Let A be a square matrix. Prove that there exists a diagonal matrix J such that A+J is invertible and each diagonal entry of J is ±1.
The best solution was submitted by Jeong, Jinmyeong (정진명), 수리과학과 2007학번. Congratulations!
Here is his Solution of Problem 2010-12.
Alternative solutions were submitted by 권용찬 (수리과학과 2009학번, +3), 심규석 (수리과학과 2007학번, +3), 정성구 (수리과학과 2007학번, +3), 정유중 (2006학번, +3), 김치헌 (수리과학과 2006학번, +3), 박민재 (KSA-한국과학영재학교, +3), 서영우 (2010학번, +2), 서기원 (2009학번, +2), 오상국 (2007학번, +2). One of them has a non-constructive solution of Problem 2010-12.