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A Hypothetical Hike

Suppose it takes six days to hike to Grandma’s house, but the most any one person can carry is four days’ worth of food. What’s the fewest number of friends who would have to accompany you, at least partway, for you to complete the journey?
Remember, your friends will need to eat on the way there and back.

The answer is two. At the end of the first day, each of you would have three days’ worth of food left. One friend would then need to give both of you and the other friend a day’s worth of food and return home himself. At the end of the second day, you and the remaining friend again would have three days’ worth of food each. That friend would need to give you a day’s provisions and then make the two day trek home. That would leave you with four days of food and four days to go.