Head Bands

[Guest]

ok ok i get it...they all like the dark

[Guest]

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...

[Guest]

hey!! come on dude!!!

wat r u tryin to prove PDR? wat do u mean by sayin "Finally, there's one more possibility no one has mentioned..." lol

haha when the question said dat one of dem has raised his hand and answered right....wats ur point mr smart?? LMAO

[Guest]

if person 1 had a red head band and person 2 had a white person 3 would not see 2 red so he would not know which he had so he would be silent.

Person 2 would see a red but that still leaves 1 red and 3 white he does not know what person 3 has.

He could assume that since person 3 did not say anything that he would not have red one as well so person 2 could have said he had a white instead of person 1 but since the question is what color was said the answer is white

[Guest]

"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!

[rookie1ja]

"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

[Guest]

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

[rookie1ja]

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).

[Guest]

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!

[Guest]

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.

[Guest]

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.

[Guest]

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

[Guest]

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.

[Guest]

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

[Guest]

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.

[Guest]

It makes perfect sense, that is correct 1 has white and his deductive reasoning was right on the money. why are ppl making it so difficult?

1 knew if 3 saw two reds he woulda yelled the answer, he also knew that 2 (based on 3's non-rsponse) knws that 3 must see a white and red or a white and white, so if 1's banadana were red, he'd (2) would know he was white, but 2 had no response leaving only one conclusion that 1 and 2 both had white so 1 yelled WHITE!

2 couldn't answer because seeing 1's white he knows he could have either white or red.

[Guest]

Note: I didn't notice that this thread was many pages long, and others already made similar posts to mine, newb here.

This can be solved for any combination of who speaks up.

Here is the full logic of how this works.

There are seven possible combinations

A w w w

B w w r

C w r w

E w r r

D r w w

F r w r

G r r w

You start with the person who has the most knowledge, that is person 3.

Person Three

The only way person three can make an assessment is if 1 and 2 both have red headbands. This means red is used up, and he must be white. He says "White" and they all go free. [layout G]

Person Two

Because person three is silent, that tells person two that person one and two are not both red. Or put another way, that either 1&2 are both white, or they are one red and one white. Now if he sees person one has a red headband, he knows he must be white (because if he and person 1 were both red, person three would have solved the puzzle). So he speaks up "White" if person three is silent and person one has a red headband. [layout D and F]

Person One

If person two is silent and person three is silent, then person one knows that he must be white, because any other combination would have been found by either person 2 or person three.

[Guest]

A1 = 1st Person

A2 = 2nd Person

A3 = 3rd Person

If A3 saw that A1 and A2 had |Red| head-bands his would be 100% |White|.

So he would pick |White|.

If A3 saw that A1 had |White| and A2 had |Red| his chance would be 66% |White| and 33% |Red|.

So he would pick |White|.

If A3 saw that A1 and A2 had |White| his chances would be 66% |Red| and 33% |White|.

So he would pick |Red|.

This is my conclusion. (It's probably wrong.)

[Guest]

I GOT IT! his headband is white cuz d other 2 red

[Guest]

I'm new to this site so I'm trying not to nit-pick too much but I'm not sure I see this as a true logic puzzle. The really good puzzles leave nothing up for interpretation and give you absolutely everything you need to know in the text of the riddle. They can usually be solved with good lateral thinking or mathematics, even if there are multiple answers.

Here are my problems with this riddle in general:

1. How do the captives know how many headbands the chief had to begin with, and that the color / distribution of them were? This should be made clear in the riddle.

2. Any of the captives could have said anything and gotten killed, the question should be, what is the one answer that could have saved them, and who could have given it without guessing?

The solution would then be "White" and "The 3rd Captive," and the only circumstances that could have led to his certainty would be if the 1st and 2nd captive had red headbands on:

Captive 1: Red, Captive 2: Red, therefore the 3rd captive could be 100% certain his was white b/c there would only be white headbands remaining. Any other combination of headbands and the 3rd captive would be guessing (66% if both 1 and 2 have white headbands and he guesses red, 66% chance if the other two have 1 red and 1 white and he guesses white).

Captive 1: White, Captive 2: Red:

[rookie1ja]

Here are my problems with this riddle in general:

1. How do the captives know how many headbands the chief had to begin with, and that the color / distribution of them were? This should be made clear in the riddle. The puzzle says: "... he had 3 white and 2 red - so 2 head bands were not used - captives were informed about these numbers ..."

2. Any of the captives could have said anything and gotten killed, the question should be, what is the one answer that could have saved them, and who could have given it without guessing? The puzzle says: "... An incorrect guess deems them to imprisonment. Only one guess can be made by the group. ..." I see, I forgot to mention that they wanted to live.

[Guest]

there are 3 white and 2 red bands, so 2 of the bands don't get used at all. the third person who can see the colors of the bands on the others' heads, would have been able to say "white" for his own headband, if and only if, the color of headbands on the two others' was red. since he does not do that, the second guy knows that the options could be either of the following:

1. both the first and second guy have white headbands.

2. one of them has red and the other has white.

if the color of the band on 1st guy's head were red, the 2nd guy would have guessed the color of his headband to be white. since he doesn't, the first guy knows that the color of his (1st guy's) headband is white.

so the correct answer is, 1st guy guesses his headband's color as white.

Edited February 9, 2008 by sunrayk

[Guest]

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. 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). Then they went out in a queue so that each man saw the head-band of those standing in front of himself (the first one did not see any head band, the second one saw the first one's head band, and the third one saw the head bands of the two others). If somebody said the colour of his head-band, they all would be free. After a quiet while one of them said: "My head-band is ...".

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

Edited:

You have to assume that all the prisoners are fairly intelligent and have confidence in the intelligence of their fellow prisoners.

An incorrect guess deems them to imprisonment.

Only one guess can be made by the group.

All the captives want to be free and live.

Head Bands - solution

The first one (he did not see any head bands) thought this way:

The last one is silent, which means, he does not know, ergo at least one of head bands he sees is white. The one in the middle is silent too even though he knows what I already mentioned. If I had a red head band, the second one would have known that he had a white head band. However, nobody says anything, so my head band is not red – my head band is white.

The 2rd and 3nd would have said something if one of the following scenarios were true:

1-red, 2-white, 3-red

1-red, 2-white, 3-white

Or of course if this scenario were true:

1-red, 2-red, 3-white

But the only plausible scenarios are:

1-white, 2-red, 3-red

1-white, 2-red, 3-white

1-white, 2-white, 3-white

Does this help anyone?

[Guest]

or one said to the other "your headband is so and so" then the other would've said "My headband is so and so"

[Guest]

The first few guesses to this riddle were overcomplicated and poorly thought out. That and the fact that you (rookie1ja) didn't explain very clearly about how the captured people got the crucial information were what made this so confusing to some people.