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3 Princess Puzzle


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11 replies to this topic

#1 O'Beckon

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Posted 30 December 2007 - 11:36 PM

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?

This is not a trick question, and the answer is not anything like "is this statement a lie?" The solution is nice and elegant.

Spoiler for solution

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#2 bonanova

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Posted 31 December 2007 - 08:25 AM

Spoiler for solution
I believe there are at least three questions that work.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#3 bonanova

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Posted 31 December 2007 - 01:35 PM

The clunker in this riddle is Princess Mischievous.
You might, unknowingly, ask your question of her, and her answer is useless!

Spoiler for solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 unreality

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Posted 31 December 2007 - 10:27 PM

I couldnt find a way around the Mischievious one answering either YES or NO randomly

Ask one princess, let's call her princess A, if princess B is older that princess C. You want to marry whichever one she indicates is younger.
If you ask the:
--Youngest: she will tell you that the eldest one is younger
--Middle: either one is good
--Eldest: she will tell you that the youngest is younger



This wouldnt work. It has to be a YES or NO question, remember?

So say you do that, and line them up, 123. Ask Princess 1 if Princess 2 is older than Princess 3.

the truthteller will say the truth (YES or NO), the liar will lie, and the mischevious princess would also say either YES or NO.

Your own answer does not work. The middle one wouldnt say "either one is good", she would say a specific one is younger as well.
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#5 unreality

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Posted 31 December 2007 - 11:00 PM

The closest I've been able to get is asking #2 a certain q about #1, and if its NO then choose #3 and you're set, and if its YES then choose #1 and there's a 4/5 chance that you're okay. However this isnt the "perfect answer"
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#6 Martini

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Posted 31 December 2007 - 11:37 PM

This wouldnt work. It has to be a YES or NO question, remember?


"Is princess B older than princess C" is a yes or no question.

So say you do that, and line them up, 123. Ask Princess 1 if Princess 2 is older than Princess 3.

the truthteller will say the truth (YES or NO), the liar will lie, and the mischevious princess would also say either YES or NO.

Your own answer does not work.


The question the OP supplied works, it's just that the OP didn't explain why.

If you get a "yes" answer from Princess A, go with Princess C. If you get a "no" answer, go with Princess B.
Possible scenario:

Princess A: eldest-truthteller
Princess B: youngest- liar
Princees C: middle- normal

Princess A could only answer no, so by going with Princess B, you don't get the middle child.

Another scenario:

Princess A: youngest- liar
Princess B: eldest-truthteller
Princees C: middle- normal

Princess A could only answer no, so by going with Princess B, you don't get the middle child.

Another scenario:

Princess A: middle- normal
Princess B: eldest-truthteller
Princees C: youngest- liar

If Princess A answers yes, you pick C and get the youngest. If she answers no, you pick B and get the oldest. Either way you don't end up with her.

The middle one wouldnt say "either one is good", she would say a specific one is younger as well.


I think what the OP meant was that it doesn't matter if the middle child decides to tell the truth or lie, since you never pick the Princess you're asking the question to, you won't end up with her.

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#7 unreality

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Posted 01 January 2008 - 01:22 AM


This wouldnt work. It has to be a YES or NO question, remember?


"Is princess B older than princess C" is a yes or no question.



Yeah I know, as I said later


So say you do that, and line them up, 123. Ask Princess 1 if Princess 2 is older than Princess 3.

the truthteller will say the truth (YES or NO), the liar will lie, and the mischevious princess would also say either YES or NO.

Your own answer does not work.


The question the OP supplied works, it's just that the OP didn't explain why.

If you get a "yes" answer from Princess A, go with Princess C. If you get a "no" answer, go with Princess B.
Possible scenario:

Princess A: eldest-truthteller
Princess B: youngest- liar
Princees C: middle- normal

Princess A could only answer no, so by going with Princess B, you don't get the middle child.

Another scenario:

Princess A: youngest- liar
Princess B: eldest-truthteller
Princees C: middle- normal

Princess A could only answer no, so by going with Princess B, you don't get the middle child.

Another scenario:

Princess A: middle- normal
Princess B: eldest-truthteller
Princees C: youngest- liar

If Princess A answers yes, you pick C and get the youngest. If she answers no, you pick B and get the oldest. Either way you don't end up with her.

The middle one wouldnt say "either one is good", she would say a specific one is younger as well.


I think what the OP meant was that it doesn't matter if the middle child decides to tell the truth or lie, since you never pick the Princess you're asking the question to, you won't end up with her.



there are 6 possibilities, not 3
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#8 Martini

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Posted 01 January 2008 - 04:39 AM

Yeah I know, as I said later


Am I missing something? You said the OP's solution wouldn't work because it wasn't a yes or no question. I pointed out that the solution given was a yes or no question. I don't see where you later retracted that comment.


there are 6 possibilities, not 3


Would you like me to go over all possible scenarios to show you that they all work? I will if you like, but I was pretty confident that you could do that on your own after I pointed out how the solution works.
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#9 bonanova

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Posted 01 January 2008 - 10:17 AM

I believe there are at least three questions that work.

Here are four questions that work.
Select the least desirable Princess and call her A.

Spoiler for solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#10 unreality

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Posted 01 January 2008 - 06:49 PM


Yeah I know, as I said later


Am I missing something? You said the OP's solution wouldn't work because it wasn't a yes or no question. I pointed out that the solution given was a yes or no question. I don't see where you later retracted that comment.



I was just pointing out that he didnt give his answer in YES or NO form. If you look at the next line I said:

So say you do that, and line them up, 123. Ask Princess 1 if Princess 2 is older than Princess 3.

which is a YES or NO question, I assumed that was the YES or NO question the OP asked with those answers. Nvm. It doesnt matter
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