Answer: Remember: Davis is 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 that Davis and/or Jones are wearing blue hats. If Smith is silent, Jones 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, Davis immediately knows that his hat is blue and says so before the 10 seconds are up.

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