Four Hats

Contributed by Peter N. Jacobson

Four men are buried to their necks in sand in a straight line so that they can only look straight ahead, as shown above. The first man, on the left, is facing an opaque barrier separating him from the other three; he can't see anyone and no one can see him. The others, all facing the barrier from the right side, can not see behind themselves. Each can only see the back of the head(s) of any men in front of him. None can see his own hat. They all know that: 1) there are two black and two white hats distributed among them and that, 2) their co-sufferers are at least intelligent, with a reasonable grasp of basic logic (although their present situation hardly demonstrates their skills in practical application of these qualities), and are certainly motivated by their imminent demise. Unless one of them can correctly identify the color of the hat he is wearing, they are about to be shot; a wrong guess will produce the same result. They are not allowed to communicate with each other in any way.
Who works out what color hat he is wearing and, of course, how?

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