[Guest]

There are three identical triplets, Adam, Alan and Alex. It is known that precisely one of them is a truthteller, exactly one of them is a liar and the remaining triad member is an alternator, that is, he alternates true statements and false statements

Frank, who is a mutual acquaintance of the three brothers is currently looking for Adam. He chances upon two of the triplets. Unfortunately, since the brothers look exactly the same he is unable to distinguish between them.

What is the minimum number of questions Frank must ask the duo to guarentee that he can determine which triplet (either one of the two, or the one who's not there) is Adam?

[Guest]

There are three identical triplets, Adam, Alan and Alex. It is known that precisely one of them is a truthteller, exactly one of them is a liar and the remaining triad member is an alternator, that is, he alternates true statements and false statements

Frank, who is a mutual acquaintance of the three brothers is currently looking for Adam. He chances upon two of the triplets. Unfortunately, since the brothers look exactly the same he is unable to distinguish between them.

What is the minimum number of questions Frank must ask the duo to guarentee that he can determine which triplet (either one of the two, or the one who's not there) is Adam?

ONE

[Guest]

There are three identical triplets, Adam, Alan and Alex. It is known that precisely one of them is a truthteller, exactly one of them is a liar and the remaining triad member is an alternator, that is, he alternates true statements and false statements

Frank, who is a mutual acquaintance of the three brothers is currently looking for Adam. He chances upon two of the triplets. Unfortunately, since the brothers look exactly the same he is unable to distinguish between them.

What is the minimum number of questions Frank must ask the duo to guarentee that he can determine which triplet (either one of the two, or the one who's not there) is Adam?

Do we only have to ask questions where the response is Yes/ No, or can we ask questions whose response can be a phrase etc.?

Cheers,

Edited November 17, 2009 by baron

[Guest]

ONE

Did you have a certain one in mind?

[Guest]

I like this one. I know the one with the two brothers, but this adds some interest.

Here is what I think...

I don't think it matters how many brothers you have (or if they are lying) because the question you need to ask will reveal the same answer with either truth or lies. I would ask:

If I were to ask you where Adam is, what would you say?

1. Truth teller would tell you where Adam is because he would have told you that anyway.

2. Liar would tell you where Adam is because he would say the opposite of what he would normally say (since you asked him what he would say if you asked him).

Of course I suppose he could come up with another lie rather than telling the truth, though. Hmm...

[Guest]

Do we only have to ask questions where the response is Yes/ No, or can we ask questions whose response can be a phrase etc.?

Cheers,

I think the correct answer is two, and you have to phrase a compound question.

Full solution to follow,

Cheers,

[Guest]

OK, here is my solution:

The secret is to ELIMINATE the Alternator at the end of the first question.

I am using T for Truth Teller, L for Liar and A for Alternator ( one who tells the lies and truth alternatively- so he can start with a lie or truth).

Line up the two guys so that one is in front of another:

The order can be:

TL

TA

LT

LA

AT1 (With Alternator speaking truth in answer to the first question)

AL1 ( With Alternator speaking truth in answer to the first question)

AT2 (With Alternator lying in answer to the first question)

AL2 (With Alternator lying in answer to the first question)

You can ask compound questions ( there are so many questions to ask, but I will just provide an indicative one).

Compound question should make use of the prepositions:

p1- A is behind L

p2- I am alive

p3- You are TruthTeller

p4 -You are alive

You can use various logic gate ( Hint: XOR = 'one or the other but not both')

The truth table is

TL F T T T

TA F T T T

LT T F T F

LA F F T F

AT1 T T T T

AL1 T T T T

AT2 F F F F

AL2 F F F F

So you can see that if the final output is FALSE ( which will only be when ALL prepositions are true or ALL prepositions are false), you have a case that the person you asked the question to is an Alternator- thus the second person is either a liar or a truth teller.

Conversely, if the final outout to the compound question is TRUE, you KNOW that this person is either a liar or a truth teller.

Then, once you have eliminated the ALTERNATOR, you can simply ask the other guy

"If I were to ask you where Adam is, what would you say?"

Voila! you have Adam.

Sorry for not expressing it more meaningfully,

Cheers,

Varun Pant

Edited November 17, 2009 by baron

[Guest]

I too would like to know if the questions have to be yes or no. Also, are all three brothers aware whether the alternator will answer truthfully or falsely to the first question posed to him?

[Guest]

It's too easy to do in 4 for that to be the correct answer...

[Guest]

Actually, the answer is one question.

See, there is NO complexity, and it is actually simpler than it looks

If this was my next (or second) question to you, and if I asked you where Adam was, what would you answer?

This way, if it is the Truth teller, he would respond correctly- for the liar, it does not make any difference if it is first or second question- he will always lie, but for the alternator, it would mean that he would always be lying ( he alternates between telling the truth and lying)- and would be similar to the case of the liar.

Cheers,

Varun Pant

[Guest]

Actually, the answer is one question.

See, there is NO complexity, and it is actually simpler than it looks

If this was my next (or second) question to you, and if I asked you where Adam was, what would you answer?

This way, if it is the Truth teller, he would respond correctly- for the liar, it does not make any difference if it is first or second question- he will always lie, but for the alternator, it would mean that he would always be lying ( he alternates between telling the truth and lying)- and would be similar to the case of the liar.

Cheers,

Varun Pant

But it would not for the alternator - he would wind up truthfully telling you a lie (or lying about the truth). You wouldn't get the cancellation you're looking for as in the liar. And since you do not know which of them is the truthteller/liar/alternator, you wouldn't be guaranteed the answer.

[Guest]

If this was my next (or second) question to you, and if I asked you where Adam was, what would you answer?

This way, if it is the Truth teller, he would respond correctly- for the liar, it does not make any difference if it is first or second question- he will always lie, but for the alternator, it would mean that he would always be lying ( he alternates between telling the truth and lying)- and would be similar to the case of the liar.

Instead of asking about the next (second) question, ask if this were in two questions (third) -- that way the alternator would cancel two lies or have two truths (truthteller and liar fall into one of these scenarios as well). Also, the question would need to be definitive so that a lie on a lie would be the truth -- i.e. if with the first lie Alex is chosen, then Alan is not a possibility for the second lie.

[plainglazed]

I believe you should be able to determine which brother is Adam by asking three simple yes/no questions:

1. Are you Adam?

2. Are you Adam?

3. Is the brother not present Adam?

Consider: If both brothers present answer yes or no to both 1. and 2. Then neither are the alternator.

If they both say "yes" to 1. and 2. then the one who says "no" to 3. is (truthful) Adam.

If they both say "no" to 1. and 2. then the one who says "yes" to 3. is (lying) Adam.

If one says "yes" and one says "no" to questions 1. and 2. then the brother not present is (alternating) Adam.

Consider: If one brother present gives alternating answers to question 1. and 2. he's the alternator and the other brother present is either the lying or truthful brother.

If the alternator says "yes" to 1. and "no" to 2. and "yes" to 3. then he must be lying to questions 1. and 3. He would have to be lying to say "yes" to both "Are you Adam?" and "yes" to "Is the brother not present Adam?" so the truthful answer to both 1. and 3. must be "no" proving the other brother present to be Adam (if that other brother present said "no" to 3. he is truthful Adam or if he said "yes" to 3. he is lying Adam).

If the alternator says "no" to 1. and "yes" to 2. and "no" to 3. then he must be truthful to questions 1. and 3. If he were lying when saying "no" to questions 1. and 3. then the truthful answer to 3. would be "yes" to "Is the brother not present Adam" and also true would have to be 2. "yes" to "Are you Adam" (since he alterantes lying and being truthful) again proving the other brother present to be Adam (if that other brother present said "no" to 3. he is truthful Adam or if he said "yes" to 3. he is lying Adam).

We still havent worked out the scenerios where the alternator says (1) "yes","no","no" or (2) "no","yes","yes"

Consider case (1):

If he's lying to questions 1. and 3. then the truthful answer to 3. is yes making Adam the brother not present.

If he's telling the truth to questions 1. and 3. then he is Adam.

Condider case (2):

If he's lying to questions 1. and 3. then he is Adam

If he's telling the truth to questions 1. and 3. then the brother not present is Adam.

Consider the other brother present with the aternator:

If the other brother present with the alternator answers "yes", "yes", "yes" then he must be lying (he can not be telling the truth and say "yes" to both "Are you Adam?" and to "Is the brother not present Adam?") and the alternator is Adam.

If the other brother present with the alternator answers "no", "no", "no" then he must be telling the truth (again, if he were lying the truthful answer to both 1. and 3. would be yes which is not possible) and the alternator is Adam.

We still have not worked out the scenerios where the other brother present with the alternator says (3) "no", "no", "yes" or (4) "yes", "yes", "no".

Consider case (3):

If he is the liar then he is Adam and if he is the truth teller then the brother not present is Adam. Either way Adam is not the alternator.

Consider case (4):

If he is the liar then the brother not present is Adam and if he is the truth teller then he is Adam. Again, either way Adam is not the aternator.

This eliminates the possibility of Adam being the alternator in cases (1) and (2) when you have the scenerio of (3) or (4).

So in case (1) and (3) or (4) and in case (2) and (3) or (4) Adam is the brother not present.

[Guest]

Instead of asking about the next (second) question, ask if this were in two questions (third) -- that way the alternator would cancel two lies or have two truths (truthteller and liar fall into one of these scenarios as well). Also, the question would need to be definitive so that a lie on a lie would be the truth -- i.e. if with the first lie Alex is chosen, then Alan is not a possibility for the second lie.

Actually, it is even simpler.

If I asked you where Adam was, what would you answer?

Truth teller would tell about where Adam is.

Liar would lie about where Adam is, but since you ask what would be your answer, he has to tell about where Adam is!

Now that we have agreed the case for Liar and truth teller, let's come to the alternator.

Two cases arise:

Case 1: He is going to tell the truth this time, so effectively, he is a truth teller!

Case 2 :He is going to lie this time , so he is equivalent to the liar!

In either of the two cases, it does not matter!

He will either be telling the truth and tell you where Adam is, or else he would lie, but STILL tell where Adam is!