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Found problems: 1

2012 USAMO, 2
Tags: rotation , USAMO , pigeonhole , 2012 USAMO , 2012 USAMO Problem 2 , Probabilistic Method
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.