## Three princesses

A forum for good logic/math puzzles.

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### Re: Three princesses

My solution:
Spoiler:
Sisters are, randomly, A, B, and C.
Ask A if sister B is older than C.
If the answer is yes, marry C. If the answer is no, marry B.
If A is the truthteller and B is the liar, the answer will be no. If A is the truthteller and C is the liar, the answer will be yes. In both instances, you marry the liar.
If A is the middle sister, it will not matter what she answers; you will marry one of the other sisters.
If A is the liar and B is the truthteller, the answer will be no. If A is the liar and C is the truthteller, the answer will be yes. In both instances you marry the truthteller.
bentomat

Posts: 4
Joined: Tue May 29, 2012 2:11 pm UTC

### Re: Three princesses

Edit: Sorry, completely misunderstood the question there!
Last edited by bananageek on Mon Jun 04, 2012 12:49 pm UTC, edited 1 time in total.
bananageek

Posts: 1
Joined: Fri Jun 01, 2012 6:19 am UTC

### Re: Three princesses

You get to ask one question, to one princess, and get one reply, not one question to all the princesses, that gets three supplies.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

jestingrabbit

Posts: 5388
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: Three princesses

Spoiler:
I heard this question from a friend yesterday. And turns out, it does have an answer.
Ask one of the sisters, say A, if one of the other two sisters, say C, is younger than the other, B.
If the answer is "yes" marry C or else, marry B.
sudhanva

Posts: 1
Joined: Mon Oct 21, 2013 2:17 pm UTC

### Re: Three princesses

I think you're supposed to put answers in spoilers so that the people who want to figure it out themselves won't find out by reading your answer.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
tomtom2357

Posts: 555
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Three princesses

You need a question that fixes the answer of the flipflopper
How about a question like "Do both of your sisters lie sometimes?"

The flipflopper must say "No" (if she is telling the truth, then the answer must be 'no' because the truth teller never lies, and if she's lying the answer is 'no' because the liar always lies)
The truth teller must say "No" (the liar always lies , while the flipper sometimes lies)
The lie teller must say "Yes" (the truth teller never lies, so the liar has to say she does)
So you can deduce which sister is the liar, and can date her
chrisboote

Posts: 1
Joined: Mon Nov 25, 2013 12:52 pm UTC

### Re: Three princesses

chrisboote wrote:You need a question that fixes the answer of the flipflopper
How about a question like "Do both of your sisters lie sometimes?"

The flipflopper must say "No" (if she is telling the truth, then the answer must be 'no' because the truth teller never lies, and if she's lying the answer is 'no' because the liar always lies)
The truth teller must say "No" (the liar always lies , while the flipper sometimes lies)
The lie teller must say "Yes" (the truth teller never lies, so the liar has to say she does)
So you can deduce which sister is the liar, and can date her

There is a question that works even if the random sister answers in a way completely unrelated to the question ie is completely random, not merely sometimes lying, and sometimes telling the truth.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

jestingrabbit

Posts: 5388
Joined: Tue Nov 28, 2006 9:50 pm UTC
Location: Sydney

### Re: Three princesses

hint (this isn't a solution, and you can deduce it from what jestingrabbit just said:
Spoiler:
Never pick the person you asked. That ensures that even if the random person answers randomly, you won't pick them and therefore the solution still works. Then you only have to worry about the truthteller or liar's answer to the question.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.
tomtom2357

Posts: 555
Joined: Tue Jul 27, 2010 8:48 am UTC

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