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
- - - - -


  • Please log in to reply
70 replies to this topic

#11 Egghead

Egghead

    Junior Member

  • Members
  • PipPip
  • 85 posts

Posted 07 December 2010 - 09:13 PM

Remember:
5. The players do not cheat.

To put the problem another way, all players of the team are housed in separate rooms. Everyone is informed about the colour of all others' caps by an arbiter. There is absolutely no possibility of learning more information than those colours.


Mirror in the room, not cheating; just not handled by the rules.
Arbiter gives away the cap's color, not a team member; so again, not handled by the rules.

The statement "There is absolutely no possibility of learning more information than those colours," makes the game impossible to win without wild guessing; so, either the statement is false and one can deduce the color of his/her own cap or it is true and there is no point in trying to figure out the game as it is always a 1/3 chance of winning (possibilities are correct, incorrect, abstain).
  • 0

#12 amateur

amateur

    Junior Member

  • Members
  • PipPip
  • 28 posts

Posted 07 December 2010 - 09:19 PM

How about this strategy

Spoiler for


Spoiler for nice try, but can you explain

  • 0

#13 Kornrade

Kornrade

    Junior Member

  • Members
  • PipPip
  • 36 posts

Posted 07 December 2010 - 09:33 PM

How about this strategy

Spoiler for


This strategy may give a "little more than 50%" winning chance, but it is still far from the optimal solution.

Edited by Kornrade, 07 December 2010 - 09:33 PM.

  • 0

#14 Kornrade

Kornrade

    Junior Member

  • Members
  • PipPip
  • 36 posts

Posted 07 December 2010 - 09:37 PM

Mirror in the room, not cheating; just not handled by the rules.
Arbiter gives away the cap's color, not a team member; so again, not handled by the rules.

The statement "There is absolutely no possibility of learning more information than those colours," makes the game impossible to win without wild guessing; so, either the statement is false and one can deduce the color of his/her own cap or it is true and there is no point in trying to figure out the game as it is always a 1/3 chance of winning (possibilities are correct, incorrect, abstain).


No mirror in the room, no other sources of indirect information
The arbiter communicates which team member was which colour, just as if they stood in the circle and everyone could see everyone else.

"makes the game impossible to win without wild guessing"
Whoever chooses to write RED/BLUE has a 50% chance of being wrong because of the statistical independence of coin toss events (that was already established). I never said that the team wins 100%!
  • 0

#15 bushindo

bushindo

    Senior Member

  • VIP
  • PipPipPipPip
  • 721 posts
  • Gender:Male
  • Location:Los Angeles, CA

Posted 07 December 2010 - 10:00 PM

This strategy may give a "little more than 50%" winning chance, but it is still far from the optimal solution.



Well, I see what you're saying.
Spoiler for

Edited by bushindo, 07 December 2010 - 10:02 PM.

  • 0

#16 Kornrade

Kornrade

    Junior Member

  • Members
  • PipPip
  • 36 posts

Posted 07 December 2010 - 10:10 PM

Yes...
Spoiler for Hint

  • 0

#17 jagdmc

jagdmc

    Advanced Member

  • Members
  • PipPipPip
  • 100 posts

Posted 07 December 2010 - 10:54 PM

Spoiler for My guess

  • 0

#18 puzzled_again

puzzled_again

    Newbie

  • Members
  • Pip
  • 3 posts

Posted 07 December 2010 - 11:52 PM

Well, I see what you're saying.

Spoiler for


Spoiler for

  • 0

#19 phillip1882

phillip1882

    Senior Member

  • Members
  • PipPipPipPip
  • 765 posts

Posted 08 December 2010 - 12:29 AM

over 70%?
Spoiler for i don't see how that's possible

  • 0

#20 puzzled_again

puzzled_again

    Newbie

  • Members
  • Pip
  • 3 posts

Posted 08 December 2010 - 12:49 AM

over 70%?

Spoiler for i don't see how that's possible


Spoiler for

  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users