# Which door should you take?

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The case of a single guard ( two doors ,one question ) is similar. Ask 'which door would a lier recommend I take', then take the opposite.

No matter who you ask, the correct answer to your question is (of course) the wrong door. Therefore, if you ask the liar, he will tell you the right door, so if you do the opposite, you'll go through the wrong door...

=Uncool-

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I still don't see how to make it any simpler.

I agree that MigL will get eaten by the tiger if he asks that question to a liar and then does opposite [ an imagined liar would recommend the bad door - and the liar you question will tell you the opposite of that ie the good door - and you do the opposite ie the bad door]

Questions must, I think, have a degree of self-reference. It is this self-reference (or reference to the other guard - same thing really) that means that the liar and the truth-teller give the same answer.

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I think I would ask, "Why are you guarding the door?"

And then I would tell the dudes to screw themselves, and I would bust out like Majin Buu in Dragon Ball Z when he got sealed into Kami's hyperbolic time chamber.

I've seen this riddle before. I've seen the answer.

And I'm pretty sure if I meet these dudes, I'm going to just pull a Majin Buu.

Maybe their job as guards is to make sure people actually do go through the doors.

Hmm.

Edited by Genecks
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Sorry, posted that wrong.

The question to ask of the single guard should have been 'If you were a lier which door would you recommend I take'.

A truth-telling guard will tell you what a lier would tell you, the wrong door, so you take the opposite

A lie-telling guard, already being a lier, will also tell you the wrong door, so you take the opposite.

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MigL - could you explain where your logic differs:

'If you were a lier which door would you recommend I take'

Guard - Truthteller

Internal hypothetical dialogue - 'if I were a liar I would say the bad-door which is on the RIGHT'

External dialogue - "the RIGHT door"

opposite - you take the LEFT door

result - safety

Guard - Liar

Internal hypothetical dialogue - 'if I were a liar I would say the bad-door which is on the RIGHT'

External dialogue - "the LEFT door"

opposite - you take the RIGHT door

result - tiger food

The lying guard must lie

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Would the lier also not lie about being a lier and so give yet another inversin betwen right and wrong door ?

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The simpler form with 1 guard is:

If I were to ask you which door led to heaven, what would your answer be?

Truthteller: Left door goes to heaven, so I would answer left door, so the final answer will be left door.

Liar: Left door goes to heaven, so I would answer right door, so the final answer will be the left door.

=Uncool-

Edited by uncool
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Would the lier also not lie about being a lier and so give yet another inversin betwen right and wrong door ?

No - because you have not asked him if he is a liar. You have to assume that he can make a logical thought progression in his head (ie "what would a liar say") - you also assume that he says the opposite of what he believes through that logic to be the truth

Uncool

Yeah - not sure it is much less convoluted than mine tho!

You could argue that you question could be compressed without loss to "what door leads to heaven" - at which point it collapses. But it has that element of self-reflexivity.

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I'd say that it is less convoluted

because it doesn't directly involve the "pretend you're the opposite of who you are"

.

=Uncool-

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i agree with you uncool - I was being facetious.

i just wrote a long post on why I thought your question was flawed - but have changed my mind and deleted it. I think many would compress it to a simple question - but the formulation (which ii guess is the future subjunctive) does not really allow it. One has to be able to rely on grammatical and logical accuracy to answer these questions - and if ones does then yours is perfect.

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I just went up to one of the guards and asked him if the other guard believed any of the alternative solutions would work and he said "Yes, all of them". lol

No more questions for you then...so what door you gonna pick?

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No more questions for you then...so what door you gonna pick?

In my younger years I must have picked the correct door since I am now retired and still living what I consider a rewarding life!

Edited by TonyMcC
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In my younger years I must have picked the correct door since I am now retired and still living what I consider a rewarding life!

Damn - that's the best answer so far!

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Well, new question time, right?

3 Guards-- One always tells the truth, one always lies, and one who tells the truth or lies randomly

Oh, and just so you can't use the 1-guard answer, there are now 2 death doors and 1 good door (that probably leads to 2 doors with no hinting guards, lol)

I don't really have an answer for this one yet...have fun!

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Well, new question time, right?

3 Guards-- One always tells the truth, one always lies, and one who tells the truth or lies randomly

Oh, and just so you can't use the 1-guard answer, there are now 2 death doors and 1 good door (that probably leads to 2 doors with no hinting guards, lol)

I don't really have an answer for this one yet...have fun!

This should not be possible. The answer to the question will either be "Yes" or "No"; that cannot distinguish between 3 doors.

=Uncool-

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This should not be possible. The answer to the question will either be "Yes" or "No"; that cannot distinguish between 3 doors.

=Uncool-

When did that become a rule? In every answer so far, the guards can indicate a door. Say in this one, they could indicate up to 2. There IS an answer, and it's super simple.

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*bump*

Come on, someone try it

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When did that become a rule? In every answer so far, the guards can indicate a door. Say in this one, they could indicate up to 2. There IS an answer, and it's super simple.

I think we need to restate the rules for this new variation. The original rule was "You walk up to a guardian and ask him the one question you are allowed and he tells you which door to take." If the guard can give more than one piece of information, why not 3? Why not ask a question that needs to be answered in essay form?

I'd interpret the original rule to mean that a guard can basically indicate a single door in answer to any question. (The precise wording is bad, because if you ask "what door would the other guard tell me to take to avoid death", a valid answer is not the same as the guard telling you which door to take.)

Edit: The rules should be that you can choose whatever door you want based on however the guard answers, however in the case of 3 doors the question would by necessity have to make the guard indicate the good door (not one of the 2 bad doors, which wouldn't give you enough information to choose).

Restated:

1. 3 Guards-- One always tells the truth, one always lies, and one who tells the truth or lies randomly. Also, by "randomly" I think we mean the guard either answers a full question truthfully or falsely, rather than giving a random answer.

2. there are now 2 death doors and 1 good door

3. You can ask any one guard any question and the guard will indicate a door in response, if it's possible and consistent with rule 1. (Otherwise their head explodes, I think is the standard rule.)

Can it still be done?

(I assume your version is not the same... can you restate it?)

Edited by md65536
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I think we need to restate the rules for this new variation. The original rule was "You walk up to a guardian and ask him the one question you are allowed and he tells you which door to take." If the guard can give more than one piece of information, why not 3? Why not ask a question that needs to be answered in essay form?

I'd interpret the original rule to mean that a guard can basically indicate a single door in answer to any question. (The precise wording is bad, because if you ask "what door would the other guard tell me to take to avoid death", a valid answer is not the same as the guard telling you which door to take.)

With this interpretation, the question would have to make the guard indicate the correct door (not one of the 2 wrong doors, which doesn't give you enough information to choose).

I had forgotten about that stipulation about taking whatever door was indicated, as uncool's riddle answer gave an indication of the death door. My intention was this:

1. 3 guards: 1 lies, 1 doesn't lie, 1 may or may not lie

2. 2 death doors, 1 good door

3. You can ask 1 guard to indicate up to two doors that match the properties you provide, and choose your door from the information provided.

From this framework, uncool's answer still works, upon review, though it's more complex than necessary. My simple 7-word query was this:

"Which of these doors lead to death?" Then, take either the door indicated, or if 2 are indicated, take the other. (The tough part is wording it with correct grammar!)

1. 3 Guards-- One always tells the truth, one always lies, and one who tells the truth or lies randomly. Also, by "randomly" I think we mean the guard either answers a full question truthfully or falsely, rather than giving a random answer.

2. there are now 2 death doors and 1 good door

3. You can ask any one guard any question and the guard will indicate a door in response, if it's possible and consistent with rule 1. (Otherwise their head explodes, I think is the standard rule.)

Can it still be done?

Yup!

Even with your forgotten rule, one could simply ask, "If asked, which door could you say leads to life?" (the conditional subjunctive keeps the guard from indicating the other death door out of spite)

And some folks say spoken language isn't as precise as math...there are just tons more functions which are too often misunderstood!

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Marqq - I don't think your answer works unless you assume a bit more than I think you are. If the guard you ask is one who lies randomly, he could think as follows:

Under straight asking (that is, if you were to ask "Which door would you say leads to life?"), he tells the truth. But under this question, he tells a lie. This means that his straight answer would be the door to life, so his answer to the full question could be either of the other doors. I don't think it was specified that he has to act consistently from one time to another, which means that this is a legitimate opportunity.

However, if the guard must indicate all relevant doors, then yes, just the question of "Which door leads to life?" is enough.

=Uncool-

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Under straight asking (that is, if you were to ask "Which door would you say leads to life?"), he tells the truth. But under this question, he tells a lie. This means that his straight answer would be the door to life, so his answer to the full question could be either of the other doors. I don't think it was specified that he has to act consistently from one time to another, which means that this is a legitimate opportunity.

I think the most useful specification of the rule is that the random guard would have to pick between being truthful or a liar, and be consistent throughout the question. If he could switch halfway through, then any multi-part question could probably essentially be given random truth values, and the final answer would probably be random and thus useless. If there's a way to phrase it so that this doesn't matter (I doubt it's possible), that would definitely be Nightmare Mode for this puzzle!

Yup!

[...]

It's so simple it took me a long while to get it. For some reason I'm reminded of NAND gates.

However, given that the random guard could one day answer truthfully and another day answer falsely,

you'd probably have to phrase the question to avoid allowing him to speak of what his answer might be some other time.

Eg. if he's truthful, he may truthfully answer that he could randomly lie if asked a question???

Perhaps, "If I were right now asking which door leads to life, which could you answer with?" resolves the ambiguity?

Edited by md65536
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I think the best you can do is something like "which door, or set of doors, among these doors leads to death?"

It depends on whether you view the liar as "blindly lying" or "deceitfully lying". If it's the latter you are toast.

If the guard you pick is honest (permanently or temporarily) he will indicate two doors that lead to death. You pick the other

If he says the opposite of the truth (again, permanently or temporarily) then he will point to the one safe door.

If he is a devious liar who wants you dead, he picks one of the death doors at random and the safe door.

Incidentally, if he always seeks to make false statements then, were he to indicate just one door he would tacitly tell you that he was the liar. In doing so, he would effectively tell you something true. But he's not allowed to do that.

The problem seems to be that "liar" is poorly defined.

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Wow! I'm seeing this for the first time, but the answer should be asking one guardian what the other would say if asked which road leads to any of the two options. If one falls in the hand of the liar, and he lies, the other would love to defend himself.

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There are 3 doors, only one of them good.

There are 3 guards, and you can ask one of them a question that can be answered with the guard pointing to one door.

One guard always tells the truth.

One guard always lies.

One guard is insane but consistent, and alternatively acts truthful or lies (you don't know which will be first), with each "atomically evaluable" part of your question.

I'm not sure is this variation is consistent. Assume the insane guard would evaluate the "parts" in order that you speak them (or reverse order, would be equivalent, but she wouldn't "optimize" or reorder your expression). Also assume that if the guard is evaluating a part truthfully, she treats any previously evaluated parts as the truth. That is, the guard "acts honest" and conveys the previous lie rather than turning a lie into a truth (which is what the consistent liar does). Assume that if you ask a question that can't properly be answered, the guard will just give you a dirty look and no answer.

What question would you ask?

(If this variation doesn't make sense, I could try to specify exactly how the insane guard is to answer a question.)

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• 1 month later...

Classic but great riddle.

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