Let f be a continuous function from [0,1] such that f([0,1]) is a circle. Prove that there exists two closed intervals \(I_1, I_2 \subseteq [0,1]\) such that \(I_1\cap I_2\) has at most one point, \(f(I_1)\) and \(f(I_2)\) are semicircles, and \(f(I_1)\cup f(I_2)\) is a circle.

The best solution was submitted by Myeongjae Lee (이명재), 2012학번. Congratulations!

Here is his Solution of Problem 2012-11.

Alternative solution was submitted by 박민재(2011학번, +3). Two incorrect solutions were submitted (W.S.J., K.M.P.).