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Head Bands

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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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Posted · Report post

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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Posted · Report post

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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Posted · Report post

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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Posted · Report post

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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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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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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Posted (edited) · Report post

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
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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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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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The person at the back would be able to say what color their headband was because if they knew how many headbands theer were then if they saw 2 red headbands then they would know that the color of theirs was white but if thay saw only 1 red in front but 2 whites and 1 red in front then you couldn't be quite sure what color anyones was. ^_^

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Couldn't the last person in the queue also be able to guess this correctly? Assuming the 3 men knew the amount of white and red bands (3 and 2) the last man could see that the first two men both have red bands. The 3rd man knowing there are only 2 red bands could then realize that he must have a white band and state that thus setting them free.

Yes, you are correct. There are two possible outcomes. Either the third man sees two red headbands and says his is white, or the third and second are silent and the first guesses his is white.

Excellent puzzle. :)

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im not sure if im right but im guessing that the head band was white, because 2 men were white and theres blended in and the other one was a different skinned color besides white, thats why they could see his... like i said, not sure

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Posted · Report post

It was dark inside the teepee so none of the prisoners saw any of the headbands. All three were white. ?? :unsure:

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No way! This answer is BOGUS! The question only states that one of them spoke up, it doesn't say the first one spoke up. It solves the puzzle equaly well to have per1 and per2 wearing white, and per3 saying he has red because he can see the two whites. And the idea that someone might pause to double check in his head how many of each color headbands there were before speaking up when his life is on the line I think is perfectly reasonable.

..but if you had paused to double check how many of each colour headbands there were, you would have found that there were a possible three whites, so if per3 saw 2 whites in front of him he would not know if he had a red or a white. That's why he didn't speak.

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Posted · Report post

a pretty easy way would be if it was red it would absorb heat and be warmer

white reflect heat and be cooler

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like senti_2k2 said....what if third sees 2 white headbands?

If the third sees only 2 white then he is unsure what color his headband is... but the first still knows 2 red were not seen by the third

Going by the second prisinors silence he still safely assumes he has a white himself.

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there r 7 cases

www 1st person

rrw 3rd

rww 2

wrw 1

rwr 2

wrr 1

wwr 1

3rd should say immediately

2nd should wait and say for a min

1st should wait for a while and should say

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The third person will be able to make out if he has for certain a white headband. if he remains quiet it means that the people before him have either two white or a white and a red headband. If he remains quit the second person will consider this and answer acording to what he sees. either he sees a red band and he knows he is white eihert he sees a white band and he cannot respond to the question since he can have either red or white

. the silence will even be lopnger so after a day or so the 1st person will realise that neither of the man can determine the colour of their headband so he know his is white because if it were red the second person would have been able to say white and the third could hhave been quite or the second person was quiet and the third person responded.

the only fact they have to know is that there are 3 white bands and 2 reds

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B))

the third guy said his head band was white, this is because there r only 2 red, so the 2 infront of him must be red, so by process of elemination he was able to conclude that his was white since that was the only color left

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ok so the way i see it is that it is the second person who answers.

It has been established that if the first 2 had red bands then the third person would know they have a white band and reply immediately.

As they did not we know that of the first two, one has a white the other has a red band. The second person can see what colour the first has and so replies with the other colour.

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Posted (edited) · Report post

The clue is in the question. "The chieftain was willing to let them go ". Therefore he will deliberately make it as easy as possible for them i.e R R W in that order so the last person can confidently say his head band is white

Edited by AliceJH
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Actually, the reason that folks are confused about the answer to this riddle is found not in the difficulty of the riddle itself. The riddle is actually designed to be rather simple, but only in its proper form. The poster of this riddle has ommited a key element of making the riddle solvable in his presentation of the riddle, but continues to view the riddle with the ommited material in mind when posting rationalizations of the simplicity of the solution.

Simply stated, you must tell the puzzlee that the chief has promised that the three captives will not all wear red head bands. The fact that at least one captive will wear a red headband is self-evident in the number of available white headbands in relation to the number of captives. However, as the riddle is currently worded, it is entirely possible that the third man in line would look forward to see two red headbands on his fellow captives and have no certainty whatsoever that he himself is not wearing a red one as well, or for that matter has been adorned with one of the white ones. His silence, or reluctance to make a guess, offers no information to either other man as to the color of his headband, except of course for the obvious point that both front men are not simultaneously wearing white.

To avoid a more exhaustive explanation, the second man cannot know in any case (as currently posed in the riddle) the color of his own headband unless a very specific order of the bands is being used (1.White,2.Red,3.Of no consequence). No.2's silence (when added to the third man's silence) does afford a bit of information to the first man in the line, but only in the circumstance that if he (the second man) sees a white headband on the man in front of him, then he can clearly only know that his own headband is not also white, as just proven in the above placement. Otherwise, the third man would have claimed his own to be red right away. (If you have trouble understanding why this is so, or perhaps do not agree right away, keep in mind that all three headbands could conceivably be red in the current wording of the riddle)

The first man would never be the only captive with the answer to the solution, no matter how the bands were arranged. I won't bother describing the logic to this, but suffice it to say that there a number of situations in which the first man could know the color of his own headband, but not without the second man already being aware of his own and speaking up.

The person who posed the riddle has given us a good logic puzzle, but unfortunately left out a key detail. There are simply too many scenerios (placements of colors coupled with silence) in which no man would be able to answer the riddle definitively at such high stakes without knowing for certain beforehand that the chief was forbidden to give every man a red headband.

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Posted (edited) · Report post

Although the "correct" solution may indeed be that the 1st man stated he had a while headband, there is truly only one other possible answer - given the information in the brain teaser. As others have pointed out, the third man could have said he had a white headband since, there being only 2 red headbands, if he saw that the men before him had red headbands, then he had to have a white one. The biggest problem with this teaser is the amount of time passing before an answer was given. We do not know for sure the reason why #3 would not make an immediate guess, but it is possible that he did not immediately respond (possibly because he was color blind, possibly because he was just slow in nature - not slow-witted) even though he knew he had to have a white headband.

So, since there is a little ambiguity, there are 2 correct answers: the first man or the third man responded white, but the only man who could answer without guessing is the third man, so that may actually be the best answer! :rolleyes:

Edited by RaDazzle1
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Posted · Report post

I don't think they made it - they can't see with a headband on - can they?

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