## Three princesses

A forum for good logic/math puzzles.

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eddiesimeon
Posts: 1
Joined: Tue Jun 10, 2008 9:56 am UTC

### Re: Three princesses

hmm or should i just pick the pretty one????
Spoiler:
Ask each princess, Are you a princess?
You will get the following answers:
Yes, Yes, No = pick the girl who said no... she is either always lying
No, No, Yes = pick the girl who said yes... she is either always telling the truth

When two girls say No then obviously one of them are lying sometimes but you don't know which one.
When two girls say Yes then obviously one of them are telling the truth sometimes but you don't know which one.
When one girl says Yes then she is the truth telling princess.
When one girl says No then she is the lying princess.

jestingrabbit
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### Re: Three princesses

eddiesimeon wrote:hmm or should i just pick the pretty one????
Spoiler:
Ask each princess, Are you a princess?
You will get the following answers:
Yes, Yes, No = pick the girl who said no... she is either always lying
No, No, Yes = pick the girl who said yes... she is either always telling the truth

When two girls say No then obviously one of them are lying sometimes but you don't know which one.
When two girls say Yes then obviously one of them are telling the truth sometimes but you don't know which one.
When one girl says Yes then she is the truth telling princess.
When one girl says No then she is the lying princess.

which is one question asked three times. You can do it with one question asked once.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Kaneda
Posts: 42
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### Re: Three princesses

OK, I can't be bothered to read through all 6 pages to see what the consensus on what happens if the answer is indeterminate so here is my answer before I look at the other spoilers

Spoiler:
If I ask your sister if your other sister would say that you are the middle sister, what would she say?
If you are asking the middle sister, she can give a yes or no. Either of the others would have to answer that she doesn't know.

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Three princesses

Kaneda wrote:OK, I can't be bothered to read through all 6 pages to see what the consensus on what happens if the answer is indeterminate so here is my answer before I look at the other spoilers

Spoiler:
If I ask your sister if your other sister would say that you are the middle sister, what would she say?
If you are asking the middle sister, she can give a yes or no. Either of the others would have to answer that she doesn't know.

You don't need to use a question that can't be answered by some of the sisters. There is a very simple, straightforward question that allows you to make the determination.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

3fj
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### Re: Three princesses

Just for myself, so i can go back and check if anyone got a different answer.
Spoiler:
You ask "Are you the middle sister?"
The eldest will answer "No" all the time
The youngest will answer "Yes" all the time
The middle will answer "Yes" some of the time and "No" the rest of the time
You then choose the sister who's answer is unique, as you only want the one you "know where your with" (which you'll know cause she'll of either said yes or no)
Everything's dead until it's alive. Man will exist, and then he will die. Just take the ride!

AvalonXQ
Posts: 747
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### Re: Three princesses

3fj wrote:Just for myself, so i can go back and check if anyone got a different answer.
Spoiler:
You ask "Are you the middle sister?"
The eldest will answer "No" all the time
The youngest will answer "Yes" all the time
The middle will answer "Yes" some of the time and "No" the rest of the time
You then choose the sister who's answer is unique, as you only want the one you "know where your with" (which you'll know cause she'll of either said yes or no)

Spoiler:
That's asking one question to EACH of the sisters. The original problem only allows you to ask a question to ONE of them.

TimM1104
Posts: 5
Joined: Tue Jun 03, 2008 7:15 pm UTC

### Re: Three princesses

Two answers were posted on page 5... Now I still am curious about the version which you can only as one one sister, one question, while she is right in front of you.(while the other two are in a different room), and afterwords are forced to decide to marry her or to have one of the other two sisters randomly chosen as my bride. -_- that one is much more tricky(if the first one wasn't tricky enough in the first place)

Buttons
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Location: Somerville

### Re: Three princesses

TimM1104 wrote:Two answers were posted on page 5... Now I still am curious about the version which you can only as one one sister, one question, while she is right in front of you.(while the other two are in a different room), and afterwords are forced to decide to marry her or to have one of the other two sisters randomly chosen as my bride. -_- that one is much more tricky(if the first one wasn't tricky enough in the first place)

That one's doable, but a lot less elegantly. You want a question where the middle sister gives one answer, and the other sisters give a different one. But in order for the middle sister to consistently give the same answer to a question, it has to be self-referential so you can "cancel out" the lying. One possibility is
Spoiler:
If I asked you whether you were the middle sister, and you answered with the same truthfulness as you are right now, would you say "yes"?

TimM1104
Posts: 5
Joined: Tue Jun 03, 2008 7:15 pm UTC

### Re: Three princesses

Buttons wrote:
TimM1104 wrote:Two answers were posted on page 5... Now I still am curious about the version which you can only as one one sister, one question, while she is right in front of you.(while the other two are in a different room), and afterwords are forced to decide to marry her or to have one of the other two sisters randomly chosen as my bride. -_- that one is much more tricky(if the first one wasn't tricky enough in the first place)

That one's doable, but a lot less elegantly. You want a question where the middle sister gives one answer, and the other sisters give a different one. But in order for the middle sister to consistently give the same answer to a question, it has to be self-referential so you can "cancel out" the lying. One possibility is
Spoiler:
If I asked you whether you were the middle sister, and you answered with the same truthfulness as you are right now, would you say "yes"?

But...
Spoiler:
if you ask thtat to the youngest, she would say yes she is, and the truthful person would say no. So if they aren't agreeing on something it makes it impossible

But I do think you are going down te right track. Different question, but correct track. ^^

greeniguana00
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Location: Albany, NY, USA

### Re: Three princesses

Spoiler:
There should be some way to name them by location, so we will assume they are on the corners of a triangle. You will ask the person on the corner which is pointing towards you, and based on their response, choose the girl to the left or right (from your perspective). We'll set a supposed order of Honest-Neither-Liar-Honest-Neither-Liar-etc. when looking from above and going clockwise and define this to be clockwise (or course it won't necesarily start in that order, but given a particular orientation, we can now say that that orientation is counterclockwise or clockwise). Counterclockwise would be Honest-Liar-Neither-etc.

Yes = go with person on left
No = go with person on right
Y/N = Doesn't matter which

|Honest | Liar | Neither |
_______________________________________________
Couterclockwise | Yes | No | Y/N |
--------------------|-------|--------|---------|
Clockwise | No | Yes | Y/N |
------------------------------------------------

So, with this we just need to formulate a question that will be answered in a way according to this table. If we are asking the person who sometimes lies and sometimes tells the truth, it doesn't matter at all what they answer because we know we will never be choosing the one we ask, so we only need be concerned with how the liar and truth-teller answer our queston. Looking at the table, the liar always must answer the question in the opposite way as the honest person, and it's not too difficult to think of question like that. A very complicated to ask question (which would work) would be, "Starting on the person who is lying, and going around in a cirlce in this direction (make gesture), is the order 'Liar-Neither-Honest'?"

It's not pretty, but it works. With more thought, one could come up with a question that works and is simpler.

Now of course they may not be in a circle like that, but you can define things in the question such that it doesn't matter that they aren't actually.

Ha, I just thought of a pseudo-answer:

Spoiler:
Ask, "How would the middle sister answer if I asked her if she were the middle sister?"

If the person does not answer, choose that person. If the girl says "yes" or "no", she is the middle sister and choose one of the other two. This hinges on the fact that with the sister who always tells the truth, she would have no way of knowing whether she is speaking the truth or not either way, so she couldn't answer or risk violating that fundamental rule. The same is true with the sister that always lies because she would know if she was saying the truth or not. Only the middle sister would how she would respond. Of course, if we are being picky, the middle sister could also decide not to respond, or not know yet how she would respond and trick you into picking her, but that's why I call this a pseudo-answer.

Clarification of the original solution:

Spoiler:
Let's say you walk into the room and you see the three girls. There must be some way to differentiate between the three, whether they are standing in different spots or in a different way or wearing different color dresses. We'll assume they are wearing different color dresses, but you could switch that out for anything and it would still work. So, lets say the girls are wearing red, blue, and green dresses. You walk up to the one in the green, and here's the question you ask:

"Are any of the following true: (#1) the girl in the blue dress is the girl who always tells the truth and the girl in the red dress is the girl who never tells the truth OR (#2) the girl in the blue dress is the girl who never tells the truth and the girl in the red dress is the girl who sometimes tells the truth OR (#3) the girl in the blue dress is the girl who sometimes tells the truth and the girl in the red dress is the girl who always tells the truth?

If you get the answer of YES, here are the possibilities:
A) You were asking the girl who always tells the truth, so statement #2 is true, so pick the girl in the blue dress (who never tells the truth).
B) You were asking the girl who never tells the truth, so statement #3 is false, so pick the girl in the blue dress (who always tells the truth).
C) You were asking the girl who sometimes tells the truth, so you really don't know which statements were true/false, but you pick the girl in the blue dress who must be either the girl who always tells the truth or the girl who never tells the truth (which is what you want).

If you get the answer of NO, here are the possibilities:
D) You were asking the girl who always tells the truth, so statement #2 is false, so pick the girl in the red dress (who never tells the truth).
E) You were asking the girl who never tells the truth, so statement #3 is true, so pick the girl in the red dress (who always tells the truth).
F) You were asking the girl who sometimes tells the truth, so you really don't know which statements were true/false, but you pick the girl in the red dress who must be either the girl who always tells the truth or the girl who never tells the truth (which is what you want).

So, as you can see, if the answer is yes, you pick the girl in the blue dress, and if it's no, you pick the girl in the red dress.

Ask me if this needs further clarification.
Goodnight, g♥♥dnight! There's something magnificent about good night with two disemboweled hearts in it, or at least it seems that way when you're so happy.

jestingrabbit
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### Re: Three princesses

greeniguana00 wrote:
Spoiler:
Are any of the following true: (#1) the girl in the blue dress is the girl who always tells the truth and the girl in the red dress is the girl who never tells the truth OR (#2) the girl in the blue dress is the girl who never tells the truth and the girl in the red dress is the girl who sometimes tells the truth OR (#3) the girl in the blue dress is the girl who sometimes tells the truth and the girl in the red dress is the girl who always tells the truth?

Which can be simplified to

Spoiler:
is the person wearing the blue dress older than the person wearing the red dress?

which is, you know, simple.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Buttons
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Location: Somerville

### Re: Three princesses

TimM1104 wrote:But...
Spoiler:
if you ask thtat to the youngest, she would say yes she is, and the truthful person would say no. So if they aren't agreeing on something it makes it impossible

No, both the youngest and oldest would answer "no," and the middle would answer "yes."

greeniguana00
Posts: 113
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Location: Albany, NY, USA

### Re: Three princesses

jestingrabbit wrote:
greeniguana00 wrote:
Spoiler:
Are any of the following true: (#1) the girl in the blue dress is the girl who always tells the truth and the girl in the red dress is the girl who never tells the truth OR (#2) the girl in the blue dress is the girl who never tells the truth and the girl in the red dress is the girl who sometimes tells the truth OR (#3) the girl in the blue dress is the girl who sometimes tells the truth and the girl in the red dress is the girl who always tells the truth?

Which can be simplified to

Spoiler:
is the person wearing the blue dress older than the person wearing the red dress?

which is, you know, simple.

Ha, yes, that is somewhat simpler to ask.
Goodnight, g♥♥dnight! There's something magnificent about good night with two disemboweled hearts in it, or at least it seems that way when you're so happy.

TimM1104
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### Re: Three princesses

Buttons wrote:
TimM1104 wrote:But...
Spoiler:
if you ask thtat to the youngest, she would say yes she is, and the truthful person would say no. So if they aren't agreeing on something it makes it impossible

No, both the youngest and oldest would answer "no," and the middle would answer "yes."

Why would the middle say yes? AAAAAAAhhhhhhhhhhhhhhhhhhhhh Lying about lying is telling the truth. Amazing Button's!!!
very sneaky, very good!.

Vieto
Posts: 1558
Joined: Sun Jun 22, 2008 10:44 pm UTC

### Re: Three princesses

Considering that the youngest lies, the oldest doesn't, and the middle varies, I would say that they would grow to become truthful.Eventually, over time, they will all become truthful.

Age-Truth

*** |**********/
*** |********/
t * |* ****/
r **|*****/
u **|** /
t **|**/
h *|*/
***|/__________
**********age

NIdoprince
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### Re: Three princesses

I have not read the entire thread so the solution may have already been found, but I believe this is the solution.
Spoiler:
You select a sister at random, walk up to them and point to one of there two sisters. Then you ask this question: If I wanted to marry either the truthful sister or the deceitful sister and I asked you if this was the sister I should marry than would you say yes?
If it is the truthful sister that I am asking than she will say yes if it is the deceitful sister and she will say no if it is the middle-ground sister. If it is the deceitful sister than she will answer the same way due to the phrasing of the question. Now if the sister says yes than I will marry the person I pointed at and if she says no than I will marry the third sister. The beauty is that if it is either the truthful sister of the deceitful sister than I will get accurate information and marry the right girl. If however I am talking to the middle-ground sister it does not matter because I won't be marrying the person I talk to in any event and it doesn't matter what she says. Thus I believe the answer is solved. If there is some problem in my logic please inform me.

jestingrabbit
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### Re: Three princesses

NIdoprince wrote:I have not read the entire thread so the solution may have already been found, but I believe this is the solution.
Spoiler:
You select a sister at random, walk up to them and point to one of there two sisters. Then you ask this question: If I wanted to marry either the truthful sister or the deceitful sister and I asked you if this was the sister I should marry than would you say yes?
If it is the truthful sister that I am asking than she will say yes if it is the deceitful sister and she will say no if it is the middle-ground sister. If it is the deceitful sister than she will answer the same way due to the phrasing of the question. Now if the sister says yes than I will marry the person I pointed at and if she says no than I will marry the third sister. The beauty is that if it is either the truthful sister of the deceitful sister than I will get accurate information and marry the right girl. If however I am talking to the middle-ground sister it does not matter because I won't be marrying the person I talk to in any event and it doesn't matter what she says. Thus I believe the answer is solved. If there is some problem in my logic please inform me.

Whilst that works, its not optimal. There is a non-tricky way.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

NIdoprince
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### Re: Three princesses

Spoiler:
I looked above and noticed the much more simple solution that is indeed significantly more optimal. However mine has one advantage that the much more elegant solution lacks. Mine would work if you did not know the whole age thing. Thus the other one is the best for the question asked, but if some data was removed than mine could still find the solution, but the more elegant one would be left in the dust. I think that the real trick is that you never marry the person you are talking to.

TimM1104
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### Re: Three princesses

NIdoprince wrote:
Spoiler:
I looked above and noticed the much more simple solution that is indeed significantly more optimal. However mine has one advantage that the much more elegant solution lacks. Mine would work if you did not know the whole age thing. Thus the other one is the best for the question asked, but if some data was removed than mine could still find the solution, but the more elegant one would be left in the dust. I think that the real trick is that you never marry the person you are talking to.

Ah, your's may work when the others work cause you phrase it such a way that you don't use age, but couldn't you change any answer and instead of "older" and "younger" to "more truthful" and "less truthful", which would make any of them work if you take out the age.

There is a better answer than just those, one that would work if you did not get to decide which one you marry. One that you get to say yes or no about marrying the girl you are talking to, and if you say no, you are given a random bride from the other two. And the other sisters are not in the room. And the question you ask would be:

Spoiler:
If I asked you whether you were the middle sister, and you answered with the same truthfulness as you are right now, would you say "yes"?

It is a quote because i didn't come up with it, someone did on this very page.

And instead of middle sister you could go "The sometimes truthful sometimes un-honest sister" and you don't need age just like your answer.

NIdoprince
Posts: 4
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### Re: Three princesses

I stand corrected. I was thinking about this problem again and I realized that age wasn't really the important issue but simply a way to phrase the question easier. As for the third solution that you described it does indeed seem to be even more stable than the other two. That one would not work if the middle sister just picked a random answer though.

AvalonXQ
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### Re: Three princesses

TimM1104 wrote:
NIdoprince wrote:
Spoiler:
I looked above and noticed the much more simple solution that is indeed significantly more optimal. However mine has one advantage that the much more elegant solution lacks. Mine would work if you did not know the whole age thing. Thus the other one is the best for the question asked, but if some data was removed than mine could still find the solution, but the more elegant one would be left in the dust. I think that the real trick is that you never marry the person you are talking to.

Ah, your's may work when the others work cause you phrase it such a way that you don't use age, but couldn't you change any answer and instead of "older" and "younger" to "more truthful" and "less truthful", which would make any of them work if you take out the age.

There is a better answer than just those, one that would work if you did not get to decide which one you marry. One that you get to say yes or no about marrying the girl you are talking to, and if you say no, you are given a random bride from the other two. And the other sisters are not in the room. And the question you ask would be:

Spoiler:
If I asked you whether you were the middle sister, and you answered with the same truthfulness as you are right now, would you say "yes"?

It is a quote because i didn't come up with it, someone did on this very page.

And instead of middle sister you could go "The sometimes truthful sometimes un-honest sister" and you don't need age just like your answer.

All solutions like that one are based on the false assumption that the middle sister chooses a truth disposition before answering your question. The questions become much more difficult/interesting if the middle sister just answers "yes" or "no" by whim.

Buttons
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Location: Somerville

### Re: Three princesses

AvalonXQ wrote:All solutions like that one are based on the false assumption that the middle sister chooses a truth disposition before answering your question. The questions become much more difficult/interesting if the middle sister just answers "yes" or "no" by whim.
I'm not sure why you think that assumption is false. It certainly seems to be the more reasonable way of interpreting the rules of the game:
The OP wrote:The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

thc
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### Re: Three princesses

Buttons wrote:
AvalonXQ wrote:All solutions like that one are based on the false assumption that the middle sister chooses a truth disposition before answering your question. The questions become much more difficult/interesting if the middle sister just answers "yes" or "no" by whim.
I'm not sure why you think that assumption is false. It certainly seems to be the more reasonable way of interpreting the rules of the game:
The OP wrote:The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.

Even using your own interpretation, you are still at a loss, since you are assuming the middle sister doesn't switch in the process of answering your question.

Buttons
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Location: Somerville

### Re: Three princesses

thc wrote:Even using your own interpretation, you are still at a loss, since you are assuming the middle sister doesn't switch in the process of answering your question.

That's a fair criticism. I guess I'm thinking of the question-answering process as being an instantaneous thing (even though clearly the asking or reading of the question takes some nonzero amount of time). Otherwise, you'd have weird behavior where you get answers like "N-yes."

But yeah, it's definitely a nontrivial assumption. I think that's why the elegant solution from page 2 is comparatively so appealing.

codyhotel
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### Re: Three princesses

I would ask "DID YOU SEE THAT!!!!" then point behind the king and his daughters, then while they turned around I would hit them all with a blunt object and render them unconscious, then check their wallets for ID to determine which is the eldest, then drag her off, give her some smelling salts to regain consciousness, then marry her.

It would work, and I only asked my 1 yes or no question, therefore I win.
Philwelch wrote:Would a prostitution enthusiast be a buy-sexual?

...sorry.

AvalonXQ
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### Re: Three princesses

codyhotel wrote:I would ask "DID YOU SEE THAT!!!!" then point behind the king and his daughters, then while they turned around I would hit them all with a blunt object and render them unconscious, then check their wallets for ID to determine which is the eldest, then drag her off, give her some smelling salts to regain consciousness, then marry her.

It would work, and I only asked my 1 yes or no question, therefore I win.

Unfortunately, you asked that question to all three sisters, as well as the king. Sorry; you only get to ask the question to ONE princess.

Luppoewagan
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### Re: Three princesses

You could ask just one, and get the ID off of her.

codyhotel
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### Re: Three princesses

AvalonXQ wrote:
codyhotel wrote:I would ask "DID YOU SEE THAT!!!!" then point behind the king and his daughters, then while they turned around I would hit them all with a blunt object and render them unconscious, then check their wallets for ID to determine which is the eldest, then drag her off, give her some smelling salts to regain consciousness, then marry her.

It would work, and I only asked my 1 yes or no question, therefore I win.

Unfortunately, you asked that question to all three sisters, as well as the king. Sorry; you only get to ask the question to ONE princess.

I would direct the question at only one of the sisters, but human nature constitutes a reaction from all of them if i act well enough, which i most certainly would
Philwelch wrote:Would a prostitution enthusiast be a buy-sexual?

...sorry.

Ghona
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### Re: Three princesses

The optimal solution is simple.

Ask the prettiest sister "if I said you had a nice body, would you hold it against me?"

win/win.
If you're taking me too seriously, you probably are making a mistake.

codyhotel
Posts: 319
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### Re: Three princesses

Ghona wrote:The optimal solution is simple.

Ask the prettiest sister "if I said you had a nice body, would you hold it against me?"

win/win.

this guy wins.

but seriously, i think i have it.

Spoiler:
i am assuming that if they don't answer, i just get to ask a different sister, so i would ask the sister " do either of your sisters always tell the truth?" the truthful one will say no, the lying one will be unable to respond (if she says yes, she wouldn't be lying about the truthful sister, if she says no, she wouldn't be lying about the middle sister), and the middle sister would either be unable to respond also if she was to lie, and if she was to tell the truth she would say yes

so, if the answer i receive is no, i marry that sister, if it is yes, i marry either of the other sisters, if i get no response, i assume i get to ask another girl until i do get one, then marry appropriately according to the response i ultimately receive

it took longer to explain then i thought it was going to, but really its very simple.
Philwelch wrote:Would a prostitution enthusiast be a buy-sexual?

...sorry.

Buttons
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### Re: Three princesses

codyhotel wrote:
Spoiler:
i am assuming that if they don't answer, i just get to ask a different sister, so i would ask the sister " do either of your sisters always tell the truth?" the truthful one will say no, the lying one will be unable to respond (if she says yes, she wouldn't be lying about the truthful sister, if she says no, she wouldn't be lying about the middle sister), and the middle sister would either be unable to respond also if she was to lie, and if she was to tell the truth she would say yes

so, if the answer i receive is no, i marry that sister, if it is yes, i marry either of the other sisters, if i get no response, i assume i get to ask another girl until i do get one, then marry appropriately according to the response i ultimately receive
Spoiler:
Huh? If you have to lie about something, and the actual answer is "yes," then you just say "no." You certainly wouldn't be left unable to respond.

Furthermore, I'm not sure you're appropriately dealing with the word "either." If I had you two marbles, one red and one blue, and I ask if either marble is red, the answer is clearly yes. It's not "lying about the blue marble" to say that one of them is red. So in reality, the oldest and youngest would both say "no," and the middle would say either "no" or "yes." This doesn't always distinguish the middle from the other two, so it doesn't work.

DanielLC
Posts: 17
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### Re: Three princesses

I figured out the main answer when I last saw this thread (and the rest since), but didn't bother posting it. It looks like you still haven't answered it (I'm not sure, I didn't bother to read more than the last page), so here's the main part:
Spoiler:
You just have to avoid the middle sister. She's the only one that wont give you any useful information, so just don't pick the person you ask. Ask a question to figure out which of the others to marry.

Spoiler:
Let's call the sisters Alice, Beatrice, and Chloe. Ask Alice, "If I asked you if Beatrice was the middle sister, would you say yes?" If she says yes, marry Chloe. Otherwise, marry Beatrice.

You could also just wait until they start talking, and see if you can tell who is who, or you could just ask someone else.

StevenJ
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### Re: Three princesses

DanielLC wrote:I figured out the main answer when I last saw this thread (and the rest since), but didn't bother posting it. It looks like you still haven't answered it (I'm not sure, I didn't bother to read more than the last page), so here's the main part:
Spoiler:
You just have to avoid the middle sister. She's the only one that wont give you any useful information, so just don't pick the person you ask. Ask a question to figure out which of the others to marry.

Spoiler:
Let's call the sisters Alice, Beatrice, and Chloe. Ask Alice, "If I asked you if Beatrice was the middle sister, would you say yes?" If she says yes, marry Chloe. Otherwise, marry Beatrice.

You could also just wait until they start talking, and see if you can tell who is who, or you could just ask someone else.

Daniel's solution works, but I have a simpler answer. The hint given in Daniel's first spoiler applies to my solution as well, but I avoid asking a question about a question.

Spoiler:
Call the sisters Alice, Beatrice, and Chloe. Ask Alice, "Is Beatrice younger than Chloe?" If she says yes, marry Beatrice. Otherwise, marry Chloe.

NThisStyle-10-6
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### Re: Three princesses

I might be crazy, but this seems a variant of the Labyrinth puzzle. (David Bowie in tights, that's all one needs in life). Also, see: http://www.xkcd.com/246/

I believe that a different variant of it was stated before by someone whose name I've forgotten. However, I think that, as a variant of this puzzle, the answer will be a variant of the answer to this puzzle.

The trick is to find an question where each answer yeilds the same result. For example, in the labyrinth puzzle, Sara asks the guard, "Which door would the other guard tell me to use," leaving her able to see, then, that whichever door the guard she asked said would be the road to certain doom. (I find this easiest explained by saying that, if she asks the liar, he says that the one who would tell the truth would tell her to go through the door that leads to certain doom, because he himself lies. If she asks the one that tells the truth, he says that the one that lies would tell her to go through the door that leads to certain doom because he - the door that lies - lies. The third one just stabs people who ask tricky questions.)

Regardless, I feel like the answer to this is along that vein.

Some notes:

As a charming and handsome, gallant, knightly prince, shooting or stabbing each princess for any length of time is completely out of the question.

I don't feel like there would have been a puzzle posted without a possible solution. Perhaps the original poster is just mean/doesn't know the answer himself, but I doubt it.

So, I think that if you ask any sister,
Spoiler:
"which sister would she (point to another sister) tell me is the oldest," you'll get an acceptable answer. If you ask A (oldest) which sister B(middle) would say is the oldest, she'll tell you honestly that B would tell you either herself(A) or C (youngest). If you ask B which one A would say, she'll tell you either honestly "A" or, dishonestly "B or C," If you as C which one A would say, she'll say either B or C (which might be a problem). If you ask A which one C would say, She'll say "B or C." This can be carried out, but I think I'll stop with the line that might be a problem...

I think I'm close, but not there yet.

Fleshpiston
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### Re: Three princesses

NThisStyle-10-6 wrote:
I don't feel like there would have been a puzzle posted without a possible solution. Perhaps the original poster is just mean/doesn't know the answer himself, but I doubt it.

To NThisStyle: I assure you that I am not mean, and I (and several others) do know the answer. As far as I can tell from your guess, your proposed question will not work. Also, you should remember that you can only ask yes or no questions.

If you ask me, the Summer of 2006 was the Golden Era of Logic Puzzles on the xkcd forum. Back when I posted this thread: you could count on many smart people quickly reading the problem and trying to solve it, there were few enough threads that you could easily peruse them all, and best of all, you could have Randall himself exchanging ideas with the rest of us.

Thanks to jestingrabbit and others who have "moderated" this thread over the past two years despite my neglect of it, and for helping people along who think they have a solution but are not quite there. I am pleased that only xkcd's blue eyes problem has a longer puzzle thread. I want to pose another logic puzzle, but I can tell that the Golden Era has passed, and it just wouldn't be the same. Plus it is hard to tell if someone has asked it already.

quintopia
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### Re: Three princesses

To all people thinking of posting in this thread with the solution: please read one of the other five or so correct solutions, including the short one-liner that has been posted many times here already, and be sure that yours is different. That is all.

skeptical scientist
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### Re: Three princesses

quintopia wrote:To all people thinking of posting in this thread with the solution: please read one of the other five or so correct solutions, including the short one-liner that has been posted many times here already, and be sure that yours is different. That is all.

Some people want to check if their solution is correct without reading solutions which might potentially spoil it if they were wrong. If they want to do that, even if it turns out to be a duplicate, I think that's completely legitimate.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.

"With math, all things are possible." —Rebecca Watson

jestingrabbit
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### Re: Three princesses

Fleshpiston wrote:If you ask me, the Summer of 2006 was the Golden Era of Logic Puzzles on the xkcd forum. Back when I posted this thread: you could count on many smart people quickly reading the problem and trying to solve it, there were few enough threads that you could easily peruse them all, and best of all, you could have Randall himself exchanging ideas with the rest of us.

Yeah, I really feel as though my stewardship hasn't been great. But then, all the really good puzzles have been done, so it was inevitable that it would go downhill. /rationalisation

Fleshpiston wrote:Thanks to jestingrabbit and others who have "moderated" this thread over the past two years despite my neglect of it, and for helping people along who think they have a solution but are not quite there. I am pleased that only xkcd's blue eyes problem has a longer puzzle thread. I want to pose another logic puzzle, but I can tell that the Golden Era has passed, and it just wouldn't be the same. Plus it is hard to tell if someone has asked it already.

Please post it. You've definitely contributed one of my favourite puzzles, and if more good ones don't get posted we just have a board full of "improbable alien" nonsenses. Please post it.

skeptical scientist wrote:
quintopia wrote:To all people thinking of posting in this thread with the solution: please read one of the other five or so correct solutions, including the short one-liner that has been posted many times here already, and be sure that yours is different. That is all.

Some people want to check if their solution is correct without reading solutions which might potentially spoil it if they were wrong. If they want to do that, even if it turns out to be a duplicate, I think that's completely legitimate.

Agree with skep on this one.Its not a bad thing that one of the better threads continues to be bumped imo. Sure it gets a little tedious sometimes, but I like this puzzle that much that I don't mind explaining that it has a nice, simple, direct answer once a month or so. Given that a couple of other forumites seem to be of a similar disposition, what does posting a possibly incorrect answer harm?
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

Cosmologicon
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### Re: Three princesses

Fleshpiston wrote:If you ask me, the Summer of 2006 was the Golden Era of Logic Puzzles on the xkcd forum. Back when I posted this thread: you could count on many smart people quickly reading the problem and trying to solve it, there were few enough threads that you could easily peruse them all, and best of all, you could have Randall himself exchanging ideas with the rest of us.

Thanks to jestingrabbit and others who have "moderated" this thread over the past two years despite my neglect of it, and for helping people along who think they have a solution but are not quite there. I am pleased that only xkcd's blue eyes problem has a longer puzzle thread. I want to pose another logic puzzle, but I can tell that the Golden Era has passed, and it just wouldn't be the same. Plus it is hard to tell if someone has asked it already.

I think you've got it all wrong. The popularity of those two puzzles has nothing to do with what "era" they were originally posted in. In fact, it's only because of people who aren't what you'd call smart continually posting wrong answers. And why would their popularity today have anything to do with what the board was like when they were first posted?

The reason they're so popular is because they're deceptively counterintuitive. If you post another puzzle and it doesn't get as many replies, I'm sorry if that would disappoint you, but most puzzles aren't like that, including most of my favorites. Maybe that shouldn't be your touchstone for success.

AzraelFish
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### Re: Three princesses

Alright...having read all six pages, and realizing several solutions have been given, I'm not even going to bother--suffice it to say, I thought about it enough for my own satisfaction, and came up with, if not a workable solution, something at least close enough to make me happy with it. So, what I DO want to say...rather than finding a question that would tell you that yes, you know that one in particular is not the middle sister, I'd rather figure out exactly whom the middle one is--if I were going to marry someone, I'd like it to be her. It's no fun talking to someone, day in and day out, if it's always...predictable. I, at least, would want some surprise from my wife.
I may post again in a couple days, if I figure out how to say for certain which is the middle sister. =P
Until then...peace, yo's!

--Fish