HMMT 二月 2002 · 代数 · 第 1 题
HMMT February 2002 — Algebra — Problem 1
题目详情
- Nine nonnegative numbers have average 10. What is the greatest possible value for their median?
解析
- 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 ≥ 5 m ⇒ m ≤ 18. Conversely, we can achieve m = 18 by taking four 0’s and five 18’s.