[Guest]

You may have seen before, but this has some kinks.

As a prince in a far-off kingdom, you decide to travel to an adjacent kingdom to find a princess to marry. The king there has three daughters: a pathological liar who cannot possibly tell the truth, a brutally honest girl who never lies, and a whimsical girl who is known to answer just about anything to any question. The girls are all beautiful and kind and would make wonderful brides, but you are certain that you don't want to marry the whimsical girl: you couldn't ever ask her anything and get a meaningful answer. One of the other two would be OK, since even if she lied all the time, at least you would then know the truth.

The three girls line up in front of you and you may ask exactly one yes or no question to one girl to find who you will marry. Can you successfully avoid the random answerer and find a suitable bride?

[Guest]

Ask a factual question (i.e. are you a girl). One will tell the truth, one will lie, and the other will choose one of those categories. We know that the whimsical one will be in the group of two (unless she answers something other than yes/no) so you're fine if you pick the girl with the other answer.

[Guest]

Ask a factual question (i.e. are you a girl). One will tell the truth, one will lie, and the other will choose one of those categories. We know that the whimsical one will be in the group of two (unless she answers something other than yes/no) so you're fine if you pick the girl with the other answer.

Woops, I guess I should have made that clearer in the original post: You get one yes-or-no question asked to one girl only. You only will get one answer, not three.

Edited February 23, 2010 by itsclueless

[Guest]

clarification...does the whimsical girl always answer in a whimsical manner? or just some times? like...if i ask..."Are you a girl?" is she going to answer something like "blue"? if this is the case...i would randomly pick one and ask "are you whimsical" if she answers "blue" or something just as strange i know she is whimsical and i pick one of the other two...if she answers "yes" then i know she is a liar andi can pick her and know that i am marrying a liar, and if she answers "no, then i can pick her and know she is telling the truth.

[Guest]

clarification...does the whimsical girl always answer in a whimsical manner? or just some times? like...if i ask..."Are you a girl?" is she going to answer something like "blue"? if this is the case...i would randomly pick one and ask "are you whimsical" if she answers "blue" or something just as strange i know she is whimsical and i pick one of the other two...if she answers "yes" then i know she is a liar andi can pick her and know that i am marrying a liar, and if she answers "no, then i can pick her and know she is telling the truth.

The whimsical girl is whimsical, so she answers "Yes" or "No" about as much as anything else. You can't count on her answer being off-the-wall.

[Guest]

Woops, I guess I should have made that clearer in the original post: You get one yes-or-no question asked to one girl only. You only will get one answer, not three.

Oh dangs! I guess I'm stumped then.

[Guest]

Assume that

A is a pathological liar who cannot possibly tell the truth

B is a brutally honest girl who never lies, and

C is a whimsical girl who is known to answer just about anything to any question.

Let say that they sit together, left to right: X-Y-Z

So that the impossible order are:

ABC

ACB

BAC

BCA

CAB

CBA

Step 1: ask X

Do Y tell the truth more often that Z?

If X say YES, continue to step 2a, if X say NO, continue to step 2b.

Bcoz of X say YES, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this weve known that Z wouldnt be C (random). It means that if we ask anything to Z, there will be the truth answer or lie answer.

We can give an absolute question, like:

Is 1+1=2?

If the answer is YES, then Z is A (truth teller), we continue to step 3a.

But if the answer is NO, then Z must be B (liar), we continue to step 3b.

Bcoz of Z say YES, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this, weve known that Z is the truth teller, so that we can ask Z:

Is X is the pathological liar?

If Z say YES, then X is B (liar), and the conclusion is:

X liar, Y random, Z truth teller.

If Z say NO, then X is C (random), and the conclusion is:

X random, Y liar, Z truth teller.

Bcoz of Z say YES, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this, weve known that Z is the liar, so that we can ask Z:

Is X is the truth teller?

If Z say YES, then X is C (random), and the conclusion is:

X random, Y truth teller, Z liar.

If Z say NO, then X is A (truth teller), and the conclusion is:

X truth teller, Y random, Z liar.

Bcoz of X say NO, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this weve known that Y wouldnt be C (random). It means that if we ask anything to Y, there will be the truth answer or lie answer.

We can give an absolute question, like:

Is 1+1=2?

If the answer is YES, then Y is A (truth teller), we continue to step 3a.

But if the answer is NO, then Y must be B (liar), we continue to step 3b.

Bcoz of Y say YES, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this, weve known that Y is the truth teller, so that we can ask Y:

Is X is the pathological liar?

If Y say YES, then X is B (liar), and the conclusion is:

X liar, Y truth teller, Z random.

If Z say NO, then X is C (random), and the conclusion is:

X random, Y truth teller, Z liar.

Bcoz of Z say YES, so that the impossible order will be:

ABC

ACB

BAC

BCA

CAB

CBA

From this, weve known that Y is the liar, so that we can ask Y:

Is X is the truth teller?

If Y say YES, then X is C (random), and the conclusion is:

X random, Y liar, Z truth teller.

If Y say NO, then X is A (truth teller), and the conclusion is:

X truth teller, Y liar, Z random.

Edited February 23, 2010 by dby

[Guest]

You pick one girl A and point to another girl B and ask her "Will she tell me the truth?" If A is the liar and B is the truth teller, then A will answer "No". If A is the truth teller and B is the liar then A will answer "No". If A is the whimsical girl then she will answer either "Yes" or "No". In any case if you get a definite answer, you choose girl B.

The kicker comes when B is the whimsical girl. If that is the case, then A cannot know whether to lie or tell the truth and therefore cannot answer the question. If that is the case then you know B is the whimsical girl and you should choose A.

[Guest]

Woops, I guess I should have made that clearer in the original post: You get one yes-or-no question asked to one girl only. You only will get one answer, not three.

oops, i didn't read carefully, sorry...

[Guest]

You pick one girl A and point to another girl B and ask her "Will she tell me the truth?" If A is the liar and B is the truth teller, then A will answer "No". If A is the truth teller and B is the liar then A will answer "No". If A is the whimsical girl then she will answer either "Yes" or "No". In any case if you get a definite answer, you choose girl B.

The kicker comes when B is the whimsical girl. If that is the case, then A cannot know whether to lie or tell the truth and therefore cannot answer the question. If that is the case then you know B is the whimsical girl and you should choose A.

Hmmm, that's pretty clever. I guess my definition of a "yes or no question" is one that is always answerable with either "yes" or "no". There is a method that still holds when questions must have well-defined answers.

[onetruth]

Assuming you know their ages, ask "Are you the youngest/oldest/middle?"

[Guest]

Ok then how about this...

You choose one girl A and point to another girl B and ask A "If I asked you if she is the whimsical one, would you answer 'Yes'"?

Let X be the question "Is B the whimsical one?".

Let Y be the question "If I asked you X would you answer Yes?"

If B is the whimsical one (X=T)

The liar would answer X "No" and therefore Y as "Yes"

The truth teller would answer X "Yes" and therefore Y as "Yes"

The whimsical one cannot answer since she is B

If B is not the whimsical one (X=F)

The liar would answer X "Yes" and therefore Y as "No"

The truth teller would answer X "No" and therefor Y as "No"

The whimsical girl would answer both X or Y as either "Yes" or "No"

Therefore

If you ask your question and the answer is "Yes" then either B is the whimsical girl or A is the whimsical girl and you should choose girl C.

If you ask your question and the answer is "No" then B is not the whimsical girl and you should choose girl B.

[preflop]

You may have seen before, but this has some kinks.

As a prince in a far-off kingdom, you decide to travel to an adjacent kingdom to find a princess to marry. The king there has three daughters: a pathological liar who cannot possibly tell the truth, a brutally honest girl who never lies, and a whimsical girl who is known to answer just about anything to any question. The girls are all beautiful and kind and would make wonderful brides, but you are certain that you don't want to marry the whimsical girl: you couldn't ever ask her anything and get a meaningful answer. One of the other two would be OK, since even if she lied all the time, at least you would then know the truth.

The three girls line up in front of you and you may ask exactly one yes or no question to one girl to find who you will marry. Can you successfully avoid the random answerer and find a suitable bride?

I believe this has been posted before (it just used a different background story), anyway

You say to the princess on the left : "If I were to ask you whether or not the princess in the middle is the whimsical girl, what would your response be?"

If she says Yes, you marry the princess on the right.

If she says No, you marry the princess in the middle.

the reasoning is:

If you are talking to either the truth teller or the liar, they will both tell you Yes if the middle girl is whimsical. and No if she is not.

If you are talking to the whimsical girl, it doesn't matter what she answers since you are not going to choose the girl you are talking to.

[Guest]

You line the three princesses up in a row and ask to the one on the left "If the mischeveous one is not you is the middle person the liar and if you are the mischevous one, is the truth teller to my right".

If the answer is yes you pick the one in the middle. If the answer is no you pick the one on the right. You discard the one on left always.

[Guest]

I like Justgus's and preflop's answers. Mbego, yours may work but you don't need the complicated nesting ifs.

For reference, here is an alternate solution that I have:

Name the girls A, B and C and ask A, "Is B more likely to tell the truth than C?"

If A answers yes: Either the truth teller knows that B is random and more likely to tell the truth, or the liar knows that C is the truth teller and is lying. If A is random it doesn't matter. C is a safe choice in all cases.

If A answers no: Either the truth teller knows that B is the liar and never tells the truth, or the liar knows that B is the truth teller and is lying. If A is random it doesn't matter. B is a safe choice in all cases.

[Guest]

You may have seen before, but this has some kinks.

As a prince in a far-off kingdom, you decide to travel to an adjacent kingdom to find a princess to marry. The king there has three daughters: a pathological liar who cannot possibly tell the truth, a brutally honest girl who never lies, and a whimsical girl who is known to answer just about anything to any question. The girls are all beautiful and kind and would make wonderful brides, but you are certain that you don't want to marry the whimsical girl: you couldn't ever ask her anything and get a meaningful answer. One of the other two would be OK, since even if she lied all the time, at least you would then know the truth.

The three girls line up in front of you and you may ask exactly one yes or no question to one girl to find who you will marry. Can you successfully avoid the random answerer and find a suitable bride?

Ask a Question that you know the truth to. The one girl who's answer is different from the rest is definitely not the Whimsical Girl.

If the one girl who's answer is different because she is telling the truth, she is the truth girl.

If the one girl who's answer is different because she is telling a lie, she is the liar girl.

Why is everyone making this so complicated?

Here is the reasoning: The truth girl will always tell the truth. The Liar will always tell a Lie. So, the Whimsical girl will either side with the truth girl or the lying girl. Therefore, if she sides with the Truth girl, the liar girl is the only answer that is different from the rest, so you know to pick her and that she is the lying girl. If the Whimsical girl sides with the liar, then the truth girl will be the only one with a different answer, and so you know to pick her and that she is the truth girl.

Edited February 24, 2010 by Shoyru95

[Guest]

Ask a Question that you know the truth to. The one girl who's answer is different from the rest is definitely not the Whimsical Girl.

If the one girl who's answer is different because she is telling the truth, she is the truth girl.

If the one girl who's answer is different because she is telling a lie, she is the liar girl.

Why is everyone making this so complicated?

Here is the reasoning: The truth girl will always tell the truth. The Liar will always tell a Lie. So, the Whimsical girl will either side with the truth girl or the lying girl. Therefore, if she sides with the Truth girl, the liar girl is the only answer that is different from the rest, so you know to pick her and that she is the lying girl. If the Whimsical girl sides with the liar, then the truth girl will be the only one with a different answer, and so you know to pick her and that she is the truth girl.

Read the string of replys. I already made that mistake. Only one question to only one girl.

[Guest]

My answer increases the odds of avoiding the whimsical girl, but does not entirely ensure the right choice. (Also I cannot get the "Spoiler" button to work.)

Ask a girl, "How many of your sisters are willing to lie?".

The truthful girl will say "2", pick her.

The liar will NOT say 1, but may say 2 or none. Pick her.

The whimsical may say 1, if she's truthful. Otherwise she may say 2, if she's lying.

So pick the girl who doesn't say "1".

Again, it doesn't help you absolutely avoid the whimsical girl when she's lying.

[Guest]

My answer increases the odds of avoiding the whimsical girl, but does not entirely ensure the right choice. (Also I cannot get the "Spoiler" button to work.)

Ask a girl, "How many of your sisters are willing to lie?".

The truthful girl will say "2", pick her.

The liar will NOT say 1, but may say 2 or none. Pick her.

The whimsical may say 1, if she's truthful. Otherwise she may say 2, if she's lying.

So pick the girl who doesn't say "1".

Again, it doesn't help you absolutely avoid the whimsical girl when she's lying.

You're getting there, but you can only ask a question for which the answer is "Yes" or "No"

[Guest]

You're getting there, but you can only ask a question for which the answer is "Yes" or "No"

Well, I could ask, "Do you have an even number of sisters who lie at least some of the time?".

Truthful sister says "Yes".

Liar says "Yes"

Whimsical may say "Yes" or "No".

I still don't see a definitive way to rule out the whimsical one.

[Guest]

@JLT type [ spoiler=Your spoiler title here ] Your spoiler text here [ /spoiler ] remove the spaces immediatly interior to the brackets.

I would definately want to marry the liar, because then no means yes and yes...well she said yes.

[Guest]

I believe this has been posted before (it just used a different background story), anyway

You say to the princess on the left : "If I were to ask you whether or not the princess in the middle is the whimsical girl, what would your response be?"

If she says Yes, you marry the princess on the right.

If she says No, you marry the princess in the middle.

the reasoning is:

If you are talking to either the truth teller or the liar, they will both tell you Yes if the middle girl is whimsical. and No if she is not.

If you are talking to the whimsical girl, it doesn't matter what she answers since you are not going to choose the girl you are talking to.

I dint get this one. Can you please explain. Why would the liar say 'Yes' if the middle girl is whimsical? She would lie instead right? so how would we make out again which is the whimsical one if the first girl (the one you ask the question to) is not the whimsical one.

[Guest]

Ask any one girl the question "Is sky blue?"

The truth telling girl will say "yes"

Lair will tell "No"

and Whimsical girl may say "Yes" or "No"

So if one girl says "Yes" and other two "No" then marry her... She is the truth telling girl.

If one girl says "No" and other two says "Yes" then marry her ...but always remember that she is a lair.

You may have seen before, but this has some kinks.

As a prince in a far-off kingdom, you decide to travel to an adjacent kingdom to find a princess to marry. The king there has three daughters: a pathological liar who cannot possibly tell the truth, a brutally honest girl who never lies, and a whimsical girl who is known to answer just about anything to any question. The girls are all beautiful and kind and would make wonderful brides, but you are certain that you don't want to marry the whimsical girl: you couldn't ever ask her anything and get a meaningful answer. One of the other two would be OK, since even if she lied all the time, at least you would then know the truth.

The three girls line up in front of you and you may ask exactly one yes or no question to one girl to find who you will marry. Can you successfully avoid the random answerer and find a suitable bride?

[preflop]

You say to the princess on the left : "If I were to ask you whether or not the princess in the middle is the whimsical girl, what would your response be?"

If she says Yes, you marry the princess on the right.

If she says No, you marry the princess in the middle.

the reasoning is:

If you are talking to either the truth teller or the liar, they will both tell you Yes if the middle girl is whimsical. and No if she is not.

If you are talking to the whimsical girl, it doesn't matter what she answers since you are not going to choose the girl you are talking to.

I dint get this one. Can you please explain. Why would the liar say 'Yes' if the middle girl is whimsical? She would lie instead right? so how would we make out again which is the whimsical one if the first girl (the one you ask the question to) is not the whimsical one.

Hi sharkie,

Welcome to the board. The reason why the liar will answer "truthfully" in this case is because of the way the question is worded. It is a trick used in these kinds of riddles. The question I posed was "If I were to ask you ..." this causes kind of a double negative situation.

Lets say that the middle girl is the whimsical one and I am talking to the liar. If I were to ask the liar "is the middle girl whimsical" the liar would say no.

but if I were to ask the liar how she would respond to that same question: "If I were to ask you whether or not the princess in the middle is the whimsical girl, what would your response be?" I am not directly asking about the middle girl any more I am asking how the liar would answer a direct question. Directly the liar would say no, but now she must lie about that answer so she must say yes.

I hope this helps.

[Guest]

For me, there’s something less than satisfying with that answer. Ambiguity of English language, I suppose. If I ask a liar the question you pose, I can see them saying NO, whether you phrase it as “Is the girl in the middle whimsical” or “If I were to ask you, is the girl in the middle whimsical, what would your answer be?” An aside, you used the words “whether or not” which I think would require a “she is” or “she is not” type of answer to be grammatically correct, not yes or no, but I'm no english professor. I understand the double negative logic that you are trying to accomplish, though. You are attempting to get them to comment on their answer, not answer.

Actually, I know the answer to this puzzle, because it is nearly the same as another age-old problem. This all works from the same principle of eliminating the wishy-washy answerer. In the classic, old puzzle, you are standing at a fork in the road. One road leads to heaven and the other to hell. You don’t know which is which. You have the same three personalities in front of you, liar, truth-teller, and wishy-washy. You want to get to heaven but have only TWO (yes only 2) yes/no questions to ask. This puzzle may already be posted here, but I’m new to the board, so apologize if so. I just signed up today.

Anyway, how about this for a conceptually easier solution to the princess question. It's a legitimate yes/no question and it works no matter which girl you ask. The goal is simply to eliminate the whimsy, and this does.

Solution----------------------------------------------

Rules:

1) We do not marry the first one we ask.

2) We ask any girl which of the others is more-likely to tell the truth (posed as a yes or no, depending on if we are asking left, middle, or right – SEE EXAMPLE BELOW)

3) We marry the APPARENT liar, based on the answer to the above question.

Proof. -------------------------------------------------

For the sake of discussion, let’s say the whimsy is in the middle, liar on left (L’s easier to remember) and righteous truth teller on right, but we don’t know that when we ask the question of course. (L W T) Lets look at each case where we ask each personality under these conditions:

WHIMSY: Assuming that you will not marry the first one you ask, if the first one you ask happens to be the whimsy in the middle, then the question doesn’t matter. You will marry either other one and you are safe.

What about the other two cases? We must address the case where the whimsy is not the first one you ask. This is where it gets interesting.

TRUTH/Right: Using the question above, lets say you ask the girl on the right "Is the girl in the middle “more likely” to tell the truth than the girl on the left?" Her answer will be YES. Now, going with the apparent liar would mean marry the girl on the left. –safe-

LIAR/Left: Ask her the same question, "Is the girl in the middle is more likely to tell the truth than the girl on the right?" It’s not true, but the liar will say YES. You will marry the apparently “less trustworthy” girl on the right.

There are six (3!=6) different ways the girls can line up, but this works with any combination of girl order.

Edited February 26, 2010 by Drummer_Geek

[Guest]

itsclueless said that here