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]

All day at work I thought this through completely convinced you couldn't isolate R which is key as you must do it on the first question. Then as I fell into a much needed nap it hit me. Use a condition question to isolate random. "1 assume that random's answer would be the same, what would the person to your right say if I was to ask him if he was a man."

Should the answer be yes then we know that is either TRL or RLT.

Should the answer be no then we know it is LRT or RLT .

Because random now has to be one of those two you not only eliminate a false answer but you also make it so 3 has to be either T or L. Now you can go from there.

I choose, "3, are you a man?". Yes mean T no means L. Then from there you can simply ask if the person to your you left is random. Knowing which one it is will let you decide how to interpret the answer. Now I can finally sleep.

[Guest]

i have a solution too and it seems simple:D

so:

we have 1 2 3

We ask 1:" do i have 5 figers at one hand?" ( and i do ) )

He answers: NO => 1 = L

then i ask 1 : " is 2 random?" => he answers yes =>2= T and 3 = R

no => 2 = R ; 3 = T

He answers YES: => 1 = T or R

then i ask 2" is 1 L?" => YES => 2 = L then i ask 2" is 1 T?" => YES => 1= R and 3= T

NO => 1= t and 3= R

=> NO => 2 = R or T and 3 = L ; so i ask 3 "if 1 is T?" = > YES => 1=R and 3=T

NO => 1= T and 3 = R

Is it OK ?

If he answers "no" he can be the random. bc of this, the rest of the logic doesn't follow

[Guest]

I was thinking of a question to make the L and T give me different answer and I found many but the problem is always with the R as he can give both answer so I thought that to know who is who I need to identify R

The L always lies and T always tells the truth but what if I ask them the following question:

If I ask the R if the man next to him is the liar will he answer yes?

For this question the T doesnt know the answer and therefore he cant say the truth, so he must say YES and NO same time or stay silent, but he cannot give one answer as yes or no

The same thing with the L, he also doesnt know the answer and therefore he cant lie so he is also cannot give one answer as yes or no

So I solve it this way

Let say the 3 men A, B, C

Question 1 Ask A: if I ask C (is B the liar) will he answer yes?

If YES then C cannot be the R, because if C=R then A cannot say yes

So we have these possibilities

1) A=T, B=R, C=L

2) A=L, B=R, C=T

3) A=R telling the truth then B=L and C=T or B=T, C=L

With these possibilities we will go to the 2nd question

Question 2 Ask C: do you know what the R will answer if I ask him who is the liar?

For this question the T will always answer NO as he really doesnt know, but the L will always answer YES as he is lying

So if C answer YES then C=L

So we ask C again: is B=T?

If YES then B=R and A=T

If NO then B=T and A=R

We go back now to 2nd question with C

Ask C: you know what the R will answer if I ask him who the liar is?

If NO then C=T

So we ask C again: is B=L?

If yes then B=L and A=R

If no then B=R and A=L

No we go back to the 1st question

Ask A: If i ask C (is B the liar) will he answer yes?

If NO then C cannot be the R, because if C=R then A cannot say no

A cannot be T because if A=T then C must be L and the answer cannot be NO

A cannot be L because if A=L then C must be T and the answer cannot be NO

So we have one possibility

A=R telling a lie then C=T and B=L, or C=L and B=T

2nd question to C: do you know what the R will answer if I ask him who is the liar?

If yes then C=L, A=R, B=T

If NO then C=T, A=R, B=L

Now we again go to 1st question

Ask A: If i ask C (is B the liar) will he answer yes?

If he answer yes and no or he remain silent then C=R

2nd question to A again: do you know what the R will answer if I ask him who is the liar?

If YES then A=L, B=T, C=R

If NO then A=T, B=L, C=R

Edited September 6, 2010 by Zak

[Guest]

three men=m1,m2-m3

m2is observed as having green eyes by me,

i ask m1 if m2 has green eyes.

no=LorR

yes=TorR

now I as m2 if he has green eyes

no=LorR

yes=TorR

if m1 is LorR

and m2 isLorR, m3 is truthteller so we follow up with him

if m1 is TorR

and m2 isT or R

m3 is liar and we follow up with him

if m1 is TorR

and m2 is LorR

m3 can't be R, he has to be T or L

if we ask him if m2 is T, if he says yes then m3 isL,m2 isR, m1isT

if he says no, m3 is T, m2 isL, m1 is R

Edited September 24, 2010 by peanut

[Guest]

three men=m1,m2-m3

m2is observed as having green eyes by me,

i ask m1 if m2 has green eyes.

no=LorR

yes=TorR

now I as m2 if he has green eyes

no=LorR

yes=TorR

if m1 is LorR

and m2 isLorR, m3 is truthteller so we follow up with him

if m1 is TorR

and m2 isT or R

m3 is liar and we follow up with him

if m1 is TorR

and m2 is LorR

m3 can't be R, he has to be T or L

if we ask him if m2 is T, if he says yes then m3 isL,m2 isR, m1isT

if he says no, m3 is T, m2 isL, m1 is R

i tried alot of direct question like that but its never right all the way, its solve 80% of the possibilities but not 100%

like now in the third possibilities you put (if m1 is T or R, m2 is L or R then m3 canot be R and has to be T or L)

but m3 can be the R, if m1 T and m2 L then m3 will be R

so in this case m3 can be R,T,L and we have one more question to go which make it impossible

[Guest]

i tried alot of direct question like that but its never right all the way, its solve 80% of the possibilities but not 100%

like now in the third possibilities you put (if m1 is T or R, m2 is L or R then m3 canot be R and has to be T or L)

but m3 can be the R, if m1 T and m2 L then m3 will be R

so in this case m3 can be R,T,L and we have one more question to go which make it impossible

Snap, I missed that somehow.

[Guest]

peanut i would like to know what you think about my solution, do you agree with me or not

[Guest]

answer in 3 qns

Get the 3 person to stand in one straight line.

the 6 possible lineups are TLR TRL RLT RTL LTR LRT, where T = truthful guy, L = liar, R = random guy whose capable to lieing and telling the truth.

Qns are asked to determine the possible lineups in that group

Qns 1 ( to the 1st guy in the line) " is the L standing directly on the right side of R"

Yes : TLR RLT RTL LTR

No : TRL RLT RTL LRT

Qns 2 ( to the 2nd guy of the group who answered Yes) " is T in the group" *to the group who answered no, ask the qns to the 3rd guy instead. This should eliminate the possible groups down to two

Yes : RTL LTR

No : TLR RLT

Qns 3 ( to the 2nd guy of the group who answered Yes) "is the lineup as follow RTL)

Yes : RTL

No : LTR

Edited October 18, 2010 by swongy

[Guest]

As them all if the capital of England is London. This will give one of two cases:

Case 1: Yes, Yes, No (in any order) (the guy with unpredictable answers tells the truth)

In this case, we now know the liar, and can simply ask him if the first 'yes' is the truth teller. Reverse his answer and that's the truth.

Case 2: Yes, No, No (again, in any order) (the unpredictable guy lies)

We know the truth teller, and can ask him if the first 'No' is the liar.

We have solved in two questions asked to a maximum total of four people. We can sometimes solve by asking the first question to only two people, if we get the first two answers the same (ie. yes, yes or no, no). If they differ we have to ask the third guy.

[Guest]

As them all if the capital of England is London. This will give one of two cases:

Case 1: Yes, Yes, No (in any order) (the guy with unpredictable answers tells the truth)

In this case, we now know the liar, and can simply ask him if the first 'yes' is the truth teller. Reverse his answer and that's the truth.

Case 2: Yes, No, No (again, in any order) (the unpredictable guy lies)

We know the truth teller, and can ask him if the first 'No' is the liar.

We have solved in two questions asked to a maximum total of four people. We can sometimes solve by asking the first question to only two people, if we get the first two answers the same (ie. yes, yes or no, no). If they differ we have to ask the third guy.

This method works, but it's technically 4 questions (the London question asked three times, one for each guy) and the fourth to either the T or L to find the solution.

[Guest]

Ask the first if I ask the others if you are the liar will they say you are and say ANSWER IN THE ORDER YOU ARE LINED UP IN. It will instantly eliminate the random because there will be a simple answer no matter what. The Random will say yes and no, the truth will say yes and he will not know which to say for the random and the liar will say no and won't know. You don't even need the other questions.

[Guest]

Picture the three persons next to eachother in a row. By asking the first and last guy in line who the guy in the middle is, and by asking the guy in the middle who he is - you can use the statments to figure out who is who.

Test and see for your self!

[Guest]

Writersblock's soution will work. This solution may be easier to follow, although the logic is similar; it creates a comparison among the three, although writersblock used physical ordering and I use the concept of "more honest".

It should be clear that any either-or question can be phrased as a yes-no question.

Choose one of the 3 at random. Call him #1. Ask him which of the other two is truthful more often. Call the one he fingers #2, and the one he doesn’t, #3.

If it's either the liar or the truthteller,he will finger the random answerer (since the random answerer tells the truth more than the liar, but less than the truth-teller). With this one question, you know that #3 is NOT the random answerer. #3 must be either the liar or the truthteller. So ask #3 any question you already know the answer to, such as, "are you the random answerer?" The liar will say yes, and the truth teller will say no. So with Q2, you know wheter #3 is a liar or a truth teller. A liar and a truth-teller can both be used to get the truth, you just invert the answer if he’s a liar. So with Q3, you just ask #3 who is the random answerer, and from his answer, you know everything.

For example, suppose #3 says he’s the random answerer. You know this to be false, since the random answerer was either #1, the guy you picked at random, or #2, the guy #1 said was “more truthful than #3”. So #3 is a liar. Ask #3 if #1 is the random answerer. If he says yes, then you know that:

#1 is the truth teller

#2 is the random answerer

#3 is the liar

Or, suppose #3 says he’s not the random answerer. You know he’s telling the truth,so he’s the truth teller. Ask #3 if #1 is the random answerer. If he says yes, then you know that:

#1 is random answerer

#2 is liar

#3 is truth-teller.

[Guest]

How can i see the answer of WritersBlock?

[Guest]

The trick to this puzzle is to force the liar into a double negative situation, and also to remember that the Random guy does not give random answers, but that he randomly tells the truth or lies. The key point is that he sometimes behaves like the truth teller and sometimes like the liar.

So you go to the first one and ask him "if I were to ask you 'is the second person is the random guy', would you say yes?"

If the first person is the truth teller, then it is easy, he would say yes if the second person is the Random guy and no if not

If the second person is the liar and the second is the truth teller, then the liar would have said yes to 'is the second person is the random guy' but since he is still telling lies, he would say no.

If the second person is the liar and the second 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.

Now what if the Random guy was the first person?

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.

If he is not, then you ask the second one a similar question

"if I were to ask you 'is the third person 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

[bhramarraj]

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 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 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 is the truth teller, then the liar [A] would have said ‘yes’ to ”is the second person 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 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 must be a Random guy and if you hear ‘no’ from the first guy [A], then second guy must not be a Random guy.

If he is not, then you ask the second one 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.

[Guest]

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

[comp_lex]

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.

[Guest]

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 December 30, 2011 by BaluTechie

[iNetsurface]

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 October 22, 2012 by iNetsurface

[Jaspreet Singh]

We will start by eliminating the position where Spy can be. There are two lines of thoughts we can go for. For simplification, take Truth-teller to be ‘T’, Liar to be ‘L’ and Spy to be ‘S’. Now lets assume, they are standing in a line in front of me as #1,#2,#3.

Q1.) Ask #1: Consider the one in the other two who do not answer randomly. If I were to ask him if #2 is Spy, would he answer ‘yes’?

Now, if the answer is ‘Yes’ then there are four possibilities: STL, SLT, TLS, LTS

        Q2.) Ask #2 if he’s the Spy? If he says “Yes” then #2 is Liar( Two possibilities: SLT, TLS). If he says “No” then #2 is Truth-Teller (Two possibilities: STL, LTS)

Q3.) Ask #2 if #1 is Spy? Its answer will eliminate one possibility in both the questions.

 

If the answer to Q1 is “No”, then there are four possibilities: TSL, LST, SLT, STL. Now #3 is not the spy. Hence ask #3 the Q2. If he says “yes” he is a Liar (TSL, STL), If he says “no” he is Truth-teller(LST, SLT). Now, ask #3 the Q3. It will eliminate one possibility in each case.

 

Hence, I got to know each and every one by asking 3 questions only.

Thanks:) Nice question:)

[bonanova]

@Jaspreet Singh greetings and welcome to the Den.

2007 really? Twelve years ago? This puzzle is a time capsule.

[Helper]

On 5/5/2008 at 11:44 AM, Guest said:

This is how I worked it out.

People:

A B C

To person B: Are you a liar?

If answer = Yes

B = Random Answerer

Go to person C and ask "Is person B the random answerer"

If answer = Yes

C = Truth Teller

If answer = No

C = Liar

****CORRECT UP TO THIS POINT******

If Answer = No ***[TO THE FIRST QUESTION]***

B = Random Answerer or Truth Teller

*******INCORRECT, IT COULD ALSO BE THE LIAR AS YOU RECOGNIZED IN THE SECTION ABOVE, BUT JUST FORGOT. (DON'T WORRY, IT HAPPENS...I DID ALMOST THE EXACT SAME THING BEFORE I READ THIS. I WAS SO EXCITED I'D FIGURED IT OUT, BUT THEN REALIZED I HAD LOST TRACK OF A POINT. :)****

 

(See **/ALL CAPS added to the quoted section.) So the first part of this is correct, and I'm convinced this is the only way to determine who's who, but you only have about a 17-22% chance of asking the Random (or Variable) Answerer AND getting the answers you need from that person. (Not sure I have the percentages right, but it's that ballpark.)

When I'm presented with a logic puzzle, I've always assumed it could be solved, but I think maybe this one has an additional layer: You have to determine whether there is a way to solve it A. everytime; B. just sometimes or C. never. This puzzle falls under B (I'm pretty sure).

So it is a good epistemological lesson: 1. It is possible to determine truth, but 2. it is sometimes by chance and 3. you can increase your odds of getting to the truth by asking the right questions, but 4. sometimes we don't (or can't) have enough information to determine something with certainty. Unfortunately, #4 is often overlooked, even in the field of science.

[Helper]

2 hours ago, Helper said:

Not sure how to delete my previous post (made same day), but I just found the answer by Prime which confirms there IS a solution which can be determined no matter who you ask or what the answers. There are other posts with the right answer, but Prime's is the clearest. It is fascinating though, how many people think they have the right answer but don't.

Prime's answer:

 

 

Edited October 7, 2021 by Helper

[Ell]

What if I  ask A if they feel bad when they lie?...if they can't  answer (because  they never lie) then they must be the truth teller.

    If they answer yes or no then ask B the same question... again if they can't  answer they are the  truth teller...

   If they answer  yes or no then C is the truth teller...

SO  NOW ASK THE TRUTH TELLER IF (A) IS THE LIER...HIS ANSWER SHOULD  SOLVE THE  ISSUE !!!