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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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94 replies to this topic

### #91 bhramarraj

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Posted 28 September 2011 - 12:43 PM

Kia, I have put your answer in terms of A, B, C, to make it clearer to me.
So you go to the first one [A] and ask him "if I were to ask you 'is the second person [B] is the random guy', would you say yes?"
If the first person [A] is the truth teller, then it is easy, he would say ‘yes’ if the second person [B] is the Random guy and ‘no’ if not.
If the second person [I think it should be the first person ‘A’] is the liar and the second [B] is the truth teller, then the liar [A] would have said ‘yes’ to ”is the second person [B] is the random guy” but since he is still telling lies, he would say ‘no’.
If the second person [I think first person ‘A’] is the liar and the second [B] is the Random guy, then the liar would have said ‘no’ to “is the second person is the random guy' but since he is still telling lies, he would say ‘yes’.
So in both cases, the truth teller and the liar would clearly indicate if the second guy was the Random guy. [Let me put it clearer: If A says ‘yes’ to the question asked, then B must be a Random guy; and if A says ‘no’ then B is not a Random guy.]
Now what if the Random guy was the first person [A]?
He would say ‘no’ if he was acting like a truth teller.
And he would say ‘no’ if he was acting like the liar.
So after the first question you know if the second guy is the Random guy or not.
In more clear words If you hear ‘yes’ from the first guy [A], then second guy [B] must be a Random guy and if you hear ‘no’ from the first guy [A], then second guy [B] must not be a Random guy.

If he is not, then you ask the second one [B] a similar question,
"if I were to ask you 'is the third person [C] is the random guy', would you say yes?"
For the same reasons as above, after this question you know for sure who the random guy is.
Now there is one more thing left, to find which one tell the truth and which one lies, and again, a similar question from the third person
"if I were to ask you 'is the first person is the truth teller', would you say yes?"
Or
"If I were to ask you 'are you the truth teller', would you say yes?"
And you know which one is which. The whole key is to ask a question.
As I said, the trick to this puzzle is to force the liar into a double negative situation, and remember that the random guy either tells the truth or lies which would mean that the follows the same thinking patters as the liar.
I hope that was clear.

Kia, definitely it is clear, and I fully agree with you.
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### #92 Lame Guesser

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Posted 11 December 2011 - 02:14 AM

I would ask them their how their day was, seeing as how you didn't set a goal, I would just be polite.
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### #93 comp_lex

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Posted 29 December 2011 - 07:06 AM

Kia and bhramarraj, I am uncomfortable with your solution. I think that the random guy would not be able to answer the first question.

So suppose your first person is the Random guy and you ask him "if I were to ask you 'is the second person is the random guy', would you say yes?". Let's break this down into 2 statements:
P - The second person is random
Q - Random guy says P is true
Now the question, as asked to the Random guy, becomes: "is Q true?"
The problem is that the validity of Q cannot be determined a-priori. Not even Random guy himself can know, beforehand, what he would say at any given moment. So there can be no answer to "is Q true?".

I might be wrong, but maybe someone can correct me.
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### #94 BaluTechie

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Posted 30 December 2011 - 12:23 PM

Ask First Man : Sun rises in the east.
If answer is Yes(First Man Could be Truth-Lier or Truthful).
Ask him to tell the person who always lies.
Then ask the same question to the lier, if he says yes then we can confirm that First Man is (Truth-Lier),SecondMan is (Truth),Third Man is (Lier).
if answer is NO for Sun rises in the east (First Man Could be Truth-Lier or Lier).
Ask Second Man: Sun rises in the east.
If answer is Yes (Second Man Could be Truth-Lier or Truth)
if Second Man is Truthfull then , we can resolve all the three.
if Second Man is Truth-Lier, we will ask him who is the lier, from there we will get to know everyone.
If Second Man says No for Sun rises in the east
then he might be (Truth-Lier or Lier). So , we can easily find the truth person who is remaining and will ask him to resolve all the three.

Edited by BaluTechie, 30 December 2011 - 12:29 PM.

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### #95 iNetsurface

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Posted 22 October 2012 - 08:22 PM

Ask FIRST man: "Are you human AND THIRD man is a liar?"
Ask SECOND man: "Are you and THIRD can lie?"

YY / YN / NY: 1=T, 2=X, 3=L
NN: 1=X, 2=T, 3=L

X toggler, T truthteller, L liar

Edited by iNetsurface, 22 October 2012 - 08:26 PM.

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