2012 USAMO 第 2 题

A circle is divided into 432 congruent arcs by 432 points. The points are colored in four colors such that some 108 points are colored Red, some 108 points are colored Green, some 108 points are colored Blue, and the remaining 108 points are colored Yellow. Prove that one can choose three points of each color in such a way that the four triangles formed by the chosen points of the same color are congruent.

一个圆被 432 个点分成 432 条全等的弧。这些点被着色为四种颜色，使得一些108点被着色为红色，一些108点被着色为绿色，一些108点被着色为蓝色，并且剩余的108点被着色为黄色。证明可以选择每种颜色的三个点，使得由所选的相同颜色的点形成的四个三角形全等。