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Thread: Combinatorics

  1. #1
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    Combinatorics

    Hi,
    I need help with the following problem:
    In order to open a safe, k keys are needed.Each one of 11 members is given m keys ,subject to the following two requests:

    1)Each 6 members can open the safe

    2)no 5 members can open the safe

    what is the minimum values of k and m that fulfill these two requests?
    Thank's in advance
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  2. #2
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    Re: Combinatorics

    why doesn't $k=6$ and $m=1$ work?
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  3. #3
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    Re: Combinatorics

    what if all are given the same key?
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  4. #4
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    Re: Combinatorics

    I suppose you are right.so there are 11 keys and 6 of them are needed to open the safe
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  5. #5
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    Re: Combinatorics

    in second tought, there yet may exist a set of 6 members that not have these 6 specific keys
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  6. #6
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    Re: Combinatorics

    you're going to have to restate the problem with some more details.

    are there k specific keys out of the 11m that open the safe?

    are all 11m keys unique?
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  7. #7
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    Re: Combinatorics

    These are also my difficulties in understating the problem.It is not clear from the formulation of the problem
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  8. #8
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    Re: Combinatorics

    But it does not make sense that every set of k keys open the safe .Also if only specific k eys open then the first request cannot be fulffiled.
    what do you thing about it?
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