Sherlock Holmes was famous as a brilliant deducer of facts and solver of problems.
He is says several times in the stories but initially in the novel The Sign of the Four (the second Sherlock Holmes novel) that:
“You will not apply my precept,” he said, shaking his head. “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth? We know that he did not come through the door, the window, or the chimney. We also know that he could not have been concealed in the room, as there is no concealment possible. When, then, did he come?”
The two commonest situations where Sherlock Holmes comes in useful are:
Remember the Sherlock Holmes Principle is most useful when you have a choice of answers and you need to eliminate some of the choices.