"How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?"
-- Sherlock Holmes, The Sign of Four, Chapter 6
Holmes says this again in "The Adventure of the Beryl Coronet." It's also one of the most frequently quoted Holmes aphorisms by other writers. Just recently, for example, I encountered the quote in The Sherlockian (no surprise there) and in Impact, a science fiction thriller by Douglas Preston.
The virtue of this quote is that it's so obviously true. It's also easier said than done. In many mystery stories what seems to be impossible really isn't. Consequently, the real solution is often considered early on but ruled out.
I plan to comment on a Quintessential Quote every week. What's your favorite quote by or about Sherlock Holmes?