What did you think of the solution to the mystery in "The Red-Headed League"?

The solution is entirely satisfactory because Sherlock Holmes not only deduces that John Clay and his accomplice are going to loot the City and Suburban Bank, but he is there on the spot with a detective from Scotland Yard at almost the exact moment that Clay breaks through the flooring of the underground strongroom. The author sees to it that Holmes himself, and not the Scotland Yard man, makes the arrest.

Sherlock Holmes had sprung out and seized the intruder by the collar. The other dived down the hole, and I heard the sound of rending cloth as Jones clutched at his skirts. The light flashed upon the barrel of a revolver, but Holmes' hunting crop came down on the man's wrist, and the pistol clinked upon the stone floor.

As is typical of many of the Sherlock Holmes stories, a man or woman comes to Baker Street to solicit the detective's help. After listening to the prospective client's story, Holmes goes out to make a personal inspection and investigation. This can sometimes take him into the country, as in "The Adventure of the Speckled Band," or to some interesting part of London, as in "The Adventure of the Blue Carbuncle" and "The Red-Headed League." The titles of the Sherlock Holmes stories frequently contain the word "Adventure." The adventure takes place when the detective and his friend Watson are out making their investigation. Holmes then solves the case and typically explains his thinking to his friend Dr. Watson at the end of the story. For example, at the end of "The Red-Headed League" Holmes explains a great deal to Watson which his friend did not understand at the time, even though he accompanied Holmes through all the action in the story.

“You see, Watson,” he explained in the early hours of the morning as we sat over a glass of whisky and soda in Baker Street, “it was perfectly obvious from the first that the only possible object of this rather fantastic business of the advertisement of the League, and the copying of the Encyclopaedia, must be to get this not over-bright pawnbroker out of the way for a number of hours every day."

Because of what Jabez Wilson had already told him about his new assistant always diving into the cellar to "develop photographs," Holmes deduced that the assistant had to be digging a tunnel. When Holmes knocks at the door of Wilson's pawn shop and asks the assistant for directions to the Strand, he sees proof of his deduction.

"I hardly looked at his face. His knees were what I wished to see. You must yourself have remarked how worn, wrinkled, and stained they were. They spoke of those hours of burrowing." 

To forestall the reader's question as to why the pawn broker never went down into his own cellar out of curiosity, the author, Sir Arthur Conan Doyle, loads Wilson with handicaps which would prevent him from even daring to venture down the steep wooden steps into the dark cellar. Wilson is fat, he is old, and his "florid face" suggests that he has high blood pressure. Doyle also makes his character Jabez Wilson a heavy user of snuff, a finely ground tobacco which would affect his breathing. Nevertheless, Wilson is obviously in the way, and his presence in the shop prevents John Clay from bringing in his accomplice, who calls himself Duncan Ross, to help him dig. That explains the invention of the Red-Headed League. Though highly unusual, the story is entirely credible and the ending conclusive and satisfactory.