2009 CMO 第 4 题

Let $P$ be a convex $n$ polygon each of which sides and diagnoals is colored with one of $n$ distinct colors. For which $n$ does: there exists a coloring method such that for any three of $n$ colors, we can always find one triangle whose vertices is of $P$ ' and whose sides is colored by the three colors respectively.

令 $P$ 为凸 $n$ 多边形，其每条边和对角都用 $n$ 不同颜色之一着色。对于 $n$ 的作用：存在一种着色方法，使得对于 $n$ 颜色中的任意三种颜色，我们总能找到一个顶点为 $P$ ' 且其边分别由三种颜色着色的三角形。