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Head Bands


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81 replies to this topic

#51 DarkCat

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Posted 04 March 2008 - 12:31 AM

7 Possibilities:

RRW - the third can correctly state his colour as White
RWR - if the third cannot identify his colour, the second knows his colour as White
RWW - if the third cannot identify his colour, the second knows his colour as White
WWW - the second and third do not know and do not speak; the first will know he MUST be white
WWR - the second and third do not know and do not speak; the first will know he MUST be white
WRR - the second and third do not know and do not speak; the first will know he MUST be white
WRW - the second and third do not know and do not speak; the first will know he MUST be white
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#52 kb3mkd

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Posted 16 March 2008 - 10:49 PM

7 Possibilities, 3 outcomes:

RRW - the third can correctly state his colour as White. if he says nothing his colour becomes irrelevant.
RWR and RWW - if the third cannot identify his colour, the second knows his colour as White. If he says nothing his colour becomes irrelevant also.
WWW, WWR, WRR, WRW - the second and third do not know and do not speak; the first will know his MUST be white


In no case can anyone logically claim a red headband.
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#53 222

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Posted 20 March 2008 - 08:09 AM

Captive 1 was in the front of the line seeing nothing remains silent.
Captive 2 saw only captive 1's headband and is unsure of whats behind him so remains silent.
captive 3 sees the two headband in front of him and is the only one who can give the most intellegent response.
He saw 2 red headbands on the men in front of him, and after his eyes adjusted to the sunlight he responds that his headband is white.
With your life on the line no one elsewould risk guessing.
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#54 kleeble

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Posted 24 March 2008 - 11:52 AM

It's possible that somebody has already posted this but I find the explanations more confusing than the problem.

All the men A, B and C. A can see both, B only C and C can see nothing.

There are only three possible scenarios :

If B and C both wear Red, A knows his is white.

If B wears white and C wears red, B knows his is white because the above declaration has not been made.

If B wears red and C wears white, C knows his is white because neither of the above declarations have been made.
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#55 sunshipballoons

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Posted 25 March 2008 - 09:08 PM

Head Bands - Back to the Logic Puzzles
Three white men were taken captive by a hostile Indian tribe. The chieftain was willing to let them go so he took them to a tepee, where there was no light.


If there's "no light" in the tepee, how do they see the headband? :rolleyes:
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#56 Talent

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Posted 25 March 2008 - 10:58 PM

I tried to logically work it out from the thrid man's frame of mind.

Which gives the same result:

They know there are 5 headbands.
The possibilities for the headbands that the third man can see are:
W W - A 1/5 chance his is white, a 2/5 it is red.
R R - 100% sure it is white
W R - A 2/3 chance that it is a white one. As 2 white unaccounted for and 1 red.
R W - Same thought process.

Therefore he would guess White for his own. The last man that it is.

If there's "no light" in the tepee, how do they see the headband?


Then they went out in a queue so that each man saw the head-band of those standing in front of himself


.........
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#57 stoica_cv

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Posted 06 April 2008 - 11:22 PM

i am going to post my explanation again, for the benefit of those confused. this time, there will be colors denoting the important parts...

the clues we have are as follows:

1st and 2nd can't both have red because 3rd person would have immediately known he had a white headband. Therefore 1st and 2nd either both have white or have one red and one white. (Note: if 1st and 2nd both have white then the 3rd sees 2 white headbands, which is what everyone seems confused about...)

The only logical conclusion is that the first person has a white headband then. Why? Because if the first person had a red headband, the 2nd person would have immediately said that he himself had a white headband if the 3rd person didn't say anything. Since the 2nd person didn't say anything (due to there being a "quiet while" - long silence), the 1st person can conclude that the 2nd person isn't seeing a red headband, so the 1st person must have a white headband.

Obviously, if the 3rd person sees 2 white headbands, the 2nd person wouldn't see a red headband on the 1st person. I guess I really needed to point that out? ><



The 3rd wouldn't say anything in both situations: 1st and 2nd have white or read; 1st and 2nd both have white. Correct?
Now, how could someone assume that he has a read headband when it could also be white?
Your assumtion starts wrong from the beginning because you completely ignore the fact that they all 3 could have 3 white headbands, there is the kesy.
So, if they all would have white headbands how could they know what headband has each of them? It's impossible. Why? Because the 3rd wouldn't know what collor his heat is,
could be white or read ,so he will say nothing.
In your explication 1st assumes he has a red headband and because (according to your solution) he and the 2nd could have a read headband or a white headband (you skip
the fact that they could also they both white headbands) the 2nd do not say anything because he sees a white band on it's head (1st's), so, the 1st say"I have a white headband".
But your solution starts from a wrong assumtion because you skip the fact that both could also have white headbands which situation the 3rd can't also
say anything (or he could also have a RED headband on it's head, but he couldn't know that right?)
Again, when you make an assumtion don't take only 1 posibility, take it all and the posibilities THAT MATTERS are :
1. they all have white headbands
2. 1st, 2nd have white headbands and 3rd can have white headband or red headband
3. 1st and 2nd have both reds and this is the only one posibility and the solution my friend is the most simple from all: THE 3RD WILL SAY "I HAVE A WHITE HEADBAND".


Conclusion: you logic is wrong because the first 2 could have:
1. read and white
2. white abd read
3. white and white
Your solution would have been good if there wasn't possible the 3rd situation which you "skiped it".
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#58 killaklown

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Posted 07 April 2008 - 04:51 PM

If the open there eyes with the head bands on, they would know if its a light one or not, then they can say which one they have. Or they can take it off and look, doesnt have any punishment for that.

Edited by killaklown, 07 April 2008 - 04:52 PM.

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#59 katemonster

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Posted 10 April 2008 - 08:00 PM

I like this puzzle told better as three Wise Men trying to prove who's wisest or some such, as it makes it more clear what the solver's thinking process should be. As it is, it sounds like the answer ought to be, "Duh, the third guy sees that the only two red bands are on the guys in front of him, so he knows his is white!"
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#60 insidexraindrops

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Posted 12 April 2008 - 01:59 PM

Assuming that the first and second man had the same color headbands, then it could have been the third man to speak. However, if the first two men had different colored headbands then the third man would have remained silent (for he could not guess upon the fact that the headbands of the men in front of him). In this case, it was the second man to speak because by the third mans silence, the second man could assume that he had the opposite colored headband of the first man.

Voila! They're free. :)
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