BrainDen.com - Brain Teasers

# ANANymous

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4

1. ## 4 hats puzzle

This would be considered cheating I believe, it is not the solution being sought, but was a nice try
2. ## 4 hats puzzle

Herein lies my initial question: How do we achieve 14/16, what is the selection method used by the 4 hat wearing participants? Is that solvable?
3. ## 4 hats puzzle

I appreciate the responses araver; however this link does not provide the solution I am looking for: http://brainden.com/forum/topic/13034-- And the answer I believe is greater than the answer to 3 people. I believe it is not 50% based on the person who asked this question initially (who also knew the answer, but whom I can no longer locate).
4. ## 4 hats puzzle

Can someone solve the following brainteaser with an explanation of how the people in the problem choose hat color: There are 4 people wearing black or white hats. They do not know the color of their own hat. They cannot communicate. They must come up with a strategy for simultaneously shouting out a hat color or keeping their mouth shut. Your goal is to come up with the solution that yields the highest probability of getting at least one hat color correct and no hat colors incorrect. For example, if the hats are black black black white in that order, and you guess black, doesn't guess, doesn't guess, doesn't guess, then this would count as a successful attempt; however if you guessed black, black, black, black, this would be unsuccessful. Semi spoiler below-the solution for 3 people: Using 0 as representation for white and 1 for black, you have the following table seating available. 000, 001, 010, 011, 100, 101, 110, 111 If every time you are at the table and you see two hats of the same color, you guess the opposite color, you will guess correctly in 6 out of 8 attempts, and if you do not see two hats of the same color, then you pass/ do not guess. This yields a 75% win rate for this game among the 3 participants. Thank you in advance for answers.
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