Tuesday, March 6, 2007

Word Problem

11 scientists are working with some very expensive and rare materials. They decide that the materials should be locked in a safe and only accessible when a majority of them are there.
What are the minimum number of locks that should be placed on the safe, and how many keys must each scientist carry (assume each scientist will carry the same number of keys)?

3 blogpoints to the first correct answer. 2 blogpoints for the second, and 1 blogpoint to anyone with correct answers after that.

5 comments:

Peter J. said...

I'll preface this with the fact that C&O was not only the subject I hated most, it's also the core course in which I did the worst. That being said, I think this makes sense....

Of the 11 scientists you need any 6 to be present, so that's (11 choose 6) = 462 combinations of scientists that can open the safe, which means you need 462 locks. Each scientist must carry a minimum of n keys, and n! > 462; the smallest n for which that's true is 6.

Jimmy said...

That's half right Peter - the # of locks is correct, but with 6 scientists each have 6 keys means at most only 36 locks could be opened - what about the other 426 locks?

Peter J. said...

Duh, yes... how about 462/6 = 77 keys?

Peter J. said...

No, wait... engage brain, then type...

Peter J. said...

Yeah, okay, 77 keys each.