If the blind man was wearing black then the only way the first guy would have not been able to guess his own correctly, is if the second guy was wearing white (two black hats would have given him his own color). When the second guy came to guess he would have seen the blind guy's black hat and thought "Hey, I must be wearing a white hat then, otherwise the first guy would have got it.". As neither of them were able to guess their own hat color, then the blind man knew he must be wearing a white hat.
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