On an internal wiki at work, people sometime post puzzles similar to those found on this website. Most of the questions are formulated as a story or word problems, but can be expressed mathematically and become simple to solve.
I had an idea for a joke, to create a problems which when expressed mathematically is actually an unsolved problems in maths. One idea I had was:
You are a prisoner sentenced to death. You are told by the warden that you can choose any room you would like, and prisoners are moved each day with the prisoner in room 1 being executed, which is the lowest room number. Prisoners in even number rooms are moved to room n/2 and prisoners in odd number rooms are moved to room 3n + 1. To avoid execution you can choose a room which will mean you never get to room 1, or you can prove that no such room exists and be freed.
If you are familiar with number theory, you might reconize that this is actually the Collatz Conjecture.
Does anyone know of any other maths puzzles that are actually unsolved problems (or have any comments on this one)?