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Since the man at the back could not determine his own hat, this means that the front two men could not have been wearing black hats and that, therefore, there must be at least one red hat on the two front men.

Therefore the middle man must not be able to see a black hat otherwise he would know he had a red one on.

Therefore the front man must be wearing a red hat - which finally he deduces. Interestingly, the other two can never determine their own hats.