3 Search Engine Optimization Specialists enter a room and a Black or White hat is placed on each person’s head. The color of each hat is determined by a coin toss, with the outcome of one coin toss having no effect on the others. Each person can see the other players’ hats but not his own.
No communication of any sort is allowed, except for an initial strategy session before the game begins. Once they have had a chance to look at the other hats, the players must simultaneously guess the color of their own hats or pass. The group shares a hypothetical $3 million prize if at least one player guesses correctly and no players guess incorrectly.
What is the optimal strategy to allow for the greatest chance to win the $3 million dollar prize? What will their odds of winning be?
Totally stumped? Check out this article for some insight.
3 Responses to “What Color is Your Hat? (Brain Teaser)”
The optimal strategy would be this:
Decided in advance that every player will pass unless the hats he sees on the other 2 players are the same color. When that happens, the player will guess that his hat is the opposite color of the other 2.
3 times out of 4, the hats will be distributed 2 of one color and one of the other. Every time this happens, the players will win with the strategy above.
Their odds of winning are 75%.
So, do I win a link or just 3 million$ ?
[…] Quadzilla puts a little black hat / white hat terminology on a unique problem reported by Sara Robinson that mathematicians and coders are trying to figure out. It’s called the hat problem and was created by Dr. Todd Ebert of California State University. […]
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That’s good. My initial response was that it was obviously a 50% chance, but the article shows how you can get better odds. Very nice.