three men and a hat

Posted in things that make you go hmmmm by beebe4 on June 6, 2007

Here is a brain teaser:

Three players enter a room and a red or blue 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.

The same game can be played with any number of players. The general problem is to find a strategy for the group that maximizes its chances of winning the prize.

I am a trained problem solver.  I am not very organized and sometimes I have lack of motivation issues, but sometimes, more rarely then I would like, I surprise myself with how obvious something seems.  Dilbert calls it “the knack “, my Mom calls it a gift from god.  I just call it common sense, but I guess that is relative.   

Apparently the above brain teaser has been caused a stir in the mathematical community, but after I read the brain teaser on an older web site post the correct answer just came to me and I knew it was right.  That is how my brain works… when I know the answer is right you cannot move me off of it unless you offer additional information.

Do other technologist and engineers feel the same way?


2 Responses

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  1. mathfriend said, on May 20, 2008 at 3:14 pm

    That is why some of us call this the “Ah ha!!” moment. Very much like Archimedes and “Eureka!” We know what he felt when he jumped out of that bath. And afterwards, you cannot believe how you didn’t know the answer before it popped into your head.

  2. Maggie said, on May 20, 2008 at 7:06 pm

    Hi! My name is Maggie. I am 13 n I am so glad to have solved your little riddle today. Me and my 8th grade friends in 6 hour spent our QOI time on it.The QOI is the Question of Inquery that we spend 5 minutes on each day at the begining of class. Thanks for extending are knowledge!! Should we post our solution here? Maybe one day we will be as brilliant as you!

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