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Three Wise Men

A bored king wanted to find out which of his advisers was the wisest, so he summoned his three oldest wise men.

“I am going to sit you in a triangle and blindfold each one of you,” he said, “and paint either a red or a blue dot on your foreheads.  I will then take the blindfolds off, and if you see at least one red dot, you will raise your hand.  The first man to determine the color of his own dot is the wisest.”

The king then blindfolded them and painted a red dot on each man’s forehead.  When the blindfolds were taken off, all three looked at each other and raised their hands.

Ten seconds later one of the wise men proclaimed, “I have a red dot.”

How did he know?

Solution
His thinking was as follows: “If I had a blue dot, the man to my right would see only one red dot, on the forehead of the man to my left.  However, the man to my left raised his hand, so the man to my right would immediately know that his own dot was red.  The same logic would be used by the man on my left.  Neither of them have announced anything, so my own dot must be red.”
Notes
Like many hat puzzles, this puzzle suffers from the “fairness problem”: if our wisest man had indeed been given a blue dot, he would never have been able to win the contest.  For that reason alone, you could argue that his own red dot should be obvious.

Of course, the puzzle doesn’t claim that the king is fair — just bored.

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This entry was posted on Wednesday, September 30th, 2009 at 9:00 am and is filed under Puzzles. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

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