Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

Head Bands


  • This topic is locked This topic is locked
81 replies to this topic

#1 rookie1ja

rookie1ja

    Senior Member

  • Site Admin
  • PipPipPipPip
  • 1341 posts
  • Gender:Male
  • Location:Slovakia

Posted 30 March 2007 - 04:13 PM

Head Bands - Back to the Logic Puzzles
Three Palefaces were taken captive by a hostile Indian tribe. According to tribe’s custom they had to pass an intelligence test, or die. The chieftain showed 5 headbands – 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly – they passed the test and could go free, if not – they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few minutes of silence, the first man in the line said: "My headband is ...".
What color was his head band? Why?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.


Spoiler for Solution


Spoiler for old wording

  • 0

rookie1ja (site admin)
Optical Illusions
Support BrainDen

"To start: Press any key... Where's the 'any' key?" - Homer Simpson


#2 cheizmann13

cheizmann13

    Newbie

  • Members
  • Pip
  • 1 posts

Posted 20 April 2007 - 08:31 PM

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.
  • 0

#3 Nitevizn

Nitevizn

    Newbie

  • Members
  • Pip
  • 1 posts

Posted 23 April 2007 - 09:16 PM

I sort of disagree with this, or I am missing something. The second one only sees in front of him. So, if the first one's band has a red, then the second one could not be sure the third has a white and would remain silent. The third would only see one white and would be unsure and would remain silent. That scenario would be the same if the first had a white and the second a red. Both second and third would remain silent in that case as well. Am I missing something?
  • 0

#4 rookie1ja

rookie1ja

    Senior Member

  • Site Admin
  • PipPipPipPip
  • 1341 posts
  • Gender:Male
  • Location:Slovakia

Posted 23 April 2007 - 11:13 PM

Try to think as if you were the first one - as I mentioned above. Of course, we have to assume that all 3 are quite intelligent to pass the test that way.
  • 0

rookie1ja (site admin)
Optical Illusions
Support BrainDen

"To start: Press any key... Where's the 'any' key?" - Homer Simpson


#5 jbstorch

jbstorch

    Newbie

  • Members
  • Pip
  • 1 posts

Posted 26 April 2007 - 08:24 PM

cheizmann13 and Nitevizn:

The key to both of your questions is that there was no immediate response from anyone.

Cheizmann13, your answer doesn't work because the guy in back would see two red head bands and respond without delay.

Nitevizn, the second guy would see one red head band, and he would know that if he also had a red head band, the third guy would respond without delay. When this doesn't happen, the second guy would know his head band was white.
  • 0

#6 MikeFalcor

MikeFalcor

    Newbie

  • Members
  • Pip
  • 3 posts

Posted 18 May 2007 - 09:21 PM

Actually, whether or not they knew the number of each color is irrelevant. "He took them to a tepee, where there was no light" - Therefore, without stating that the headbands were in the possession of the Chief PRIOR to taking them out to the tepee, this puzzle cannot be solved as they would not be able to see the colors (or anything else for that matter) of the headbands nor the quantities.
  • 0

#7 senti_2k2

senti_2k2

    Newbie

  • Members
  • Pip
  • 1 posts

Posted 05 June 2007 - 12:53 PM

I don't know whether i'm right or wrong.Pls clarify.

If the 1st guy sees 2 white bands, he might think whether he has a white or red.

So the 2nd guy has 2 options
1)either both of them are white
or
2)one of the 2 headbands is white.

So he can't answer even if the first guy(who doesn't see anything) is red or white.

If that's the case how come the first guy(who doesn't see anything) can confirm he is white.
It might be red too, becoz i see the solution to be justified for only option 2 for the 2nd guy.

Correct me if have missed something.
  • 0

#8 larryhl

larryhl

    Junior Member

  • Members
  • PipPip
  • 68 posts

Posted 06 June 2007 - 03:52 PM

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.

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.
  • 0

#9 malu_nike

malu_nike

    Newbie

  • Members
  • Pip
  • 4 posts

Posted 07 June 2007 - 07:56 PM

like senti_2k2 said....what if third sees 2 white headbands?
  • 0

#10 larryhl

larryhl

    Junior Member

  • Members
  • PipPip
  • 68 posts

Posted 07 June 2007 - 08:21 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? ><
  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users