On the road to the Marrakesh Multiplex

May 08, 2006

RAY: This puzzler was sent in by a young lady named Sarah Zimmerman, age 13. I had to mess around with it a little bit, but she did a pretty good job. Here it is:

A pilgrim needs to make a journey on foot between Casablanca and Marrakesh, to deliver movies to the new Marrakesh multiplex. It's an arduous and dangerous trip at best, and it takes six days. The most a traveler can carry for food and water is four days' worth.

TOM: I hope there's a hotel someplace in between.

RAY: There are no hotels. Here's the question: How many people must start out together, so that one of them can make it all the way to Marrakesh from Casablanca?

One other thing: the others who start out along with the pilgrim? They can't die along the way.
RAY: The answer is three people.

Let's say person number one is the one we're trying to get to Marrakesh.

Day one, three people start out together.

That day, each of them eats the food that person number three is carrying.

Person number one eats none of his own food. Person number two eats none of his. All three of them eat three days' worth of person number three's food.

They go to sleep. The next morning person number three has to turn back to Casablanca. He has one day's worth of food and water left. And one day's journey back. If he doesn't leave, the buzzards get him.

Day two begins, person number one and two continue their trip, and they eat person number two's food. They eat half of it.

TOM: Right. I'm with you! Keep going.

RAY: This leaves person number two with two days worth of food and water left.

TOM: Just enough to get back.

RAY: Right. He can just make it before the buzzards get him. Person number one hasn't touched any of his food and water. How much of a trip does he have left to get to Marrakesh? Four days, and he has all of his food and water left.

Do we have a winner?

TOM: Yes! The winner this week is Dave Woodwell from Las Cruces, New Mexico. And for having his answer selected at random from among all the correct answers that we got, just two, Dave gets a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com with which he can get the Car Talk baseball shirt, or the Car Talk football shirt, depending on which bench he prefers to warm. I have both of those.

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