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 The Pipe Smokers Of Mombaru

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Roqsan



Age : 673
Location : Somerset, England
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PostSubject: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 3:08 pm

Actually, although I didn't say so on the welcome thread I had an ulterior motive in joining BoB and that is to get the help of such knowledgeable pipe smokers on a little problem that I have. I think it's probably best if I give you the whole story:

Recently, I was travelling in the South Pacific and due to a storm my plane was forced down on a landing strip on the small island of Mombaru; The pilot told me that there were many such islands in the area that aren't on any map. Curiously, on this island there is a an old culture of pipe smoking that dates back into the misty labyrinths of time. According to the pilot, the islanders grow a very interesting tobacco, which is almost identical to the original Balkan Sobranie, but with a subtle casing akin to the mythical ambrosia of the gods. Also, this sublime weed has the interesting property that the mystical, contemplative life that results from smoking it (they use conch shell pipes, I think, but one cant be sure...) acts as a truth drug and so it's absolutely impossible for a Mombaran pipe smoker to ever tell a lie.

I understand that at one time all the islanders were in fact pipe smokers (who wouldn't be with such a miraculous weed to toke on), but some time ago an anti-smoking zealot arrived on the island as a missionary and converted about half of the population into non smokers. So now, tragically, about half the population are smokers and the other half are not. And worse, the lies and deceit of the anti smoking lobby, along with the enforced lack of pipe smoke has resulted in an unfortunate situation whereby none of the non smokers on the island can ever tell the truth. Sad, but true.

When, the pilot told me this story, over the sound of the engines as he wrestled the twin engined plane into the tiny Mombaran landing strip, I asked him if I could obtain some of the wonderful tobacco grown by the islanders. But he told me that it would be very difficult. What you need to do, he said, is to determine which of the islanders are pipe smokers and which are not. That's very hard, he said, because, not only do the pipe smokers do all their smoking in secret (so that the missionary can't catch them at it), but the islanders are given to answering any questions about pipe smoking in oblique ways, again so as not to offend the missionary. if you combine that with the fact that smokers always tell the truth and non smokers always lie, you can see the problem.

On landing, I noticed three houses quite close to the landing strip and I immediately went to visit them:

At the First house, I knocked on the door and it was immediately opened by a Mombaran native and his wife. Gauging my words carefully I said: "Which, if either of you is a pipe smoker and which if either is a non smoker?". "Neither of us are smokers", the Mombaran native yelled and slammed the door.

At the Second house, thinking that it might be like the first, I asked: "Are you both non smokers?". "At least one of us is", replied the native turning his back contemptuosly.

At the third house the native, when questioned on the subject, responded: "If I am a pipe smoker then so is my wife".

After that the pilot came to fetch me and we had to leave without having scored any tobacco. Now in order to return to Mombaru to get some tobacco I need to know in each case which of the natives and their wives in the huts near to the landing strip are pipe smokers and which are not pipe smokers. It would never do to approach a non smoker as the missionary would get to know and I need to approach as many pipe smokers as possible to get the maximum amount of weed. So can anyone help? If all works out you will, of course, be rewarded with Mombaran pipe weed (if you aren't married).
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bruins

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Age : 48
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 3:20 pm

cheers cheers cheers i love it! i don't have the answer yet, but i love it! (i'll put my daughters to work on this, they're little puzzle machines...)
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 3:39 pm

At the first house the person that didn't answer you is a pipe smoker.

At the second house the person who spoke is a pipe smoker.

At the third house both are pipe smokers.

Question

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ZeroContent

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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 3:50 pm

Didn't the government use pot as a truth serum? So it's probably closer to our mary jane than it is our tobacco. :-)

So the smokers are the wife in the first house and the respondent in the second and the wife in the third, the native in the third may or may not.
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Roqsan



Age : 673
Location : Somerset, England
Registration date : 2010-11-02

PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 4:27 pm

@JH&Zero Well I'm not sure since you don't give any reasons. I'm not going to make the long trip back to Mombaru based on such bare faced assertions, I'd need to be convinced of the reasoning behind these deductions, I think. Oh and besides you both disagree on the third house.


Last edited by Roqsan on Wed Nov 03, 2010 4:40 pm; edited 1 time in total
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 4:38 pm

You mean I have to go through all that convoluted logic again to try and remember how I arrived at my conclusion? I processed that in RAM and quickly dumped it as soon as I was finished. Laughing

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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 4:48 pm

First one is pretty easy. Stating that neither of them are smokers means it is a lie by default because nonsmokers can't tell the truth. If they both weren't smokers that would make the statement true, so the person not speaking must be a smoker.

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Roqsan



Age : 673
Location : Somerset, England
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 4:54 pm

jhuggett wrote:
First one is pretty easy. Stating that neither of them are smokers means it is a lie by default because nonsmokers can't tell the truth. If they both weren't smokers that would make the statement true, so the person not speaking must be a smoker.

That seems pretty convincing, now why didn't I think of that? But I'm still puzzled by the 2nd and 3rd houses.
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 5:00 pm

The second one. The statement is "at least one of us is" a non smoker.

If both are non smokers then that statement is true but non smokers can't tell the truth.
If both are smokers that statement would be a lie so that can't be the case.
If the speaker was a non smoker that statement would be true but non smokers can't tell the truth.
Only conclusion is that the speaker smokes and the other person doesn't because then the statement would be true and wouldn't break the rules of a smoker always telling the truth.

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Roqsan



Age : 673
Location : Somerset, England
Registration date : 2010-11-02

PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 5:08 pm

jhuggett wrote:
The second one. The statement is "at least one of us is" a non smoker.

If both are non smokers then that statement is true but non smokers can't tell the truth.
If both are smokers that statement would be a lie so that can't be the case.
If the speaker was a non smoker that statement would be true but non smokers can't tell the truth.
Only conclusion is that the speaker smokes and the other person doesn't because then the statement would be true and wouldn't break the rules of a smoker always telling the truth.

Ah, I see
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 5:11 pm

The third house. The statement is "If I'm a pipe smoker than so is my wife."

This one is harder for me to explain. Being it's a conditional statement of fact it has to be true in order to state anything. If it's not stating anything, it's not technically a lie. If neither of them smoke that statement is still not a lie and a non smoker always lies. So to make it a statement of fact and for it to be true they must both be smokers.

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Roqsan



Age : 673
Location : Somerset, England
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 5:43 pm

jhuggett wrote:
The third house. The statement is "If I'm a pipe smoker than so is my wife."

This one is harder for me to explain. Being it's a conditional statement of fact it has to be true in order to state anything. If it's not stating anything, it's not technically a lie. If neither of them smoke that statement is still not a lie and a non smoker always lies. So to make it a statement of fact and for it to be true they must both be smokers.

That's a really interesting way of looking at it! If the guy is a smoker then because, in that case, he must be speaking the truth, both he and his wife must both be smokers, given that he is a smoker. And that's exactly what he said so the statement "if I'm a smoker then so is my wife" is true on Mombaru and can only imply that they are both smokers.

Unfortunately, I was in a bit of a hurry when writing the OP and I now remember that I actually visited four houses and not just the three mentioned previously. Now what happened at the fourth house was that the native husband said: "My wife and I are either both smokers or both non smokers".

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hobie1dog

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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 6:31 pm

You just had to complicate things with that fourth house, didn't ya? Suspect
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pistolero

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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 6:32 pm

scratch scratch scratch

Go back where you came from and take your evil ways with you.
AAAARRRRGGH!!!
affraid

J/K, welcome to BOB.
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 7:13 pm

The entire time I was killing my weak brain over these little problems I kept thinking that there has to be a formula for these types of logic problems. Low and behold there is an entire system of these logic problems based around this scenario. Pretty cool actually. Thanks for making me learn something new Roqsan!

Hint if you want to read about it do a google for "knights and knaves".

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Roqsan



Age : 673
Location : Somerset, England
Registration date : 2010-11-02

PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 8:15 pm

jhuggett wrote:
The entire time I was killing my weak brain over these little problems I kept thinking that there has to be a formula for these types of logic problems. Low and behold there is an entire system of these logic problems based around this scenario. Pretty cool actually. Thanks for making me learn something new Roqsan!

Hint if you want to read about it do a google for "knights and knaves".

Well I suppose the cat is out of the bag. knight/knave problems were invented by Raymond Smullyan to illustrate some ideas in propositional logic, such as Godel's theorem. I think they're a lot of fun and had a laugh trying to reformulate them in terms of pipe smoking. I see that I'll have to work a bit harder... Pretty neat to get the answer to those first three problems so quickly having never seen this stuff before! Grrr Sad
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jhuggett
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PostSubject: Re: The Pipe Smokers Of Mombaru   Wed Nov 03, 2010 8:21 pm

I probably shouldn't of let the cat out of the bag. Oops. I was just so excited to read about it.

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Roqsan



Age : 673
Location : Somerset, England
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PostSubject: Re: The Pipe Smokers Of Mombaru   Thu Nov 04, 2010 6:08 am

jhuggett wrote:
I probably shouldn't of let the cat out of the bag. Oops. I was just so excited to read about it.

Yes, I was sorry to have to admit that the natives of Mombaru are probably not pipe smokers at all and just common or garden knights and knaves as described by Raymond Smullyan. Also, I have to admit that the tobacco I mentioned was also somewhat mythical. Nevertheless, it may be that there is actually tobacco on Mombaru and one of the natives might know something about it. It looks like I'll be able to make a quick stop over at Mombaru on my next trip to the South Pacific, but I'll only have time to ask this particular native one question, and apparently he will only answer questions with a simple yes or No. Given that I'm not sure whether the native is a knight or a knave, I'm having some difficulty in formulating a suitable question...
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