You have a friend living in a police state. The police open everything they can, inspect and read it, and then deliver it. They deny they do this. You want to send your friend something in a box that the police won't see.
Both you and your friend have your own sturdy boxes, pad locks, and keys. Neither of you has keys to the other's locks. If you send your friend a box with no pad lock, and he sends it back with one of his locks, you won't be able to open it because you won't have the key. If you send him an unlocked box with your pad lock and matching key inside, the police will copy the key before delivering it.
How can you send him something in a box so that the police can't get to it without it being obvious that they broke into the box?
I heard this puzzle this morning on an NPR show, Car Talk.