Ultimate brain teaser#7

[nate]

Of three men, one always tells the truth, one always lies, and one answers yes or no randomly. Each man knows which one each of the others are. You may ask three yes/no questions, each of which may only be answered by one of the three men, after which you must be able to identify which man is which. How can you do it?.


Take your time, you'll need it for this one.Good luck

[BamaCracker]

This has to revolve around asking each one the same question. I am working under the assumption that the question would be about the random guy. But, I have not been able to figure out the wording of the question that will show me the answer.

If you only had to no one of them, you can ask, "Is the liar here?" The liar has to say "No." But we know the liar is there. Now, if the random guy says "no" you have to guess between them. If the random guy says "Yes". . .

I just thought of something. The answer has to involve asking one guy what the other two will say. What will "A" say if I ask him if he is a liar? Liar say's, "No" and truth teller also says, "No." But random guy still says, "whatever." And, we're left guessing which one is lying.

Ok, how about this; we ask we ask one guy three questions; Are you the random guy? Yes. Is "A" the random guy? Yes. Is "B" the random guy? No. If we are talking to liar, we now know which is which. But, if we are talking to random guy, we still don't know.

OK, pick a guy. Ask him, "If I ask "A" if he is random guy, what will he say? If we talk to liar, and "A" is random guy, he says, "No." If we are talking to . . .

hell, I don't know! OK, so these ideas help someone else figure it out?

[Guy]

I don't know the answer to this one (and I haven't really tried either) but I think Bama is on the right track, because I remember a similar problem involving a liar and a truthful guy, and I remember that the question was based on asking what the other guy would anser to a certain question. This caused the the truth and the answer (or lie and the answer) to cancel each other out.

[BamaCracker]

I saw one once along the same lines about two prostitutes and their health card. With only two, it's pretty easy, but adding the random guy makes it hard.

[Edited by BamaCracker on 12-11-2001 at 08:39 PM]

[BamaCracker]

Pick one of the men and ask, "If I were to ask you whether "A" is a liar, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"

That way, the truthteller will say "yes" if "A" is the liar and "no" otherwise. The liar will answer the same, since he will lie about who is the liar, and he will lie about lying. The third man may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly report which one is the liar.

I don't see any flaw in that one, do you?

[jayz]

if b is truthful than ask b if a lies if yes than b would be truth a would be the one that lies and c would be randomly.if no than b truthful c lies a randomly i think??

[Diceman]

and hold it to the first guys head and ask him who is what. Tell him if you find out he was lying you are gonna turn his head into a squash. That way you can solve it with only one question. Am I close?

[Guy]

Dice, you have been officially nominated to lead the effort to convert the United States to the metric system. Now that you have mastered introducing millimeters into everyday activities, your next assignment will be to intoduce units of weight, for example: "How would you like me to blast away that 2 kilogram meatball on your shoulders with my 9 millimeter". This will allow the general population (well, the ones you are having "encounters" with at least) to learn to associate the two types of units. Thank you.

[BamaCracker]

So? Am I wrong or not?

[Diceman]

pretty funny..........
Bama, no,er I mean yes, mmmm what are you asking?

[nate]

That is the correct answer to a similar but differant question.

You come to a fork in the road while traveling.Your'e not sure which fork to take, but each of three men do.One tells the truth, one lies and the other tells the truth sometimes and lies the other times.Each of the three men know each of the others, but you don't know who is who. If you could ask one man at random one yes or no question, what question would you ask to determine the road you need to take.

This will get you to your destination but you still don't know who is who.In brain teaser #7,one guy is random, differant than lies sometimes and tells the truth sometimes.I will post the answer later today.

[Carl Roberts]

Question #1: Ask guy A, “Is B more honest than C?” If A says “yes”, then you can ask C question #2 because you know C is not the random guy. If A had said “no”, then you can ask B question #2 because you know B is not the random guy.

Question #2:
If A answered “yes” to question #1, ask C, “Is A more honest than B?” If C answers “yes”, then A is the random guy. If C answers “no”, then B is the random guy.
If A answered “no” to question #1, ask B, “Is A more honest than C?” If B answers “yes”, then A is the random guy. If B answers “no”, then C is the random guy.

Now (finally) you know who the random guy is. You just need to identify the liar and the truth-speaker.

Question #3: Pick either of the remaining two, unidentified guys. Ask him, “Is he the random guy?” while pointing at the guy who you know is the random guy. Based on the answer, you can identify the liar and the truth-speaker.

Got anything harder?

<just kidding, nate – i hope you don’t have anything harder; that is one of the best logical brain teasers i’ve ever seen! thanks for that one and all the other ones that preceded it>

[Diceman]

it took 2 weeks to solve this, so it must have been pretty tough. I would have figured it out, but besides the dizzy thing, I am writing a novel over in the other thread.

[Carl Roberts]

Nate said, "Take your time." (although I suppose two weeks was pushing it, eh?)

[nate]

Good job Carl.That isn't the same approach used in the answer to the question.The fact that your strategy is different tells me that you actually figured it out instead of having access to the answer.

[Edited by nate on 12-17-2001 at 06:52 PM]

[BamaCracker]

I still don't see the flaw in my answer, even if it is/was an answer from some other question. :D

[El Tel]

....but trying to understand the answers is giving me a headache. I'll go with Diceman - the one question approach.

[Carl Roberts]

...I like Diceman's answer, too. Surely, it is much, much faster!

[Training Guru]

You boys have WAAAAAYYYYY too much time on your hands!!

:P