SOLUTION: A backpacker wishes to cross the desert, an 8-day trip. The packer and each of her helpers can carry a maximum of 5 days� worth of supplies. What is the smallest number of people

Question 289733: A backpacker wishes to cross the desert, an 8-day trip. The packer and each of her helpers can carry a maximum of 5 days� worth of supplies. What is the smallest number of people who must start the hike in order for the backpacker to cross the desert and each helper to return safely to the starting point?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

You need 3 helpers to start with the backpacker.

Call them persons 0 (the backpacker), 1, 2, and 3

During day 1, each uses 1 day worth. Each has 4 at the end of day 1. 3 gives one day's worth to each of the three others, leaving person 3 with one day's worth to get home.

0, 1, and 2 start day 2 with 5 day's worth, use one, having 4 at the end of the day. 2 gives one day's worth each to 0 and 1, leaving 2 with which to get home.

0 and 1 start day 3 with 5 day's worth, use one, having 4 at the end of the day. 1 gives one day's worth to 0 leaving 3 with which to get home.

0 starts day 4 with 5 day's worth and that is sufficient to carry him/her through the 8th day.

John

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