I like the lies and statistics question, but it is a bit too violent, so I suggest a (slightly harder) and way less violent version.
You are looking at the basement of your house, and you see three doors out of place: one leads to the rest of the basement (you want to explore it, because you are sure it is safe), one leads out of the basement and locks it forever (you don't want it), and one is a ticket room, but you don't know which is which.
You can double back, ask more questions and choose more doors after you enter the ticket room, but not the other two doors.
There are 5 strangers near the doors, called A to E, and you don't know who is who. They all know their own and each others' identities, as well as which door leads where.
- A tells only the truth.
- B answers your first question truthfully, but copies the behaviour (if A, tell the truth, if D, yes or no randomly, etc) of your last asked person after that.
- C answers your first question telling the opposite, but copies the behaviour (if A, tell the truth, if D, yes or no randomly, etc) of your last asked person after that.
- D answers yes or no randomly.
- E behaves like A, but will give you a ticket.
After you have a ticket, you must go to the ticket room to permanently destroy all your tickets. If you ask two questions with at least one ticket with you, you will be sent straight out of the basement, locking the basement.
You can only ask Boolean combinations of the following questions (and, or, not, exactly one of, all of, none of, if and only if), to avoid paradoxes:
- "Is 2+2=4?"
- "Are you / Is this guard [A-E]?"
- "Does this door lead [to the rest of the basement, out of the basement, to the ticket room]?
Question: Can you find out which room leads to the rest of the basement, asking 5 questions or fewer? If so, how?
