We should also add districts with restrictions based on some parameter.
To enter the "musclemen" district, you would need to win an arm wrestling match against the guard.
In the "agile" district, you would need to shoot at targets.
In the "runners" district, you would need to run a timed distance.
In the "intellectuals" district, you would need to solve puzzles.
And so on.
Added 2 minutes later
Why do you even need that district? Do you want to be knight-idols? Or haven't you had enough of polishing boots yet? I really don't understand the point of going there.