The Wise Queen

Puzzler time.

We have used this one before. A long, long time ago. But it is time to bring it back.

Once upon a time in a land far, far away, there lived a queen who wished to find the wisest woman in the realm to be her assistant.

She searches far and wide. She finally summons the three known wisest women to her court. She decides to administer the following test.

She says, "I'm going to put either a red hat or a white hat on each of your heads."

She faces them in a circle, and standing behind them, she proceeds to place three red hats on their heads, one red hat on each of their heads. They are facing each other, but they cannot see themselves. They can only see each other.

Then she says, "If you can see another red hat, raise your hand."

Then they all raise their hands, because they are all wearing red hats. Although they cannot see themselves, only the other people in the room.

Then she says, "If you can tell what color hat you have on, stand up."

Time goes by. Nothing happens. They all look around at each other. Finally, after a time, one woman stands up and she says, "I'm wearing a red hat."

The question is, how did she know that she was wearing a red hat? Remember there are no mirrors, and she can only see the other women in the room, not herself.

So, how did she know that?

Good luck.

Answer the Puzzler »

Remember last week's puzzler?

Only Works For Squares

Puzzler time.

Here it is.

Everyone remembers from their school days, the Pythagorean Theorem.

A squared + B squared = C squared.

And there are numbers which satisfy that little equation, of course.

Many hundreds of years ago, a French mathematician by the name of Fermat said that this only works for squares. There is no A cubed + B cubed = C cubed. There is no A to the fourth + B to the fourth = C to the fourth... You get it.

As luck would have it, a young mathematician issues a statement that he has three numbers which prove Fermat's theorem is incorrect. He calls a press conference. Of cours he doesn't want to divulge everything right away. He wants to dramatize, build a little bit, right?

So he gives them all three numbers. But he doesn't tell the power. So this is what he gives them.

A equals 91.

B equals 56.

C equals 121.

So, it just so happens that at this little impromptu press conference, there are all these science reporters from all the newspapers that are around this town. And one of the guys, one of the reporters has his 10-year-old kid with him, because this happens to be a holiday. He's off from school.

So the kid very sheepishly stands up and raises his hand, and he says, "I hate to disagree with you, sir, but you're wrong."

The puzzler question is, how does he know that this is wrong?