¶ 2020 AMC8 Problem 6
Problem:
Aaron, Darren, Karen, Maren, and Sharon rode on a small train that has five cars that seat one person each. Maren sat in the last car. Aaron sat directly behind Sharon. Darren sat in one of the cars in front of Aaron. At least one person sat between Karen and Darren. Who sat in the middle car?
Answer Choices:
A. Aaron
B. Darren
C. Karen
D. Maren
E. Sharon
Solution:
It is given that Maren sat in the last car, Aaron sat directly behind Sharon, and Darren sat in one of the cars in front of Aaron. Based on these three conditions, the possible seating arrangements are:
The last condition states that Karen and Darren did not sit in adjacent cars, which eliminates the second and third possibilities. That leaves the first arrangement as the only one that satisfies all of the conditions, with Karen sitting in the fourth car and Aaron in the middle car.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions