Suppose that \(n\) points are chosen randomly on a sphere. What is the probability that all points are on some hemisphere?

The best solution was submitted by 채석주 (수리과학과 2013학번). Congratulations!

Here is his solution of 2014-24.

An alternative solution was submitted by 이병학 (수리과학과 2013학번, +3).

Let \(G\) be a group such that it has no element of order \(2\) and \[ (ab)^2=(ba)^2\] for all \(a,b\in G\). Prove that \(G\) is abelian.

The best solution was submitted by Chae, Seok Joo (채석주), 수리과학과 2013학번. Congratulations!

Here is his solution of problem 2014-20.

Alternative solutions were submitted by 박민재 (수리과학과 2011학번, +3), 박지민 (수리과학과 2012학번, +3), 장기정 (2014학번, +3), 박훈민 (수리과학과 2013학번, +3), 이병학 (수리과학과 2013학번, +3), 한미진 (순천향대학교 2014학번, +3), 한대진 (인천신현여중 교사, +3), 김경석 (경기과학고 3학년, +3), 진형준 (인천대학교 수학과 2014학번, +3), 장일승 (인천대학교 수학과, +3), 조현우 (경남과학고 3학년, +2).