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]

Martini,

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.

[Guest]

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

If Answer = No

B = Random Answerer or Truth Teller

Go to person C and ask "Are you a liar?"

If answer = Yes

C = Random Answerer

B= Truth Teller

A = Liar

If answer = No

A = Liar

Ask person C "Are you the truth teller?"

If answer = No

C = Random Answerer

B = Truth Teller

[Pirate8]

Ask the first man "if he is a man." If the answer is no then he is a liar.

If the answer is yes he’s either a truth teller or Mister random so you ask the 2^nd man "are you a man?" If the answer is no he is the liar.

If the answer is yes then the 3^rd man is the liar.

Now that you know who the liar is you ask the liar while pointing to one of the other 2 men "is this man the truth teller?" If he says yes then that man is Mister random. However if the answer is no then that man is the truth teller.

[Guest]

Have you found a solution, or are you just seeing what people come up with?

I've thought about it and can't a way except this.

Ask two men if they are men.

You will definately ask the other man if he is (by other I mean the man that lies and tells the truth.)

Since he can do both, I'm sure he'll yes yes. So will the truthteller.

If on says no then you know who the liar is.

If both say yes, then you still know who the liar is.

Ask the liar if the first is the truthteller and the second is the liar (the first and second being the two that aren't the liar obviously.)

If he says yes then it is the other way around. If he says no then you are right.

Again, this is assuming that the man that can choose to tell the truth aor a lie will choose to tell teh truth and say he is a man. If he doesn't, then this could work, if you ask the right people. But, asking the right ones would be by chance and would not be reproducably effective.

[Guest]

Have you found a solution, or are you just seeing what people come up with?

Both.

Ask two men if they are men.

You will definately ask the other man if he is (by other I mean the man that lies and tells the truth.)

If you only ask two men if they are men, how do you come up with "you will definitely ask the other man if he is"?

Since he can do both, I'm sure he'll yes yes. So will the truthteller.

If the man can both lie and tell the truth, how did you come to the conclusion "I'm sure he'll yes yes"? (I'm guessing you meant to write "I'm sure he'll say yes.") There's no reason to be sure the man who lies and tells the truth will answer "yes".

The rest of your reply is incorrect based on your above conclusions.

[unreality]

ask them if the first man is the liar:

if the first man says Yes, you know he's the Random man ®, because neither the Liar (L) or Truth-teller (T) could say "yes" to that.

now if the first man said no, he is either L or T. If he is L, T will say "yes he's L" and R will say either. If he is T, L will say "yes he's L". R will say either. Hmm. Is this the right start to solving it?

[Guest]

Is this the right start to solving it?

It's not the start to the solution that I came up with, but I do believe you are on your way coming up with an alternate solution that also works. If he answers 'yes' to your question, you can actually solve the riddle with only two questions.

[Guest]

Martini very good question...

to solve this you have to... line them up back to back and ask ur questions? (at least this is how I started it)

I solved this puzzle before. Its actually very fun to work on

I hope this hint helps...

good luck...

[Guest]

but I do believe you are on your way coming up with an alternate solution that also works.

I take it back. I can't think of any following questions that would solve the riddle if starting off with the question you asked.

[unreality]

lol k

[Guest]

ask them if the first man is the liar:

if the first man says Yes, you know he's the Random man ®, because neither the Liar (L) or Truth-teller (T) could say "yes" to that.

now if the first man said no, he is either L or T. If he is L, T will say "yes he's L" and R will say either. If he is T, L will say "yes he's L". R will say either. Hmm. Is this the right start to solving it?

This isn't correct. R could also say No to the question. Yes will give you R but No will not eliminate him.

[unreality]

niiiiiiice!

[Guest]

Yes, very nice job, Writersblock, and a good job at providing an explanation also.

[Guest]

*CHEERS*

[propsguy]

Holy crap is that good Writersblock!

I'm looking for the "Bow-down" key on my computer.

[Guest]

ask them if the first man is the liar:

if the first man says Yes, you know he's the Random man ®, because neither the Liar (L) or Truth-teller (T) could say "yes" to that.

now if the first man said no, he is either L or T. If he is L, T will say "yes he's L" and R will say either. If he is T, L will say "yes he's L". R will say either. Hmm. Is this the right start to solving it?

If you had written, ask one of them if he is a liar, this could easily be done with that as a first question. Can anyone tell me how?

[Guest]

If you ask the first man " if i asked him (pointing to the middle man) if he was a liar what would he say?"

If the first man was the liar and the middle man is the truth he would answer " Yes"

If the first man was the truth and the middle man the liar he would answer "No"

If the first man answered "yes" I would then ask him if he is a liar. If he is indeed is the Liar he will answer "NO"

If the first man answered "no" I would then ask the second man if he is a liar. and again he will answer "NO" if he is.

Once the liar and the truth telled have been determined i would then ask the liar if the third person (who hadent been asked anything so far) was the random one being a liar he will say "No" if we are correct. However if he says "yes" Then this means that the Random person was having a truthful day and we have mistaken them for each other and there you go!

Right??

[Guest]

Did you leave out an option if the liar answers the first question yes? If he answers yes it could either be LTR or LRT. That means the second question doesn't work because there will be a random guy in every possible position. This is in response to Writersblock.

Edited March 11, 2008 by spishak8

[Guest]

I have heard a version of this one before but with the additional challenge that they will only answer Og or Ug. Og and Ug mean Yes and No but you don't know which is which (you don't speak their language). How does this effect the solution?

[bonanova]

I have heard a version of this one before but with the additional challenge that they will only answer Og or Ug. Og and Ug mean Yes and No but you don't know which is which (you don't speak their language). How does this effect the solution?

Post #7 in this thread explains how to get around the uncertain meanings of the Yes/No words.

[Guest]

i need ask one question only....

the question is: is the one on the left the liar?

and i ask it to you (the originator of the quandary)

[Guest]

Lets say there are three people A, B and C.

Q1: Ask B: If i ask A if he is a toggler (S) will he say yes?

Three possibilities: (i) No answer (ii) No (iii) Yes.

(i) No answer

You get no answer for the following combinations: A is S, B is L; A is S, B is T.

As you see is the above combinations A is always S.

Q2: AskB: Is A a toggler?

Two possibilities: Yes or No

Since we already know A is S, if the answer is Yes then B is T and C is L. END

If the answer is No then B is L, C is T and A is S. END

For this option we find out who is who with only two questions. Lets see the other options to the first question:

(ii) No

You get No for the following combinations: A is T, B is S (1); A is L, B is S (0) /* S (1) and S (0) implies that the toggler told the truth or a lie respectively for the first question.

Q2: Ask A: Is B a toggler?

Two possibilities: Yes or No. If yes, A is T, B is S, C is L. END

If No, A is L, B is S, C is T. END

We also find out who is who in this case in two questions. The last option of the first question will need three questions shown below.

(iii) Yes

We get yes for the following combinations: A is T, B is S (0); A is L, B is S (1); A is T, B is L; A is L, B is T.

Q2: Ask B: Is A a liar?

Two possibilities: (a)Yes or (b)No

(a)Yes

the combination are: A is T, B is L; A is L, B is T.

Q3: Ask B: If I ask A if u r a liar would he say yes?

Yes: A is L, B is T and C is S. END

No: A is T, B is L, C is S. END

(b) NO

Combinations are: A is T, B is S; A is L, B is S.

Q3: Ask A: is B a toggler?

Yes: A is T, B is S, C is L. END

No: A is L, B is S, C is T. END

[Guest]

NICE

Edited April 8, 2008 by Multee-Pass

[Guest]

Ask one man if he is a man. If he says yes, he is either the random or the truthteller. If he says no, he is the liar.

Ask a second man if he is a man. If he says yes, he is either the random or the truthteller. If he says no, he is the liar.

If one of the first two answers you get is no, then that man is the liar, and ask him which of the other two men is the truthteller. Whichever man he chooses is the random, and the last man is the truth teller.

If the first two answers you get are Yes, then ask the third man, who must be the liar, which if the first two men is the truthteller. Whichever man he chooses is the random, and the last man is the truth teller.

[Guest]

If one of the first two answers you get is no, then that man is the liar.

Not necessarily. He may be the random answerer.