What methods did holmes use to solve the crime?

Holmes spoke with Watson about his ability to reason backwards; this method helped him solve the case. He further elucidated the ways in which he figured out certain aspects of the case, especially that it was about a woman. The novel ends with Holmes and Watson reading a newspaper article about the end of the investigation; it only mentions Holmes as an amateur detective who helped but gave primary credit to Lestrade and Gregson.