'The Red-Headed League' is a story about how a detective uses his reasoning skills to?

uncover a plan to rob a bank
Hum!" said Holmes, sinking back in deep thought. "He is still with you?"

"Oh, yes, sir; I have only just left him."

"And has your business been attended to in your absence?"

"Nothing to complain of, sir. There's never very much to do of a morning."

"That will do, Mr. Wilson. I shall be happy to give you an opinion upon the subject in the course of a day or two. To-day is Saturday, and I hope that by Monday we may come to a conclusion."

"Well, Watson," said Holmes when our visitor had left us, "what do you make of it all?"

"I make nothing of it," I answered frankly. "It is a most mysterious business."

Watson comments that while he is still confused by the case it appears that Holmes has solved the mystery. At this point in the story, are you confused or do you have a hunch about solving the case?

"As a rule," said Holmes, "the more bizarre a thing is the less mysterious it proves to be. It is your commonplace, featureless crimes which are really puzzling, just as a commonplace face is the most difficult to identify. But I must be prompt over this matter."

"What are you going to do, then?" I asked.

"To smoke," he answered. "It is quite a three pipe problem, and I beg that you won't speak to me for fifty minutes." He curled himself up in his chair, with his thin knees drawn up to his hawk-like nose, and there he sat with his eyes closed and his black clay pipe thrusting out like the bill of some strange bird. I had come to the conclusion that he had dropped asleep, and indeed was nodding myself, when he suddenly sprang out of his chair with the gesture of a man who has made up his mind and put his pipe down upon the mantelpiece.

"Sarasate plays at the St. James's Hall this afternoon," he remarked. "What do you think, Watson? Could your patients spare you for a few hours?"

"I have nothing to do to-day. My practice is never very absorbing."

"Then put on your hat and come. I am going through the City first, and we can have some lunch on the way. I observe that there is a good deal of German music on the program, which is rather more to my taste than Italian or French. It is introspective and I want to introspect. Come along!"Sherlock Holmes often smoked his pipe while reflecting on the details of a case and trying to reach the solution.