94 replies to this topic

[Martini]

Welcome to the boards, smarties. See the post immediately before yours.

[etisayus]

Keep asking the men if they are the liar and when one of them says yes he is the random man...lets lable them L T R

We have eliminated R it might take a few times but that is the only possible way to elminate him is to keep asking.

Now ask either the L or the T (the two left) but since we dont know which is which we will say 1 and 2

Ask 1 if 2 would say he is a liar if 1 says YES then he is the one telling the truth if he says NO then he is the liar.

THIS IS THE SOLUTION im sure there are probably more ways but this is the easiest

There is no gurantee that random man will say yes as we have to ask only 3 questions.

[AnwarSiddiqui]

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 question 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?

After implementing all the set theory that I knew of, I had to get down to drawing a flow chart of possible combinations and a flowchart of all the possibilities. Well one thing is pretty well defined that there will be a yes or no answer to any question that I will as. But for every question the Truth teller will always answer the truth, the liar will always tell a lie and the random person may either tell the truth or a lie, there is no way of being confirm about that.

I tried my best and the problem does solves in three questions but in two particular cases I can only identify one of these three as a lier or a truth teller. This means that if I have atleast 1 more question then I can be sure about all three of them.

Will such a solution that I am 100% sure to find the identity of atleast one person be acceptable?

[AliceJH]

Q1 - To first man "Do either of the other two ever tell lies?"

At least one of them must be a compulsive liar (given) so
If first man's answer = Yes, he is either T (always tells truth) or R(random - on this occasion telling truth)
If first man's answer = No, he means the other two always tell truth which is not possible , so he is either L (compulsive liar) or R (random - telling lie on this occasion)

I'm not sure how to proceed but is this along right lines?

[EyesOfTheDead]

I have become particulary interested in this site, and I have heard this riddle long ago. The solution...

Spoiler for Solution

The trick is asking a question that the liar and truth teller will give the same answer to. Consider the question (to man number 1) "Is man number 2 random?" If he is obviously the truth teller will say yes and the liar will say no. So you ask, "Would you tell me that man number 2 is random?" If number 2 is random, the truth teller would tell you he is, so he says yes. The liar would tell you no, so he also answers yes. So if the answer is yes, either number 2 is random, or number 1 is random answering randomly, you KNOW 3 ISNT random. If he says no, either number 2 ISN'T random, or number 1 is random. So by that answer to that question you know for sure who ISN'T random. With that, you can ask any question to that person, such as "Am I standing in front of you?" to determine truth teller or liar. Depending on that, the last one is pretty simple

[nogox5]

I really dont like the "no answer" solutions because then its not really a yes or no question anymore, it now has an extra answer, and if the truth teller and liar have the option of not answering then the random person might randomly decide not to give an answer either, and then it would be unsolvable.
Also a person wouldnt just stare blankly into a question they couldnt answer, they would say "i dont know", of course the liar couldnt admit that he didnt know and so he would have have to lie about knowing and would just have to guess, and even if it got it right, he would still be lying, he was just lying correctly, but still lying at the moment that he gave the answer. And under the same logic the random could lie and give the "i dont know response", again leading to an unsolvable solution.

Spoiler for A non-no-response solution

As far as I can see there is only one way to solve this without the no response option and that is to figure out who either the truth teller is, or who the liar is in two questions, and then using the third to easily figure out the other two. Ill call the three men Truth, liar, and random. The key to it is that to any given question both the truth and the liar have only one possible answer, but the random has two. So we must some how force random's answer to be different than either the truth teller or the liar. The easiest way to do this is to give him a question such that one of the answers is a paradox, forcing him to use the other answer.

Ask person 1: "Are you the random and are you going to lie to me?"
The truth teller will have to say "no", because hes not the random.
The liar will have "yes", because hes not the random either but will have to lie and say he is, and the second part of the question would be irrelevant.
The random will have to say "no", because saying yes would be a paradox (the answer "no" is simply a lie)

If he says "yes" you know hes the liar and you can easily figure out the other two (just ask if 2 is random and you know its the opposite)
If he says "no" ask the second person. If the second person says "yes" then he's the liar and you can easily figure out the other two. If the second person says "no" you know the third is the liar and you can easily figure out the first two.

Edited by nogox5, 08 August 2008 - 04:02 PM.

[EyesOfTheDead]

If he says "yes" you know hes the liar

How do you KNOW he's the liar? No matter what the answer to that question is you can never distinguish who is who.

[Loaner]

Spoiler for This will Work

Ask person one "Will the Liar tell me the truth?"
If he answers no we know he is either Truth (T) or Random ®. We ask the same question again. If he answers no again we know he is T and can ask him if Person 2 is the Liar. Yes means 2 is Liar (L) and by elimination 3 is R. If he answers Yes to the second question we know he is R. Now we ask person 2 if person 1 is the R. Yes means 2 is T and 3 is L. No means 2 is L and 3 is T.

Now, if we ask person one "Will the Liar tell me the truth?" and he answers no we know he is either L or R. We ask again and apply the same methodology as above, just in reverse.

[Loaner]

Spoiler for This will Work

Ask person one "Will the Liar tell me the truth?"
If he answers no we know he is either Truth (T) or Random ®. We ask the same question again. If he answers no again we know he is T and can ask him if Person 2 is the Liar. Yes means 2 is Liar (L) and by elimination 3 is R. If he answers Yes to the second question we know he is R. Now we ask person 2 if person 1 is the R. Yes means 2 is T and 3 is L. No means 2 is L and 3 is T.

Now, if we ask person one "Will the Liar tell me the truth?" and he answers no we know he is either L or R. We ask again and apply the same methodology as above, just in reverse.

Of course this implies random alternates between truth and Lies. This is how I heard this riddle before and assuming it is the intent.

[Martini]

Of course this implies random alternates between truth and Lies.

"and one that sometimes answers truthfully and sometimes lies"