Asume we are the first of the three men. If we see two white hats, we know we must be wearing black, and could immediately proclaim so.
But we don't, so we must either wear black or white
so far as stated in the the puzzle.
but, if we were wearing a white hat, then the others would see a black and white, and THEY could reasonably deduce themselves to be wearing black, because if they were also wearing white then THE OTHER OF THE TWO would be seeing two white and would proclaim black immediately and because they don't do so, we know we must be wearing black!
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