How does Cal know what color hat he is wearing?

Question

Alan, Ben, and Cal are all sitting in chairs with their eyes closed. Denise walks around with a box of hats, 3 red and 2 blue. She gives each one of them a hat from the box. When they open their eyes and look forward, Alan says "I cannot deduct what color my hat is." Ben says the same thing, but Cal says he can.

How does Cal know what color his hat is?

Answer 1

 

When they  open their eyes,they can see hats of two others.Cal can see hats of Ben and Alan.If hat of one of them is blue and the other is red,the hat of Cal may be blue or red.if hats of both of them are red,again the hat of Cal may be blue or red.but if hats of both of them are blue ,the hat of Cal must be red.Because there are two blue hats.

Answer 2

 

Ben and Cal cannont possibly wear blue hats because then Alan would know his hat is red which leaves the possible combinations:


 Alan   Ben   Cal
    B      B     R
    B      R     B
    B      R     R
    R      B     R
    R      R     B
    R      R     R

Now if Ben can see that Cal's hat is blue, he can deduce that his hat 
is red, because Ben and Cal cannot both have blue hats. Since Cal 
cannot deduce this either, the second and fifth possibilities above 
are out.  That leaves this:

   Alan   Ben   Cal
    B      B     R
    B      R     R
    R      B     R
    R      R     R

You can see that in every remaining case, Cal is wearing a red
hat.