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mogiaw
10-20-2003, 01:49 PM
Is there a correct solution to the riddle featured in the Jennifer Connolly/David Bowie film, Labyrinth?
There are two doors, one leads to hell, the other to heaven, and one is guarded by a keeper who always tells the truth and the other is guarded by a keeper who always lies. What question do you ask to find out which door is which*?
In the film Connolly's logic is wrong and she gets the wrong door.


*that is if there is an actual answer to the riddle.

I could perhaps have been a bit clearer so apologies but hopefully someone will know what i'm on about,
thanks,
Mogiaw

Beastal
10-20-2003, 01:56 PM
"If I were to ask you which door leads to heaven, how would you respond?"

nocturnal_tick
10-20-2003, 01:56 PM
You ask either one, what door would the other keeper say leads to heaven. If you get the truth teller, he will tell you the truth and that door leads to hell. If you ask the liar he will lie about the door and you get the door to hell. Either way you choose the other door. ;)

Cabbage
10-20-2003, 01:57 PM
Ask one of the guards, "If I asked you which door leads to heaven, which door would you tell me?"

If the guard tells the truth, he'll show you the door leading to heaven, of course.

What if the guard is a liar? Well, if you asked him which door leads to heaven, he'd point to the door leading to hell.

But that's not the question we asked--we asked, "If I asked you which door..." So he's going to lie about that and point to the door leading to heaven.

So either guard will point out the correct door.

(This may not be the only question that works, of course).

Bryan Ekers
10-20-2003, 02:00 PM
Yes, it's logic puzzle 101.

Ask guard A the following: "If I asked guard B which was the door to Hell, what would he say?"

If A is the truthteller and B is the liar:
A knows that B would indicate the Heaven door, since B is a liar. A, being a truthteller, correctly reports what B's choice would be and indicates the Heaven door.

If A is the liar and B is the truthteller:
A knows that B would indicate the Hell door, since B tells the truth. A would then lie about this, and thus A indicates the Heaven door.


In either case, the Heaven door is indicated.

Bryan Ekers
10-20-2003, 02:01 PM
Hmm, if four simulposts fall in the forest, do they make a sound?

Bricker
10-20-2003, 03:09 PM
Why do you think her answer in the film was wrong?

ricksummon
10-20-2003, 03:16 PM
In fact, Sarah's logic is correct in Labyrinth. If it hadn't been, the door would have led to certain death and the movie would have been over. :)

But this is quite the elementary logic puzzle. A more complex variant is "God, the Devil, and Bob." There are three identical people in front of you. One is God, who always tells the truth. One is the Devil, who always lies. One is Bob, whose answers are completely random. Your objective is to determine who is who by asking three yes/no questions.

bryanmcc
10-20-2003, 06:24 PM
Why not just ask if it is raining? Or if rhinoceri are purple?

Yllaria
10-20-2003, 06:24 PM
I prefer the way they answered a similar question in 10th Kingdom.

JRootabega
10-20-2003, 06:55 PM
You can't ask if it's raining because you only get one question. They don't say that outright, but that's usually how the puzzle works.

And I always thought that
she fell down the hole because "things aren't always as they seem" and she had been tricked (well, LIED to, I guess). She only lived because Hoggle freeing her from the oubliette, and that was unplanned. Maybe I got that from the book.

JRootabega
10-20-2003, 06:59 PM
*watches a little further* Well, unplanned as far as the guards knew.

panamajack
10-20-2003, 07:34 PM
If you only get one question, none of the already given answers(questions) necessarily work without further provisions. Though nocturnal tick & Cabbage's are arguably better.

The reason:
The liar is perfectly free to answer your question in any way, as long as it's a lie. Thus if you happen to ask the liar what the liar or the other person would say, the liar may answer, "Green apple pig!" (an obvious lie). You now know who's the liar, but that doesn't help you pick a door.

Arguing in this way against the question that asks about the doors themselves seems more questionable, since "green apple pig" is really a non-answer to your question, not the same as a lie. The key is to give the respondent only two choices (in Cabbage's question it's implicit that only a door can be answered). The stipulation that either a 'yes' or a 'no' is the only answer is the clearest way to present this; I'm pretty sure I've seen the problem stated that way somewhere.

ultrafilter
10-20-2003, 08:52 PM
For the three-person variant, it's possible to get the information you want in two questions.

Beastal
10-21-2003, 04:17 AM
You mean one question.

Diceman
10-21-2003, 07:33 AM
Does anybody remember what, exactly, Jennifer Connolly asked those guys in Labyrinth? I remember the scene but it's been years since I've seen that movie and I don't remember if she got the riddle right or not.

Frank #2
10-21-2003, 09:05 AM
Labyrinth Script (http://scifiscripts.com/scripts/labyrinth_transcript.txt)

excerpt:

Sarah: All right. Answer yes or no. Would he tell me that this door leads to the castle?
Alph: Uh... What do you think? Really? Yes.
Sarah: Then the other door leads to the castle, and this door leads to certian death.
Alph: He could be telling the truth.
Sarah: But then you wouldn't be. So if you said he said yes, the answer is no.
Alph: I could be telling the truth.
Sarah: Then he'd be lying, and the answer would still be no.
Alph: Is that right?
Ralph: I don't know. I've never understood it.
Sarah: No, it's right. I've figured it out. I couldn't do it before. I think I'm getting smarter. It's a piece of cake. Aaaaahhh!!!!!!

ultrafilter
10-21-2003, 12:09 PM
Originally posted by Beastal
You mean one question.

Well, if it can be done in one, it can be done in two, right?

I've seen the two question solution, but never just one.

Diceman
10-21-2003, 12:24 PM
It looks like she solved the riddle correctly. Maybe the oubliette is the correct way, and the other door would have dropped her into a pit of spikes or something.

nocturnal_tick
10-21-2003, 02:30 PM
originally posted by panamajack
Thus if you happen to ask the liar what the liar or the other person would say, the liar may answer, "Green apple pig!"
By this logic either one could just remain silent. Therefore neither breaks the rules governing them and neither of them can be identified. There has to be some limit to what they can say and I think we can assume yes/no answers will be said.

ArrMatey!
10-21-2003, 02:57 PM
My theory as to why Sarah fell-
It's a good riddle, but it's always possible that the door guard that was telling her the rules... Was lying.

Azi
10-21-2003, 03:04 PM
I had considered that at one point, Diceman. And the "helping hands" did offer to return her to the surface, so she didn't drop straight into the oubliette; she chose to go down into it.

Sarah's logic was correct, assuming they were playing fair. I must wonder... what if the guard who presented the challenge was a liar? Wouldn't he be lying as he gave the details? Maybe both pairs always lied or both said whatever they felt like in order to stop her progress.

Revtim
10-21-2003, 03:10 PM
Originally posted by Beastal
You mean one question. Is that dependent on the 66 percent chance that you don't ask Bob the question? Seems to me that no matter what you ask, if you ask Bob your first question you are screwed (unless he randomly gives you the answer, but of course you cannot depend on it).

panamajack
10-21-2003, 04:14 PM
Excerpting from just before the above excerpt

ALPH: You can only ask one of us.
RALPH: It's in the rules. One of us always tells the truth, and one of us always lies. He always lies.
ALPH: I do not! I tell the truth!
RALPH: Oh, what a lie!
TIM: Ha ha ha!
ALPH: He's the liar!

From this it's clear that she could have asked both of them a question, or that the 'rules' did not exist as stated. All that's clear is that they're not both constant liars.

Originally posted by nocturnal_tick
By this logic either one could just remain silent. Therefore neither breaks the rules governing them and neither of them can be identified. There has to be some limit to what they can say and I think we can assume yes/no answers will be said.

The truth-teller staying silent would be a 'non-answer' while the liar staying silent is a valid lie, given that questions must be answered, so that has less provisions than I'd made in my first case.

Nonetheless, this is a valid point. There's probably a convoluted way to force a correct answer even if they aren't required to answer all questions, but I can't think of it right now.


If I'd been more clever, I would have made the liar say, "I'd tell you to go to hell if you asked me that."

Phage
10-21-2003, 04:32 PM
I think that Azi hit on the answer when he mentioned the helping hands. Supposing the riddle was actually a riddle and not some elaborate ruse with no correct answer, Sarah solved it correctly. However, she didn't respond well when she met the helping hands.

The hands were willing to help her in whatever way they could: "Up or down?" Sarah had found the correct path to the castle but fallen off of it. Instead of asking the helping hands to put her back on the right path, she doubted herself and told the hands to go along with the flow. Essentially she told those who were willing to help her to help whoever set the trap. I think that this is yet another one of the many great morals in the movie: "Friends can be enemies if you tell them to."

Another annoying thing about that scene is that she didn't ask the hands if they knew the way to the castle. They were probably the friendliest creatures in the maze, but does she even think of asking which way she should go when they ask? Nope, not even when she is clueless herself...

Bryan Ekers
10-21-2003, 05:15 PM
Most likely, the scene was just a parody of all "truthteller/liar" logic puzzles. It makes no more sense, nor does it pretend to, than the "Keep him here until I get back" scene from Monty Python and Holy Grail.

Shade
10-21-2003, 07:16 PM
I think 'green apple pig' is cheating, as it's not false, it's not even a statement. However, if the liar is only described as a liar, I think saying 'neither door' or 'both doors' would be a valid answer for him.

I also think it's fair to assume the guards will answer a question, else the puzzle is obviously unsolvable. What a liar can be relied upon to do is a subject of contention in these sorts of things :) I think 'to respond with a a false answer' is reasonable, despite the real-life answer 'respond possibly falsly' or the too-generous 'respond with the as nearly as possible complete opposite of the true answer.'

panamajack
10-21-2003, 08:49 PM
But my point is that 'green apple pig' is only a lie in response to a specific question. To avoid any of the other complications I brought up, assume for the rest of this post the proviso "All questions must be answered". Not to pick on him, but Beastal provided :

"If I were to ask you which door leads to heaven, how would you respond?"

Since the liar would not respond "green apple pig" to the "which door" question, the answer "green apple pig" to your question is, in fact, a lie. To say otherwise is to require something like the 'respond with the as nearly as possible complete opposite of the true answer' condition.

Earlier I made two mistakes: the liar can only stay silent under the assumptions I made if you ask about what the other person would say, not what the liar himself would say (assuming you know that all questions deserve a response, silence is another lie, since no direct & answerable question is met with silence). Also, Ralph & Alph can't both be truthtellers, but I think I agree with Bryan Ekers on the purpose of that scene, especially given its outcome.

Diceman
10-21-2003, 10:25 PM
It's a good riddle, but it's always possible that the door guard that was telling her the rules... Was lying.
Sarah's logic was correct, assuming they were playing fair. I must wonder... what if the guard who presented the challenge was a liar? Wouldn't he be lying as he gave the details?
I never thought about this possibility. It would fit in with the Goblin King's personality, since he never really plays fair. And his comments after she falls in ("She shouldn't have gotten as far as the oubliette. She should have given up.") do kinda suggest that the whole bit with the doors is just a trick.

Meeko
10-21-2003, 11:01 PM
Im just sitting here thinking.

I think the God Bob and the Devil (or what ever) is just a variant of the
Three boxes have incorrect labels (out of "Apples" "oranges" "Half and half")
on them.

one has all oranges, the other all apples, and the third half and half. You can only look in two boxes and then must figure out what is which box.
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Also, where does the following fit into this conversation;

Statement A: Statement B is True.
Statement B: Statement A is False.

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I would think that the solution to the God Bob and Devil include asking for verification of the first question.

I dont know the code for a spoiler box....
Below is what I think can be a
"close" answer to GBD there is more commentary after this answer,,, after more slashes.
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I think this is close (but I admit not the 'real' answer

"What is 2+2?" (Some question you know the "truth" to)
If you get a wrong answer... then ask that same person;
"was that last answer correct?"

if you get a right answer then say (to another person)
"Was that last answer correct?"

This accounts for the "concreteness" of Devil and God.
Bob is still the odd man out. He could still randomly emulate God or Devil. Perhaps, if a third question where allowed, you could ask the loaded question "Would the person to your left say that you are God?"

In any case, the second question can not be "fixed" you must ask your second question based on information collected with the first exchange of a question. (Even if that information is "false")
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I think that it is impossible to ask just one question. You could Have bad luck and get Bob.... what value would a question be to him. if you only had one question? You would need a concrete answer, and bob is not concrete.

If Bob was Truth Lie Truth Lie Truth Lie... etc, then perhaps he would be of more value.

Call me Frank
10-22-2003, 02:53 AM
Maybe I missed someone who answered it, but seriously, why couldn't you just ask "What is 2+2?" or something along those lines?

Moe
10-22-2003, 03:17 AM
Originally posted by Call me Frank
Maybe I missed someone who answered it, but seriously, why couldn't you just ask "What is 2+2?" or something along those lines?

OK, so you get your answer. You've used up your one (;)) question. Now what?

KP
10-22-2003, 04:06 AM
Interestingly, Nocturnal Tick's answer works (assuming a responsive direct answer must be made) whether you know if the liar is in front of the door to hell or not.

However, unless you are exceedingly careful in formulating your question a perfectly reasonable, but (possibly unintentionally) ambiguous answer -by either liar or truth-teller - could still foul you up, whether or not you know which door the liar stands by. e.g.:

YOU: What would the other guy say if I asked which door leads to Heaven?
GUARD: My door
YOU: Wait! Do you mean he'd say -quote "My door leads to Heaven" unquote- or do you mean he'd say YOUR door led to Heaven?
GUARD: Either you have a degree in semantics, or you watch too much Monty Python. Either way, you deserve what you get.

KP
10-22-2003, 04:20 AM
Moe -

Under the conditions stated, the liar stands before the door to Hell. Therefore, if the answer to "What is 2+2?" is false, you know that is the door to Hell, regardless of the question

Preferably, you'd choose some more unambiguous question of fact. I can answer "What is 2+2?" in many ambiguous ways, like "One zero zero" [true in binary, false in base ten] or "It depends what you are adding." and that's not even getting into the really annoying ones like "An equation" [It isn't technically an equation, but most people would honestly say it was] "A math problem" [it is not mathematics, it is arithmetic; and it is not a problem, since it's not an equation. See Whitehead and Russell "Principia Mathematica" to understand of how elementary adding 2 to 2 *isn't*. They were the first to rigorously prove 1+1 = 2 -under the unstated conventions of common arithmetic- and they didn't get that far until Volume II)

God may always tell the strict truth, but he's not always helpful. Not in my experience, anyway.

Shade
10-22-2003, 04:52 AM
panamajack:
:smack: Sorry, I'd read that quite quickly. Yes, if you're asking the lying guard what someone would say 'green apple pig' is fine.

Specifying both inner and outer questions to be yes/no still gets round this, though, I think.

I think my favorite comment on puzzles of this type comes from a book whose title I can't remember (probably by Raymond Smullyan). There's several puzzles where the the setter specifies that one the statements engraved on a pair of boxes is a lie, and the guesser has to find something hidden in one or the other box, and so on. Then in the final puzzle, the setter gives no clues and shows the guesser two boxes inscribed:

The statement on the other box is false, and the prize is in this box.

The statement on the other box is true.

The guesser reasons thatIf the first statement is true, the second must be false as it says so, but it says the truth, that the first is true. Contradiction. So the first statement is false. Hence, the second is false (as it says the first is true.). So the first part of the first statement is true, but the whole thing is false, hence the second part is false, so the prize is in the second box.He opens that box, but he's wrong!The setter never made any guarantees that the statements could be parsed as true or false, they become equivalent to 'this statement is false' which is possible to carve on boxes, but not analyze logically!

bienville
10-22-2003, 06:13 AM
Originally posted by KP
Under the conditions stated, the liar stands before the door to Hell.

Danger! It's a trap!

We are conditioned to assosiate liars with Hell and Truthtellers with Heaven but it is NEVER stated that the Liar guards the door to Hell. The Liar could be guarding the door to Heaven whilst the Truthteller guards the door to Hell.

It's gotta be a "yes" or "no" question:

Would that guy say that he leads to Heaven? (the Castle, big Rock Candy Mountain, whatever the desired location may be).

or
Would that guy say he leads to hell?
or
Would that guy say you lead to heaven?
or
Would that guy say you lead to hell?
or
Would you say . . . yadda yadda yadda

Sarah got it right, Bowie's just a dick.

Diceman
10-22-2003, 07:38 AM
bienville is right; you've got to ask the question so that the guy must give a yes or no answer. You ask, for example, "Would the other guy say that this door leads to Heaven?"

As for asking what 2+2 equals, or some similar strategy, I've read stories where the two people just refuse to answer the question, or claim that they don't know any math, or give some other non-answer.

tanstaafl
10-22-2003, 01:49 PM
The version I usually hear is to ask, while pointing at a door, "If I asked the other guard if this door leads to (whatever), would he say 'yes'?"

This forces a yes/no answer (since that is what the question is asking). If the answer is 'yes' then you choose the other door; if it is 'no' you go though the one you are pointing at.

As an alternate, I have also heard "If I asked the other guard which door leads to (whatever), which one would he tell me to use?" Presumably the guard would somehow indicate one of the doors. You then go through the other door.

panamajack
10-22-2003, 02:22 PM
I realize I didn't make it quite clear which question the liar was responding "green apple pig" to initially; sorry for the confusion. I don't know if you were making a joke, Shade, but I think the Smullyan book might be What is the Title of This Book?.

I thought of a way that seems to work for the two doors puzzle given only the following provisions:

The truthteller (hereafter T) must only make true statements or actions.
The liar (L) must only make false statements or actions, except for '-'.

'-' is indicated by holding both hands up, palms forward, and means that the person cannot respond to the statement ( either without logical contradiction of his or her character, or due to insufficient knowledge ).

No attempts to alter the meaning of '-' are allowed (i.e. "Answer with '-' if 2+2 = 4"), and '-' may not be used at any other time (esp. by the liar).

Note that they are not required to answer questions, or be helpful in any way.

Two doors, A & B lead to heaven (H) and hell (O). (A=H) means A leads to heaven.
Two guardians, one T and the other F. You may make one question to determine which door leads to where.

This is one answer I think works :

If you were the other person, how would you respond to the statement, "Respond with something other than 'A=H' unless you're L"?


Here's how I see it working out:
Considering the statement within the question. If posed to T, the response will be anything other than "A=H". If posed to L, you get '-' if A does lead to heaven, and "A=H" if it doesn't.

So the response to the question posed will be :

x A B (x is the person you ask)
T H O "I'd say '-'".
T O H "A=H".
F H O '-'.
F O H "A=H".

T's responses are easily understood. F is forced to respond to the question, since anything else would be a valid T response to the statement, thus a true answer to your question, which F can't do.


Using the table, you can tell from the response which door leads where.

Meeko
10-22-2003, 11:31 PM
I re-read the God Devil and Bob post, I drove myself crazy trying to figure it out. I told my mom that you had only 2 questions... we figured it out with three.

Bryan Ekers
10-27-2003, 03:11 AM
Originally posted by Shade
I think my favorite comment on puzzles of this type comes from a book whose title I can't remember (probably by Raymond Smullyan). There's several puzzles where the the setter specifies that one the statements engraved on a pair of boxes is a lie, and the guesser has to find something hidden in one or the other box, and so on. Then in the final puzzle, the setter gives no clues and shows the guesser two boxes...

I dunno if you're being ironical or not, but one of Smullyan's books that contained this type of "engraved box" puzzle was (wait for it) What is the Name of This book?. Chapter five is "The Mystery of Portia's Caskets". The premise is that Portia will marry the man who can figure out which of a group of engraved caskets contains the gold ring (or whatever the prize was). The caskets (typically gold, silver and bronze) have engravings like "Either the statement on this casket is true, or the bronze casket contains the ring" and whatnot.

The chapter goes on to describe the daughter and then grandaughter of Portia (each also named Portia), who present suitors with increasingly difficult puzzles. The chapter closes with a distant descendant of Portia (also named Portia) who presents a suitor with caskets engraved with statements that are deliberately misleading, I guess to prove a point that just because a statement says it is true, doesn't necessarily make it so.

Smullyan finishes the story by saying this final Portia marries her suitor anyway, despite him being tricked by the misleading statements. Then (somewhat sexistly, I thought) her new husband promptly puts her over his knee and gives her a good spanking, thus discouraging her from any future thoughts of playing such games.

Shade
10-27-2003, 03:22 AM
Yep, that's it. No, I knew the title was something like that, but I hadn't spotted the irony in my genuinely not remembering it.

Sexist? Maybe, but not if you assume she'd have done the same thing to him if he'd have played silly buggers with her like that - I think all the women I know would :)

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