5 ms·
> Eleven scientists are working on a secret project. They wish to lock up the documents in a cabinet so that the cabinet can be opened if and only if six or mor
by itsmemattchung 4y ago
> Eleven scientists are working on a secret project. They wish to lock
up the documents in a cabinet so that the cabinet can be opened if
and only if six or more of the scientists are present. What is the
smallest number of locks needed? What is the smallest number of
keys to the locks each scientist must carry?
> it is not hard to show that the minimal solution uses 462
locks and 252 keys per scientist
Probably obvious to most on HN but the answer didn't jump out at me immediately: 11! / 5!6! = 462
- water554 4y agoI wager this answer wasn’t obvious to most on HN…
- tromp 4y agoIt becomes obvious only after making the less than obvious assumption that locks can work in OR fashion rather than the usual AND fashion. How does one put 462 locks on a cabinet such that opening any one lock opens the cabinet?
- simongr3dal 4y agoYou could put several doors the cabinet. If using a chain, connecting locks in parallel between the links would be AND, and locks in series between the links would be OR.
- tromp 4y agoI've seen cabinets with multiple doors, and can even imagine them reaching the same space. But I've yet to see a cabinet lockable with a chain:-(
- Arrath 4y agoWhy, it simply requires the cabinet to be accessible all-around so you can fully wrap the chain, and a handle or the like to thread the chain through!
- queuebert 4y agoIn physics we use the term "straightforward" for something that doesn't require a conceptual leap but might take a bit of thinking.
- whatshisface 4y agoCircumnavigating the earth in an airplane is straight forward.
- bombcar 4y agoDepending on your frame of reference "straight forward" will launch you into space.
- DiggyJohnson 4y agoAdded to my “style” notebook. Cheers