Posted:

**Sun Aug 05, 2007 7:56 pm UTC**sorry then, Ihad missunderstood the problem and had just a assumed that the random sister was more like a coin toss 50% yes 50% no and didnt care what your question was.

Page **5** of **12**

Posted: **Sun Aug 05, 2007 7:56 pm UTC**

sorry then, Ihad missunderstood the problem and had just a assumed that the random sister was more like a coin toss 50% yes 50% no and didnt care what your question was.

Posted: **Sun Sep 16, 2007 8:45 am UTC**

How about if you asked a question that took a lot of working out. The middle girl would answer instantly, as she can lie or tell the truth, but the liar MUST ensure she is lying, and the truth teller MUST ensure she is telling the truth? So if the princess take a long time in answering marry her. If she takes little time in thinking do not.

Posted: **Sun Sep 16, 2007 6:23 pm UTC**

Mr Cool wrote:How about if you asked a question that took a lot of working out. The middle girl would answer instantly, as she can lie or tell the truth, but the liar MUST ensure she is lying, and the truth teller MUST ensure she is telling the truth? So if the princess take a long time in answering marry her. If she takes little time in thinking do not.

The actual answer is a lot more satisfying than that. Its in white at the top of page two. So don't read that if you want to work it out yourself, but you can safely read the first page and get some good hints.

[fannishness]Some of the posts are actually by xkcd!![/fannishness]

And, though you don't have to, you might want to visit the intro thread so we have a vague idea of who we're talking to.

Posted: **Mon Sep 17, 2007 6:53 pm UTC**

I didn't read all five pages of the thread. Sorry if my answer has come up.

Edit: I guess this wouldn't be a solution, because you must select one princess and ask the question of only her.

Ask them this question: Are you the middle sister?

The oldest sister will answer no, the youngest yes. The middle sister will answer either yes or no. You simply pick the sister with the unique answer.

Edit: I guess this wouldn't be a solution, because you must select one princess and ask the question of only her.

Posted: **Mon Sep 17, 2007 7:40 pm UTC**

I've been trying to solve this for a while now and I have yet to find a solution. I decided yesterday to read what was the solution and none of the answers in this tread actually work

What is the answer

What is the answer

Posted: **Mon Sep 17, 2007 9:11 pm UTC**

nufan wrote:I've been trying to solve this for a while now and I have yet to find a solution. I decided yesterday to read what was the solution and none of the answers in this tread actually work

What is the answer

Ummm... what? Have you looked at

http://forums.xkcd.com/viewtopic.php?p=988#988

??

Its the answer, but you have to highlight the text to see it. If you don't think it works, I'd be interested to hear why not.

Also, here's a hint, in case you want to keep trying.

The only questions that wont have a different answer for the youngest and oldest, with the middle answering arbitrarily, are ones which refer to the sisters

Not much of a hint, but it might help you out somewhat.

Posted: **Tue Sep 18, 2007 4:56 am UTC**

Thx jestingrabbit

Posted: **Fri Oct 12, 2007 12:44 am UTC**

"Are you incestuous lesbians?"

Screw marriage, if the sisters are !ugly, it'll be months before you need to worry about them.

Screw marriage, if the sisters are !ugly, it'll be months before you need to worry about them.

Posted: **Fri Oct 12, 2007 3:45 pm UTC**

Caveat: I've only read the first page of this thread, so I'm certain to be repeating a solution that has already been rehashed several times.

I reason as follows:

**Spoiler:**

EDIT: Having now read the whole thread, I see I was missing one important point:

I reason as follows:

EDIT: Having now read the whole thread, I see I was missing one important point:

(STRATEGY: Pose the question to the least attractive one!)

Posted: **Tue Oct 16, 2007 1:45 am UTC**

I didn't read through...**Spoiler:**

Posted: **Tue Oct 16, 2007 2:32 pm UTC**

If you had read through, you would have noted that you only get to ask one sister one question. It'd be too easy if you could ask all three.

Posted: **Thu Oct 18, 2007 6:04 pm UTC**

I came to the conclusion to look for the sister who gave a unique answer too, but somehow forgot that you only get one question to one girl.

This isn't a guarenteed question, but if you ask "Are you the youngest?" you get a 1/4 chance of correctly identifying the eldest or youngest. (Might be wrong, don't feel like doing probability right now.) Either of those girls will answer "no", guarenteed, and you have a 2/3 chance of picking them. The middle girl will either say "yes" or "no". If she says "yes", you know she's the middle girl. If she says "no"... Well, you messed up, but on the bright side I think she sounds like the more interesting of the three anyways. Consistent truth or lies is dull and boring.

This isn't a guarenteed question, but if you ask "Are you the youngest?" you get a 1/4 chance of correctly identifying the eldest or youngest. (Might be wrong, don't feel like doing probability right now.) Either of those girls will answer "no", guarenteed, and you have a 2/3 chance of picking them. The middle girl will either say "yes" or "no". If she says "yes", you know she's the middle girl. If she says "no"... Well, you messed up, but on the bright side I think she sounds like the more interesting of the three anyways. Consistent truth or lies is dull and boring.

Posted: **Sat Oct 20, 2007 3:18 am UTC**

Im sorry if this has come up already, but I read the first page and the last page. This seems a lot more like people comming up with not good answers out of frustration, so I am not going to wade through 5 pages of it. Some may consider my solution cheating, but it isnt really... I also changed the question from yes/no to true/false for simplicities sake

**Spoiler:**

Im new at HTML, sorry about the formatting

also how do I find harder pure logic problems (Such as this which require basic knowledge of things not logic ie. not probability math questions or something)?

Im new at HTML, sorry about the formatting

also how do I find harder pure logic problems (Such as this which require basic knowledge of things not logic ie. not probability math questions or something)?

Posted: **Tue Oct 23, 2007 12:14 am UTC**

I didn't read all 5 pages, so sorry if this answer has already been discussed.

**Spoiler:**

Edited for grammatical clarity.

Edited for grammatical clarity.

Posted: **Tue Oct 23, 2007 4:42 pm UTC**

that is similar to the correct answer in a way, but, unfortunately, it's not a yes/no question.

Posted: **Tue Oct 23, 2007 9:33 pm UTC**

It doesn't matter, you can point to a sister and ask if she is the one who lies more. If the answer is yes, choose her, otherwise, choose the other one. It's still a nice new idea for this problem. But it is, in a sense, similar to the already stated solution; actually, I think that any difference between all of the sisters can be used to find the right answer in this same manner (of course, presuming you know about said difference).

OK, I've said nothing useful, you can flame me now

OK, I've said nothing useful, you can flame me now

Posted: **Thu Oct 25, 2007 1:15 am UTC**

Ummm the answer that you ask which one lies the most is incorrect...

lets say you ask the middle sister, or the youngest sister, "who lies the most?".

Either could point to the middle sister or the oldest; to lie they just cant point to the youngest.

to illustrate: if you ask a liar what one plus one equals, they can answer anything aside from 2. or more generally, if the answer to a question is A, anything not A is a lie; the lie is not nessesarily the opposite of A. if I am facing north and you lie about what direction I am facing, NorthEast is a legitimate answer, because I am not.

That kind of reasoning only works when the solution set is bounded to two choices, sorry :-\

im fairly sure my answer works though *see my previous post*

lets say you ask the middle sister, or the youngest sister, "who lies the most?".

Either could point to the middle sister or the oldest; to lie they just cant point to the youngest.

to illustrate: if you ask a liar what one plus one equals, they can answer anything aside from 2. or more generally, if the answer to a question is A, anything not A is a lie; the lie is not nessesarily the opposite of A. if I am facing north and you lie about what direction I am facing, NorthEast is a legitimate answer, because I am not.

That kind of reasoning only works when the solution set is bounded to two choices, sorry :-\

im fairly sure my answer works though *see my previous post*

Posted: **Thu Oct 25, 2007 1:22 am UTC**

I think the following comic applies to this riddle. Btw, my opinion is that there is no solution, citing all the reasons described above.

I have to add the extra text, it's brilliant: "And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out."

I have to add the extra text, it's brilliant: "And the whole setup is just a trap to capture escaping logicians. None of the doors actually lead out."

Posted: **Thu Oct 25, 2007 1:26 am UTC**

Except that the posts immediately above yours all contain valid, non-tricky solutions.Gyvulys624 wrote:Btw, my opinion is that there is no solution, citing all the reasons described above.

Posted: **Fri Nov 23, 2007 10:37 pm UTC**

Why can't I ask the King?

Posted: **Fri Nov 23, 2007 10:48 pm UTC**

J Spade wrote:Why can't I ask the King?

Because you can't, that's why. Even if you could, what yes/no question would you ask?

There is a very simple question which you can ask of precisely one princess that allows you to identify the eldest or youngest. This makes it one of the best puzzles here. If you had to ask the king, it would be a real 169.

Posted: **Fri Nov 23, 2007 10:49 pm UTC**

Is this daughter the one that sometimes tells the truth and sometimes lies?

Then you can get either the true one or the lying one every time.

Then you can get either the true one or the lying one every time.

Posted: **Fri Nov 23, 2007 10:58 pm UTC**

J Spade wrote:Is this daughter the one that sometimes tells the truth and sometimes lies?

My communication there wasn't as clear as it might be. I should have said something like "there is a yes/no question which, when asked of any one princess, allows you to identify one of the princesses that is eldest or youngest."

Posted: **Thu Nov 29, 2007 4:31 am UTC**

Another fairly straightforward solution:

So we know how we can avoid the flip-flopper. A question arises: is it possible to avoid any of the others? The answer seems like it should be no, since if we are unlucky enough to have picked the flip-flopper (middle daughter) we have no useful information about how to avoid anybody else. HOWEVER, if the middle daughter instead of picking randomly, consciously decided beforehand whether she would lie or tell the truth then I bet such a solution (although meta) would exist.

Ask the middle person: "Is the person on your left the middle child, or are you the truth teller, but not both?" (Logical XOR). If 'Yes', hit up the person on the right, if no, the left.

So we know how we can avoid the flip-flopper. A question arises: is it possible to avoid any of the others? The answer seems like it should be no, since if we are unlucky enough to have picked the flip-flopper (middle daughter) we have no useful information about how to avoid anybody else. HOWEVER, if the middle daughter instead of picking randomly, consciously decided beforehand whether she would lie or tell the truth then I bet such a solution (although meta) would exist.

Posted: **Thu Nov 29, 2007 5:49 am UTC**

Do you mean that you want to ask a single question to determine a not-eldest or not-youngest or do you mean that you want to ask a single question to determine the youngest or eldest? The first is probably doable, but second isn't.

Posted: **Fri Nov 30, 2007 2:37 am UTC**

I meant the first, but like I said we need a middle child who isn't random in her answer but instead random in her approach to the answer (lying or truthful frame of mind).

The second probably isn't doable, but probably doable in two questions. Its interesting, but I've never seen a good proof that some problem like this is impossible. (except for very trivial cases). For example, before the solution to this one came around, many people thought it would be impossible, but I don't think anybody knew how to try to approach proving it. (Though this is kind of a bad example, since any proof of its impossibility would have obviously been incorrect).

The second probably isn't doable, but probably doable in two questions. Its interesting, but I've never seen a good proof that some problem like this is impossible. (except for very trivial cases). For example, before the solution to this one came around, many people thought it would be impossible, but I don't think anybody knew how to try to approach proving it. (Though this is kind of a bad example, since any proof of its impossibility would have obviously been incorrect).

Posted: **Fri Nov 30, 2007 3:00 am UTC**

imatrendytotebag wrote:The second probably isn't doable, but probably doable in two questions. Its interesting, but I've never seen a good proof that some problem like this is impossible.

Hm? There are three daughters. You want to find out which of them is the youngest, say. There are three possible solutions, but you only get a single yes or no answer to a single question. There aren't enough bits of information to encode which daughter is the youngest (or middle, or oldest), so clearly it's impossible.

Posted: **Fri Nov 30, 2007 3:30 am UTC**

Buttons wrote:imatrendytotebag wrote:The second probably isn't doable, but probably doable in two questions. Its interesting, but I've never seen a good proof that some problem like this is impossible.

Hm? There are three daughters. You want to find out which of them is the youngest, say. There are three possible solutions, but you only get a single yes or no answer to a single question. There aren't enough bits of information to encode which daughter is the youngest (or middle, or oldest), so clearly it's impossible.

Yeah, of course. Good call.

When I was talking about "some problem like this" I was actually referring to more complicated things (ie variations on the 4 gods problem), but at any rate well said about the impossibility of this one.

Posted: **Sat Dec 01, 2007 3:33 pm UTC**

GUYS!!!!!!!!!!!!!

I have the answer.

I went to sleep yesterday trying to figure it out, and I have it now.

SPOILER ALLERT!!!!!!!!!

**Spoiler:**

I am going to post the explanation on my next post, because it could use an explanation.

I have the answer.

I went to sleep yesterday trying to figure it out, and I have it now.

SPOILER ALLERT!!!!!!!!!

I am going to post the explanation on my next post, because it could use an explanation.

Posted: **Sat Dec 01, 2007 3:57 pm UTC**

That would help, as would a table with possibilities and consequences.

Posted: **Sat Dec 01, 2007 4:10 pm UTC**

This is my explanation for my solution

**Spoiler:**

Continuing:

**Spoiler:**

A compilation of all tables:

**Spoiler:**

I just noticed Aaronspook's answer from over a year ago.

Ok guys, my explanation could certainly use some fixing up.

I am going to wait until I get enough feedback about it before I merge all of the explanations and put them together.

Thanks!

thanks jr

Continuing:

A compilation of all tables:

I just noticed Aaronspook's answer from over a year ago.

Ok guys, my explanation could certainly use some fixing up.

I am going to wait until I get enough feedback about it before I merge all of the explanations and put them together.

Thanks!

thanks jr

Posted: **Tue Jun 03, 2008 7:32 pm UTC**

Swamp, I am unsure if I agree with your answer. It seemed tobe three questions asked in one?

A much shorter or easier question would be:

**Spoiler:**

Table would be:

**Spoiler:**

Now maybe your's is saying the same thing, But I just didn't understand the answer haha.

A much shorter or easier question would be:

Table would be:

Now maybe your's is saying the same thing, But I just didn't understand the answer haha.

Posted: **Wed Jun 04, 2008 9:10 am UTC**

Here's another version of the problem that I've solved. (actually, the partial solution to it is floating in this thread somewhere.)

Same setup with the princesses and your preference, different procedure. This time the king brings to you one princess randomly. You may ask one yes-no question to her. After she responds, you must choose to accept or reject her. If you reject her, however, the king chooses you bride randomly from the remaining two.

Same setup with the princesses and your preference, different procedure. This time the king brings to you one princess randomly. You may ask one yes-no question to her. After she responds, you must choose to accept or reject her. If you reject her, however, the king chooses you bride randomly from the remaining two.

Posted: **Wed Jun 04, 2008 5:14 pm UTC**

My question works for both versions of the question.

The Random sister would answer no, so I would ask the king/father to marry one of the others.

Both the lying sister and the truthful sister would answer yes, so I would marry the sister in front of me.

My question in two versions:

The bad Version:

**Spoiler:**

The Good Version:

**Spoiler:**

No, the actual question is the second version, which is obviously one question.

The Random sister would answer no, so I would ask the king/father to marry one of the others.

Both the lying sister and the truthful sister would answer yes, so I would marry the sister in front of me.

My question in two versions:

The bad Version:

The Good Version:

TimM1104 wrote:Swamp, I am unsure if I agree with your answer. It seemed tobe three questions asked in one?

No, the actual question is the second version, which is obviously one question.

Posted: **Fri Jun 06, 2008 12:08 pm UTC**

I feel i may have discovered an alternate solution, assuming that "i dont know" is a legitimate answer"

ask: If i asked your sisters a question, will they give the same answer?

if i have stubled across the lying sister, she will likely say yes, or no, and thus be recognisable as the middle sister.

either of the other sisters will be unable to predict their sisters behavior, and thus answer "i dont know"

This probably isnt a legit answer, but i like it anyway, even if its not as foolproof as the other way.

ask: If i asked your sisters a question, will they give the same answer?

if i have stubled across the lying sister, she will likely say yes, or no, and thus be recognisable as the middle sister.

either of the other sisters will be unable to predict their sisters behavior, and thus answer "i dont know"

This probably isnt a legit answer, but i like it anyway, even if its not as foolproof as the other way.

Posted: **Fri Jun 06, 2008 7:57 pm UTC**

jestingrabbit wrote:Do you mean that you want to ask a single question to determine a not-eldest or not-youngest or do you mean that you want to ask a single question to determine the youngest or eldest? The first is probably doable, but second isn't.

isn't this trivial? Just ask a question whose value you already know. E.g., "1+1=2?" The oldest will answer no, the middle random, the youngest yes. If the princess you ask answers yes, then you know that princess is not the youngest. Vice versa for non-oldest.

Posted: **Sat Jun 07, 2008 5:33 am UTC**

thc wrote:jestingrabbit wrote:Do you mean that you want to ask a single question to determine a not-eldest or not-youngest or do you mean that you want to ask a single question to determine the youngest or eldest? The first is probably doable, but second isn't.

isn't this trivial? Just ask a question whose value you already know. E.g., "1+1=2?" The oldest will answer no, the middle random, the youngest yes. If the princess you ask answers yes, then you know that princess is not the youngest. Vice versa for non-oldest.

But that's asking three questions, one to each of the daughters. The trick is to identify a non-random-answerer with only one question to one daughter.

Posted: **Sat Jun 07, 2008 7:32 pm UTC**

jestingrabbit wrote:thc wrote:jestingrabbit wrote:Do you mean that you want to ask a single question to determine a not-eldest or not-youngest or do you mean that you want to ask a single question to determine the youngest or eldest? The first is probably doable, but second isn't.

isn't this trivial? Just ask a question whose value you already know. E.g., "1+1=2?" The oldest will answer no, the middle random, the youngest yes. If the princess you ask answers yes, then you know that princess is not the youngest. Vice versa for non-oldest.

But that's asking three questions, one to each of the daughters. The trick is to identify a non-random-answerer with only one question to one daughter.

No, what I mean: ask "1+1=2," if you get a "no" answer, then you know that that daughter is not the oldest. If you get a "yes" answer, that daughter is not the youngest. So no matter what response you get, you determine non-eldest or non-youngest.

Posted: **Sun Jun 08, 2008 2:14 am UTC**

thc wrote:jestingrabbit wrote:thc wrote:

isn't this trivial? Just ask a question whose value you already know. E.g., "1+1=2?" The oldest will answer no, the middle random, the youngest yes. If the princess you ask answers yes, then you know that princess is not the youngest. Vice versa for non-oldest.

But that's asking three questions, one to each of the daughters. The trick is to identify a non-random-answerer with only one question to one daughter.

No, what I mean: ask "1+1=2," if you get a "no" answer, then you know that that daughter is not the oldest. If you get a "yes" answer, that daughter is not the youngest. So no matter what response you get, you determine non-eldest or non-youngest.

But you don't get to pick which kind of person you're identifying using that strategy. After you ask the question you either determine a non-eldest or a non-youngest, but if you set out to determine a non-eldest and you get a truthful response you don't know whether you are dealing with the truthful or the random, and so haven't IDed a non-eldest person.

But you're right that you can determine either a non-eldest or a non-youngest with one question, so long as you don't care which it is that you want to identify.

Posted: **Mon Jun 09, 2008 8:57 am UTC**

Without asking any question to the girls, a priori you have a 2/3 chance to make a good decision.

Suppose that you were unable to come up with the right question to ask, and instead just ask one sister "Are you the oldest one?" and she answers with yes or no. Does this give you any new information?

Suppose that you were unable to come up with the right question to ask, and instead just ask one sister "Are you the oldest one?" and she answers with yes or no. Does this give you any new information?