This question requires a bit of logical distortion to get the information required to answer the question.
However, I've never seen it asked before what would happen if more modes of question unanswerability were introduced.
I'm thinking of a number from 1 to 5, and you're allowed to ask one yes-no question to which I can answer one of the following things:
- Sometimes (Both yes and no are known to be true with a nonzero frequency.)
- I don't know (There is a definite answer, but it is not known.)
- Not applicable (This question does not have an answer for my number.)
What question can you ask to determine what number I'm thinking of?
There may be many correct answers to this question, but try to make it as elegant as possible.