1. Nine nonnegative numbers have average 10 . What is the greatest possible value for their median?
Solution: 18 If the median is $m$, then the five highest numbers are all at least $m$, so the sum of all the numbers is at least $5 m$. Thus $90 \geq 5 m \Rightarrow m \leq 18$. Conversely, we can achieve $m=18$ by taking four 0 's and five 18 's.