What methods does Sherlock Holmes use to solve the murder in the story The Hound of the Baskervilles?
Holmes uses his usual analytical and empirical methods to solve the crime. He dismisses from the start any superstitious notion of a legend of a mysterious demonic hound and applies logic to his search for a murderer and motive.
One method Sherlock Holmes uses to solve the crime is simply background research. He discovers that Stapleton has only a few people between him and inheriting the Baskerville estate, which makes him a very likely suspect.
Holmes also uses subterfuge. He doesn't want a mastermind like Stapleton to know that he, Holmes, is on his tail, for fear it will make him extra cautious. Therefore, he sends Watson up alone to investigate, but also sneaks up himself in disguise to do sleuthing, unbeknownst even to Watson.
Finally, near the end, Holmes makes bold moves to confront the hound and manages to do so, saving Sir Henry in the process and revealing that Stapleton has been using a very large dog painted with phosphorus to kill the other people in the way of his...
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