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Comment by itsmemattchung | Hacker News Reader

> 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

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I wager this answer wasn’t obvious to most on HN…

In physics we use the term "straightforward" for something that doesn't require a conceptual leap but might take a bit of thinking.

Circumnavigating the earth in an airplane is straight forward.

Depending on your frame of reference "straight forward" will launch you into space.

Depending on your frame of reference "keep perfectly still" will launch you into space. But how would that be a useful choice?

I was referring to whether a "straight forward line" would be tangent to the surface of the Earth (i.e., straight) or curved to follow the globe.

Added to my “style” notebook.

Cheers

It 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?

You 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.

I'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:-(

Why, 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!

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