Death at the President's Lodging - 1 (New edition)

Inspector Appleby is called to St Anthony's College, where the President has been murdered in his Lodging. Scandal abounds when it becomes clear that the only people with any motive to murder him are the only people who had the opportunity - because the President's Lodging opens off Orchard Ground, which is locked at night, and only the Fellows of the College have keys?