly Archives: October 2020

Solution: 2020-18 A way of shuffling cards

Consider the cards with labels \( 1,\dots, n \) in some order. If the top card has label \(m \), we reverse the order of the top \( m \) cards. The process stops only when the card with label \( 1\) is on the top. Prove that the process must stop in at most \( (1.7)^n \) steps.

The best solution was submitted by 길현준 (수리과학과 2018학번). Congratulations!

Here is his solution of problem 2020-18.

Other solutions was submitted by 김유일 (2020학번, +3), 이준호 (수리과학과 2016학번, +3).

GD Star Rating
loading...

2020-18 A way of shuffling cards

Consider the cards with labels \( 1,\dots, n \) in some order. If the top card has label \(m \), we reverse the order of the top \( m \) cards. The process stops only when the card with label \( 1\) is on the top. Prove that the process must stop in at most \( (1.7)^n \) steps.

GD Star Rating
loading...

Solution: 2020-16 A convex function of matrices

Let \( A \) be an \( n \times n \) Hermitian matrix and \( \lambda_1 (A) \geq \lambda_2 (A) \geq \dots \geq \lambda_n (A) \) the eigenvalues of \( A \). Prove that for any \( 1 \leq k \leq n \)
\[
A \mapsto \lambda_1 (A) + \lambda_2 (A) + \dots + \lambda_k (A)
\]
is a convex function.

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

Here is his solution of problem 2020-16.

Other solutions were submitted by 길현준 (수리과학과 2018학번, +3), 이준호 (수리과학과 2016학번, +3).

GD Star Rating
loading...