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#78410 08/22/02 02:31 PM
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That proves my point - when there is only one representative of each sort (be it from a collection of two or two thousand) it is reasonable to ask which one.

If you had shown me seven glasses made up of four pints of Thwaites Best Bitter, and three of Greene King's Abbot Ale Everard's Beacon Ale, and asked me, "here are 7 pints of ale, which one would you like to try first," I would still think you were asking which glass, not which ale. (And I would select the furthest away, on the grounds that by the time I got to the seventh, I would need it to be near at hand!)



#78411 08/22/02 02:47 PM
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Quite the otherwise, my good Rhuby. I would be asking you which one of the two choices you would like to try first. Although I might (I don't know if they are distinguishable by color) be attempting to see if you can distinguish between them by taste. In fact I would probably have you blindfolded, which is really a good analog to the Blackfeet/Whitefeet situation.

Perhaps we are arguing Pondial differences here, in which case, forget it.


#78412 08/22/02 02:53 PM
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Hmmm. The analogy falls down (as usual) if you try to push it too far - both ales are models of probity and the best way to tell which is which is to taste them (and, Yes, I could tell which was which from the taste! - not from the colour, which is very similar, but possibly from the head. [the froth on top])

Why don't you pop across, and we can put it to the test?



#78413 08/22/02 02:56 PM
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I would love to hear TEd's question, if indeed it is, as I interpret your comment on it to imply, valid in general but not in the specific.


#78414 08/22/02 03:13 PM
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Cannot be done with one question if there are two who may be from the same tribe:

Assume two Indians, A and B. There are four possibilities:

Both are whitefeet, so they both tell the truth
Both are blackfeet, so they both lie.
A is a whitefeet, who always tells the truth. B is a blackfeet, who always lies.
A is a blackfeet, who always lies, and B is a whitefeet, who always tells the truth.


First question, asked of A:

What will B say when I ask him to predict your answer if I ask you what color your feet are.

If both are whitefeet, A would answer the underlying question by saying “I have white feet.”
B would predict that A would say that.
A truthfully says that B would predict that A would answer by saying that A has white feet..

If both are blackfeet, A would answer the underlying question by lying: “I have white feet.”
B would predict that A would answer the question by saying, “I have black feet”, which is a lie because a blackfeet would say that he had white feet, so a liar would predict that he would say just the opposite.
This means that A would say that B would predict, “A would say that he has white feet.” Which is the truth, but we didn’t ask A what color feet he had.

If A is a whitefeet and B is a blackfeet, A would have answered the basic question by telling the truth: “I have white feet.
B would have to say that A would say he has black feet, because he has to lie.
A, knowing that B would lie, would have to predict that B would say that A has black feet.

If A is a blackfeet and B is a whitefeet, A would have answered the basic question by saying that he has white feet (a lie).
B would say when asked that A would say he has white feet, because that’s the truth about the lie A would tell.
A would then say that B would say that A has black feet.

If the answer to the first question is white feet, then you know that both of them are from the same tribe, since that’s the only combination that elicits that answer. Ask A: What will B say if I ask him what color his feet are? If B is a blackfeet, he will answer the question by lying: I have white feet. A would then predict that B would answer black feet, since he has to lie. If both of them are white feet, B would say I have white feet and A would agree with him. Thus, if A answers black feet, you know they both have black feet. If A answers white feet then you know that they both have white feet.

If the answer to the original question was black feet, you know that one of them has black feet and the other has white feet.

Ask A: what will B say when I ask him what color feet he has.

IF A is a whitefeet, he knows that B will answer that he has white feet, and will tell the truth: B will say that he has white feet.

If A is a blackfeet, he knows that B will truthfully say, “I have white feet”, so he will say, “B will say he has black feet.




TEd
#78415 08/22/02 03:37 PM
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What will B say when I ask him to predict your answer if I ask you what color your feet are.

a beautifully reasoned response based on not knowing whether there were representatives of both the tribes present.

A beautifully reasoned response, indeed, but disallowed since it is a question about what he would *say not about the *colo(u)r of their feet.

I hereby withdraw my defense of TEd's claim to anything in particular.




#78416 08/22/02 04:00 PM
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Only one way to settle this, Rhuby. When the ASp and I come over there to visit y'all we'll head on over to your favorite local and you will set me down, blindfolded, and lay in front of me, three pints. One of Thwaites Best Bitter, one of Greene King's Abbot Ale Everard's Beacon Ale and one of either of those to be decided at a later date by a disinterested third party. You will then ask me which one I want to try first. I will try them all and attempt to determine which two pints are of the same variety.


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Assume two Indians, A and B. There are four possibilities...

Now hold on a minute.

Did I miss something? I don't recall the question indicating that Indian A and Indian B knew each other, or more specifically which tribe the other was. (Maybe the tribes are very small, and everybody knows all the members of both tribes? But that isn't stipulated, either, or excluded. And if the tribes were visually identifiable, the questioner would be able to tell, too.) So neither one necessarily knows what the other will say, and the argument fails.

All of which is quibbling, of course, because we all know very well exactly what was meant, and all we're doing is pointing out the lack of perfection in phrasing the question initially, which [imperfection] is permitted. Or ought to be.


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You have to assume that the Indians know one another's tribal affiliation, otherwise the problem has no solution.

And since the questions I set out can be answered with only "black feet" or "white feet" I think my solution's technically correct for the most general of cases.



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You have to assume that the Indians know one another's tribal affiliation, otherwise the problem has no solution.

This problem is a specific instance of a generic truth teller/liar problem. I alluded to one of the others in my comment above about free beer in the city. In that case you only had one person to ask the question of and had to determine, not the status of the person you asked the question of but which road was the road to the city. In milum's problem, milum's solution, asking if the person's feet were green, satifies any possible interpretation of the problem from the original, poorly stated (and done so because it was being dredged up from the memory of what appears to have been a night when it was rather drunk out) statement of the problem. It also meets the criterion normally used in these problems, but not stated in this case, that the questions be yes/no questions.


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