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Your soul is on its way to the afterlife when suddenly you arrive in a room.
You look around and notice six humanoids staring at you.
You walk toward them and you can suddenly hear them talk between themselves.
They said "Not another one of those...".
Perplexed, you ask them, "is something wrong?".
Then they tell you "Of course something is wrong, we don't like your kind around here, you make our job too complicated!"
You then reply, "My kind?".
To which they reply "Yes! your kind! You did as many bad things as good things in your life and we don't know if we should send you to hell or heaven... You know what... Just choose by yourself!".

You quickly decide that heaven is where you want to go(of course).
So you look around for the door to heaven and then notice that the door to hell and the door to heaven, against all expectations, are identical plain wooden doors.
You then decide to ask them which one is the correct door.

NEED TO KNOW

-3 of them are demons working for hell and 3 of them are angels working for heaven.
-Against all expectations, demons and angels look identical.
-Angels are pure are holy and never lie.
-Demons are cruel and want you to go to hell no matter what. They will lie to you most of the time, but may tell the truth if they have a reason to believe it will make you fail.
-Demons can hear everything you ask to the others.

What is the best way to find the door to heaven if at all possible?
I will accept the cleverest answer!

Clarifications :
The demons are smart but not THAT smart.
They are trying to actively make you go to hell and will always tell you the answer that seems the most obvious to achieve their goal at the moment the question is asked to them. For example, if the very first question you ask happens to be to a demon, they will obviously tell you that the hell door is the heaven door.
Also note that no one is omniscient, that is why the detail that demons can hear everything in the room is important. That is the only source of information they get to fool you.

UPDATE
Some people seem hell-bent on closing my question , so I will try to lower the difficulty and perhaps post a few plausible answers of my own to let the people judge them in all fairness in an hour or so, after a few hours I will select the answer that seems the most liked by reading the comments before it is too late and the question do get closed.

New clarifications
Although the best way to find heaven was asked, the best does not have to be infallible, but simply the most likely to succeed. This does not mean that there is no sure way to do it, but for making it easier, the answer with the highest probability to succeeding will be chosen.
Also keep in mind that the demons are smart but not THAT smart, they are not prodigies that will be able to read 2-3 moves ahead of you. If you can come up with a very clever scheme, maybe you will get lucky.
Also keep in mind that asking a question simultaneously to everyone can be a good way to prevent demons to collect info and form a plan and change their answer.
Also keep in mind that the demons lie most of the time, except when needed. Which means that if the answer does not "appear" to help you in anyway to discover heaven or who is lying, they will always choose to lie.

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closed as off-topic by Beastly Gerbil, kaine, Alconja, Ankoganit, gtwebb Oct 26 '16 at 5:48

This question appears to be off-topic. The users who voted to close gave this specific reason:

If this question can be reworded to fit the rules in the help center, please edit the question.

  • 4
    $\begingroup$ I did not believe it was relevant to mention. They will always tell the truth so they don't need "info" to deceive you. $\endgroup$ – stack reader Oct 25 '16 at 14:28
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    $\begingroup$ As many as you want. But the one with the most efficient/clever solution will win. $\endgroup$ – stack reader Oct 25 '16 at 14:36
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    $\begingroup$ What happens if you ask a question that can't be answered truthfully? $\endgroup$ – ffao Oct 25 '16 at 14:49
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    $\begingroup$ Good! Finally a Knights + Knaves where the Knaves aren't brain-damaged. $\endgroup$ – Joshua Oct 25 '16 at 18:29
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    $\begingroup$ What if the one who told you the rules was a demon? There is no guarantee that you can even trust the rules for this puzzle. All six could actually be demons that are trying to mess with you (would explain why you cant tell them apart). $\endgroup$ – Anketam Oct 25 '16 at 22:13

23 Answers 23

47
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Simple:

You don't need to ask any questions. Just be patient and wait for the next person to show up. If the person does not have a balanced life like you did, you will overhear their path and can then decide which door to take.

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  • $\begingroup$ +1 Thinking outside the box, I like it. I might even select your answer as correct if I don't get a better one. $\endgroup$ – stack reader Oct 25 '16 at 17:23
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    $\begingroup$ What if the angels tell the next soul that they're going to heaven, and the demons say that they're going to hell, just to mess with you? It's possible that you can't tell which door even if it's open until you enter it. $\endgroup$ – Kevin Long Oct 25 '16 at 18:02
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    $\begingroup$ Good point @KevinLong . We should wait long enough to see someone who is going to hell, and then take the other door. $\endgroup$ – Ryan27 Oct 25 '16 at 18:30
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    $\begingroup$ What if the next person comes in, and all they're told is "Go through the door on your left." $\endgroup$ – user12284 Oct 25 '16 at 19:55
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    $\begingroup$ And when the next person comes in, there are seven humanoids staring at them, saying, "Not another one of these.." $\endgroup$ – Trevor Powell Oct 26 '16 at 4:44
26
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Ask all you want...

you're doomed to just guessing...

Imagine two people like you in identical rooms, with identical demons and angels, except in Room A, the door to heaven is on the left, and in Room B, the door to heaven is on the right. Also, in Room A, the angels are standing on the left, and in room B, the angels are standing on the right.

The demons in Room A deviously answer any question exactly the same as an angel in Room B would, and vice-versa.

Any question you ask of a particular creature in either room would get the exact same answer as the same question of the equivalent creature in the other room. Thus, there is no way to determine which room you are in, and thus you cannot determine which door is which.

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    $\begingroup$ Agreed. Assuming both demons and angels are omniscient, then in any strategy of asking questions, the demons will just opt to answer identically to the angels. Yes, they prefer to lie, but if there is a strategy that will give you the right answer if they lie, the demons' omniscience will make them aware of that, and they'll just keep acting exactly as the angels (except acting as if the other door was the door to heaven). If I were a demon, why would I take a risk? Just make it a coin flip on whether or not the person can find the right door. $\endgroup$ – Kevin Long Oct 25 '16 at 15:45
  • $\begingroup$ @KevinLong: Once into two groups of only like kind, we can start asking devious questions. $\endgroup$ – Joshua Oct 25 '16 at 17:58
  • $\begingroup$ "Demons will answer exactly as the angels in the other room" - no, that's not a winning strategy. Imagine that you ask things which are certainly true in your room, but may be true or false in the other room, like "is my hair black". As soon as you find dissent over such a thing, you know who's the demon. $\endgroup$ – rumtscho Oct 25 '16 at 18:03
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    $\begingroup$ In fact this is the strategy the demons have to follow, because any answer that is not consistent with it would give them away immediately -- at least once you have split the creatures into two groups of three by asking each of them separately which door leads to heaven. The demons' only hope of obscuring the truth is to pretend they are the angles, the true angles are impostors, and the doors are the other way around -- and give the answers that would be true under that pretense. $\endgroup$ – Henning Makholm Oct 25 '16 at 18:30
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    $\begingroup$ The demon's prospensity to "lie most of the time" is a red herring: they never really have a choice between truth and falsehood if they want to avoid losing. $\endgroup$ – Henning Makholm Oct 25 '16 at 18:34
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What if...

If the demons want me to go to Hell, and want me to fail, I could technically short-circuit them by convincing them that I actually WANT to go to Hell. After I succeed, while they are writhing on the ground in existential agony, I saunter up to the angels and say, "Just kidding, folks. Lead on!"

Of course, then what follows is that...

The angels, disgusted at how I lied so smoothly to manipulate the servants of Hell itself, decide that I committed that last sin to swing the balance against my favor, and strip me of the right to decide, banishing me to Hell regardless. Oh well.

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  • $\begingroup$ nice answer. everyone only thinking about heaven when hell may be interesting lol the thing is ... the need to know do not specify if the angels can be affected by your choice. do they care, @stackreader? $\endgroup$ – lois6b Oct 25 '16 at 15:41
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    $\begingroup$ Yup... I think I owe this train of thought to Sir Terry Pratchett and Neil Gaiman: if nothing else, Hell has all the best musicians. :) $\endgroup$ – Xenocacia Oct 25 '16 at 15:45
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    $\begingroup$ +1 That's original, I like it. But it is specified that you want to go to heaven, and when I wrote that they want you to fail, it meant they want you to go to hell. $\endgroup$ – stack reader Oct 25 '16 at 15:52
  • $\begingroup$ @stackreader: I understand that Heaven is the ultimate aim, but I meant to lie to the demons to convince them otherwise (assuming they cannot read minds). Of course, I'm sure there are tons of better answers out there. Just having some fun. Thanks! $\endgroup$ – Xenocacia Oct 25 '16 at 16:00
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Right off the bat you can separate them into two groups by asking "is the door on the right heaven?" 3 people will say yes, 3 people will say no. (because if all 6 - or even just 4 - said one thing, then you would know it to be true)

Now you have two groups of 3 people each. You tell them to close their eyes and ask them questions about heaven that only angels would know. Only allowing them to answer with their hands.

So you say, "is heaven more gold or yellow? if its gold, put 1 finger up, if its yellow put two". You asking these questions until you see a member of either group provide a dissident answer. You then know that group is the group of demons.

The logic here is that if you ask a question that only angels will know, the demons have to guess. And if they don't know what the other demons guessed ("demons can hear everything in the room is important. That is the only source of information they get to fool you.") they will eventually have differing guesses. Angels on the other hand cannot have different answers because they cannot lie.

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  • 3
    $\begingroup$ Very good. This seems to get around user3294068's impossibility proof. The demons are not omniscient, they are "smart but not that smart". $\endgroup$ – deep thought Oct 26 '16 at 2:44
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    $\begingroup$ This answer needs more upvotes. It's a simple and elegant way to solve the problem. $\endgroup$ – Thane Brimhall Oct 28 '16 at 16:39
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    $\begingroup$ This assumes that the angels are cooperative as well as honest. If three beings refuse to close their eyes, well, you'll have to see if the unseeing ones trip up and lie. If six beings refuse, you're back to the impossible. $\endgroup$ – Wildcard Apr 29 '17 at 7:39
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"Of course something is wrong, we don't like your kind around here, you make our job too complicated!"

If you ask me, this does not sound like an Angel who is holy. Every soul is something to be cherished by a holy individual, and they would consider this an opportunity to bring one more to the light!

Take the 5 individuals who didn't say this, have them arrive at a quorum about which door to walk through. Let the 6th one fume at giving away extra information before the start of the game.

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  • 2
    $\begingroup$ Well since they didn't want to decide themselves, this may not work. However, you could go down the line asking "which door do you want me to go through?" until you get three nominations for one door. If the remaining two demons choose their own door they're still "outvoted", and if they choose the "heaven" door they're hastening your departure to Heaven. They're damned if they do and damned if they don't -- which is just how it should be! You will need to ask 3-5 times. $\endgroup$ – Doktor J Oct 25 '16 at 19:02
  • $\begingroup$ @DoktorJ True, I assumed that the angels wanted to vote you into heaven, which means that they'll help you out if given a majority vote, tipping the quorum towards heaven. If that assumption is unsafe, your implementation by asking 3-5 questions is the slightly-more-brute-force equivalent. $\endgroup$ – Cort Ammon Oct 26 '16 at 0:16
  • $\begingroup$ I upvoted, but I think Doktor J's idea of just asking until you get 3 answers that match. I wouldn't ask about what they want. I'd ask "Which door is heaven". $\endgroup$ – TecBrat Oct 26 '16 at 17:54
  • $\begingroup$ @DoktorJ their demons, I'm pretty sure they were dammed long before answering your question actually :p $\endgroup$ – dsollen Nov 25 '16 at 19:46
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This is not in the spirit of the puzzle, but my answer is

My good / bad work balance is irrelevant. I will sit quietly and wait for my Lord and Savior Jesus Christ to take me through the correct door! :-)

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  • 2
    $\begingroup$ You are not without intelligence. Nevertheless, it might be amusing to play the game. I'm reasonably certain a solution exists. $\endgroup$ – Joshua Oct 25 '16 at 18:01
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    $\begingroup$ Given the question already establishes the existence of heaven and hell, waiting for divine intervention is actually a pretty good option. $\endgroup$ – user1717828 Oct 25 '16 at 18:49
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    $\begingroup$ My answer was more well-received than I expected. Thank you! $\endgroup$ – TecBrat Oct 25 '16 at 19:19
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    $\begingroup$ @TecBrat Ah but apparently the path to Heaven and Hell doesn't work the way you were led to expect (no pearly gates, St. Peter and all that), so what's your reasoning that anyone will show up to save you? Perhaps that assumption is inaccurate as well. $\endgroup$ – thanby Oct 25 '16 at 19:22
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    $\begingroup$ @vsz: He of course already has. $\endgroup$ – Joshua Oct 25 '16 at 20:31
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As a start, you can divide the group into

angels and demons by asking everyone "Does the door on the left go to heaven?"

If you get more than 3 "yes"es to this question, that would mean that indeed the door on the left goes to heaven (because if not, all three angels would've said "no"). So the demons, not wanting to reveal this, will smartly say the opposite of what the angels say in this circumstance. Therefore, assuming crafty demons, you'll have 3 of the humanoids saying "yes" and three saying "no" to this question, which allows you to separate the 6 into two groups of three.

But

You still don't know which three are which...


Below here doesn't really work.

So then, you ask questions in the following pattern.

Group A (unknown) and Group B (unknown).

To A1: "Does the door on the left lead to heaven?"
To B1: "Was my previous question answered truthfully?"
To A2: "Were my previous two questions answered truthfully?"

If the answer to the first two are ever both "Yes", you've asked about the correct door, because either you asked an angel first (and thus the first yes is true) or you asked a demon first and he answered truthfully, which is confirmed by the second "Yes".

So demons will try to ensure that the first two answers are not "yes", because that would reveal the door to heaven.

So we have some specific cases:

Case 1: Angel first, correct door asked about
A:Yes D:No A:No → Y N N
Note: Demon must answer "no" or gives it away.

Case 2: Demon first, correct door asked about
D:No A:No D:No/Yes → N N Y/N
Demon must begin with "no" or gives it away.

Case 3: Angel first, incorrect door asked about
A:No D:Yes A:Yes → N Y Y
OR
A:No D:No A:No → N N N
Demon has a choice, but angel's following answer will match.

Case 4: Demon first, incorrect door asked about
D:Yes A:No D:Yes/No → Y N Y/N
OR
D:No A:Yes D:Yes/No → N Y Y/N

You can see from this that

If you ask those questions about the correct door, the second answer will never be "yes". If the second answer is ever "yes", take the opposite door to the one you asked about. And thus demons will probably seek to not ever answer "yes" to the second question.

Also, the N N Y answer pattern only exists if you asked about the correct door to start, so if you hear that, pick that door. And demons will seek not to answer that way because it'd give heaven away.

And the Y N Y case only exists if you picked the wrong door to ask about, so demons will avoid that.

Left with:

Case 1: Angel first, correct door asked about
A:Yes D:No A:No → Y N N

Case 2: Demon first, correct door asked about
D:No A:No D:No/Yes → N N Y/N N N N (because a "yes" would give it away)

Case 3: Angel first, incorrect door asked about
A:No D:Yes A:Yes → N Y Y → Take the other door
OR
A:No D:No A:No → N N N

Case 4: Demon first, incorrect door asked about
D:Yes A:No D:Yes/No → Y N Y/N → Y N N (Y N Y would give it away) OR
D:No A:Yes D:Yes/No → N Y Y/N → Take the other door

So if the answers are

N N N, then either you've asked a Demon first about the correct door, or an Angel first about the incorrect door.

And if they're

Y N N, then either you've asked an Angel first about the correct door, or a Demon first about the incorrect door.

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  • 1
    $\begingroup$ Neither side should say yes to the second question- if the angel says it's the wrong door, the demon will try to convince you otherwise. If you ask the demon first and it's the wrong door, the demon will say it's right. Essentially, if both sides ever agree about a door being right or wrong, you'll know at least one of them is an angel, and so it must be what they say it is. $\endgroup$ – Kevin Long Oct 25 '16 at 17:45
  • $\begingroup$ I have worked through all cases on the ladder, and this solution is complete except for receiving Y Y N. In this case, group A must be demons so you have the answer anyway. $\endgroup$ – Joshua Oct 25 '16 at 20:36
  • $\begingroup$ @Joshua I think it actually doesn't work because Y N N and N N N are basically opposites, and even if you switch groups, you'll get the other one. (I.e. ask group A first, get Y N N, then ask group B, get N N N, and therefore are none the wiser.) $\endgroup$ – Dan Russell Oct 25 '16 at 20:42
  • $\begingroup$ To be clear, isn't this just equivalent to asking just the first question as only YNN and NNN are possible (assuming smart demons)? $\endgroup$ – kaine Oct 25 '16 at 21:07
  • $\begingroup$ @kaine Yep, I think so after further review. The idea was to force the demons to answer in a certain way, and indeed you can force them to make certain answers so as to not give away the truth, but I think this approach at least doesn't have quite enough. $\endgroup$ – Dan Russell Oct 25 '16 at 21:12
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Start by proclaiming the following:

I will enter the right door if you all have the same answer to my next question, and I will enter the left door if there is disagreement.

Then ask the following question:

Does the door on the right lead to Heaven?

Then take the following action:

If they all answer "no" enter the left door. If there is disagreement, enter the right door

Basically, the Demons have to call your bluff. If they take your statement as truth, you will go to heaven every time.

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  • 1
    $\begingroup$ But perhaps the demons would discern your strategy here and simply answer the opposite of what the angels would say. $\endgroup$ – Dan Russell Oct 25 '16 at 16:42
  • $\begingroup$ That's clever, but I don't think the demons would fall for that. If they ever agree with the angels, then you would know for sure the correct door and they won't tell you what door is the correct one hoping that you will stay true to your word and voluntarily walk into hell. They will probably always go against the angels, and then you gonna have to decide if you are willing to bet your life on if they called your bluff or not. $\endgroup$ – stack reader Oct 25 '16 at 16:43
  • $\begingroup$ Yup! But they will then have to also think if you also know that they know... etc. Reminiscent of a certain scene from the Princess Bride involving poison. It comes down to who bluffs better, which is the best you can hope for with the given scenario. $\endgroup$ – Skroll Oct 25 '16 at 16:49
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    $\begingroup$ I gave the +1 because I thought it was clever, though admittedly it just becomes a game of bluffs on bluffs. $\endgroup$ – Kevin Long Oct 25 '16 at 17:38
  • $\begingroup$ Appreciate it! If the Demons do "...always tell you the answer that seems the most obvious to achieve their goal at the moment the question is asked..." then this should always work. I suppose it depends how clever those pesky Demons are! $\endgroup$ – Skroll Oct 25 '16 at 18:02
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Lots of answers already, but I didn't see one like this yet:

Starting with a few assumptions:

1. All beings are compelled to answer whatever questions they are capable of answering. If not, then all 6 could just tune you out and let you make your own decisions; I mean gosh, they already have said that they "don't like you," why answer questions if they don't have to?

2. When asked a question with options (ex: "do you prefer Coke, Dr. Pepper, or Pepsi"), a demon must answer either with the true option, or one of the untrue options. This may seem obvious from the question, but the precision here is key.

We're also given that

Angels ... never lie

Also, all 6 beings told you

we don't know if we should send you to hell or heaven

Then for the angels to have said that, that must have been true for them. Which implies that

The angels have no preference for whether you should go to Heaven or Hell.

However, we also know that

Demons ... want you to go to hell

So, to find out if any given being is an angel or demon, ask them

Do you think that I should I go to Heaven, or that I should go to Hell?

Based on the assumptions before,

Demons must give one of the options, as they do have a preference. Angels, however, have no preference. So they cannot truthfully give either answer, and must either stay silent or, if they are compelled to give some answer, say something like "I have no preference."

Then, you can find an angel by asking the questions to beings until you get your first angel answer (so 4 times at most). Then ask the angel

Which door leads to Heaven?

And take that door. 2 to 5 questions.

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  • 6
    $\begingroup$ I think assumption #2 is a big one that might not apply. Seems like demons could still answer "I have no preference." $\endgroup$ – Dan Russell Oct 25 '16 at 20:07
  • $\begingroup$ Oh it's absolutely a big assumption. But as per user3294068's answer, if there are no further restrictions (or a definition of just how smart these demons are) they might as well be angels who got the words "Heaven" and "Hell" swapped. There would have to be some difference in how angels and demons could answer, I think. $\endgroup$ – Kokiomot Oct 25 '16 at 20:15
  • $\begingroup$ Note that "we" could refer to the group as a whole rather than just the angels or a single angel. All angels could want a happy ending for you. (and again demons are not obligated to answer in any particular way if it does not suit their goal). $\endgroup$ – kaine Oct 25 '16 at 21:10
  • $\begingroup$ About your assumptions: From the question posed "To which they [All] reply ... we don't know if we should send you to hell or heaven... " So it seems that they all, on some level, lack a preference. $\endgroup$ – Kevin Fegan Oct 25 '16 at 21:51
  • $\begingroup$ @kaine that reminds me of an old joke that goes along the lines of: 3 logicians walk into a bar, barkeeper asks "would you all like a drink?", the first one says "I don't know", the second says the same, and the third says "yes". If any one of them saying "no" would have made the answer to the question "no", and I figured the same general idea would apply to the angels speaking for themselves if they did actually have a preference. $\endgroup$ – Kokiomot Oct 25 '16 at 22:17
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It seems like there are too many variables in this riddle to actually come up with a solution that will get you 100% into heaven. The following is the closest I've come up with.

Say, "On the count of 3, everyone point to the door that the opposite spiritual being would most likely say is the heaven door." Then count to 3.

Having everyone point ensures that the demons won't overhear any of the other responses. Having everyone point at the same time ensures that the demons don't get a chance to plan ahead in case they can also see the others' responses.

If you asked a demon which was the heaven door, they would most likely point to the hell door. The 3 angels, unable to tell a lie, will therefore point to the hell door.

If you asked an angel which door is the heaven door, they would all point to the heaven door. The demons, knowing this, would then all point to the hell door as well.

Therefore you would know that the door that everyone didn't point to is the heaven door.

Now at this point, some of you might say that the demons are smarter than that. However it was stated that:

The demons are smart but not THAT smart.

so some demons may realize the trap they were put in and point to the heaven door instead, but unless all the demons point to the heaven door this trick still works. You might end up with 4 of the humanoids pointing to the hell door and 2 pointing to the heaven door. But because the angels have to point to the hell door the majority is most likely pointing to the hell door and therefore the other is the heaven door.

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  • $\begingroup$ I like that you are looking for asymmetry but you are assuming that the angels are smarter than the demons. Do you know this? Angels never lie but can they make mistakes? $\endgroup$ – kaine Oct 25 '16 at 21:36
  • $\begingroup$ hence is why i asked "everyone point to the door that the opposite spiritual being would most likely say is the heaven door." also the angels don't have to be smart. they just can't be dumb. $\endgroup$ – mikelt21 Oct 25 '16 at 21:38
  • 1
    $\begingroup$ Eh... the angel question is easier... You are right there. This is as good as any other solution. $\endgroup$ – kaine Oct 25 '16 at 21:40
2
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I'd ask them all a similar question to "Describe you go home to when you have finished deciding the fate of the damned each day?", but not similar enough to a devil to steal the answer (e.g. where do you go home to, describe where the angel next to you goes home to, etc.)

That way you should be able to at least determine which at least 1 of the angels are actually a demon.

Next, as you haven't said only 1 question per angel (I will refer to all as angels, unless there is a known demon), I would simply ask all but the one which we have worked out is a demon the simple question "If I was to walk through a door and enter into heaven, which door would I walk through?". You know for a fact that 3/5 of the answers HAVE to heaven, so you go through the door which gets pointed to the most.


Potentially sarcastic answer!

Either that, or open both doors at the same time and look inside. Whichever looks nicer, you jump inside.

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2
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Working off of Ryan27's answer:

Ask the first person you see if they mind if you wait awhile to see where the person after you goes. The demons will immediately object and demand that you chose now. Ask anyone who didn't demand you chose what door leads to heaven.

This assumes that

The angels don't care if you go to heaven or not.

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2
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Ok, since Stack Reader responded "Thinking outside the box, I like it" to Ryan27's answer, I'm also going to suggest some outside-the-box ideas, since they are not yet overtly prohibited:

Open each door and see what's inside--so far there is no statement you cannot return once you go through a door. Maybe you can explore each place & even live in each for a while to see which you like best.

This is supported by the fact the angels themselves can't tell which is better for you: if souls get stuck in heaven or hell once they went through a door, it would be a very serious problem from an all-good, perfectly just God's perspective to have good souls getting stuck in hell, and so a fool-proof system would have been put in place to make sure good souls only went to heaven. The lack of a fool-proof system to save good souls suggests souls cannot get stuck in an incorrect location.

Also potentially beside the point of logic-riddle solving, yet still philosophically/logically interesting and outside-the-box is this:

It may be a false assumption that heaven is better than hell for the ex-human in question. If you did as many bad things as you did good things, you might be just as happy in hell as you would in heaven. Perhaps if you do all bad deeds, your soul is fully demonic and so you are no different from the demons at the doors. This theory is supported by the quandary's premises that the angels and demons are visibly impossible to distinguish. If the demons reside happily in hell, then maybe you could too.

Also,

Just because the demons are stated to be "cruel", it does not follow that human souls will suffer in hell--being cruel may simply be a behavioral trait of beings that do bad deeds. Perhaps to demons who do bad things only, cruelty to each other is appropriate social etiquette, and hence not something to which bad ex-human souls are averse.

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  • 1
    $\begingroup$ So now, how do SE readers choose who to upvote & who to downvote?!?! $\endgroup$ – Thom Blair III Oct 25 '16 at 19:35
2
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Assuming the Demon/Angel must provide an answer to your question.

Think of a number between 1 and 1 million in your head, hold it there. Ask one of the six to tell you the number. If they are an angel they are unable to lie and through some divine power give you the correct number. Just in case of extreme luck, perform this multiple times rotating through until one was consistently correct and one was consistently incorrect. Then ask the consistently correct angel which door leads to heaven.

The assumption:

The angel (and therefor a demon) will not respond with 'I do not know'. You could be stubborn and say you will not enter a door until your question is answered, hopefully prompting some divine intervention to keep things moving. Otherwise, eternity in a room with some demons and angels is better than 50% chance at landing in hell.

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  • $\begingroup$ Why would a demon (with supposedly equal access to divine powers) give you an incorrect answer to your test question? They apparently have the ability to tell the truth if it furthers their ends, and once they pass your test, the demon would then be able to convince you to use the wrong door. $\endgroup$ – speedfranklin Oct 25 '16 at 21:12
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    $\begingroup$ @speedfranklin Very last line of the original post - "That is the only source of information they get to fool you". There is nothing which indicates equal access to divine powers. $\endgroup$ – Isaac Oct 25 '16 at 21:26
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As the demons are smart they will realize what several people have before. All they need to do is answer all questions as if all angels were demons, demons were angels, heaven was hell, and hell was heaven.

As they are not that smart, they will not realize that this can take several forms:

  • They each pretend to be one of the exact angels in front of them (6 permutations) (A)
  • They pretend their demon names are the names of angels (B)

If Demons have two strategies that are equivalent and do not know which the other two will pick, you may be able to trip them up.

Therefore you should do the following:

  • Choose a random being and request: "What is the name of one of you 6 humanoids?"
  • Assume they answer "Bob"
  • Ask all of them to face the walls
  • Ask each of them in turn to nod their head if "Bob" is a demon

If all demons were genius, they would already have a plan set up for this.

If they are not "that" smart, however, you can expect that they may not know which strategy to adopt. This is compounded by my understanding that demons do not like to give their real names but that giving their real names is the better strategy.

  • If there are 1, 2, 4, or 5 "No"s, then just separate them into two groups by asking "Does the door on the left go to heaven?" and see which group in inhomogeneous. This is what you are hoping for.
  • If there are 0 or 6 "No"s, they agree to keep the angels names correct but may not have decided who adopts which identity. Ask for all names and move around asking at random whether each humanoid has each name.
  • Finally, if there are 3 "No"s, they probably gave the demons' names as angel names. Try again with a different name to see if you can trip them up but I assume you won't.

If you do not succeed, ask yes or no questions about the "demons" opposing each "angel" and see if either group disagrees amongst itself. (Maybe "which demon is most badass?")

This can all be beaten by having the demons plan ahead as to which strategy to take or recognizing that giving their demon names is a slightly better idea (assuming no names are recognizable to you). They can also make up odd names or claim that someone has a duplicate name in the hopes of confusing you. I have to assume though that the demons aren't that smart because you said they aren't.

It may be a good idea to have demon's and angels pair up before starting so that both strategies are just as good but I would guess that aversion to revealing their names would bias them all to adopt the angels' names

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  • $\begingroup$ This is sort of along the lines of what I've been thinking about. Providing some subset with knowledge that can't be seen by others, then asking the right questions. $\endgroup$ – Dan Russell Oct 25 '16 at 21:13
  • $\begingroup$ @Dan Russell... Um.. Not really. If you provide the subset with knowledge, the demons with or without the knowledge just behave as angels with or without that knowledge. The demons will lie to you when appropriate. You need to take advantage of the fact they might not have planned out their lie in advance. $\endgroup$ – kaine Oct 25 '16 at 21:18
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    $\begingroup$ Four college students are hungover before an exam. They call the professor and say they have a flat tire. The professor reschedules and sticks an extra question of the test worth 50%. "Which Tire?". That is the essence of this answer. $\endgroup$ – kaine Oct 25 '16 at 21:20
  • $\begingroup$ Yep, that seems to be the case. And that's what I was getting at with the "right questions" part. $\endgroup$ – Dan Russell Oct 25 '16 at 21:21
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Ask anyone who are the angels, this will split the 6 into two groups of 3, although we don't which are the true angels.

Now, spit in your hands and ask the first group to bless the spit. Then fling it at the second group. If the first group were angels, your spit was turned into holy water and should burn the second group. If that is the case, ask the first group for the door and be on your merry way.

If the second group does not get burned but is merely pissed off (because after all you did just throw your spit at them) they must be the angels. Humbly apologize and bring them back towels and ice cream from heaven when they've shown you the way.

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Firstly you need to:

Ask each angel/demon "What would the other 5 will say to the question 'are you an angel'?" Each of the angels will say the other 2 angels will say "yes" but they will say they "don't know" what the demons will say, as they can only tell the truth and there is always a chance the demons will say something other than "yes".

From this:

The demons will give the same answers, only lying and pointing out the other 2 demons saying yes instead of angels, as they will know if they answer differently you will immediately know them for demons. This way you can immediately establish which 3 are equal to which other 3, though not which is which.

Then:

You only need 1 angel and 1 demon to answer your questions, so then ask the angel "Which door would (opposite number) tell me is heaven?", to which the angel will point out the door to hell, and asking the demon "Which door would (opposite number) tell me is heaven?" will also point to hell, as that is where it wants to trick you into going.

If the demon knows this:

it will point to the opposite door, as it will try to trick you. If this is the case, you simply need to ask "which door will (opposite number) say leads to hell?" in the opposite order and the demon will be asked first, and as the angel has not yet been asked it will invariably point to heaven, as will the angel afterwards.

You can then take the door you know points to heaven.

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    $\begingroup$ Hmmmm...except that in the last part the angel really doesn't know what the demon would say, and thus must answer "I don't know", and therefore the crafty demon would answer everything "I don't know" as well to obfuscate the truth. $\endgroup$ – Dan Russell Oct 25 '16 at 16:30
  • $\begingroup$ I'm a little confused here- wouldn't the demon point to the door to hell in the last part, in order to keep up the illusion that the angel is the demon, and that the door to hell is the door to heaven? $\endgroup$ – Kevin Long Oct 25 '16 at 16:37
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The door to Heaven should be located on the right hand side of the room. There are many biblical references which provide evidence for this.

Acts 2:34

"For it was not David who ascended into heaven, but he himself says: 'THE LORD SAID TO MY LORD, "SIT AT MY RIGHT HAND

Hebrews 8:1

Now the main point in what has been said is this: we have such a high priest, who has taken His seat at the right hand of the throne of the Majesty in the heavens

Mark 14:62

And Jesus said, "I am; and you shall see THE SON OF MAN SITTING AT THE RIGHT HAND OF POWER, and COMING WITH THE CLOUDS OF HEAVEN."

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    $\begingroup$ But if it is on the right from God's view, who is behind the door, then from your side it should be the left door, shouldn't it? $\endgroup$ – celtschk Oct 25 '16 at 20:27
  • $\begingroup$ There is only one door on the other side. One leads to Heaven, the other to Hell. $\endgroup$ – Jason Hutchinson Oct 25 '16 at 20:30
  • $\begingroup$ God is omniscient, so he knows where the door is even if he's on the other side. When coming from heaven, you'd find the other door either on your left or on your right. And even if God doesn't do that, he could. $\endgroup$ – celtschk Oct 25 '16 at 20:43
  • $\begingroup$ And Jesus will sort the lambs from the goats. He won't leave it up to 6 underlings who don't really care. $\endgroup$ – kaine Oct 25 '16 at 21:26
  • $\begingroup$ Suppose the room is round and the doors are on opposite ends of the room. =) $\endgroup$ – Kevin Fegan Oct 25 '16 at 22:00
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Solution 1:

Since the demons cannot simply choose to say "Yes" or "No", but only to either say the truth or to lie, just ask: "Is it true that either this door goes to hell or your answer is a lie, but not both?"

If the asked one says the truth (either due to being an angel, or due to being a demon choosing to say the truth), then his answer is not a lie, therefore he will say "yes" if the door goes to hell, and "no" otherwise.

If the asked one lies (a demon who decides to lie), then his answer is a lie, therefore if the door goes to hell the correct answer would be "no", but since he is lying, he'll answer "yes". And if the door leads to heaven, the correct answer would be "yes", but due to lying the given answer will be "no".

Either way, if the answer is "yes", the door leads to hell, and if the answer is "no", the door leads to heaven.

Solution 2, out of the box:

If you are a true believer, you'll of course figure that God will make sure you get where you belong, so you don't ask at all, but just arbitrarily choose one door. If it wasn't the one to heaven, you didn't deserve that anyway.

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    $\begingroup$ I don't think that Solution 1 quite works, because smart demons will always answer this question as the opposite of whatever angels would say. With 3 yes and 3 no, there's no way to distinguish. $\endgroup$ – Dan Russell Oct 25 '16 at 20:48
  • $\begingroup$ @DanRussell: Please read carefully the first part of the first sentence. $\endgroup$ – celtschk Oct 25 '16 at 20:53
  • $\begingroup$ You mean your first sentence? "Since the demons cannot simply choose..." Why not? They can say whatever they want, right? $\endgroup$ – Dan Russell Oct 25 '16 at 20:57
  • $\begingroup$ @DanRussell: From the question: "They will lie to you most of the time, but may tell the truth if they have a reason to believe it will make you fail." Nothing about saying whatever they want; they just can choose to either say the truth or to lie. $\endgroup$ – celtschk Oct 25 '16 at 21:01
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    $\begingroup$ No second guessing of what the OP might not have meant is required. The question says: "They are trying to actively make you go to hell and will always tell you the answer that seems the most obvious to achieve their goal." In other words, they can say whatever they want. Sometimes what they tell you will have been a lie, but not by them actually choosing "for the next N minutes everything I say will be a lie". They are free to lie or tell the truth about the door, and then separately, they are free to lie or tell the truth about the "but not both" part. $\endgroup$ – Kevin Fegan Oct 25 '16 at 22:35
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I'd feel each door and/or doorknob, just like you're taught to when there is a fire. Whichever is warm is Hell; take the other one.

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Assumptions:

This works on the assumption that all six would be in consensus about a truly evil being (Adolf Hitler, a demon, whatever) getting sent to Hell...

  1. To start,

Pick any arbitrary pair of humanoids (we'll call them A and B). Ask B, "If I asked A which door he would choose to send an evil being (we'll call it "E") through, which would he respond?", then ask B, "Which door would A choose to send E through?".

  1. You may need to repeat this...

one more time if the answer to both questions is the same

  1. Once you have...

different responses, you know you have one demon and one angel.

  1. For your last question,

ask A, "Which door would B send me through"?

  1. And you can walk through

the opposite door

assured of the path to heaven!


Explanations:

  1. If you were to ask an angel directly which door he'd send E through, he'd point to the Hell door; thus if you were to ask a demon directly which door he'd send E through, he would of course point to the Heaven door so you'd go through the opposite and go to Hell.

    Now if B is an angel, he will respond to the indirect questioning with the Hell door twice if A is an angel as well, or Heaven then Hell if B is a demon.

    If B is a demon, he'll want you to believe he's an angel and also that A is the opposite of his actual nature (but also invert the answers to try to mislead you), so he'll respond with the Heaven door twice if A is a demon, or Hell then Heaven if B is an angel.

    Depending on your initial pairing choice (○ = angel, ⋔ = demon, + = heaven, - = hell), this would be your truth table:

     A B
     ○ ○  =  - -
     ⋔ ○  =  + -
     ○ ⋔  =  - +
     ⋔ ⋔  =  + +

  2. So when you get different responses you know you've got one demon and one angel.

  3. (see truth table in explanation #1)

  4. If A is an angel, he would of course respond with the Hell door (since B is a demon).

    If A is a demon, (hopefully) he's more concerned with painting B as a demon than puzzling all this out so far, and will claim that B would send you through the Hell door.

  5. Since both responses would point to the Hell door the other door is of course the heaven door.

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    $\begingroup$ This does not work. If A is an angel he will point to the hell door. If A is a smart demon, he will point to the heaven door because he knows B would point to the hell door. The demon is smart... not a simple liar. He just acts as if he were an angel and the doors were reversed. $\endgroup$ – kaine Oct 25 '16 at 21:32
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Ask them all what the door is made of.

Angels will say wood, demons will say something else. Since its obvious that the doors are made of wood, the demons have no reason to tell the truth (to cause failure), and will lie (say it's made of metal, glass, etc.).

Of the six answers, 3 will be obviously false, and you can ask any one of the 3 identical looking humanoids who said the door was made of wood, which one the door to heaven would be.

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    $\begingroup$ The demons are somewhat intelligent, and capable of telling the truth, and therefore would tell the truth to avoid tipping you off that they were demonic liars. $\endgroup$ – TecBrat Oct 25 '16 at 17:41
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Ask the leftmost one: Do demons lie?
Ask the one next him: Do demons lie?
Ask the one next him: Do demons lie?
Ask the one next him: Do demons lie?
Ask the one next him: Do demons lie?
Ask the rightmost one: Do demons lie?

If a demon always lie the 3 demons will say "no". Angels will alway say "yes".

The demon can say "yes" to make you fail. But since a demon tell lie to you most of the time, asking him : Do demon lie? 3 times will force him to say "no" somehow. Demon are not that smart so they would lie.

So repeat the same question another 2 rounds

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    $\begingroup$ Its not like that at all, demons lie most of the time but will say whatever is necessary to make you go to hell $\endgroup$ – Beastly Gerbil Oct 25 '16 at 18:29
  • $\begingroup$ How smart are they? $\endgroup$ – TSLF Oct 25 '16 at 18:35
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    $\begingroup$ Smart enough to work out what answer will be most likely to send you to hell $\endgroup$ – Beastly Gerbil Oct 25 '16 at 18:37
  • $\begingroup$ But they are not that smart to tell truth 3x. Otherwise we need to establish their level of smartness. $\endgroup$ – TSLF Oct 25 '16 at 18:43
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    $\begingroup$ personally I think this is a bit too broad, but I also am assuming that they are as smart enough to tell a lie to the same question each time $\endgroup$ – Beastly Gerbil Oct 25 '16 at 18:46

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