Let's start with A.
If B and C had white feathers on their heads, then he would correctly name
the color of his own feather. But he is silent, which means that this is not the case.
Now B (Well, he's smart and he understood everything)
Then 1) if C has a black feather on his head, then B has a white or black feather,
2) if C has a white feather on his head, then B has a black feather.
Since he is silent, it means he is not sure, and he can only be unsure in the first case.
And in the first case, it says that C has a black feather.
That