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Head Bands


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81 replies to this topic

#41 bigcitybrom

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Posted 30 November 2007 - 09:04 PM

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.
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#42 cbcarey

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Posted 04 December 2007 - 12:46 AM

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.
Spoiler for ...

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#43 Smithsps

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Posted 09 December 2007 - 05:35 AM

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.)
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#44 kashmoney

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Posted 24 January 2008 - 12:34 AM

;) I GOT IT! his headband is white cuz d other 2 red
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#45 CGT

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Posted 01 February 2008 - 07:46 PM

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:
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#46 rookie1ja

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Posted 02 February 2008 - 12:46 AM

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.


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#47 sunrayk

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Posted 09 February 2008 - 06:00 PM

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 by sunrayk, 09 February 2008 - 06:03 PM.

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#48 W!3N3R

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Posted 12 February 2008 - 07:42 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. 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.


Spoiler for Solution



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?
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#49 im_stupid_hehehe

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Posted 14 February 2008 - 04:20 AM

or one said to the other "your headband is so and so" then the other would've said "My headband is so and so" :P
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#50 MysteryKidakaJohnDoe

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Posted 17 February 2008 - 02:11 PM

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.
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