# Solution: 2012-10 Platonic solids

Determine all Platonic solids that can be drawn with the property that all of its vertices are rational points.

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

Here is his Solution of Problem 2012-10.

Alternative solutions were submitted by 박민재 (2011학번, +3, Solution), 정우석 (서강대학교 2011학번, +3), 박훈민 (대전과학고 2학년, +2). One incorrect solution was submitted (G.S.).

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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.