HMMT 二月 2002 · 代数 · 第 1 题

英文解析

1. Nine nonnegative numbers have average 10. What is the greatest possible value fortheir median?
   Solution: 18 If the median is m , then the five highest numbers are all at least m , sothe sum of all the numbers is at least 5 m . Thus 90 ≥ 5 m ⇒ m ≤ 18. Conversely, we canachieve m = 18 by taking four 0’s and five 18’s.