How to add user that can add users

[Rickard Andersson]

I'm setting up a MySQL server for a university. The database contains some sensitive data such as the backend for our website. This data is stored in a database called 'website'. In the spring, we will be giving a course on databases and in this course each student will be given an individual login and a database in which they can roam free. We want the course supervisor to create all the users and databases, BUT, we don't want the course supervisor to have access to the 'website' database. Essentially, what I'm asking is:

Is it possible to create a user that can create databases and users and have full control over these without allowing this user access to our 'website' database?

I get the impression that in order for a user to be able to create new users, he or she must have INSERT access to the 'mysql' table. And if so, can't that user just grant himself permissions to the 'website' database?

If this isn't possible, how do you suggest we solve the problem? I guess running two instances of MySQL is one way, but I don't like it.

Any help would be appreciated.

Cheers,
Rickard