Math Challenge question help??

Question

Alan, Ben, and Cal are seated as shown with their eyes closed. (3 chairs in a vertical row, so you see the persons head in front of you, in the order of Alan first, Ben in the middle, and cal last.)

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."

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

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

What color is Cal wearing and how does he know?

**Please Help me with this problem! Also please show your work and what you did to get the answer so i could understand what you did :) thankes!!

Where it says "hearting that, Ben says" its actually suppose to say "hearing that, Ben says."
sorry! typo :)

hmmm those good answers so far :) but I'm still confused because how would Cal see what color hats Alan and Ben have if he's at the end of the row and see's no one elses hats?

seating is like this:

> > >
alan ben cal

the arrows point what way they are looking

Answer 1

Here's the complete answer...

Alan looks forward... if he were to see two blue hats, he would deduce he had a red hat. Because he said he couldn't deduce his hat color, that means that the two hats ahead of him are *not* both blue.

Ben and Cal hear this and know that they together do not have blue hats.

So Ben looks forward. If he saw a blue hat on Cal's head, he would know that he has *red* (because he knows they both can't have blue.)

But Ben can't deduce this. This means he must have looked forward to see a *red* hat on Cal's head.

Finally Cal, listening to all this just says, "I have a red hat!"

It's just logic...

Answer 2

That's an awesome question. We had something similar to that a while ago.

I'm pretty sure it's red. The only possible way Cal could be sure of what she is wearing is if she knows that it cannot possibly be the other color. So, she had to exclude something. This means that both boys must have been wearing blue hats. Because there are only two blue hats, Cal knows that her hat must be red.

Answer 3

The only way that Cal knows what color hat he's wearing is if he sees that both Alan and Ben are wearing blue hats. Since there are only 2 blue hats, he knows that his hat must be red.

Answer 4

Alan and Ben both wore blue hats and Cal then had to wear red. Cal wore RED hat. because there was no more blue hat for Cal.

Answer 5

OK

Not sure if this is what you are looking for but:

Alan is wearing blue. He sees Ben (who is also wearing blue) and Cal (who has a red). Alan cannot know what he has since, he "sees" one red and one blue.

Same is true for Ben. But Cal "sees" two blues and knows he must be wearing red.

That's what I think. Hope that helps.