Question 53
There are 2005 young people sitting around a (large!) round table. Of these at most 668 are boys. We say that a girl $G$ is in a strong position, if, counting from $G$ to either direction at any length, the number of girls is always strictly larger than the number of boys. ($G$ herself is included in the count.) Prove that in any arrangement, there always is a girl in a strong position.