## Friday, March 09, 2007

### Amusement Park Roller Coaster

An amusement park roller coaster includes five cars, numbered 1 through 5 from front to back. Each car accommodates up to two riders, seated side by side. Six people—Tom, Gwen, Laurie, Mark, Paul and Jack—are riding the coaster at the same time.

The following four statements are true:
1. Laurie is sharing a car.
2. Mark is not sharing a car and is seated immediately behind an empty car.
3. Tom is not sharing a car with either Gwen or Paul.
4. Gwen is riding in either the third or fourth car.
If Gwen is riding immediately behind Laurie's car and immediately ahead of Tom's car, all of the following must be true EXCEPT?

(A) Gwen is riding in the fourth car.
(B) Paul is riding in the third car.
(C) Tom is riding in the fifth car.
(D) Laurie is riding in the third car.
(E) The first car is empty.

1. My analysis:

Car 1 - empty
Car 2 - Mark (alone)
Car 3 - Laurie (alone)
Car 4 - Gwen and Paul
Car 5 - Tom and Jack

So, (B) Paul is riding in the third car, is False.

2. I agree with Mr. Don that the correct answer is B, but the order is slightly different:

1 - X - X
2 - M - X
3 - L - J
4 - G - P
5 - T - X

Note that Laurie had to be sharing a car, so he could not have been alone.

3. Mr Don, I'm afraid Laurie must share a car with someone, (see the original conditions) so you're scenario can't work.

Gill, your scenario works out.

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