All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Hats revisited (Posted on 2013-12-19) Difficulty: 2 of 5
Three people are trying to win the following game as a team:

Each of them is put on a hat of either red or blue. Assume an equal chance of getting a red or a blue hat, separately for each participants.
Each one can only see the other people's hats, but not his own.
He has to guess the color of his own hat by writing down either "Red", "Blue", or "Don't know".
After all three people submit in writing their guesses, they would jointly win if:

1. At least one of them guessed right,
2. None of them guessed wrong .

"Guessed right" is defined as guessing a color that is the color of the hat.
"Guessed wrong" is defined as guessing a color that is NOT the color of the hat.
It's neither "right" nor "wrong" if "don't know" is submitted as an answer.

Those three people can establish a joint strategy before the hats are put on their heads.
After the hats are on, they can neither communicate to each other nor see other guesses.

What strategy would give them the best chance of winning and what's the probability of winning under that strategy?

Source: Allegedly posted in the elevator of UC Berkeley Math department.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
QuestionI give up....tomarken2014-05-06 14:50:18
Some Thoughtsre(4): Logicians don't discuss strategy (spoiler?), buttomarken2014-02-28 11:04:14
re(3): Logicians don't discuss strategy (spoiler?), butAdy TZIDON2013-12-21 06:50:30
re(2): Logicians don't discuss strategy (spoiler?), butSteve Herman2013-12-20 18:44:27
Some Thoughtsre: Logicians don't discuss strategy (spoiler?), butAdy TZIDON2013-12-20 11:00:36
SolutionLogicians don't discuss strategy (spoiler?)Steve Herman2013-12-19 12:28:22
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2020 by Animus Pactum Consulting. All rights reserved. Privacy Information