The Final Problem

"The Final Problem" is a short story by Sir Arthur Conan Doyle. In it Sherlock Holmes and Professor Moriarty die in the Reichenbach Falls. 
The author used this plot as a device to kill Holmes. Later, pressed by public demand, Holmes was shown to have survived the fall.
"The Adventure of The Final Problem" is the original title of the short story by Sir Arthur Conan Doyle. It appears in book form as part of the collection "The Memoirs of Sherlock Holmes". It is the only Conan Doyle story to include the apparent death of Sherlock Holmes. It is also the only one in which Moriarty actually appears instead of just being talked about.