Camel in the Desert

One man is trying to cross the desert to reach the neighboring village. It takes 4 days to get there, but his camel can carry bananas which will feed him for 3 days only. How can the man reach the neighboring village without starving?

The man travels one day, leaves one portion of bananas in the desert and returns back to his village. Then he leaves again with 3 new portions of bananas, picks the portion left in the desert on his way and ends up in the neighboring village on the sixth day.

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  1. Assume the man need 1 banana per day and his camel can only carry at most 2 bananas.
    If he carry 2 bananas, it takes him half a day to 1/8 of the way and half a day to return. He eats 1 banana and can leave there 1 banana. So 1 day to transport 1 banana. So we get these results:
    – At the half point of the way he needs to leave 2 bananas
    – At 3/8 of the way he needs to leave 4 bananas
    – At 1/4 of the way he needs to leave 8 bananas
    – At 1/8 of the way he needs to leave 16 bananas
    Thus he needs about: 16+8+4+2+2 = 32 days
    For more exactly, with each progress from one point to the next point, the last turn takes only half a day and half a banana. Then we can recalculate:
    – At the half point of the way he needs to leave 2 bananas
    – At 3/8 of the way he needs to leave 3.5 bananas
    – At 1/4 of the way he needs to leave 6 bananas
    – At 1/8 of the way he needs to leave 11.5 bananas
    Finally he needs at least: 10.5 + 5.5 + 2.5 + 1.5 + 2 = 22 days

    1. So sorry, Khong, there was a typo in the problem. The camel can carry enough bananas for whole 3 days.
      If the camel can carry bananas for only 2 days though, I believe that your solution with 22 days is optimal. It will be an interesting puzzle itself to prove that:)

      1. It looks like someone has already posted the general formula on math stackexchange.
        The idea is to show that there is an optimal solution of a special form, and then find a recursive formula. If you would like to discuss this problem further (or any other), let me know and I will make a topic about it in the forum.