There is a well-known quote from Sir Arthur Conan Doyle, the author of Sherlock Holmes, to which I have always been partial. It goes, "When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth." Doyle's quote speaks to the mechanics of problem solving—those sincerely interested in getting to the heart of a matter must be willing to put all options on the table. This is especially true when the difficulty is seemingly insoluble and defies easy explanation. In such cases, when all obvious options have been exhausted, reason dictates that we proceed down the line to those less obvious. We already know what doesn't work; our task is to discover what does, however counterintuitive it might seem.
