"I am accustomed to have mystery at one end of my cases, but to have it at both ends is too confusing."If you don't remember the context of this epigramatic quote, you may think it means exactly the opposite of what it does.
-- Sherlock Holmes, "The Adventure of the Illustrious Client"
When Holmes talks about being accustomed to having mystery at "one end of my cases," that's sounds (to me, at least) as if he's talking about the front end. There's a mystery at the beginning of every case, right?
But he's actually referring to having a mystery at the client end of the case as opposed to the villain end of the case. Sir James Damery, acting as intermediary, refuses to tell Holmes the identify of the "illustrious client." The continuation of Holmes's quote is, "I fear, Sir James, that I must decline to act."
Nevertheless, Holmes takes the case without finding out the identity of the client. And it is hard to see why.
Sir James makes an appeal that Holmes listen to the facts of the problem. Holmes agrees, stressing that "I commit myself to nothing." After Sir James the presentation, Holmes says the problem interests him and "I shall be prepared to look into it." But he doesn't find out who the client is until the end of the case.
One can only assume that Holmes decided to live with the confusion.