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Head Bands


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#31 rookie1ja

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Posted 22 September 2007 - 10:51 AM

"Three white men were taken captive by a hostile Indian tribe."

Why do they have to be white? Are you saying that Caucasian people are all victims now? Or is it that all other races are of such subordinate value that nobody would want to take them captive? Is that it? Why do you have to bring race into the whole thing? Does it even need to be species-specific? Couldn't we have the same brain teaser with an organism taking another organism captive? I'm here to tell you that it's a C-O-N.... um... -spiracy! That's what it is!


right, it is conspiracy ... I have hidden a secret message for sleeping agents
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#32 BoilingOil

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Posted 26 September 2007 - 12:19 AM

it looks like most responses have somewhat missed the mark. The question asked was:


What colour was his head band? And how would you reason it?


Several responses called it out correctly. Seven scenarios exist with 3 total results:
W R R
-3rd man sees 2 reds - knows his own is white

R W R
W W R
-2nd man sees 1 red - knows his can't be red or 3rd man would have seen 2 reds and called white, therefore 2nd man knows his own is white

R W W
R R W
W R W
W W W
-1st man hears no response from 2 & 3, deduces 3rd man didn't see 2 reds and deduces 2nd man didn't see one red, so 1st man knows his own is white.

Therefore one of the 3 called out white correctly. We don't have enough info to know which man it was though. This of course hinges on enough time passing for 1st or 2nd man to assume the men behind them had a chance to reason it out correctly.

Finally, there's one more possibility no one has mentioned...
3rd man gives some indication to 2nd (or 2nd to 1st) of the color of the other man's headband. The puzzle said they were quiet, but it doesn't preclude one of them communicating the color of another's headband to him - perhaps by tapping morse code on the other man's back or writing a note and passing it to him. Cheezy answer? Sure, but possible given the rules...



I have to agree with PDR here, because I came to the same conclusion before joining the crew
However, there are a few more things to point out:
1. If it is pitch dark in the tepee, the Chieftain himself must not be seeing what he is doing. So unless he knows exactly which is which by some other method, it must be a gamble for himself as well
2. The original question does not say that the white men are told how many red and white bands there are... I think they MUST have been told for this test to even work. Still to me it seems better if the question were edited to include this, only to assure that nobody says: this makes no sense!!!

Thank you,
BoilingOil
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#33 rookie1ja

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Posted 26 September 2007 - 09:02 AM

2. The original question does not say that the white men are told how many red and white bands there are... I think they MUST have been told for this test to even work. Still to me it seems better if the question were edited to include this, only to assure that nobody says: this makes no sense!!!


I have edited the puzzle long time ago ... and it includes the condition:

He put one head band on each of their heads (he had 3 white and 2 red - so 2 head bands were not used - captives were informed about these numbers).


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#34 BoilingOil

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Posted 26 September 2007 - 03:53 PM


2. The original question does not say that the white men are told how many red and white bands there are... I think they MUST have been told for this test to even work. Still to me it seems better if the question were edited to include this, only to assure that nobody says: this makes no sense!!!


I have edited the puzzle long time ago ... and it includes the condition:

He put one head band on each of their heads (he had 3 white and 2 red - so 2 head bands were not used - captives were informed about these numbers).



I completely overlooked that... I stand corrected!
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#35 music5

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Posted 14 October 2007 - 10:59 PM

ok ok,..so theres 3 white headbands and 2 red headbands,...if two men had the red headbands then the last guy would know that he has the white headband. but if all three of them has white headbands,..they would have to make a risky guess saying that they all had white bands.
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#36 orthopod911

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Posted 19 October 2007 - 04:19 AM

Constraints demand there will be either 2 red and 1 white, 1 red and 2 white or 3 white. If front and middle men both have red, man in back immediately knows his is white and says so. Since he does not, front and middle men now know they don't have reds, so they have to have 1 white and 1 red or 2 whites. If the middle man now sees the front man has red, he knows he must have white and speaks up. Since he does not, this leaves only white for the front man, who now knows this and speaks up.
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#37 ali500

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Posted 22 October 2007 - 04:06 PM

This is alot like the master ones so it must have been fair meaning the head band was white. the guy used logic or magic
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#38 howelegant

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Posted 22 October 2007 - 06:31 PM

I thinking that the first guy was color blind and could not see reds! So logically the other guts knew that he had a red band assuming they know he could not see red.
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#39 mujoma

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Posted 06 November 2007 - 08:37 AM

you cant change the parameters mid way through!

there is no logical way to deduce the outcome.

either they guessed right or they were scalped

simple answer: a leap of faith
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#40 scottI

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Posted 09 November 2007 - 07:22 AM

I think this answer is a little better. The person at the end of the line knows there are at most 2 red head bands for him and the people in front of him. If he sees two red head bands his is white. Otherwise he does not answer. This tells the middle person in line that there are at most 1 red head bands for him and the people in front of him. If he sees one red head band his is white. Otherwise he does not answer. This tells the person at the front of the line there are at most 0 red head band for him and the people in front of him. If he see zero red head bands his is white.

This may be generalized to n people and n-1 red head bands. The scheme is just to have the mth person in the line wait n-m+1 seconds to answer if he decides to answer. If no one has answered and he only sees red head bands in front of him, he knows he is white.
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