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

#11 nicksyl

nicksyl

    Newbie

  • Members
  • Pip
  • 3 posts

Posted 09 June 2007 - 09:15 PM

There was no light so i don't think this riddle is even a riddle. One of the men must have randomly guessed and hoped for the best.
Edit: oh i understand, he put their headbands on in the room with no light, then took them outside >< sorry!
  • 0

#12 malu_nike

malu_nike

    Newbie

  • Members
  • Pip
  • 4 posts

Posted 10 June 2007 - 05:06 PM

oh ok i understand larryhl, thanx for the explanation.

If 3rd is confused and 2nd is seeing a red on 1st - then 2nd has to be wearing white and 2nd would not have stayed silent or confused.

if 3rd is confused and 2nd is seeing a white on 1st, then 2nd could be wearing white or red. Therefore 2nd would be confused and silent, so 1st would know that he is wearing white.
  • 0

#13 MissMaryKathryn

MissMaryKathryn

    Newbie

  • Members
  • Pip
  • 2 posts

Posted 21 June 2007 - 12:47 AM

I get it!

The one thing that people don't understand is that, the 2nd guy is quiet because
the the 1st guy is white AND that the 3rd guy is quiet! If the 3rd guy spoke up, then the first two would have to be red,
but since the 3rd guy is quiet, the 2nd guy knows that the combinations possible are:

2nd=White 1st=White

2nd=Red 1st=White

2nd=White 1st=Red

But since #2 is quiet, the 1st must be white, because if the first was red,
2 would have to be white, but if #1 is white then 2 is either Red or White and he doesn't
want to take that 50/50 chance. The first notices this and speaks up. He has to be white!
  • 0

#14 Incognitum

Incognitum

    Junior Member

  • Members
  • PipPip
  • 51 posts

Posted 22 June 2007 - 01:16 PM

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.
  • 0

#15 Riddari

Riddari

    Junior Member

  • Members
  • PipPip
  • 48 posts

Posted 27 June 2007 - 07:04 PM

I understand the solution as given, but I don't feel that it is a complete solution. It only explains the case of the 4 of the seven possibilities. It implies potential solutions for the other possibilities, but I think all possibilities should be explicitly covered in the solution.

The seven possibilities are as follows:
P 1 2 3
1 R R W
2 R W R
3 R W W
4 W R R
5 W R W
6 W W R
7 W W W

In case 1, the third prisoner would (or at least should) immediately know that his headband is White because the two red headbands are on the other prisoners. In cases 2 and three, the second prisoner should know that his headband is white because he can see that the first prisoner's headband is red and would expect the third prisoner to respond immediately if he saw two red headbands. The color of the third prisoner's headband would be irrelevant. In cases 4 through 7, the first prisoner could eliminate that the first three possibilities by the lack of response from the other prisoners, leaving only possibilities where his own headband is white. In all cases, you have to assume that all the prisoners are fairly intelligent and have confidence in the intelligence of their fellow prisoners.

A couple people above seem to be confused about how the prisoners would know how many of each headband were available. I think it is reasonable to accept that the chief was testing the intelligence of the prisoners and would give them the information they needed to succeed. Otherwise, there would not be much point in the exercise.

Another possible solution would be for all three prisoners to state that they had white headbands. The instructions simply state that "If somebody said the colour of his head-band, they all would be free." Nothing says that an incorrect guess deems them to imprisonment. So, since they all know there are only two red headbands, at most only two of them could be wrong, making at least one of them correct. In the same light, one of the prisoners could claim to have a white headband and then if he is incorrect immediately state that he has a red headband. Again, this does not violate the instructions. I think both of these are cheesy solutions, though, and can both be eliminated by simply adding a condition to the puzzle stating that only one guess can be made by the group.
  • 0

#16 anuraag

anuraag

    Newbie

  • Members
  • Pip
  • 6 posts

Posted 30 June 2007 - 09:46 PM

second person will say that he has white. the first one has red. third's hat is indeterminate
  • 0

#17 anuraag

anuraag

    Newbie

  • Members
  • Pip
  • 6 posts

Posted 30 June 2007 - 09:50 PM

rather it depends upon who speaks out. if 2nd and third are quiet then the first one can know that he is wearing white
  • 0

#18 teriincali

teriincali

    Newbie

  • Members
  • Pip
  • 4 posts

Posted 01 July 2007 - 11:28 PM

I've got it. It's much simpler than any of you think.

Assuming they saw the headbands before the darkness:

The 2 unused headbands were red and the third man saw two white headbands.
  • 0

#19 teriincali

teriincali

    Newbie

  • Members
  • Pip
  • 4 posts

Posted 01 July 2007 - 11:28 PM

oops... so he said mine is white lol
  • 0

#20 TEX

TEX

    Newbie

  • Members
  • Pip
  • 13 posts

Posted 02 July 2007 - 06:55 AM

Since there were only 2 red bands, The last person could confidently assume that his is WHITE because he saw that the other two people had(the only two) red ones.
  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users