Circles colored with arcs
Source: 2012 USAMO problem #2
April 24, 2012
rotationUSAMOpigeonhole2012 USAMO2012 USAMO Problem 2Probabilistic Method
Problem Statement
A circle is divided into congruent arcs by points. The points are colored in four colors such that some points are colored Red, some points are colored Green, some points are colored Blue, and the remaining 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.