SOLUTION: Alan, Ben and Cal are seated as shown with their eyes closed. A B C ....Cal is sitting in the front, behind him, Cal, and behind him Alan (in train style). Diane places a hat o

Question 335127: Alan, Ben and Cal are seated as shown with their eyes closed. A B C ....Cal is sitting in the front, behind him, Cal, and behind him Alan (in train style). Diane places a hat on each of their heads from a box they know contains 3 red and 2 blue hats. They all open their eyes and look forward.
Alan is sitting behind Ben, who is sitting behind Cal. Alan says; "I cannot deduce what color hat I'm wearing" Hearing that, Ben says, "I cannot deduce what color I'm wearing either." Cal then says, "I know what color I'm wearing!"
How does Cal know the color of his hat?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's the deal:

There are 3 red hats and 2 blue hats.

A sits behind B sits behind C

All look forward.

A says he doesn't know what hat he is wearing.

B says he doesn't know what hat he is wearing.

C says he knows.

The color of the hat C is wearing has to be red.

Here's how:

Assume C has a red hat on.

This means that B could have a red or a blue hat on.

A looks and sees either 2 red hats or 1 blue and 1 red hat.

A can't determine what color hat he has on because he cannot know unless both B and C had a blue hat on, which they don't.

So A doesn't know which means that B and C either have 1 red and 1 blue or 2 red.

B looks at A and sees a red hat.

This means that B could have a red hat on, or a blue hat on, so he doesn't know either.

C knows that the only way A would know is if both B and C had blue hats.

C also knows that the only way B would know is if C had a blue hat on.

C concludes he has a red hat on.

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