"they don't know that all the blue-eyed people know that the blue-eyed people know" Yes, they do. In the three-person case, a blue-eyed person can see two othe

"they don't know that all the blue-eyed people know that the blue-eyed people know" Yes, they do. In the three-person case, a blue-eyed person can see two other blue-eyed people, A and B, and they know that A can see B, and vice-versa, so they know that A and B both know that there are blue-eyed people, and they know that both A and B would be able to us the same logic they used, so they also know that A and B know that A and B know that there are blue-eyed people.