What is the first mystery presented to Dr. Watson in The Hound of the Baskervilles?

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 In Holmes' office, a walking stick has been left behind.   First, Watson offers his own conclusions, based on the inscription on the cane, which reads:  "To James Mortimer,  M.R.C.S., from his friends of the C.C.H."  Waston surmises :  1)  the walking stick was a retirement gift, awarded to a man after many years of faithful service.  2)  The fact that the stick is well-used suggests that it was not merely ornamental, but consistently used.

Holmes, however, reaches a different conclusion.  Examining the cane, Holmes decides that the object must have belonged to a young man. CCH, he argues, is the abbreviation for Charing Cross Hospital, an enviable place in which to practice.  Only an extremely successful young doctor would leave such a prominent position in order to practice rural medicine.   Holmes also notices the indentions of tooth marks at the bottom of the cane, and reasons that the impresssions must have been left by a small dog, probably a spaniel, something Watson had completely missed.

Holmes, of course, is proved correct.  The mystery is solved when Mortimer, the phrenologist, arrives to claim the cane.  Holmes has inside knowledge of Moritmer, which he witholds from Watson, making his deductive abilities seem more acute than they actually are. 

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