[LennonCook]

I can do this easily if we take the number of people down to 3.
They are in a Line as Follows-

We will say that person 3 has a black hat on. He can see the hats of both person 1 and person 2. If he sees 2 white hats, he knows that his must be black because there is at least 1 black hat in the lineup. If however, he sees 1 Black and 1 White hat, he says nothing.
If person 3 doesnt say anything, Person 2 knows that his hat must be different to person 1's, so he knows the colour of his hat.

Then, out of the remaining 2, 1 further can be saved. If person 3 calls out that he has a Black hat, Person 2 knows his must be the same as person 1s ie. White.

If person 2 figured his out, person 3 cant do a thing.


So the maximum which can be saved is 2/3. And this riddle is not mathematical, but rather scientific. It is a control experiment- the results are recorder twice, the seond time after changing 1 variable.