Three wise men are told to stand in a straight line, one in front of the other. A hat is put on each of their heads. They are told that each of these hats was selected from a group of five hats: two black hats and three white hats. The first man, standing at the front of the line, can’t see either of the men behind him or their hats. The second man, in the middle, can see only the first man and his hat. The last man, at the rear, can see both other men and their hats.
None of the men can see the hat on his own head. They are asked to deduce its color. Some time goes by as the wise men ponder the puzzle in silence. Finally the first one, at the front of the line, makes an announcement: “My hat is white.”
He is correct. How did he come to this conclusion?



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1st, wise man don't speak until they are quite certain they must be right.
[possible cases - outcome]
www - no one behind him know for sure
wwb -  no one behind him know for sure
wbb -  no one behind him know for sure
wbw -  no one behind him know for sure

bww - middle man speaks
bbw - rear man speaks
bwb - middle man speaks

If there was a black hat in the 1st man he would know, therefore as time passes he gets more convinced that he has a white one.
When he spoke he was very sure that we was correct.