We have advertised for an additional question setter at Quiz Master Shop and had 36 replies (We haven't really, this is just a puzzle), and all can cover at least one of the subjects where we feel we are lacking expertise. 25 can write questions on TV, 20 can cover Literature and 21 have knowledge of the Arts.
On closer inspection seven could do TV and Literature, nine who can cover TV and Arts, and six who know Arts and Literature. After a great deal of discussion we decided to interview only those who could write questions on all three subjects.
How many people were invited for interview?
This problem is best solved using Venn diagrams - and the answer is four.