This answer reminded me of a nice puzzle. I present it as a challenge for you.
N thieves had stolen a magical artefact. They bought a lock with N keys and attached the artefact to a loop on a wall in their garage, so that each of them could use the artefact at any time. Immediately a big problem came up: if one of them decided to take the artefact from the garage, then they would not be able to find out who had done it. As they couldn't trust each-other, they were eager to always know who had taken the artefact whenever it was not in the garage. Meanwhile, any thief alone should be able to take it when he needed it.
How could they achieve this goal, if they could buy any number of locks with any number of keys to each lock? How can this be done with the minimum number of locks?
P.S. I do not know whether proof of minimality exists.
- Thieves can use only padlocks and keys, other things are forbidden.
- They can attach locks to the loop and to the artefact. They can attach the locks to each other. Shackles of the locks are wide enough to be attached to any number of other shackles simultaneously.
- They can distinguish locks by serial number.
- Thieves can't break locks. Also they can't open locks then do not have keys to.
P.S. A common mistake is to not take into account that a thief, once the artefact is stolen, is free to leave his lock whenever he wants.