Suppose that we color integers 1, 2, 3, …, n with three colors so that each color is given to more than n/4 integers. Prove that there exist x, y, z such that x+y=z and x,y,z have distinct colors.
The best solution was submitted by Chiheon Kim (김치헌), 수리과학과 2006학번. Congratulations!
Here is his Solution of Problem 2009-12.
Alternative solutions were submitted by 백형렬 (수리과학과 2003학번, +3), 조강진 (2009학번, +2), 권상훈 (수리과학과 2006학번, +2).