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Post Info TOPIC: Labyrinth Riddle


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There are two doors with faces on them. One door always tells the truth and one door always lies. Also, one door leads to Heaven and one to Hell. You do not know which one is which or where each leads. You can only ask one door one single question to find out which door leads to Heaven. But remember, you don't know if it is lying or not. What is the question and why?

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Hmmm....if the door that tells the truth is the door that leads to heaven and the door that lies is the one that leads to hell, I would ask....does God love me? If the answer was no, I would know I was at the door to hell. If the answer was yes, I would be at the door to heaven. I would think you would have to ask a question you are positive of the answer to...maybe I am making it too simple though and missing something here. *lol*

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That was creative. I'm going to post the answer tomorrow, give a bit of suspense and time to think about it. Thanks for your interest!!

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'Are you a door?'

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Frodo wrote:

'Are you a door?'


 that was my first thought, or 'how many doors are there?'  biggrin



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How do you know which one leads to heaven?

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I would ask door #1 a simple question: Is door #2 the way to heaven? Why might you ask? One door always lies, and one door always tells the truth, that's why. So when I ask door #1 to tell me what door #2 would say, I know it would lead me somewhere safe. If door #1 were the liar, he would have to lie about what door #2 would say. Since door #2 would have told the truth, door #1 would then have to tell the lie. However, if Door #2 were the liar, he would obviously have lied. However, door #1 would then have to answer the question truthfully which would be the lie from door#2. Hence, no matter which door is the liar and which door is the truth-teller, the answer would still have one and exactly one lie in it. Knowing this, I'll take the other door. It's a win, win proposition either way. Great riddle Ruhig, thanks.



-- Edited by Mr_David on Saturday 30th of June 2012 04:15:19 PM

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Mr.David


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If you were the liar, would you tell me this door leads to Heaven? Or visa versa maybe.


If you think the liar could possibly be telling the truth you could over-think the situation and make a decision based on the vibe that the face on the door is giving you biggrin



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"There ain't no Coupe DeVille hiding in the bottom of a Cracker Jack Box."



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Deciding which socks to wear is a big decision for me. Maybe I'd ask the door which are my favourite socks, or maybe I would go round in ever decreasing circles, finally disappearing up my own exhaust pipe.

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Fyne Spirit

Walking with curiosity.



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you ask either door "What would you tell me if I asked which door is the way to Heaven?"

 

The double negative ensures the lying door tells the truth, and is irrelevent to the truth door

 

easy peasy

 




-- Edited by LinBabaAgo-go on Saturday 30th of June 2012 04:20:57 AM

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Ruhig wrote:

How do you know which one leads to heaven?


 after asking either door "how many doors are there?".    If lying door responds 3 or 1...   then ask the other door does their door lead to heaven, knowing that this is a true answer.  If asking the the truth telling door first "how many doors are there?"  and you get a truthful answer, then ask the lying door if his door leads to heaven, knowing that the answer is false.  



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I believe I am in melt down.
Toad


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Going out the window :)

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I love 'Stairway to Heaven' ... ... ... thanks LinBaba ...

Pappy



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I'm with Fyne spirit, Toad and Leeau... thanks for the song Andrew... David... you cheated!

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David cheated and looked up on google. Lol and Pete: you forgot that you only get one question, and one should never assume the truth door leads to heaven. Hp works in mysterious ways putting a liar infront of his door. But as I said... David either watched this movie too many times or cheated:) thanks for playing

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Ruhig wrote:

David cheated and looked up on google. Lol and Pete: you forgot that you only get one question, and one should never assume the truth door leads to heaven. Hp works in mysterious ways putting a liar infront of his door. But as I said... David either watched this movie too many times or cheated:) thanks for playing


 The movie got the riddle from a famous mathematician named Raymond Smullyan, and there are many many variations of this riddle, Knights and Knaves which involve the double negative and Boolean Algebra.

The version I learned in school was "truth town" and "Lie town" and you came to a fork in the road and there was a man there who was either from one or the other, same concept. If you took enough math in school you eventually encountered this.

There is more then one correct answer on this thread

There are several ways to find out which way leads to freedom. All can be determined by using Boolean algebra and a truth table.

One alternative is asking the following question: "Will the other man/door tell me that your path leads to freedom?"

 

 

Knights and Knaves involves knights (who always tell the truth) and knaves (who always lie). This is based on a story of two doors and two guards, one who lies and one who doesn't. One door leads to heaven and one to hell, and the puzzle is to find out which door leads to heaven by asking one of the guards a question. One way to do this is to ask "Which door would the other guard say leads to hell?". This idea was famously used in the 1986 film Labyrinth.

 

Knights and Knaves

From Wikipedia, the free encyclopedia
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Knights and Knaves is a type of logic puzzle devised by Raymond Smullyan.

On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie. The puzzles involve a visitor to the island who meets small groups of inhabitants. Usually the aim is for the visitor to deduce the inhabitants' type from their statements, but some puzzles of this type ask for other facts to be deduced. The puzzle may also be to determine a yes/no question which the visitor can ask in order to discover what he needs to know.

An early example of this type of puzzle involves three inhabitants referred to as A, B and C. The visitor asks A what type he is, but does not hear A's answer. B then says "A said that he is a knave" and C says "Don't believe B: he is lying!" To solve the puzzle, note that no inhabitant can say that he is a knave. Therefore B's statement must be untrue, so he is a knave, making C's statement true, so he is a knight. Since A's answer invariably would be "I'm a knight", it is not possible to determine whether A is a knight or knave from the information provided.

In some variations, inhabitants may also be alternators, who alternate between lying and telling the truth, or normals, who can say whatever they want (as in the case of Knight/Knave/Spy puzzles). A further complication is that the inhabitants may answer yes/no questions in their own language, and the visitor knows that "bal" and "da" mean "yes" and "no" but does not know which is which. These types of puzzles were a major inspiration for what has become known as "the hardest logic puzzle ever".

Contents

Examples

A large class of elementary logical puzzles can be solved using the laws of Boolean algebra and logic truth tables. Familiarity with boolean algebra and its simplification process will help with understanding the following examples.

John and Bill are residents of the island of knights and knaves.

Question 1

John says: We are both knaves.

Who is what?

Question 2

John: We are the same kind.

Bill: We are of different kinds.

Who is who?

Question 3

Here is a rendition of perhaps the most famous of this type of puzzle:

John and Bill are standing at a fork in the road. You know that one of them is a knight and the other a knave, but you don't know which. You also know that one road leads to Death, and the other leads to Freedom. By asking one yes/no question, can you determine the road to Freedom?

This version of the puzzle was further popularised by a scene in the 1986 fantasy film, Labyrinth, in which Sarah (Jennifer Connelly) finds herself faced with two doors each guarded by a two-headed knight. One door leads to the castle at the centre of the labyrinth, and one to certain doom. It had also appeared some ten years previously, in a very similar form, in the Doctor Who story Pyramids of Mars.

Solution to Question 1

John is a knave and Bill is a knight.

John's statement can't be true because nobody can admit to being a knave (see Liar paradox). Since John is a knave this means he must have been lying about them both being knaves, and so Bill is a knight.

Solution for Question 2

John is a knave and Bill is a knight.

In this scenario they are making contradictory statements and so one must be a knight and one must be a knave. Since that is exactly what Bill said, Bill must be the knight, and John is the knave.

Solution to Question 3

There are several ways to find out which way leads to freedom. All can be determined by using Boolean algebra and a truth table.

One alternative is asking the following question: "Will the other man tell me that your path leads to freedom?" If the man says "No", then the path does lead to freedom, if he says "Yes", then it does not. The following logic is used to solve the problem. If the question is asked of the knight and the knight's path leads to freedom, he will say "No", truthfully answering that the knave would lie and say "No". If the knight's path does not lead to freedom he will say "Yes", since the knave would say that the path leads to freedom. If the question is asked of the knave and the knave's path leads to freedom he will say "no" since the knight would say "yes" it does lead to freedom. If the Knave's path does not lead to freedom he would say Yes since the Knight would tell you "No" it doesn't lead to freedom.

The reasoning behind this is that, whichever guardian the questioner asks, one would not know whether the guardian was telling the truth or not. Therefore one must create a situation where they receive both the truth and a lie applied one to the other. Therefore if they ask the Knight, they will receive the truth about a lie; if they ask the Knave then they will receive a lie about the truth. Note that the above solution requires that each of them know that the other is a knight/knave. An alternate solution is to ask of either man, "What would your answer be if I asked you if your path leads to freedom?' If the man says "Yes", then the path leads to freedom, if he says "No", then it does not. The reason is fairly easy to understand, and is as follows:

If you ask the knight if their path leads to freedom, they will answer truthfully, with "yes" if it does, and "no" if it does not. They will also answer this question truthfully, again stating correctly if the path led to freedom or not. If you ask the knave if their path leads to freedom, they will answer falsely about their answer, with "no" if it does, and "yes" if it does not. However, when asked this question, they will lie about what their false answer would be, in a sense, lying about their lie. They would answer correctly, with their first lie canceling out the second. This question forces the knight to say a truth about a truth, and the knave to say a lie about a lie, resulting, in either case, with the truth.



-- Edited by LinBabaAgo-go on Saturday 30th of June 2012 09:07:13 PM

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Wow Lin, thanks for the background. I wasnt aware of any of that. And i failed algebra 3x in high school so I still have difficulty with the logic behind the answer. And Pete... I'm gonna take that as a compliment... So thanks? :)

-- Edited by Ruhig on Saturday 30th of June 2012 09:21:08 PM

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Ruhig wrote:

David cheated and looked up on google. Lol and Pete: you forgot that you only get one question, and one should never assume the truth door leads to heaven. Hp works in mysterious ways putting a liar infront of his door. But as I said... David either watched this movie too many times or cheated:) thanks for playing


I've watched this movie numerous times so I knew how to respond. I'm also a math major so I know a little bit about theories. Google helped a little also, but I didn't mean to 'cheat' -for lack of a better word. Do you forgive me?   



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Mr.David


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I told you alcoholics are brilliant people. We only have a disease. We are not stupid. lol.

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Actually David, you saved me from having to copy and paste the answer myself! Of course your "forgiven" for "cheating" :)

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