1. ## 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?

2. ## Re: Combinatorics

why doesn't $k=6$ and $m=1$ work?

3. ## Re: Combinatorics

what if all are given the same key?

4. ## Re: Combinatorics

I suppose you are right.so there are 11 keys and 6 of them are needed to open the safe

5. ## Re: Combinatorics

in second tought, there yet may exist a set of 6 members that not have these 6 specific keys

6. ## 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?

7. ## Re: Combinatorics

These are also my difficulties in understating the problem.It is not clear from the formulation of the problem

8. ## 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?