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

[Guest]

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?

[Guest]

What about this?

Ask person 1: If I ask person 2 if he is the Liar, will he say no?

Ask person 2: If I ask person 3 if he is the Liar, will he say no?

Ask person 3: If I ask person 1 if he is the Liar, will he say no?

One of the men will not answer, because he can't honestly (or dishonestly) predict what the random man would say.

Let's call the man who refused to answer B. The man we asked him about is C, and the other man is A.

B's lack of response identifies C as the random answerer. C's response is random and therefore worthless.

We know that if we actually asked B man if he was the liar, he would deny either way.

Therefore:

If A says no: he tells the truth, and B lies.

If he says yes, he is the liar, and B tells the truth.

[Guest]

Hello Ppl. Whats up. I hope im not copying anyone with this answer, and if i am im terribly sorry. Now here's my answer

L=liar T=truthteller B=both(random answers person)

Ok. Now, this depends on if the sun is out or not.

If the sun is out, you ask the question "is the sun outside"

Now, the L will say no, the T will say yes, and the B will say yes or no

if B says yes, then you ask the L (the only one that lied) who the T is

He'll tell you the B (because he lies)

With this you can tell that the person that the L said the T was is the B, and so the person that the L didnt talk about it the real T

Now, if the B says a lie, then you should ask the T (the only person that said the truth), who the L is, now, the person the T says is the L, really is the liar.

Also, if the sun isnt out you ask the question (is the sun away.

BTW- "the sun is out" means that you can see the sun; it is not dark outside

"is the sun away" means that it is dark outside

Just in case i wasn't clear

[Guest]

Sorry if i didnt mention this, because i know people will try to say "what if you are in a room and there is no way to tell where the sun is right now"

Well, the question i gave was an example of a good question.

A type of question you need to ask is something you know the answer to, and so do the 3 ppl (T,L,B)

you could ask the colour of something or ask where you 4 ppl are in the world

as long as it is something that all 4 of u ppl know the answer to

[Guest]

What about this?

Ask person 1: If I ask person 2 if he is the Liar, will he say no?

Ask person 2: If I ask person 3 if he is the Liar, will he say no?

Ask person 3: If I ask person 1 if he is the Liar, will he say no?

One of the men will not answer, because he can't honestly (or dishonestly) predict what the random man would say.

Let's call the man who refused to answer B. The man we asked him about is C, and the other man is A.

B's lack of response identifies C as the random answerer. C's response is random and therefore worthless.

We know that if we actually asked B man if he was the liar, he would deny either way.

Therefore:

If A says no: he tells the truth, and B lies.

If he says yes, he is the liar, and B tells the truth.

There are actually two men who can't answer, not one, so the solution the way you proposed it won't work. Also, it assumes that not answering is permissable, so the random answerer can also choose not to.

Hello Ppl. Whats up. I hope im not copying anyone with this answer, and if i am im terribly sorry. Now here's my answer

L=liar T=truthteller B=both(random answers person)

Ok. Now, this depends on if the sun is out or not.

If the sun is out, you ask the question "is the sun outside"

Now, the L will say no, the T will say yes, and the B will say yes or no

if B says yes, then you ask the L (the only one that lied) who the T is

He'll tell you the B (because he lies)

With this you can tell that the person that the L said the T was is the B, and so the person that the L didnt talk about it the real T

Now, if the B says a lie, then you should ask the T (the only person that said the truth), who the L is, now, the person the T says is the L, really is the liar.

Also, if the sun isnt out you ask the question (is the sun away.

BTW- "the sun is out" means that you can see the sun; it is not dark outside

"is the sun away" means that it is dark outside

Just in case i wasn't clear

"if B says yes, then you ask the L (the only one that lied) who the T is"

What if two of them lied?

[Guest]

There are actually two men who can't answer, not one, so the solution the way you proposed it won't work. Also, it assumes that not answering is permissable, so the random answerer can also choose not to.

"if B says yes, then you ask the L (the only one that lied) who the T is"

What if two of them lied?

I don't see how two men can't answer, as only one was asked an unanswerable question. And since the random answerer must either lie or tell the truth, i disagree that he could choose not to answer.

[Guest]

I don't see how two men can't answer, as only one was asked an unanswerable question. And since the random answerer must either lie or tell the truth, i disagree that he could choose not to answer.

Okay, I got you now. That's actually pretty clever. The only problem I have with it is assumes that not answering is an option. If not answering is an option for the one that can't answer without knowing if his statement will be truthful or not, why can't any of them decide not to answer? Besides that, I like the logic.

[Guest]

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?

Using slightly oblique questions and given that the two consistent answerers are obliged to follow their path (ie the truth teller has to be right and the liar has to be wrong) . Would it not be possible to follow a line by which an 'I cannot answer that' answer is forced - providing the necessary piece of info.

i.e To any given person - "If I asked him (one of the other men) the question 'is the sky blue?' what would his answer be?"

As soon as a 'I cannot answer that' repsonse is gained, you know the subject of the question is the random answerer.

The only man who could answer that question about both the other men is the random answerer. Leaving a full question to deduce the other's identities with a simple question you know the answer to. Ie Is the sky blue?

[Guest]

Hi,

I don't know if this counts but I hope it does.

These are the 6 possible ways they may be standing.

1 2 3

T L R

T R L

L T R

L R T

R T L

R L T

If you ask the 1st person, "If I were to ask the 2nd person if the 3rd person always told the truth would he say yes?," three things will happen. You will get either a yes, no, or no response. The only one who will be able to give a yes/no answer is Random. The truth teller and the liar will be stuck without an exact reply. So, if the was no response then you have narrowed the order down to:

1 2 3

T L R

T R L

L T R

L R T

Now, you ask a similar question to the 2nd person. "If I were to ask the third person if the 1st person always told the truth will he say yes? You will once again have three things happen. You will get either a yes, no, or no response. If you got a yes/no then they are the Random. No response implies truth teller or liar. So, if you received no response then this will be the remaining choices.

1 2 3

T L R

L T R

Finally, you ask the 1st person if the 3rd person always tells the truth. Seeing as you know the answer to that you will automatically know if they are telling the truth or they are the liar. That is the easiest question I could think of.

Theoretically you could solve this in 2 questions if the first person gives you a yes/no answer on the first question because you will know they are the Random on the first shot. Like I said, I don't know if this solution counts but I wish this was a real scenario so I could see these guy's reactions when I asked them the questions. LOL

[Guest]

To be honest a "No response" type of solution is a little cheating...but I do have a way to solve this:

1. Ask the first man of the second man: Does he lie or tell the truth?

2. Ask the second man of the first man: Does he lie and tell the truth?

3. Ask the third man of the second man: Does he lie or tell the truth?

Here is the decision tree:

Note, the man on the left hand side of the arrow is the askee and the man on the right hand side is the subject

Question 1 - Ask the first man of the second man: Does he lie or tell the truth?

We can determine if

A yes will yield:

T->R

T->L

R->L

R->T

Basically, the first man is either the Truther or the Random guy

A no will yield:

L->R

L->T

R->T

R->L

Basically, the first man is either the Liar or the Random guy

**

Question 2 - Ask the second man of the first man: Does he lie and tell the truth?

If a yes was given for question 1, question 2 will yield:

A yes will yield:

R->T

L->T

NOTE: This will tell us the first one is the Truther, and the third question should simply be asking the truther if 2 is the liar.

A no will yield:

R->T

L->R

Move on to question 3...

If a no was given for question 1, question 2 will yield:

A no will yield:

R->L

T->L

NOTE: This will tell us the first one is the Liar, and the third question should simply be asking the liar if 2 is the truther.

A yes will yield:

R->L

T->R

Move on to question 3...

**

NOTE at this point, the results of these answers cancel several possibilities, leaving us with only two possible positions depending on the branch we're on (Yes, No or No, Yes)

Question 3 - Ask the third man of the second man: Does he lie or tell the truth?

If the previoues two questions were Yes, No

A yes willl yield

T->L

A no will yield

L->R

Either answer tells you who the last two are...

If the previous answers were No, Yes

A yes will yield

T->R

A no will yield

L->T

Either answer tells you who the last two are...

/end

It's a little convoluded, but the basic idea is to force the response of the liar/truther to find the random guy. My BIG assumption here is that Yes/No logic follows standardized logic (True/False) where the liar simply states the inverse answer to the question. For instance, if I'm asking the liar if the random guy lies and tells the truth, the liar MUST answer no whereas the truther MUST answer yes.

[Guest]

i think i have it.... ask two of the men if they are men ? truthful answer is yes the liar could only say no since that would be the lie(obviously)......... therefore ,singling out the liar, then you ask the liar to tell you out of the other two which one always tells the truth(must specify him to tell you based on the other two otherwise he could say himself).... since he lies he will tell you the one who is the random answerer.....................

[Guest]

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

[Guest]

There are actually two men who can't answer, not one, so the solution the way you proposed it won't work. Also, it assumes that not answering is permissable, so the random answerer can also choose not to.

"if B says yes, then you ask the L (the only one that lied) who the T is"

What if two of them lied?

Well Martini, i already explained that if 2 of them lied, then you should ask the T (the one that only told the truth (you know, the second part of my first answer (and yes, i did use 3 brackets at once))) who is the liar and the both

<_<

[Guest]

Well Martini, i already explained that if 2 of them lied, then you should ask the T (the one that only told the truth (you know, the second part of my first answer (and yes, i did use 3 brackets at once))) who is the liar and the both

<_<

You don't get four questions; you get three.

[Guest]

so we have three people in a room, number 1, number 2 and number 3. One of them speaks only the truth(T), one can only tell lies(L) and one can do both(B).

my first question will be directed to all three of them:''Is there anyone among you three that only tells lies?''

I know that T will say yes to this question and that L will say no. So depending on what B will say I have two possibilities:

1) the answers i get are: yes, no, yes(if B will tell the truth)

lets say that i get the answers in that turn: 1=yes, 2=no, 3=yes. Then i will know that 2 is L. I will ask him if 1 is the truthteller.

If he says yes then i will know that 1=B, 2=L, 3=T. If he says no then I will know that 1=T, 2=L,3=B

2)the answers i get are:yes, no, no(if B will lie)

Assume that i get the answers in that way:1=yes, 2=no, 3=no. Then i will know that 1 is T. I will ask him if 2 tells only lies.

If he says yes then i will know that 1=T, 2=L, 3=B. If he says no then i will know that 1=T, 2=B, 3=L

[Guest]

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

[Guest]

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.

[Guest]

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?

[Guest]

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?

[Guest]

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

[Guest]

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.

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 August 8, 2008 by nogox5

[Guest]

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.

[Guest]

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.

[Guest]

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.

[Guest]

Of course this implies random alternates between truth and Lies.

"and one that sometimes answers truthfully and sometimes lies"

[Guest]

Ask person A the first question:

"Would you currently answer yes to the statement 'I sometimes tell the truth and sometimes lie' ?"

If A is the truth teller, he will truthfully say no.

If A is the liar, he would say yes to 'I sometimes tell the truth and sometimes lie', but will lie about his agreement, answering no.

If A is the random in the truth-telling mood, he would truthfully answer yes.

If A is the random in the lying mood, he would not answer yes to 'I sometimes tell the truth and sometimes lie', but will lie and say he would, answering yes.

If A answered yes, we know he is random. We then ask B a second question 'Would C say that you are a liar ?'. If B says yes, he is the truth-teller and C is the liar; if he says 'no' he is the liar and C is the truth-teller. In this case we know the identies of all three with two questions.

If A answered no, we know he is either the truth-teller or the liar. Ask him a second question 'Would B or C ever agree that you are a liar ?". If yes , A is the truth-teller. If no, A is the liar. Know we know whether A is a liar or truth-teller with one question left. Ask him the last question, 'Is B random ?'.

If A is the truth-teller, yes implies B random, C liar. No implies B liar, C random.

If A is the liar, yes implies B liar, C random. No implies C liar, B Random.

All three identies known with only 3 yes / no questions.