Everyone has always known that at least one prisoner is green-eyed.
The facts:
- No prisoners are not green-eyed.
- Everyone has always known that at most one prisoner is not green-eyed.
- Everyone has always known that everyone has always known that at most two prisoners are not green-eyed.
- Everyone has always known that everyone has always known that everyone has always known that at most three prisoners are not green-eyed.
- For all i, (Everyone has always known)^i that at most i prisoners are not green eyed.
What is the information contained in hearing the statement “at least one person is green-eyed” addressed to everyone?
- At most n-1 prisoners are not green-eyed
- Everyone knows that at most n-1 prisoners are not green-eyed
- For all i, (Everyone knows)^i that at most n-1 prisoners are not green-eyed
- Specifically, a new piece of information: (Everyone knows)^n that at most n-1 prisoners are not green-eyed
