Problem:
The numbers and are rearranged according to these rules:
The largest isn't first, but it is in one of the first three places.
The smallest isn't last, but it is in one of the last three places.
The median isn't first or last.
What is the average of the first and last numbers?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The largest, smallest and median occupy the three middle places, so the other two numbers, and , are in the first and last places. The average of and is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions