Minimum number of persons needed to cross a Desert


In the middle of the confounded desert, there is the lost city of “Ash”.

To reach it, you will have to travel overland by foot from the coast. On a trek like this, each person can only carry enough rations for five days and the farthest we can travel in one day is 30 miles. Also, the city is 120 miles from the starting point.

What is the fewest number of persons, including yourself, that you will need in your Group so that you can reach the city, stay overnight, and then return to the coast without running out of supplies.
How many persons (including yourself) will you need to accomplish this mission?
desert puzzle
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    Answer – Total 4 persons (including you) required.

    It is given that each person can only carry enough rations for five days and as there are 4 persons.
    Hence, total of 20 days rations is available.

    1. Day 1 : 4 days of rations are used up. One person goes back using one day of rations for the return trip. The rations remaining for the further trek is for 15 days.

    2. Day 2 : The remaining three people use up 3 days of rations. One person goes back using 2 days of rations for the return trip. The rations remaining for the further trek is for 10 days.

    3. Day 3 : The remaining two people use up 2 days of rations. One person goes back using 3 days of rations for the return trip. The rations remaining for the further trek is for 5 days.

    4. Day 4 : The remaining person uses up one day of rations. He stays overnight. The next day he returns to the coast using 4 days of rations.

    Thus, total 4 persons, including you are required.

    Detective Expert Answered on 18th October 2015.
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    This question is ambiguous: it needs to tell us whether we can leave supplies alone in the desert, or if the supplies must be minded by someone.

    If we can leave supplies lying around, then remember that carrying 5 days’ provisions means that starting out, you’ve got enough to travel for 2 days, travel 2 days back, and leave 1 days’ rations on the ground.  We also should remember that we only need one person (i.e., ourselves) to make it to Ash, 4 days’ travel away.   Lastly, recall that anyone returning to the coast can stock up again and set out again.

    So if we think of the midpoint (2 days’ travel) as our refueling stop, and the person going to Ash (me) will need 4 days’ additional supplies to get the further 2 days’ distance and back, then let’s think about this experimentally…

    Suppose I take 4 people with me.  We start with 5 days’ rations each.  After 2 days, they each drop 1 day of rations on the ground (so 4 total), I pick up 2 of them (so I again have 5 total), and then turn around and with their 2 remaining days they hike back to the coast.  I take 4 further days to go out to Ash and back to that midpoint.  I pick up the last 2 days’ rations on the ground, and finish the journey home alone.

    OK, now what if instead they turn around, and come meet me halfway again?  Maybe I only need 2 companions.  So we start out with 15 rations; 2 days in, we have 9 left.  I take 5 of them, leave them with 2 each.  They head back to the coast, I continue on to Ash.  The night I’m in Ash, they’re back at the coast, stocking up again.  The next morning, I leave Ash with 3 (will have 1 at the midpoint), and they set out again with 5 each.  We meet 2 days later, I have 1 day of rations left, but they have 3 each and give me 1 apiece, and then we trot back.  Okay, that works.

    Let’s think about this rationally, though… if I COULD leave supplies alone in the desert, then I wouldn’t need any companions, I could just progressively build up piles of stuff at each day’s waypoint all by myself until I can make the journey given the supplies I’ve left out there.  So that doesn’t seem like a fair interpretation of the question.  So that’s my answer: 2 companions, 3 of us total.

    Denzera Curious Answered on 18th October 2015.
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    Assuming everyone is to be kept alive the answer should be 4.

    After every day of travel you are left with 4 days ration.
    After 1st day one would return – He would distribute 3 days of ration to remaining others and use 1 to return. So remaining three would be back up to 5.
    Similarly after 2nd day one would return distributing two to the others to get them back to 5 and keep 2 for his return.
    On 3rd day end another would return giving one to you to get back to 5 and keep 3 for his return.
    This five will take you through 5 more days needed to complete the trip.

    DK0305 Curious Answered on 17th October 2015.
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