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SuperGrover
Lets meet as little as we can


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PostPosted: Tue Jan 04, 2005 5:56 am    Post subject: Reply with quote

theandygrant wrote:
Yes, but since we don't know from Moe's answer of "yes" whether he is lying or telling the truth, we don't know whether to ask Larry or Curly the second question.


Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.

If Moe answers randomly, then we can ask the second question of either Larry or Curly, because exactly one of them is the liar and the other is the truth-teller. As we will see, a Yes answer means we will ask Curly and a No answer means we will ask Larry.

So let's examine the other two cases. If Moe is the liar, then a Yes answer (that Larry tells the truth more often than Curly) means that Curly is the truth-teller. So Yes means ask Curly. And a No answer (that Larry lies more often than Curly) means that Larry is the truth-teller. So No means ask Larry.

If Moe is the truth-teller, then his answer to the first question is truthful. A Yes answer means that Curly is the liar. So Yes means ask Curly. A No answer means that Larry is the liar. So No means ask Larry.
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theandygrant
This is the foul fiend Flibbertigibbet


Joined: 07 Feb 2004
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PostPosted: Tue Jan 04, 2005 6:22 am    Post subject: Reply with quote

SuperGrover wrote:

Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.


We can't use the same question.
"If I asked the other guard, what would he say?" only works because the guards were polar opposites.

If we successfully identify the random-answerer with the first question, then we could indeed use the original question again.

Its not a case of "If Moe tells the truth" or "If Moe answers randomly".
It's a case of "If Moe says Yes" and "If Moe says No"

Say you ask Moe "Is Larry more likely to tell the truth than Curly?" and he says "Yes."

The four possible outcomes are:
1. Moe always tells the truth; Larry answers randomly; Curly always lies.
2. Moe always lies; Larry answers randomly; Curly always tells the truth.
3. Moe answers randomly; Larry always tells the truth; Curly always lies.
4. Moe answers randomly; Larry always lies; Curly always tells the truth.

We know now that Curly is not the random-speaker, which is useful, but not useful enough, since we still don't know who the opposite guard to Curly is.

It may be possible to construct some sort of double-negative trap question to ask Curly....
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theandygrant
This is the foul fiend Flibbertigibbet


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PostPosted: Tue Jan 04, 2005 6:50 am    Post subject: Reply with quote

From what I can see, there are three generic solutions to this riddle.

Solution A:
Use the first question to identify the Truth-teller.
Use the second question to ask the Truth-teller which door leads to riches.
Go through that door.

Solution B:
Use the first question to identify the Liar.
Use the second question to ask the Liar which door leads to riches.
Go through the other door.

Solution C:
Use the first question to identify the Random-answerer.
Use the second question to ask the second guard what the third guard would say.
Go through the other door.

Now, I notice that the wording of the riddle says "You may ask the guards two questions", with guards in plural. This may be ambiguous, but I don't think this outlaws asking the questions to all three guards at the same time. Solutions to riddles have lain in more pedantic interpretations than that, I'm sure. So it may be that Clare's solution is indeed an acceptable one.
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SuperGrover
Lets meet as little as we can


Joined: 12 Nov 2004
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PostPosted: Tue Jan 04, 2005 5:10 pm    Post subject: Reply with quote

theandygrant wrote:
SuperGrover wrote:

Remember that the goal here is to find a guard who either always lies or always tells the truth. Then we can ask him the trick question mentioned up in the thread.


We can't use the same question.
"If I asked the other guard, what would he say?" only works because the guards were polar opposites.

The four possible outcomes are:
1. Moe always tells the truth; Larry answers randomly; Curly always lies.
2. Moe always lies; Larry answers randomly; Curly always tells the truth.
3. Moe answers randomly; Larry always tells the truth; Curly always lies.
4. Moe answers randomly; Larry always lies; Curly always tells the truth.

We know now that Curly is not the random-speaker, which is useful, but not useful enough, since we still don't know who the opposite guard to Curly is.

It may be possible to construct some sort of double-negative trap question to ask Curly....


I thought that the trick question would be "If I were to ask you if Door A were the door to riches, what would you say?"
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Shiz
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PostPosted: Tue Jan 04, 2005 6:26 pm    Post subject: Reply with quote

There's also the version of question which goes 'If I had asked you yesterday which door was the door to riches, which door would you have pointed to?'

With this question both the liar and the truth teller must point to the door to riches, but I still can't work out how to apply that to the random guard. Confused
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Robin
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PostPosted: Tue Jan 04, 2005 9:39 pm    Post subject: Reply with quote

I can't be bothered right now to wade through the labyrinthine logic of all these replies, but I did read SuperGrover's answer, and it quite clearly works. There is quite clearly no way, in one question, to work out who is the liar, or who is the truth-teller (since the other guard can always answer anything to any question), but all you need is to identify one person who definitely isn't the random-answerer. SuperGrover's question, as far as I can see, achieves that. Nice one Thumbs up
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Hatfielder
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Joined: 19 May 2004
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PostPosted: Wed Jan 05, 2005 2:58 pm    Post subject: Reply with quote

That took a lot of wading through.

I still like my answer and was shocked I came up with it as I'm ususally dreadful at answering these kinds of problems. Razz

Reading the resulting chat you do seem to have come up with a workable answer between you all.

Quote:
Ask one of the guards (Moe) if the second (Larry) is more likely to tell the truth than the third (Curly). If Moe answers Yes, then we actually know something about Curly:

If Moe always tells the truth, then Curly is the liar;

If Moe always lies, then Curly is the truth-teller;

If Moe answers randomly, then Curly is either the liar or the truth-teller (we don't know which, but that's okay).

And if Moe answers No, then we know something about Larry:

If Moe always tells the truth, then Larry is the liar;

If Moe always lies, then Larry is the truth-teller;

If Moe answers randomly, then Larry is either the liar or the truth-teller.


SuperGrover allows us to be certain that we are addressing the second question to either the liar or the truth teller. If we got an answer of No we can be sure that larry is not the random speeker, and if we got an answer of yes we can be sure that Curly is not the random speeker.

Quote:
There's also the version of question which goes 'If I had asked you yesterday which door was the door to riches, which door would you have pointed to?'

With this question both the liar and the truth teller must point to the door to riches.




Shiz's post gives us a question that both the liar and the truth teller will point to the door to riches, but which importantly doesn't rely on the guards polarity with another guard.

There now. No-one can argue with that combined solution.

But then I liked my simple one better, working through the possibilities of this one made my brain spin.

Clare Angelic
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theandygrant
This is the foul fiend Flibbertigibbet


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PostPosted: Wed Jan 05, 2005 3:27 pm    Post subject: Reply with quote

Yep. I like all that.
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SparkPlug
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PostPosted: Wed Jan 05, 2005 5:29 pm    Post subject: Reply with quote

Why don't you all go together - then you'll have loads of questions Wink
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theandygrant
This is the foul fiend Flibbertigibbet


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PostPosted: Wed Jan 05, 2005 8:50 pm    Post subject: Reply with quote

Or we could just not ask any questions and send Shiz through one of the doors first Evil or Very Mad Angelic Wink
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Rosie Ragdoll
Drunkenness is thy best virtue


Joined: 28 Sep 2004
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PostPosted: Wed Jan 05, 2005 9:42 pm    Post subject: Reply with quote

theandygrant wrote:
Or we could just not ask any questions and send Shiz through one of the doors first Evil or Very Mad Angelic Wink


That's just cruel but of course if there were any gentlemen out there they'd offer to go first Razz

Rosie
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theandygrant
This is the foul fiend Flibbertigibbet


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PostPosted: Wed Jan 05, 2005 9:58 pm    Post subject: Reply with quote

Which is why Gentlemen make poor adventurers.
I can't quite see Harrison Ford offering to go first Razz

Gentlemen are all well and good,
but rogues and rapscalions are where it's at Wink
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Rosie Ragdoll
Drunkenness is thy best virtue


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PostPosted: Wed Jan 05, 2005 10:52 pm    Post subject: Reply with quote

But the bad guy never gets the girl, so it looks like you are going to be whisked away to a life of luxury by a real gentleman Shiz.

Rosie
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Shiz
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PostPosted: Thu Jan 06, 2005 2:24 am    Post subject: Reply with quote

Real Gentlemen? Suddenly beginning to think they no longer exist! Surprised

Shiz Wink
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