Question 121
Let $x_{1}, x_{2}, \ldots, x_{n}$ be real numbers with arithmetic mean $X$. Prove that there is a positive integer $K$ such that the arithmetic mean of each of the lists $\{x_{1}, x_{2}, \ldots, x_{K}\}$, $\{x_{2}, x_{3}, \ldots, x_{K}\}$, $\ldots$, $\{x_{K-1}, x_{K}\}$, $\{x_{K}\}$ is not greater than $X$.