The Science of Deduction

'The Science of Deduction', an article allegedly written by Mr. Sherlock Holmes, is perhaps more than an article. It is the base of everyday life, but sometimes it just depends on how deep the deducting goes. Deduction is not only a fictional detail of lives as great as Sherlock Holmes, but it is also everywhere around us. For example, parents try to find out which of the children had stolen from the cookie jar, or students try to find out why a teacher is absent. For me today, I came across a question in my geometry textbook: Alan, Ben, and Cal are seated with their eyes closed, one infront of the other (Alan looking at the back of Ben's head, but can also see Cal, and Ben looking at the back of Cal's head). Diane places a hat on each of their heads from a box they know to contain 3 red and 2 blue hats. They open their eyes and look forward. Alan says, "I cannot deduce what color hat I'm wearing." Hearing that, Ben says the same. Cal then says, "I know what color I'm wearing!" How does Cal know the color of his hat?
This question took me a few minutes to work out. And here is my answer: The only way for Cal to know what color hat he's wearing is only if his hat is red. If Alan says he cannot deduce what color hat he's wearing, then that meants that the 2 sitting in front of him cannot both be wearing blue (then Alan would know he's wearing red). Thus, it leaves us with 3 possibilities: they are both wearing red, or one or the other is wearing either blue or red. But then Ben announces that he too cannot deduce what color he is wearing, eliminating the possibility of Cal wearing blue. Because if Cal was wearing blue, that meant that he could then deduce that he himself must be wearing red, for if he was wearing blue, Alan would know that he (Alan) is wearing red. So that leaves us with Ben having to wear a red hat. This took me a while to work out, but when I did, I felt a sense of achievement.
As Sherlock Holmes would say, "Elementary, my dear Watson!" (though in actual fact, this has never been said through the original 60 stories, but was in fact coined by a 1915 novel, Psmith Journalist, by P. G. Wodehouse)