[Jehar]

That's a good point, but then the critical factor is that nobody knows how many people have blue eyes. More specifically, each person has to hold the possibility that n = observed persons with blue eyes + 1, which is himself.

[maxerickson]

That's why it takes n days.

Each blue eyed person can see n-1 others. If nothing happens on day n-1, they learn that they have blue eyes.