calamarain
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I know I said that the final one had been posted... I may have lied

Angels tell the truth, demons lie. Mortals can do either.

Suppose you visit a high society party. No mortals there, only angels and demons. Now, this is a very very high society party, so half of the guests are completely insane. This means that everything that's true they believe to be false and vice versa.

So, if I asked a sane angel whether 2+2 was 4, they'd say "Yes"
If I asked an insane angel whether 2+2 was 4, they'd think it wasn't and answer "No"
If I asked a sane demon whether 2+2 was 4, they'd know it was, but lie and say "No"
If I asked an insane demon whether 2+2 was 4, they'd think it wasn't, but lie and say "Yes"

There is a box that contains either a green piece of paper or a red piece of paper, you do not know which. If you can guess correctly what colour the paper is, you win a rather large diamond. If you guess wrongly, you must listen to the Greatest Hits of George Bush Volumes 1-100,000. So understandably, you do not want to guess randomly, but be absolutely sure what colour the paper is before you guess.

But it gets worse. The people at the party are speaking in code! There are two words they're using - "Mushroom" and "Artichoke". One of them means yes, and one of them means no, and you don't know which is which.

So the riddle is this. What *single* yes/no question could you ask to an inhabitant of the party to find out conclusively what colour the paper is in the box? Bear in mind that you don't know which word means yes and which means no (and they're going to answer with one of the words). And that you don't know whether the person you're talking to is angel or demon. And you don't know whether they're sane or insane.

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silver
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but do they know what's in the box? you didn't say. I might take it as an assumption, but then I risk making a donkey of you and Mption.


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Maurog
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Also, do they know whether they are sane?

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calamarain
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Maurog wrote:
Also, do they know whether they are sane?

Everyone at the party besides you knows what's in the box. And no, you don't know if the person you're talking to is sane. All you know is that they're either an angel or a demon, either sane or insane, and that they'll answer "Yes" or "No"... but in code. "Mushroom" and "Artichoke" mean "Yes" and "No", but not necessarily that way round.

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My Holds

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[Last edited by calamarain at 09-25-2007 03:51 PM]

silver
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of course _I_ don't know if the person I'm talking to is sane, but are the other inhabitants aware of the sanity/insanity of the other inhabitants (including their own)? (and that is what Maurog asked)



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[Last edited by silver at 09-25-2007 03:53 PM]

calamarain
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silver wrote:
of course _I_ don't know if the person I'm talking to is sane, but are the other inhabitants aware of the sanity/insanity of the other inhabitants (including their own)?

Other inhabitants are aware of the sanity and nature of the other inhabitants. They're all really quite well informed, but you (the guest) are the ignorant one

Just a hint - the solution doesn't actually need to involve other people, there is a question you can ask that doesn't need a second person there to refer to.

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Maurog
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There is a problem. I asked an insane angel whether "mushroom" means "yes", and it exploded. Can you fix it?

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calamarain
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Maurog wrote:
There is a problem. I asked an insane angel whether "mushroom" means "yes", and it exploded. Can you fix it?

I'm sorry, but the angel was out of warranty.

If you asked an insane angel whether "mushroom" meant yes, they'd either answer "mushroom" or "artichoke".

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Maurog
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No, it couldn't answer "artichoke" by any means. If mushroom really means yes, it will think mushroom means no, and as an honest angel answer no, i.e. mushroom. If mushroom really means no, it will think it really means yes, and as an honest angel answer yes, i.e. mushroom.

Interesting...

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calamarain
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Maurog wrote:
No, it couldn't answer "artichoke" by any means. If mushroom really means yes, it will think mushroom means no, and as an honest angel answer no, i.e. mushroom. If mushroom really means no, it will think it really means yes, and as an honest angel answer yes, i.e. mushroom.

Interesting...

Follow the table through

Sane Demon - Does Mushroom mean yes?

If it does, it will answer "No", i.e. "Artichoke"
If it doesn't, it will answer "Yes", i.e. "Artichoke"

Sane Angel - Does Mushroom mean yes?

If it does, it will answer "Yes", i.e. "Mushroom"
If it doesn't, it will answer "No", i.e. "Mushroom.

Insane Demon

If it does, it will answer what it believes to be "Yes", i.e. "Artichoke".
It it doesn't, it will answer what it believes to be "No", i.e. "Artichoke".

So asking the question tells you nothing about whether Mushroom actually means yes or no, but it does tell you whether you're dealing with an angel or a demon

Unless I've screwed up the logic somewhere I deliberately didn't look at the answer for this puzzle, so it's possible I may have entered it wrongly (which I'd have known if I looked at the answer). I do *have* the answer though, in the book.

If I have, it's going to be really embarassing Let's find out.

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My Holds

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[Last edited by calamarain at 09-25-2007 04:27 PM]

Ezlo
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Whoa, this goes WAY above my head. I'll try and think of one, but one question?? Yikes.

calamarain
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Ezlo wrote:
Whoa, this goes WAY above my head. I'll try and think of one, but one question?? Yikes.

Mmmmm. It's an easy problem if you're allowed four questions (one to determine sanity, one to determine type, one to determine mushroom/artichoke and the last to determine the box). Perhaps even three. But one? That's hard.

I've been looking over the question again... and I think the author of the book may have assumed something I have not. If so, then the problem is still solvable, but will have a different solution (it's a parity thing). Both versions are valid, but his is simpler. I will double check this tonight and read the entire answer. After I've tried my utmost to build one myself.

I think it's a building thing - each question seems to only be able to yield one piece of information (sanity, type, mushroom). Building enough conditions into it, and engineering the different types of answer possible, one could presumably get a question that the only thing you can tell is what's in the box. Nothing about the sanity/type/mushroom of the person you ask.

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My Holds

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[Last edited by calamarain at 09-25-2007 07:33 PM]

Albert
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I think I may have got something. It's a bit convoluted and there are plenty of ways I could have gone wrong though.

Tahnan
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OK, this was either (a) taken from What is the Name of this Book? by Raymond Smullyan, in which it's humans and vampires instead of angels and demons, and bal/da for mushroom/artichoke; or (b) taken from a book that plagiarized Smullyan shamelessly.

Either way, this problem appears at the end of a chapter that builds up to it extensively. Asking it out of the blue is perhaps incredibly unfair.

Tahnan
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Albert wrote:
I think I may have got something. It's a bit convoluted and there are plenty of ways I could have gone wrong though.

Click here to view the secret text

×
"Please count the number of yeses you would have given me if I had asked you these three questions before you started speaking in code.

1. Are you sane?
2. Does 'mushroom' mean 'yes'?
3. Is the card red?

Now, is your number even?"

Artichoke means red, mushroom means green.

Suppose you ask an insane angel, when mushroom means "yes" and the card is red. His answer:

Albert
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Tahnan
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Albert wrote:
...then says the word he thinks is 'yes', which is 'artichoke'.

What? No. If he wants to answer "yes", he'll say "mushroom"; if he wants to answer "no", he'll say "artichoke".

Albert
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We're interpreting the rules differently then.
I was under the impression that insane people get the codewords wrong, along with everything else.

Blondbeard
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This might work. Depending on if it's a legal question...

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[Last edited by Blondbeard at 09-25-2007 10:01 PM]

calamarain
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Tahnan wrote:
OK, this was either (a) taken from What is the Name of this Book? by Raymond Smullyan, in which it's humans and vampires instead of angels and demons, and bal/da for mushroom/artichoke; or (b) taken from a book that plagiarized Smullyan shamelessly.

Either way, this problem appears at the end of a chapter that builds up to it extensively. Asking it out of the blue is perhaps incredibly unfair.

Yep, it's from What is the Name of This Book. I love that book, though I think The Lady Or The Tiger? is better.

And yes, people are interpreting the rules differently. Either that, or Smullyan assumes that yes/no are implicitly replaced by the codewords.

Say M = yes and A = No

An insane angel will think that M = no, and when asked "Is M yes?", he will answer honestly, using the word *he* thinks is no, i.e. M. This is a different outcome from the book, since there's a teensy bit of parity arising.

And regarding the fact that it's at the end of the chapter... I've asked a few heavenly logic ones before, and they've been answered quite easily, even the one about the three possible statements in court.

So I thought I'd go all out and put the hardest logic puzzle I could find out there, and see if anyone could actually get it. If you lot are able to solve larrymurk's holds then this should be trivial

____________________________
My Holds

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[Last edited by calamarain at 09-26-2007 01:07 PM]

Tahnan
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calamarain wrote:
And regarding the fact that it's at the end of the chapter... I've asked a few heavenly logic ones before, and they've been answered quite easily, even the one about the three possible statements in court.

So I thought I'd go all out and put the hardest logic puzzle I could find out there, and see if anyone could actually get it. If you lot are able to solve larrymurk's holds then this should be trivial

For the former: the ones before could be solved by simple trial and error--just assign all the possibilities and run through them to see which one is consistent. This is a puzzle of a different color.

And as for the latter, well, speaking as someone who works professionally in formal logic, ability to solve DROD rooms and ability to do logic are, I think, two very different ways of thinking. ("You can solve a larrymurk room...I figured you'd have no trouble curing this disease!")

In all seriousness, I'd encourage people to get the book and work through it, rather than reading the answer here if (and when) someone solves it. It's a fine book, and you'll be somewhat better prepared to face this one if you've done the ones before it.

calamarain
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Tahnan wrote:
And as for the latter, well, speaking as someone who works professionally in formal logic, ability to solve DROD rooms and ability to do logic are, I think, two very different ways of thinking. ("You can solve a larrymurk room...I figured you'd have no trouble curing this disease!")

I was being sarcastic I am fully aware that the two are different. Too many of my friends are computer scientists for me not to be aware. Why do you think I included the winking smiley?

In all seriousness, I'd encourage people to get the book and work through it, rather than reading the answer here if (and when) someone solves it. It's a fine book, and you'll be somewhat better prepared to face this one if you've done the ones before it.

Oh, definitely. And his other book "The Lady or the Tiger?" is even better, the Monte Carlo Lock puzzle is to die for. It's got a whole mathematical novella behind it

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My Holds

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[Last edited by calamarain at 09-26-2007 06:22 PM]

Ezlo
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*Bump*

I don't know about you, but I'd like an answer.

calamarain
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Ezlo wrote:
*Bump*

I don't know about you, but I'd like an answer.

Blondbeard posted one.

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Ezlo
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Oh, I don't think you ever said so.

Bunches
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I don't know about you guys, but I'd open the box, and find out.

Jatopian
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Bunches wrote:
I don't know about you guys, but I'd open the box, and find out.

Ah, but that is an action, and the riddle asked what question you could ask.

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Bunches
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Jatopian wrote:

Bunches wrote:
I don't know about you guys, but I'd open the box, and find out.

Ah, but that is an action, and the riddle asked what question you could ask.

So I'd ask a random question, ("Are your socks blue?) and then open the box. It'd work!

BenStandeven
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Following the rules everyone here seems to be using, try:

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[Last edited by BenStandeven at 11-05-2007 04:45 PM : oops, forgot secret tag.]

Blondbeard
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Yes. That's definitly cleaner than my variant. Have a mod point!