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The liar, the truth teller....and the random answerer


Best Answer Writersblock , 30 July 2007 - 01:31 AM

Martini,

Spoiler for ...
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#61 Phatfingers

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Posted 20 January 2009 - 07:37 PM

Spoiler for Yet another solution...


It seems I had more than one error in my approach. (Nice catch by Prime, by the way). Oh, plates of crow!

NN	NY	YN	YYLRT	X	X	[A]	[C]LTR	[B]	[A]	X	XRLT	[B]	X	X	[C]RTL	[B]	X	X	[C]TLR	X	X	[A]	XTRL	X	[A]	X	X

The subjects in square brackets are proven non-random by the first two questions, but the third question is not sufficient to eliminate all but one possibilities in all cases.

NNY implies LTR or RTL
YYY implies LRT or RLT
All the others reduce to one option.
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#62 Prime

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Posted 20 January 2009 - 11:18 PM

If A is Random, then his "No" answer to Q1 is a lie.
If C is Liar, then his affirmation of Q2 would be "Yes".
B therefore must answer yes, making "NNN" an impossibility for combination RTL.
...

I beg to differ. If the arrangement for ABC was RTL, then
1. A, the Random, could have answered truthfully to the first statement, saying that C was not a Random.
2. Your second question directed to B was "Could C affirm A's answer?" Then B, the Truth-teller, knowing that C, the Liar, could not affirm the truthful answer just given by Random. So his reply would also be "No".
3. And the third question 2+2=4 directed to the Liar, would also draw the "No" response.
Thus with RTL arrangement, you could receive NNN answers (if Random chose to tell the truth). As well TRL arrangement could produce NNN in case Random spoke the truth.
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Past prime, actually.


#63 Prime

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Posted 20 January 2009 - 11:41 PM

...
NNY implies LTR or RTL
YYY implies LRT or RLT
All the others reduce to one option.

Oops, sorry, I did not notice your last post. So you have caught the error already.
Looking through the posts I see that the problem has been solved by Writersblock soon after it was originally posted.
I gave a similar solution in my earlier post using a different relation between the Random, Truth-teller, and Liar. I believe the key to the solution is to come up with a question that uses some relation between the men. I think your question "Could C affirm A's answer?" is that type of the question. However, not excluding Random from some position(s) on the very first question makes things difficult.
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Past prime, actually.


#64 Prime

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Posted 21 January 2009 - 09:10 PM

Spoiler for Answer<br />


If (2) answers 'no' than (2) is the liar. Point to one of the men you know to be either a truth teller or random, at this point in the example either (1) or (3), and ask the liar, (2) if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is the type of man you asked about. If the liar says yes, than he is the other man.

Hope that made sense.

This is a good solution! The first question eliminates 2 possibilities out of 6, the second question eliminates two more possible arrangements, and the third question decides between the remaining 2 variations.
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Past prime, actually.


#65 Phatfingers

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Posted 27 January 2009 - 02:07 AM

This is a good solution! The first question eliminates 2 possibilities out of 6, the second question eliminates two more possible arrangements, and the third question decides between the remaining 2 variations.


In the first question, couldn't 2 have randomly answered "No"? He's not necessarily "the" liar, just proven to have lied to that particular question.
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#66 Prime

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Posted 30 January 2009 - 04:29 AM

In the first question, couldn't 2 have randomly answered "No"? He's not necessarily "the" liar, just proven to have lied to that particular question.

You are right. That was not a solution. Nothing works here, unless you eliminate Random teller from one of the positions with your very first question. Here is why...
Spoiler for Deep analysis

Edited by Prime, 30 January 2009 - 04:35 AM.

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Past prime, actually.


#67 TheFirstSymptom

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Posted 31 January 2009 - 07:32 AM

There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no questions to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them?



This is my solution:

For the first question ask the first man if he is a man. Or I am a woman, something all of you know to be true. This can lead you down two different paths. For the first letís say he says no. Then you know he is the liar, leaving you with R and T as the other two. Now to figure out those you simply as the first man, L if the second man is the truthteller. If he says yes you know it goes L, R, T. If he says no you know it goes L, T, R.

BUT the first man could also answer yes. This means that he is either R or T. So now you ask the second man the same question. He could also answer either way. Lets say he says yes. That means the second man is also either R or T. This means the third man must be L. So now you direct your third question to the third man and ask him if the first man is the truthteller. If he says yes, you know the order is then R,T, L. If he says no you know the order is T, R, L.

BUT if the second man answers no then you know that he is the liar and you can continue to ask him if the first man in the truthteller. If he says yes you know that the order is R, L, T. If he says no you know the order is T, L, R.

Please let me know if this is correct. Thanks : )
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#68 TheFirstSymptom

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Posted 31 January 2009 - 07:44 AM

There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no questions to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them?



This is my solution:

For the first question ask the first man if he is a man. Or I am a woman, something all of you know to be true. This can lead you down two different paths. For the first letís say he says no. Then you know he is the liar, leaving you with R and T as the other two. Now to figure out those you simply as the first man, L if the second man is the truthteller. If he says yes you know it goes L, R, T. If he says no you know it goes L, T, R.

BUT the first man could also answer yes. This means that he is either R or T. So now you ask the second man the same question. He could also answer either way. Lets say he says yes. That means the second man is also either R or T. This means the third man must be L. So now you direct your third question to the third man and ask him if the first man is the truthteller. If he says yes, you know the order is then R,T, L. If he says no you know the order is T, R, L.

BUT if the second man answers no then you know that he is the liar and you can continue to ask him if the first man in the truthteller. If he says yes you know that the order is R, L, T. If he says no you know the order is T, L, R.

Please let me know if this is correct. Thanks : )
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#69 TheFirstSymptom

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Posted 31 January 2009 - 07:49 AM

This is my solution:

For the first question ask the first man if he is a man. Or I am a woman, something all of you know to be true. This can lead you down two different paths. For the first letís say he says no. Then you know he is the liar, leaving you with R and T as the other two. Now to figure out those you simply as the first man, L if the second man is the truthteller. If he says yes you know it goes L, R, T. If he says no you know it goes L, T, R.

BUT the first man could also answer yes. This means that he is either R or T. So now you ask the second man the same question. He could also answer either way. Lets say he says yes. That means the second man is also either R or T. This means the third man must be L. So now you direct your third question to the third man and ask him if the first man is the truthteller. If he says yes, you know the order is then R,T, L. If he says no you know the order is T, R, L.

BUT if the second man answers no then you know that he is the liar and you can continue to ask him if the first man in the truthteller. If he says yes you know that the order is R, L, T. If he says no you know the order is T, L, R.

Please let me know if this is correct. Thanks : )



Ya. Realized there was a flaw in that solution right away. haha.



So I think I have a good idea going...but still can't figure out everything

For the first question ask the first man something that all of you know to 100 percent true. This can lead you down two different paths. For the first letís say he says no. Then you know he is L or R. Now you can ask the second man the same question. This can lead you down two different paths as well. If he says no also. then you know the third man is T. You direct your third question to T and ask if the first is L. If he answers yes, you know that the order is L, R, T. If he says no then you know the order is R, L, T.

BUT if the first man says yes, you know that he is either T or R. So now you ask the second man the same question. If he responds yes, then you know the third is the liar. You simply ask the third man if the first man in T. If he says yes you know the order is R, T, L. If he says no you know the order is T, R, L.

If the second man says no than I am lost what to do....please help
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#70 Prime

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Posted 31 January 2009 - 08:21 PM

Ya. Realized there was a flaw in that solution right away. haha.



So I think I have a good idea going...but still can't figure out everything

For the first question ask the first man something that all of you know to 100 percent true. This can lead you down two different paths. For the first letís say he says no. Then you know he is L or R. Now you can ask the second man the same question. This can lead you down two different paths as well. If he says no also. then you know the third man is T. You direct your third question to T and ask if the first is L. If he answers yes, you know that the order is L, R, T. If he says no then you know the order is R, L, T.

BUT if the first man says yes, you know that he is either T or R. So now you ask the second man the same question. If he responds yes, then you know the third is the liar. You simply ask the third man if the first man in T. If he says yes you know the order is R, T, L. If he says no you know the order is T, R, L.

If the second man says no than I am lost what to do....please help

For help see correct solutions in this topic. One by Writersblock posted first.
I gave another one a year later. There may be some more, I didn't go through the entire topic closely.
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Past prime, actually.





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