A logic problem

[Andrew Green]

Stolen from elsewhere (yes, there is a answer):


You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

 

[Touch Of Death]

Stolen from elsewhere (yes, there is a answer):


You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

I know the answer only when refering to Parots. Now that they are princesses, it puts a whole new spin. LOL
Sean
PS what do you think? LOL

 

[Andrew Green]

I know it too, but don't want to give anything away quite yet

 

[MA-Caver]

Gotta be the most obvious question for ANY woman...

Are you fat?

ok, ok I was just kidding... also thought it over and realized that what if they all answer "no?"

how about... Would you mind being poor?

 

[tradrockrat]

"Are you the middle sister?"

The oldest must say no, the youngest must say yes. The middle sister can say either, but that just excludes her and the other that answered the same as her.


am I right?

Oh crap - just realized only one has to answer - -be back later... lol

 

[tradrockrat]

Ask them all a bunch of questions that are NOT yes or no answers - how about THEM apples... lmao


logic tells me that no yes or no question can ever satisfactorily tell you whom is whom if you can only ask it once to one person. sorry.

whats the answer?

 

[terryl965]

Is it ask the one that will tell you the truth and add every single one in a single question Right.

 

[Andrew Green]

No, you get one question, to one girl, and you don't know which of the girls is which.

 

[tellner]

You ask any one of them "Are you the middle daughter? No funny stuff because if I find out you're lying we're moving to a split level pig sty in Lower Slobbovia which doesn't have an extradition treaty with your daddy's kingdom."

 

[michaeledward]

You need to ask the yes or no question to one daughter but about a different daughter. This will allow you to eliminate two. I'm still struggling to get an answer (actually, I struggled for about 5 minutes yesterday, and then gave up).

Let's assume the daughters have blonde, red, and brown hair, respectively.

You ask the redhead "Is the blonde haired daughter the middle daughter?"


Think along those lines ... and you may have more success.

 

[tradrockrat]

You need to ask the yes or no question to one daughter but about a different daughter. This will allow you to eliminate two. I'm still struggling to get an answer (actually, I struggled for about 5 minutes yesterday, and then gave up).

Let's assume the daughters have blonde, red, and brown hair, respectively.

You ask the redhead "Is the blonde haired daughter the middle daughter?"


Think along those lines ... and you may have more success.

but with only one question to one daughter, you always run the risk of getting the middle daughter who can answer either way.

I still don't see it.


EDIT: OK called in favor from a friend - she says this - ask a question that excludes the princess who is answering - you WILL NOT pick the sister answering. My friend love logic riddles, but didn't have the actual answer (at least not that she'd admit).

 

[shesulsa]

crap ... not enough caffeine for this

 

[Rich Parsons]

Stolen from elsewhere (yes, there is a answer):


You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.

The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?

Given:

All three sisters look a like.

Sister 1 (S1) = S2 = S3 in looks


Truthfulness
S1 = Truth

S3 = Lies = ~Truth

S2 = Mischievous

Age
S1 > S2 > S3 in age


If you ask a sister if she is the oldest then youngest will answer Yes. Then the Oldest will answer Yes and then middle child will given different answers depending.

If you ask the question, Are you the oldest who always tells the truth?

S1 will answer Yes
S2 can answer with anything
S3 will answer Yes

If you ask the question Are you not the Oldest who tells the truth?

~ = Not

Read ~(Oldest & Truth) = ~Oldest & ~Truth = ~Oldest & Lies


S1 will answer No
S2 will answer with anything
S3 will answer No to the Oldest part and No to the Lies.

So How about Are you the youngest who tells the truth?

S1 would not be able to answer for she is not the youngest
S2 anything
S3 would be able to answer yes - but S2 coudl still answer yes so not enough




Still thinking

 

[Andrew Green]

Micheal Edwards is on the right sort of path...

 

[exile]

Awraight. First, I call on Andrew (or any of the admins) to verify that (i) I have not logged in to this thread since last night before 11 or so, enough to read the problem and notice that no correct answers were given (or attempted, in most cases ), and (ii) that I have spent no more time in this thread at this moment than was required to upload the following text.

Second, I've not encountered this variant of the problem before, but I'm familiar with some simpler versions (of which the path-in-the-woods problem is the most familiar version). The point is that a question must be designed which allows you to infallibly sort the compulsive truth-teller and the compulsive liar's examples together, as vs. the unpredictable sisters. My take on the answer---arrived at after cominng back from a hellish week of family visits, in the hope of a relaxing evening instead of several hours of preoccupied distraction involving a logic problem that my family has zero interest in (thanks very much Andrew :EG---is the following, based on the assumptionn that the sisters know which of them has which habits so far as truthful responses to yes/no questions is concerned:

Does the truth of your answer to any particular question Q coincide with the truth value of the statement `A true inference is possible here' which your sisters can infer with respect to that question?

Here are the possible outcomes:

(i) you ask the truth-teller. She always tells the truth, and her sisters know it. The truth value of her answer is always 1, and her sisters, knowing that, know that the truth value of her answer is always 1; hence her sisters can invariably infer the true answer, so that the value of `A true inference is possible here' is 1; therefore she must answer Q `yes'.

(ii) you ask the liar. She never tells the truth, and her sisters know it. The truth value of her answer A is always 0, and her sisters, knowing that, know that the truth value of A is always 0, therefore can always infer that the true answer is invariabley ~A; therefore the answer to `Is a true inference is possible here' is yes, i.e, the value of `A true inference is possible here' is 1; therefore the truth value of her answer (0 by hypothesis) and the the truth value of `A true inference is possible here' (1) do not coincide, therefore a truthful answer would be `no'. But since this sister invariably lies, her answer must be `yes'.

(iii) you ask the human one (i.e., the one who sometimes lies and sometimes tells the truth... are we allowe to editorialize here? :lol Let's assume

a. She decides to tell the truth. That means the value of her answer is 1, but since her sisters know that she is not always truthful, the value of `A true inference is possible here' is 0; therefore a truthful answer (which ex hypothesi she is giving) is `no', since the two value (1 and 0) do not coincide.

b. She decides to lie. That means that the value of her answer is 0, and since her sisters know that she is not always truthful, the value of `A true inference is possible here', is 0; therefore the value of her answer and the truth value of the statement coincide. A true answer is yes. But ex hypothesi, she's lying. Therefore she says `no' in answer to the question.

Short summary: the eternal liar and eternal truth-teller both answer yes to this question. The one you don't want to marry is the one who answers `no', since, whether she's lying or telling the truth in answer to this particular question, the anwswer she gives, `no', distinguishes her from her sisters.

Am I warm?

 

[Lisa]

Awraight. First, I call on Andrew (or any of the admins) to verify that (i) I have not logged in to this thread since last night before 11 or so, enough to read the problem and notice that no correct answers were given (or attempted, in most cases ), and (ii) that I have spent no more time in this thread at this moment than was required to upload the following text.

Second, I've not encountered this variant of the problem before, but I'm familiar with some simpler versions (of which the path-in-the-woods problem is the most familiar version). The point is that a question must be designed which allows you to infallibly sort the compulsive truth-teller and the compulsive liar's examples together, as vs. the unpredictable sisters. My take on the answer---arrived at after cominng back from a hellish week of family visits, in the hope of a relaxing evening instead of several hours of preoccupied distraction involving a logic problem that my family has zero interest in (thanks very much Andrew :EG---is the following, based on the assumptionn that the sisters know which of them has which habits so far as truthful responses to yes/no questions is concerned:

Does the truth of your answer to any particular question Q coincide with the truth value of the statement `A true inference is possible here' which your sisters can infer with respect to that question?

Here are the possible outcomes:

(i) you ask the truth-teller. She always tells the truth, and her sisters know it. The truth value of her answer is always 1, and her sisters, knowing that, know that the truth value of her answer is always 1; hence her sisters can invariably infer the true answer, so that the value of `A true inference is possible here' is 1; therefore she must answer Q `yes'.

(ii) you ask the liar. She never tells the truth, and her sisters know it. The truth value of her answer A is always 0, and her sisters, knowing that, know that the truth value of A is always 0, therefore can always infer that the true answer is invariabley ~A; therefore the answer to `Is a true inference is possible here' is yes, i.e, the value of `A true inference is possible here' is 1; therefore the truth value of her answer (0 by hypothesis) and the the truth value of `A true inference is possible here' (1) do not coincide, therefore a truthful answer would be `no'. But since this sister invariably lies, her answer must be `yes'.

(iii) you ask the human one (i.e., the one who sometimes lies and sometimes tells the truth... are we allowe to editorialize here? :lol Let's assume

a. She decides to tell the truth. That means the value of her answer is 1, but since her sisters know that she is not always truthful, the value of `A true inference is possible here' is 0; therefore a truthful answer (which ex hypothesi she is giving) is `no', since the two value (1 and 0) do not coincide.

b. She decides to lie. That means that the value of her answer is 0, and since her sisters know that she is not always truthful, the value of `A true inference is possible here', is 0; therefore the value of her answer and the truth value of the statement coincide. A true answer is yes. But ex hypothesi, she's lying. Therefore she says `no' in answer to the question.

Short summary: the eternal liar and eternal truth-teller both answer yes to this question. The one you don't want to marry is the one who answers `no', since, whether she's lying or telling the truth in answer to this particular question, the anwswer she gives, `no', distinguishes her from her sisters.

Am I warm?

Can you repeat that in English please? :lol2:

 

[exile]

Can you repeat that in English please? :lol2:

English??? You are having the want I say the logic theorem she be the English??? So yes, now I try to say what she want to say, the logic theorem...

The terms of the problem are: you get one question, only one, and it has to be of the yes/no variety. Sigh... that limits your choices a lot. And it's worse than that. If you ask a question which separates the truth teller from the liar, that doesn't help with the third sister, because her answer might be the truthful one, in which case it'll be the same as that of the truth teller. And you don't get a second question to sort those two out. If she decides to lie, her answer will be the same as that of the compulsive liar sister. And again, you don't get to sort the two out with a followup question.

The only way you can get at the true/false sister, so far as I can see, is to ask a question which, whether she's telling the truth or lying, results in a different answer than the compusive truth-telling sister and compulsive liar will give. Yes? So there are two parts to this trick (I think):

Part 1: figure out a question that both the truth-teller and the liar will give the same answer to. Now one thing about them (something the original question shoves in your face): they're at least consistent—you `know where you stand' with them. And the point is, the sisters know who tells the truth, who lies, and who does both. So the strategy is, ask the question about the sisters and what they know from each other's answers. The question has to allow us to group the two `extreme' sisters together—well, since all the sisters know what the true answer is from either the truth-teller's or the liar's answers (because they know who is who), make your one shot at the answer a question which, no matter which of the sisters you ask, will yield the same result for the liar and the truth teller.

So here's a question Q. And the truth teller will always answer Q truthfully (A = 1) and the liar will always answer Q falsely (A = 0). But in both cases, the sisters all know how to get at the truth. Take the truth-teller's answer's literally, but flip the value of the liar's answers. In one case, a literal answer is necessary, in the other, a flip is necessary. Think of my bolded question as, `can you take my answer literally?' The truth teller says, truthfully, yes you can take my answer literally. The liar says—because she's a liar—yes, you can take my answer literally. So for both of them, the answer is `yes—take my answer literally'.

Part 2: Make sure that the true/false sister has to answer differently from the other two, whether or not she's telling the truth. And here the idea is, you have to play on the fact that unlike the first two, the third sister's answers can't automatically be used as pointers to the truth, because no one knows (including her sisters) what she's doing in any given answer.

That means, if she answers the bolded question truthfully, she has to admit that no, her truthful answer cannot be taken as a literal truthful answer to the question Q, because her sisters know she might be lying, hence they cannot answer the statement `we can infer the correct answer' with a `yes'. So even though her answer is truthful, her sisters cannot make the right inference automatically; hence: is she telling the truth—yes!Can her sisters know that for sure?—no! Therefore her truthful answer tow whether the truthfulness of her answer and the truthfulness of `your sisters know what the truth is from your answer' are identical has to be `no': you cannot take my truthful answer to the particular question you're asking literally as what my sisters can say about the answer to the question.

But if she's lying when she answers, it means that the truth value of her answer (false) is the same as the truth value of the statement that her literal answer to the question is truthful—namely, uh-uh. Under no circumstances do we, or her sisters, know what she's up to, hence we can't conclude that what she says is true. So the statement that we can would be false, just as her answer to Q is false. So the two overlap, and when she's lying, she knows that the two overlap. But because she's lying, she can't answer Q truthfully, by saying yes, the two overlap. On the contrary: by assumption, since she's lying, she has to claim that the two don't overlap. In other words, she has to answer the statement contained in Q with a resounding `no'.

So the true/false sister always has to answer the bolded question with a big fat `no'. And the other two must answer it `yes'. And that's how you can tell 'em apart...

... does that help at all??

 

[Andrew Green]

So the true/false sister always has to answer the bolded question with a big fat `no'. And the other two must answer it `yes'. And that's how you can tell 'em apart...

The the middle sister will be able to answer either "yes" or "no". The other two will answer based on the fact that they always tell the truth, or always lie.

 

[Lisa]

English??? You are having the want I say the logic theorem she be the English??? So yes, now I try to say what she want to say, the logic theorem...

<snip>

... does that help at all??

No.

 

[exile]

The the middle sister will be able to answer either "yes" or "no". The other two will answer based on the fact that they always tell the truth, or always lie.

Wait a mo. The middle sister has a question Q, the bolded question I gave. A `yes' answer to that question means that the truth of her answer to any question (including the one she's answering) is the same as the truth value of the claim that her sisters can tell for sure if her answer is truthful. But her sisters can't tell for sure if her answer is truthful, 'cause she can always lie. So a `yes' answer means that the truth value of her answer (`true') is the same as the value of the claim that her sisters know what's going on (`false'). Since, on hypothesis a, she's answering truthfully, this outcome entails that her answer (the two values match) is false—which is a contradiction to the assumption on this scenario that she's answering truthfully. So she can't answer `yes' on this scenario (=hypothesis a). And on hypothesis b., when her answer to the question is false, her `yes' answer' would true—the falseness of her answer and the falseness of the claim that her sisters know what's going on match exactly. But since by hypothesis she's got to be lying this time, she can't give the true answer, which is `yes' (the two truth-values do match, this time). The lying answer is `no'. In other words, for the true/false sister, when she tells the truth, her answer to the question is `no' and when she lies, the answer to the question is also `no'. So she can't answer `yes' in either case w/o violating the assumed truth, or untruth of her answer.