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I have been told that Sherlock Holmes is never actually quoted saying his famous phrase "Elementary, my dear Watson." However, all of his detective stories focus on the "simplicity" of mysteries once they have been explained. Does the famous Baker Street detective rely more on deductive reasoning than inductive, or are both processes of reasoning equally important? Can you give a couple examples of each?

Eureka! There is a two-in-one example in The Hound of the Baskervilles. When a guest leaves his walking stick behind, Holmes (with Watson, this time!) makes several conjectures about its owner; here both deductive and inductive methods of reasoning are used:

Inductive:

Watson notices the quality of the stick and its evident wear. He  speculates that it might belong to an elderly revered gentleman, possibly of his own professsion (a doctor).

Inductive:

Holmes attempts to decipher the engraving on the handle, proposing that the 'C.C.H.' initials could eventually stand for 'Charing Cross Hospital.'

Deductive and Inductive:

He also notices the scratches in the middle of the stick and supposes they are the bite marks of a small hunting dog:

“Has been in the habit of carrying this stick behind his master. Being a heavy stick the dog has held it tightly by the middle, and the marks of his teeth are very plainly visible. The dog's jaw, as shown in the space between these marks, is too broad in my opinion for a terrier and not broad enough for a mastiff. It may have been—yes, by Jove, it is a curly-haired spaniel.”

How holmes pay for his fault or never mistakes