# A question from Bob to Bob

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?

• If the game was about, say a hundred bucks, then I wouldn't need to ask: does John want to kill Bob?
– Bass
Nov 15, 2023 at 20:14
• How about "Are you within range of my gun?" Nov 15, 2023 at 20:25
• It seems like there are a whole category of questions that allow John to change the answer, but can still be answered correctly. "Are you wearing shoes?" "Is there a lamp on that table?" "What am I holding in my left hand?" John can affect the answer to any of these questions, but it doesn't prevent Bob from answering them correctly. Nov 15, 2023 at 20:33
• Perhaps you are implying that Bob should be writing down both the question and the answer, and that the answer still needs to be the same when John asks the question as it was when Bob wrote it down? Nov 15, 2023 at 20:35
• puzzling.meta.stackexchange.com/questions/7410/… makes me concerned that the intended solution to this puzzle is "it's impossible" Nov 16, 2023 at 23:12

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.

• In case anyone thinks this answer breaks the rules, here's why it doesn't: John mutilating himself only open up for the potential of the rules being broken (if Bob answers incorrectly). However, if it was disallowed to open up for the potential for the rules being broken, John could not do anything, because doing anything carries the risk of death. If John dies, the rules are broken. So, obviously, opening up for the potential of broken rules is not the same as breaking the rules. So, this answer works. Nov 17, 2023 at 19:57
• However, if John mutilates himself, and Bob answers incorrectly, then the game never ends due to incompletion. That is of no consequence to the puzzle however, because Bob still gets his guarantee that John won't shoot him dead. Good job! Nov 17, 2023 at 19:59
• I have a feeling that a few of us thought of questions like "Am I able to kill you?" but dismissed them because of the paradox rule. But that's not a paradox, it's a tautology. Nov 17, 2023 at 20:28
• @user110391 The rules stipulate the question must "concern facts regarding only the next day". This does not, it requires knowledge that John will never kill Bob at any point in the future. This requires knowledge of facts we are not allowed to ask about - it's effectively asking "On Day 2, did John make it so that he could not kill Bob on Day 3?" That does not concern "only Day 2". Nov 20, 2023 at 13:44
• It asks if on day 2 John did permanent damage on himself. Damage that can not be repaired. Nov 20, 2023 at 20:55

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.

• It is possible. I know of multiple solutions. It's just a tricky one. A hint is to break it down into abstract knowledge-restricting devices (so as to not distract yourself with the hows at first), and then take it from there. You are futher along this path than the other answers. Nov 17, 2023 at 14:31
• @user110391 What possible information can Bob base his answer on? He's a brain in a vat hearing a disembodied voice ask a question. He doesn't know anything about the world whatsoever. John is allowed to change the correct answer at will, and as far as I can see, is perfectly capable of blocking every possible way of Bob collecting information. Nov 17, 2023 at 14:38
• If I were to answer that, I would be answering the puzzle. I guess if no-one finds an answer across a long period of time, I will answer the puzzle myself (if that's allowed on this site). Nov 17, 2023 at 17:03
• @user110391 Self-answers are allowed, and I expect you're going to have to... so far the best answer is that it can't be done. How about one of the multiple solutions? Nov 17, 2023 at 17:15
• Okay, I will probably wait a while. I want to give people a good opportunity to get it. Nov 17, 2023 at 19:14

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)
Bob: No. Then, yes.

Explanation:

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.

• I assume the question you refer to is "Did John visit the room on day 2?" This almost works, but John has a strategy against it. Firstly, John makes sure Bob doesn't have a way to tell time. Bob cannot do anything for the remainder of the game (except answer the question of course), so he cannot resist John taking his time-telling devices. Then, John shows up at day two, near midnight. Given your strategy, Bob would always answer no. John shows up, waits the few seconds it takes for it to become day three, and then legally asks the question. Bob answers "no" incorrectly and gets the glock. Nov 16, 2023 at 20:13
• fixed, i think.. Nov 16, 2023 at 20:56
• Your new solution has good logic, but misses the dirty tactics John can use. It has gotten to the point now that it is unlikely for John to win, but it is still possible, and thus Bob won't have a guarantee. So, what can John do? He can give Bob something to wipe his memory. Alcohol is not difficult to get one's hands on, and for all Bob knows, John has access to drugs that are even better at wiping memory. So, if John does this Bob on day 2, Bob might not remember whether or not John asked him the question on day 2 or not. Thus, Bob does not get any guarantees with this question. Nov 16, 2023 at 21:03
• Based on the fact that my solution is based on a different puzzle at the time of my answering (eg rule 3 is different) and now John can do anything to Bob even with unguarantee success from John (eg. Force to drink alchol = wipe memory), my answer is no more valid. Nov 17, 2023 at 10:19
• How did my rewriting of rule 3 change the validity of your answer. I made sure that my rewrites didn't invalidate any answers. Nov 17, 2023 at 14:22

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."

• That is not an answer to the question, but rather a response. To answer a question is to attempt to provide the information requested by the question. A question does not (explicitly at least) ask for whether or not you know the answer to it; a question asks for the answer. Saying "I don't know" is thus not answering the question, and is thus not within the game. Nov 16, 2023 at 20:16