Bob and Alice want to marry each other, so Bob decides to send Alice a ring. The problem is that they both live in different countries, and any valuables they send through the mail are sure to be stolen, unless they are sent in a locked box. The box can be locked by a padlock which can only be opened by the right key. Both Alice and Bob have an infinite supply of boxes and padlocks with corresponding keys. However, neither Alice nor Bob have keys to each other's padlocks, only for their own. Suppose you can put boxes inside each other. How can Bob send Alice the ring? Of course, the solution to the problem must end with Alice putting the ring on her finger. To reiterate, anything outside of a padlocked box is guaranteed to be stolen.
This problem has numerous solutions as well as interpretations which makes for a fun discussion. It can also be solved in your head without pencil or paper.