Question 289733
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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
*[tex \LARGE e^{i\pi} + 1 = 0]
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