Unless you move the Number of Essays field into its own table linked to your current table in a one to one relationship, I don't see a way for a "formula" to control access to just two of these three fields. You can then use a formula in a lock expression that controls access to the entire record where the name and list number data is recorded.
Here's a simple interface design method you might use instead:
Put the Name and List Number fields on your layout, but set their behavior options in the Inspector's data tab to deny Browse mode access. Then have the user click a button to create a new record. This record can open a custom dialog for the name and list number of the new record. This allows the user to click the button to create new records, but eliminates their ability to edit the name and list number fields on this particular layout for an existing record.
Thanks a lot. I'll see if I am able to do it. Thanks again