"B does not know whether C can see anybody with blue eyes." - that's not true. C can see A. Yes. But what you quoted was part of A's reasoning. A doesn't know

"B does not know whether C can see anybody with blue eyes." - that's not true. C can see A. Yes. But what you quoted was part of A's reasoning. A doesn't know that he has blue eyes. If he doesn't, then C can only see B with blue eyes. And if C can only see B, then B doesn't know if C can see anyone. So A doesn't know whether B knows C can see a blue-eyed person (implying A has blue eyes) or not (implying he doesn't). It's not about what people know directly. It's about what people know about other people's knowledge. In the three-person case, I know that there is at least one blue person. I know that everyone knows it. But I don't know that everyone knows that everyone knows it. If K(0) is "I know there is at least one blue-eyed person", and K(n) is "I know that everyone knows K(n-1)", then (assuming I have blue eyes), K(0) is false only if I am the only blue-eyed person. K(1) is false if there are one or two of us. In general, K(n) is false if there are n+1 or fewer people with blue eyes. The foreigner makes K(n) true for all n.