A prison warden liked to play mind games with his prisoners. One day, he retrieved three of the brightest -Â Davis, Jones and Smith - and made a deal with them.
"I'm going to line the three of you up in a column alphabetically, facing forward, and then blindfold you. I'll then place a hat upon each of your heads - I've got two yellow ones and three blues one to choose from. Then, I'll remove the blindfolds.Â You're not allowed to move or communicate with one another in any way.Â I'll give you ten seconds, and ifÂ the first one of you to speak canÂ correctlyÂ blurt outÂ what color hat you're wearing, I'll pardon all three of you and set you free. But ifÂ that first guess is wrongÂ wrong, all three of you will go before the firing squad."
After a quick huddle, the three readily agreed to the warden's deal. They spent the night celebrating, and theÂ next day, the three happy prisonersÂ were being processed and released. How did theyÂ succeed in outsmarting the warden?
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Answer: Remember:Â Davis isÂ in front, Jones is behind him, and Smith is behind Jones. And the warden has two yellow hats and three blue hats. Here's how they figured it out.
If Smith (in the back) sees two yellow hats in front of him, he knows he's wearing a blue hat and says so immediately. If he says nothing, then it becomes apparent thatÂ Davis and/or Jones are wearingÂ blue hats. If Smith is silent, JonesÂ looks at Davis's hat. If it's yellow, he knows his own hat is blue and says so. (If his hat were yellow as well, Smith would have spoken up.) But if Davis's hat is blue, Jones is uncertain about the color of his own hat.
If neither Smith nor Jones speaks up,Â Davis immediately knows that his hat is blueÂ and says so before the 10 seconds are up.