Crossing the Desert

Date: 08/19/98 at 00:50:24
From: Justin Starnes
Subject: Word puzzle

I have tried for a week to answer this question, and can't get it to 
work out. Can you help me?

Assume that one person can carry a 4-day supply of food and water for 
a trip across a desert that takes 6 days to cross. One person cannot 
make the trip alone because the food and water would be gone after 
4 days. How many people would have to start out in order for one 
person to get across and the others to return to the starting point?

Date: 08/19/98 at 16:15:02
From: Doctor Jaffee
Subject: Re: Word puzzle

Hi Justin,

I came up with a solution which, I believe, works. Obviously, one 
person can't make it alone. So, I tried it with two people. At the end 
of the first day of travel they will have eaten some of their food and 
they now have three days' supply. If they both travel another day 
together, the second person will have just enough food to get back home 
and that won't do the first person any good. If the second person could 
give the first person 2 days of supplies at the end of the first day, 
then the second person would have enough to get home safely and the 
first person would have 5 days of supplies for the remaining 5 days. 
However, he can only carry 4! So, that doesn't work. Conclusion, you 
can't make it with two people.

Next, try three people. At the end of the first day, they all have 3 
days worth of supplies. So, the third person can give each of the other 
two people 1 days worth and the third person will have a 1-day supply 
to get home. So, at the end of the second day the first two people are 
back to three days of supplies and the third person is safely home. 
Now, if the second person gives the first person 1 day's worth, the 
second person will be able to get home safely and the first person will 
have 4 days of supplies to travel 4 days and the problem is solved.

Try this out with models, and I think you will see that it works. If I 
misunderstood the problem and this is not the correct solution, write 
back and I'll try again.

- Doctor Jaffee, The Math Forum
Check out our web site! http://mathforum.org/dr.math/