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#164546 12/22/06 07:14 AM
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stranger
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This is an excerpt from the script for The Labyrinth.

Quote:

Sarah: What am I supposed to do?
Red Guard (Bottom Head): Well, the only way out of here is to try one of these doors.
Blue Guard (Bottom Head): One of them leads to the castle, at the centre of the Labyrinth, and the other one leads to—
Blue Guard (Top Head): Ba ba ba bum!
Blue Guard (Bottom Head): Certain death!
All: Ooh! Ooh!
Sarah: Which one is which?
Red Guard (Bottom Head): We can't tell you.
Sarah: Why not?
Red Guard (Bottom Head): Uh... I, uh... We don't know.
Blue Guard (Bottom Head): But they do.
[Both Bottom Heads look up to Top Heads]
Sarah: Oh. Then I'll ask them.
Red Guard (Top Head): Ah, no. You can’t ask us. You can only ask one of us.
Blue Guard (Top Head): It's in the rules. And I should warn you that one of us always tells the truth, and one of us always lies. That’s a rule too. He always lies.
Red Guard (Top Head): I do not! I tell the truth!
Blue Guard (Top Head): Oh, what a lie!
All: Ha ha ha!
Red Guard (Top Head): He's the liar!
Sarah: [To the Top Head of the Red Guard] All right. Answer yes or no. Would he tell me that this door leads to the castle?
Red Guard (Top Head): Uh...
[Confers privately, at length, with Bottom Head behind shield]
Red Guard (Top Head):: Yes.
Sarah Then the other door leads to the castle, and this door leads to certain death.
All: Ooooh.
Red Guard (Top Head): How do you know? He could be telling the truth.
Sarah: But then you wouldn't be, so if you told me that he said yes, I know the answer is no.
Red Guard (Top Head): But I could be telling the truth.
Sarah: But he would be lying. So if you told me that he said yes, I know the answer would still be no.
Red Guard (Top Head): What a minute. [To Blue Guard (Top Head)] Is that right?
Blue Guard (Top Head): I don't know. I've never understood it.
All: Ha ha ha ha ha!
Sarah: No, it's right. I've figured it out. I could never do it before. I think I'm getting smarter. This is a piece of cake.




Images

Sarah opens the door behind the Blue Guard and enters. She looks over her shoulder, smiling. A trap door opens. Sarah falls down into the pit of Helping Hands. But her formulation seems correct. What went wrong?

Discuss.

Last edited by 251413913519; 12/22/06 09:37 AM.

The poster formerly known as Hydra.
#164547 12/22/06 11:01 AM
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A bit complex to handle first thing in the morning. I'll get back to you later. But if the Red Guard (bottom head) is the liar there's another way out and if the Blue Guard (bottom head) is the liar it's not true that one of them leads to the castle, at the centre of the Labyrinth, and the other one leads to certain death.

#164548 12/22/06 11:50 AM
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No idea how to solve that! But a good example of why I am not a fan of computer games. I cannot concentrate on the imaginary as my head is too full of real Holiday!
But the images were delightful.
And welcome, don't let me discourage you!
My brain is just too logy from hollydaze. And I was up and awakke at 5:30 this a.m. - that's reedikoolus.!

#164549 12/22/06 12:34 PM
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stranger
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Sarah's solution is correct, and very clever, but only if the Blue Guard was telling the truth when he said "one of us always tells the truth, and one of us always lies"!

First, let us proceed on the assumption that the Blue Guard was telling the truth: One of the doors always lies, and one always tells the truth.

Sarah asks the Red Guard to tell her if the Blue Guard would tell her that the door behind the Red Guard was the correct door. The Red Guard answers: "Yes".

From this answer, Sarah can infer which is the correct door because it's now an "either/or" scenario, but both scenarios yield the same answer to the question "Which is the correct door."

Observe:

1. The Red Guard is lying. In that case, the Blue Guard would actually say, "No: The Red Guard's door is not the correct door" and would be telling the truth: The Blue Guard's door is the correct door.

2. The Red Guard is telling the truth. In that case, the Blue Guard would say, "Yes: The Red Guard's door is the correct door"", but he would be the liar: The Blue Guard's door is still the correct door.

Solution: When you ask one of the guards: "Would he tell me you guard the correct door?" the answer will be either a direct lie, or a lie truthfully reported: Open whatever door the guard has told you the other guard would tell you is the wrong door.

Question: Why didn't it work?

Sarah's formulation is the correct solution to the scenario described by the Blue Guard ("One of us always tells the truth, and one of us always lies"); however, she overlooked the possibility that the Blue Guard, when he explained this rule, was lying. If the Blue Guard were lying, other scenarios are possible. In some of these, her formulation is useless—such as one in which all four guards lie and tell the truth inconsistently, and both doors lead to certain death.

Your thoughts.


The poster formerly known as Hydra.
#164550 12/22/06 01:13 PM
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thanks (i suppose) for a lesson in MATHS logic.

i recognize this lesson is a 'word lesson' but i still don't understand what is really has to do with words.

in the real world, it would be helpful if some always told lies, and some always told the truth. then with logic, we could navigate the world.

unfortunately, most liars occational tell the truth, and most truthful people occationally tell a lie.

and while Your thoughts is a bit more inviting, DISCUSS sound like a command.

i have very little interest in discussing the logic problem--especially when commanded to!

#164551 12/22/06 01:45 PM
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Sorry this thread is not your cup of tea, of troy. Still, there have been a few threads in this Miscellany forum about logical problems, like the Wason Card Problem, and the Monty Hall problem, and what have you, and they seemed to arouse a bit of interest.

By the way, the imperative "Discuss" and "Your thoughts" was just meant to give the post a facetious, pedagogic air. I wasn't commanding anyone to respond!

Last edited by 251413913519; 12/22/06 01:53 PM.

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#164552 12/22/06 01:49 PM
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Long number person --

Unfortunately you formulated the problem incorrectly, to the extent that Sarah cannot arrive at the correct answer. Here is what you had one of the heads saying:

And I should warn you that one of us always tells the truth, and one of us always lies. That’s a rule too. He always lies.

If the head imparting this important information is telling the truth, the scenario can play out substantially as you have set forth.

But what if the head giving this rule is the liar? If so, everything thereafter is indeterminate.

To wit:

If the head is lying about the phrase one of us, then the sentence becomes (when reversed to reverse the lie) Neither of us always tells the truth and neither of us always lies. Or it could be both of us always tell the truth and both of us always lie.

If the head is lying about the second conditional (always) then the true sentence would be One of us sometimes tells the truth and one of us sometimes lies.

If though, the head is lying about the third conditional, the opposite becomes: One of us always lies and one of us always tells the truth.

In previous versions of this puzzle that I've seen, the information about the lying head and the truthing head has been imparted by another party. Only in this way can your contestant always arrive at the correct conclusion.


TEd
#164553 12/22/06 01:52 PM
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Quote:


If the head imparting this important information is telling the truth, the scenario can play out substantially as you have set forth.

But what if the head giving this rule is the liar? If so, everything thereafter is indeterminate.




I know. You seemed to have "skip-read" the following portion of my post:

Quote:

Sarah's formulation is the correct solution to the scenario described by the Blue Guard ("One of us always tells the truth, and one of us always lies"); however, she overlooked the possibility that the Blue Guard, when he explained this rule, was lying. If the Blue Guard were lying, other scenarios are possible. In some of these, her formulation is useless—such as one in which all four guards lie and tell the truth inconsistently, and both doors lead to certain death.




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#164554 12/22/06 02:50 PM
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>What went wrong?

the poser of the conditions was probably prevaricating.

#164555 12/22/06 07:03 PM
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I, too, have come across this puzzle in the past and (as previously stated) "the rules" are imparted by a neutral party; often the storyteller.
In this case, around all this discussion by those who love language there is an important point that has been missed.
Suppose, in reality, one of the heads always tells the truth and the other always remains in a reclined position*?

*lies, is lying

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