Ok, we start with sage 1. He can see 1 of 3 different things on the other 2 heads.

bw, ww, or bb
If he sees BB he knows he has white, anything else he passes.

If we reach sage 2, he KNOWS that either he or sage 3 has a white ball. If he sees a black ball on sage 3's head...

But if he sees a white ball on sage 3's head he's not sure what is on his head, because it could have been WW that sage 1 saw, or BW.

So if sage 2 sees white he passes, and sage 3 KNOWS he has white.



I think that covers all the possibilities.