I need help with a logic problem
I need help with a logic problem.
To receive credit, you have to explain the steps of your reasoning. Simply giving the right answer will not qualify.
Professors of logic Dr. Amber, Dr. Boyle and Dr. Chatsworth are prisoners of war. Dr. Chatsworth has lost both of his eyes during the war, so he is blind. The enemy officer offers them a puzzle to solve and whoever gets it right will be freed.
Then the officer tells them that out of three white and two black hats, he will be choosing only three of random colors putting them on their heads. Professors will not know what color hat they are wearing. After putting the hats on the heads of the professors, the officer asks Dr. Amber what color he is wearing. Dr. Amber looks at the hats of Dr. Boyle and Dr. Chatsworth and says: I don’t know.
Then the officer asks the same question to Dr. Boyle. He also looks at his friends sees their hats and says he doesn’t know. The officer ironically tells Dr. Chatsworth there is no reason for him to try, because he is blind anyway. Dr. Chatsworth says he doesn’t need his eyes to know what color hat he is wearing.
He answers correctly. The color Dr. Chastworth’s hat is _________________
What color is he wearing and how did he know? Write down the steps of your reasoning.