94 replies to this topic

[Phatfingers]

Spoiler for Yet another solution...

1. Ask A if C is Random
2. Ask B if C could affirm that A's answer was truthful.
If both give the same answer, then C is non-random, otherwise A is non-random.
3. Ask the non-random person if 0+1=1.

If the answers to questions 1, 2, 3 are:

NNN: A=Random, B=Truthteller, C=Liar
NNY: A=Liar, B=Random, C=Truthteller
NYN: A=Liar, B=Truthteller, C=Random
NYY: A=Truthteller, B=Random, C=Liar
YNN: A=Liar, B=Truthteller, C=Random
YNY: A=Truthteller, B=Random, C=Liar
YYN: A=Random, B=Truthteller, C=Liar
YYY: A=Random, B=Liar, C=Truthteller

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.

[Prime]

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.

[Prime]

...
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.

[Prime]

Spoiler for Answer<br />

First, have them stand next to each other facing you, 1,2,3. Ask (2) if there is a liar or a truth teller on either side of him.

Spoiler for If (2) answers 'yes:

than (2) is either a truth teller or random. Realign the men so that the original middle guy, (2), is now on the outside, such as (2),(3),(1). Ask (3) if there is a truth teller or random on either side of (3).

Spoiler for If (3) answers 'yes:

Than you know (3) is either a truth teller or random, making the other man, (1), the liar by process of elimination. Point to one of the men you know to be either a truth teller or random, at this point in the example either (2) or (3), and ask the liar, (1), if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is a truth teller. If the liar says yes, than the man you are pointing to is random.

If (3) answers 'no' than (3) 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 (2) or (1), and ask the liar, (3), if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is a truth teller. If the liar says yes, than the man you are pointing to is random.

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.

[Phatfingers]

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.

[Prime]

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

There are 6 possible variations:
LRT
LTR
RLT
RTL
TLR
TRL
Any question that determines a Liar from Truth teller eliminates 2 variations out of 6. Such question could be "Are you a Random teller?" The Truth teller cannot answer "Yes" and the Liar cannot answer "No" to that quesion. There would be only 4 variations left. Say, the answer was "Yes", then the possibilities are:
LRT
LTR
RLT
RTL
In all those variations there is a possibility of at least one random teller in any of the positions. So there is always a possibility of at least 3 identical answers, leaving you with 3 variations for your last question, which cannot be solved. For example, in the above arrangement, the middle man's answers could be "Yes", "Yes", and "No" for the three cases where it was either Truth teller, or Liar. Then the case where it was Random teller could throw another Yes into the pot. And then you are left with 3 variations and one question left.
Also, note that with the very first question there is no way to ensure eliminatin of more than 2 possibilities. Thus the first question must eliminate possibility of random in one of the positions, or the problem is unsolvable.

To simplify the process of solving, don't invent a question. Just assign "Yes" and "No" answers as you like to possible Truth teller or Liar bearing in mind that Random could answer either way. Then see how many variations you have left in the worst case scenario.

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

[TheFirstSymptom]

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 let’s 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 : )

[TheFirstSymptom]

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 let’s 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 : )

[TheFirstSymptom]

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 let’s 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 let’s 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

[Prime]

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 let’s 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.