[Guest]

Alan, Ben, and Cal are seated in a straight line with Alan being in the back and Cal being in the front and Ben in the middle. Their eyes are closed. Diane places a hat on each of their heads from a box they know contains 3 red and 2 blue hats. They open their eyes and look forward.

Alan says, "I cannot deduce what color hat I'm wearing."

Ben says, "I cannot deduce what color hat I'm wearing either."

Cal then says, "I know what color I'm wearing!"

What color hat is Cal wearing? Explain how he knows what color he is wearing.

[Guest]

Red.

Alan's statement means that Ben & Cal's hats are not both blue (otherwise Alan would know the color of his hat to be red).

Ben's statement means that Cal's hat is not blue (otherwise Ben would know the color of his hat to be red since both are not blue from above).

Edited December 3, 2009 by ljb

[Guest]

If Alan had seen two blue (B-B)hats, he would know his was red. Any other combination (R-B, B-R, R-R) and Alan does not know.

Ben realizes this and dedices that if he sees a blue hat, his must be red. But he does not know. So Alan sees R-B or R-R.

Cal then can deduce that his hat is Red.

[Guest]

Cal is wearing a red hat If Alan had seen two blue hats he would have known that his hat was red. And would have been able to tell that he was wearing a blue hat. So he either saw one blue hat and one red hat - or two red hats. Knowing the previous bit of information, if Ben had seen a blue hat in front of him, he would have known that he was wearing a red hat. However, since he did not know, that means that Cal was wearing a red hat. Since Ben did not know what color he was wearing, that means that Cal could only be wearing a red hat

[Guest]

Alan must see at least one red hat or he would know his hat was blue.

Thus, Ben must see a red hat or he would then know his hat was red.

So, Cal now knows he is wearing a red hat.

[Guest]

I saw this once on an advertisement on a train in New York (I couldn't tell you what it was for, so it must be a bad ad). However, the riddle was posed as models and colored pashminas. And it asks what color the last model determines her pashmina to be. I decided the riddle was flawed - models wouldn't be able to figure that out! Here it is from a quick search:

Three supermodels are invited into a swanky and exclusive Fifth Avenue shop. They are shown a shelf upon which are five pashminas - three in deep cerulean and two in saffron. All three are then blindfolded, and one pashmina is draped over each. The remaining two pashminas are returned to the shelf. The models are lined up so that none of them can see the shelf.

The third supermodel's blindfold is removed, and she is asked whether she can tell, by looking only at the other two supermodels, what color pashmina she is wearing. She replies that she cannot.

The second supermodel's blindfold is removed, and she is asked whether she can tell, by looking only at the first supermodel (and, obviously, having heard the third supermodel's reply), what color pashmina she is wearing. She, too, replies that she cannot.

The first supermodel, before her blindfold can be removed, says "I am wearing a ___________ pashmina - may I keep it?".

What color pashmina was the first supermodel wearing, and how do you know?

Edited December 3, 2009 by ljb