red caps

[THEMOUSSEMAN]

the legend of the red caps?

[THEMOUSSEMAN]

Once upon a time in a faraway country, the king wanted to marry the smartest woman in the kingdom. All women were SAT tested. Three tied with the highest score. The king seated these three women at a round table. He informed them that he was about to blindfold them, then would place a cap on each of their heads positioned so that, with the blindfolds removed, each would be able to see the caps on the heads of the other two but be unable to see their own. The caps would be either red or white.

The king instructed, 'When your blindfolds are simultaneously removed you will see two caps. If one or both of them is red you are immediately to raise your hand. When you deduce the color of the cap on your head, lower your hand, rise, announce and explain.' Then the king placed a red cap on each head and removed the blindfolds. Each of the three women raised her hand. Ten seconds passed with all three hands raised.

Then the smartest of the three lowered her hand, rose, announced that the cap on her head was red, and explained.

How did she do it?

[dundurn]

The winner (call her A) works it out as follows. I can see two red caps so I have my hand up. If I had a white cap then B would have raised her hand because she could see C's red cap but she would know that the only reason C could have raised her hand was because she, B, was wearing a red cap. The same would be true for C. She could work out in exactly the same way that she too was wearing a red cap. But neither of them have dropped their hands. So I can't be wearing a white cap. So I'm wearing a red cap.

[eltelioni]

The one who raised her hand was, of course, the least intelligent. The other two also worked out the answer but realised how tedious life would be married to such a nerd.