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You are standing at an airport (that lies somewhere) on equator (of the earth) and have an unlimited number of identical aircrafts (same model, make and fuel capacity etc.) to make a complete trip of equator. Each of the aircraft has the fuel capacity to fly exactly 1/3 (one-third) around the earth along equator. Any flying plane can transfer fuel to any other plane in air instantaneously (without spillage) but after transfer, it should have left with sufficient fuel to come back to the airport (or get refuel again by someone else to eventually come to airport). In any case no plane should get crashed due to fuel outage.

Q(1). What is the minimum number of aircraft necessary to get one plane all the way around the equator assuming that all of the aircraft must return safely to the airport? Assume no other airport is available and unlimited supply of fuel is available (at the airport).

Q(2). What is the minimum number of aircraft necessary for a straight line to reach one of them from start to end point (assuming airport at the start point) and the fuel capacity is 1/3 (one-third) of the straight line (and other conditioned are same as that of Q1).

I can solve it using head and trial but I am looking for a mathematically way to derive the solution.

  • 1
    This is another incantation of [the jeep problem](http://en.wikipedia.org/wiki/Jeep_problem) - this is popular today! It was [asked in a different form](http://math.stackexchange.com/questions/157207/math-puzzle-farmer-delivery-problem) earlier. At least this version has a more interesting solution.2012-06-12
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    jeep problem is equivalent to n fleet problem but there the condition was that we can left aeroplanes in the middle just one plane should reach the destination point .... but here we can't left them in the middle... we have to bring them back to the airport safely.2012-06-14
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    To clarify is the original question: "What is the minimum number of aircraft necessary to get one plane all the way around the ***equator***..." Or "What is the minimum number of aircraft necessary to get one plane all the way around the ***world***..." Because you can play tricky games with the north or south pole with the latter (like they do in round the world yacht races).2014-05-13
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    Q2 is not clear to me."straight line to reach one of them" does not make sense. Can you please rephrase? Also what happens at the end? The plane crashes?2016-10-02
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    The much easier problem where the plane can go 1/2 of the equator is discussed in this TED Ed video https://www.youtube.com/watch?v=dzrwnwOx0fw We just need 2 support planes in this case, and it is relatively easy to figure out.2016-12-12

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