A question from Bob to Bob

Question

Set-up:

John and Bob are playing a game that goes like this:

1. Bob is alone in a completely opaque, featureless room.
2. 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.
3. 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.
4. John makes sure to be in the room two days after Bob made the question, and asks Bob the question Bob himself formulated.
5. 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?

1. The question cannot have a paradoxical answer. So, for example, Bob's not allowed to choose the question "Is this sentence false?"
2. 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.

The puzzle:

What question can Bob choose such that he guarantees that John does not shoot him dead?

Answer 1

Bob could request John to ask:

Did I mutilate myself yesterday in a way to make it totally impossible for me to ever kill you ?

Then Bob replies "No."

If John proves him wrong, it doesn't matter, he won't be able to kill Bob.
If John concedes Bob is right, he has no right to kill him.

Of course, John is obviously a madman, so he might as well kill Bob to cover up the evidence of his failure at this game.

Answer 2

I don't think it's possible.

John can put Bob into a medical coma the moment after he reads the question on Day 1, and can rouse him on Day 3 immediately before asking it. Bob has zero new information when coming out of the coma. He hears John read the question, which he already knew would happen. He knows that between 24 and 72 hours have passed since he wrote the question, but he already knew that would be the case, too. Whatever Bob thought the answer was when he wrote the question, he has learned absolutely nothing new that would cause him to change his response, yet John could have changed the correct answer at will.

As far as Bob is concerned, his entire universe consists of John reading him a question. By Day 3, John can make it so that Bob has no memories, nor any meaningful sensory inputs, nor any source of information whatsoever. Bob can be reduced to a pair of ears with no input other than John's voice, and no memories or other sensory information with which to draw conclusions. Bob cannot know the correct answer when he is put into the coma, and it is impossible for him to recall or infer the correct answer when he comes out of the coma.

Answer 3

Brief:

• Day 1: Bob shares with John a question about day 2 of a fact that John can physically control. John leaves the room.
• Day 2: Nothing/Something happens.
• Day 3: John enters the room. John read the question to Bob about day 2.

The omniscent box said (if I got it correctly from comments):

- John is unable to break the rules. So everything that could make John violating the rules is physically impossible for him. (Eg. take pills to sleep 3 days on day 2 or kill himself)
- Also asking anything about if rules are (not) respected is forbidden. (ie. Is John following the rules?)
- Bob is unable to measure time.

Solution:

John: Was John here on day 2? (bugged as pointed out in comments)
John: Was this question asked to Bob from John on day 2?
Bob: No. Then, yes.

Explanation:

Bob immediately answers No.
If it is day 2 then John would not shoot Bob, he has no reason to do it as potentially messup/broke the 5th rule. At soon a second question is posed, Bob knows that John asked him on day 2, so the answer will be Yes from now on. On day 3 he will be left alive.
If it is day 3 then John would not shoot Bob, because he is right.

I add the additional constraints because if John can break the rules Bob survability is not guaranteed in any case.

Answer 4

John: "Who won the baseball game that occurred between steps 3 and 4?"

Bob, answering to the best of his ability: "I don't know."

Answer 5

How about:

"Is John alive?"