John and Bob are playing a game that goes like this:
- Bob is alone in a completely opaque, featureless room.
- Bob chooses a question, though some types of questions are off-limits, which will be listed. After doing this, he cannot do anything else except speak until the game is over. The question must concern facts regarding only the next day.
- John enters the room that same day and reads the question. Between step 3 and 4 (and only between step 3 and 4), he may do whatever he wants, except cause Bob's death in any other way than potentially making his answer incorrect.
- John makes sure to be in the room two days after Bob made the question, and asks Bob the question Bob himself formulated.
- Bob answers the question to the best of his ability. If Bob is correct, John will never kill Bob. If he is wrong, John will shoot him dead.
So, what questions are off-limits?
- The question cannot have a paradoxical answer. So, for example, Bob's not allowed to choose the question "Is this sentence false?"
- The question cannot be regarding a fact outside of John's physical power to change, or regarding a fact John is disallowed by the game to change. So, he can't choose e.g. "What is 2 + 2", or "What did you eat yesterday?"
There's an omniscient box there to tell them if John is physically and/or game-wise unable to change a fact with the time has. If he is physically unable, Bob must ask a new question. John and Bob are average men. Also, John perfectly understands exactly what Bob's words refer to; no ambiguities exist in his question.
What question can Bob choose such that he guarantees that John does not shoot him dead?