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?

[Prime]

This is a very interesting problem. After checking the posts, I see that Writersblock had solved it a year ago. The solution that I found is the same in essence. Though, I found a different kind of relation between the three men (other than LEFT RIGHT).

Let's designate the men as 1, 2, and 3. There are six possible arrangements for them to be Truth-teller (T), Liar (L), and Random R:

1 2 3

T L R

T R L

L T R

L R T

R T L

R L T

The first question must get rid of Random in one of the positions, otherwise the problem is unsolvable. So you ask the man 1:

1) Is it possible for 2 to tell truth more often than 3?

T in the first arrangement would answer "NO". T in the second arrangement would answer "YES".

L in the 3rd arrangement would answer "NO". L in the 4th arrangement would answer "YES".

(For it is not possible for R to tell truth more often than T, and for L more often than R.)

And we don't care what Random would answer, for her answer gives no useful information.

Thus "YES" leaves us with 4 possible arrangements:

1 2 3

T R L

L R T

R T L

R L T

Here man 3 can only be either L or T, but not R.

"NO" will leave for us:

1 2 3

T L R

L T R

R T L

R L T

Where man 2 can only be L or T, but not R.

The second question would be directed to the man who can be only T or L:

2) Are you a Random-teller? To which T answers "NO" and L answers "YES".

And the third final question to the same man would be:

3) Is man 1 a Random-teller? Which would narrow your choice to just one possible arrangement.

Edited August 16, 2008 by Prime

[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 ?

[Guest]

establish which man is the truth-teller. ask man1(m1) if he always speaks truth. if he replys no ask m2 the same question. if he replys no, u know m3 is the truth-teller. ask him if the man to his left (or right) always lies. weather he replies yes or no you can deduce who the remaining 2 men are. if u find the truth teller on the first question u can find out in 2 questions

[Guest]

establish which man is the truth-teller. ask man1(m1) if he always speaks truth. if he replys no ask m2 the same question. if he replys no, u know m3 is the truth-teller.

That won't work; two men can't answer that question with a "no".

[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 ?

You have a problem if 1 is Random. He might answer "NO".

[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?

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

[Prime]

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

Just looking at your first case, NNN could mean A=Truth-teller, B=Random, C=Liar; or A=Random, B=Truth-teller, C=Liar. So those three questions do not resolve who is who. Correspondingly, your arrangement for the YNY implies that the Truth-teller lied to the first question. As well the YNN arrangement implies that the Liar answered the first question truthfully...

Edited January 20, 2009 by Prime

[Guest]

Just looking at your first case, NNN could mean A=Truth-teller, B=Random, C=Liar; or A=Random, B=Truth-teller, C=Liar. So those three questions do not resolve who is who.

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.

Correspondingly, your arrangement for the YNY implies that the Truth-teller lied to the first question. As well the YNN arrangement implies that the Liar answered the first question truthfully...

Got me there. I originally solved it where A and C were asked the questions of B and I tried to swap them in my head as I was transcribing. Let's see if it was a transcription error or a logic error:

YNY should imply:

A is determined non-random, therefore A is asked second question, and proven truthful.

Truthful A claimed C is Random, so C is Random and B is Liar.

YNY should have equated to A=Truthteller, B=Liar, C=Random

YNN should imply:

A is determined non-random, therefore A is asked second question, and proven a liar.

Liar A claimed C is Random, so C is Truthteller and B is Random.

YNN should have equated to A=Liar, B=Random, C=Truthteller

Yup. I shouldn't try to sort and copy at the same time... I still assert (randomly?) that the logic is sound. The questions are sufficient to determine who's who.

[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?

[spoiler='Answer

'] 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 (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.

Hope that made sense.

[Guest]

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	YY

LRT	X	X	[A]	[C]

LTR	[B]	[A]	X	X

RLT	[B]	X	X	[C]

RTL	[B]	X	X	[C]

TLR	X	X	[A]	X

TRL	X	[A]	X	X

[/codebox]

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='Answer

'] 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 (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.

Hope that made sense.

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.

[Guest]

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...

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 January 30, 2009 by Prime

[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?

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 : )

[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?

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 : )

[Guest]

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.

[Guest]

This i think is the soultion ok.ask the first two if they are male if yes yes then you know who the liar is

then ask the liar if the first man is the truth teller if no he is if yes he isnt thats only half solved it

but i think to find out the liar is the key to solving it.

[Guest]

ask the 2 men if they are male if yes yes then the third man is the liar then ask the liar if the first man is the random teller if the liae responds yes then the random teller is the middle man and the first man is truth teller

then you know who is who if the liar responds no then the first man is the truth teller etc etc.second answer if you ask first two men are you male and the answer

is yes no then the secon is the liar ask the liar if the first man is the truth teller if yes the truth teller is the third man etc etc.

Edited September 20, 2009 by carlo1974

[Guest]

You could ask them to stand in a row. Let’s name them A, B and C. So ask A if there is a person standing in front of him/her , if he/she says YES he/she could either be the R.A or the T if he/she says NO then he/she is the L. Then ask B the same question, he/she again can say YES so he/she is the R.A or the T, if he/she says NO we are dealing with the L. Now what we have to determine, and after doing this we will, is who is the L so when we get him/her we must ask “Is the person next to you or in front of you (depends where the liar is spotted) the T? If he/she says NO then we know it IS (because he/she will lie) and if he/she says YES we know it isn’t so we know the other person is. That way we will know who the T is, the L is and finally the R.A.

Does it make sense?

[Guest]

Martini,

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</div><div class="alt2" style="margin: 0px; padding: 6px; border: 1px inset;"><div style="display: none;">Originally I thought this was impossible, but I think I have solved it. Nice one.

I saw that:

There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT

There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL.

Theoretically it's possbile if you could figure out a way to get any of the 8 combinations of answers assigned to the states, but with the unreliability of Random's answers, I thought it was impossible. There is always a possiblity in any solution where Random will exactly mirror T or L for answers. He could always lie or always tell the truth and you can never tell when he is lying or telling the truth. This being given, I thought you can NEVER separate 6 distinct answers to apply to the 6 states, and therefore can never be sure who is who.

After a minute though, I saw through my own error in logic. I was always dealing with questions where T and L would give the same answer regardless of the order of the men. I saw that if you can get T and L to give a Yes/NO answer, then you can figure out where R's worthless answers are. The only way I saw to do this is to ask about the order of the men themselves.

So:

Ask #1 if L is standing on R's right arm (our left if they are facing us).

The answer gives you a split in the order they are standing:

If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT.

If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT.

Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3.

The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know:

Yes, Yes: Has to be LTR, or RTL

Yes, No: TLR, RLT

No, Yes: LRT, RLT

No, No: TRL, RTL

Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers.

For example:

Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL

Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR

No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT

No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL

So we have the order and know who is who.</div></div></div>

I like where you are going with this, however you can't answer it in 3. Your solution involves 4 which is still the random check. At best you can get lucky.

'Truth is T

'Lie is L

'Random is R

'Three men and lined up.

'No other given

'Possibilities TRL TLR LRT LTR RTL RLT

Ask 1 if it is R

Yes

'Possibilities LRT RLT RTL Senario 1

No

'Possibilities TLR TRL RLT RTL Senario 2

Senario 1

Ask 3 if person to your left is a liar

Yes

'Possibilities RLT RTL Senario 1a

No

Answer is RLT

Senario 1a

3 are you a man

Y = RLT

N = RTL

Senario 2

2 is the person to your left truth?

Yes then insolvable in 3 as random is not isolated.

No TRL RTL Senario 2a

Is the person to your left T?

Yes, answer is TRL

No answer is RLT

Ashamed I can't think of 3 which wins every time and to think it is impossible and sorry for my sloppy format. It is nearly 6am and I am in bed on a stubborn iPod. Let me know if anyone has better.

[Guest]

You could ask them to stand in a row. Let’s name them A, B and C. So ask A if there is a person standing in front of him/her , if he/she says YES he/she could either be the R.A or the T if he/she says NO then he/she is the L. Then ask B the same question, he/she again can say YES so he/she is the R.A or the T, if he/she says NO we are dealing with the L. Now what we have to determine, and after doing this we will, is who is the L so when we get him/her we must ask “Is the person next to you or in front of you (depends where the liar is spotted) the T? If he/she says NO then we know it IS (because he/she will lie) and if he/she says YES we know it isn’t so we know the other person is. That way we will know who the T is, the L is and finally the R.A.

Does it make sense?

That makes sense but should you run into N Y then you have

LRT

RTL

LTR

Thusly you haven't narrowed down R, where to go from there?

[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.