What is the problem presented in the story?
The presenting problem in "The Red-Headed League" is brought to Sherlock Holmes by Jabez Wilson, who tells him and Watson a long story about how he became involved with the Red-Headed League and earned four pounds a week for eight weeks for copying articles out of the Encyclopedia Britannica, but then was thunderstruck to find that the Red-Headed League had just been dissolved. When Holmes tells him that he doesn't seem to have much to complain about, since he did realize a profit of thirty pounds, Wilson exclaims:
“No, sir. But I want to find out about them, and who they are, and what their object was in playing this prank—if it was a prank—upon me. It was a pretty expensive joke for them, for it cost them two and thirty pounds.”
Holmes takes the case on a pro bono basis because he feels sure there is something more behind it than just a prank. But the problem remains the same, although it only becomes bigger and more complicated. Why did someone invent this phony league and employ Wilson for eight weeks, then dissolve the league without notice and without leaving a legitimate forwarding address?
After visiting Wilson's pawnshop with Watson, Holmes deduces that Wilson's new assistant, whom he knows to be John Clay, a notorious criminal, is digging a tunnel and wanted to get his employer out of the way so that he could devote more time to the digging and also bring in his partner to help him. Then the problem becomes: What is the purpose of the tunnel?
Holmes realizes that the tunnel must be leading in the direction of the nearby Coburg branch of the City and Suburban Bank. When Clay emerges into the underground strong room that night, he finds Holmes, Watson, a Scotland Yard detective, and Mr. Merryweather, chairman of the bank's board of directors, all waiting for him.
The trivial problem of the invention and subsequent dissolution of the Red-Headed League has led to the capture of a dangerous criminal and the prevention of the theft of 30,000 gold Napoleon coins from Mr. Merryweather's bank. The thieves wanted to get Wilson out of the way, and then when they dissolved their phony Red-Headed League it was a sign that they had finished their tunnel and were ready to loot all the gold.
"The Red-Headed League" is one of the best-liked Sherlock Holmes stories because of its unusual plot, the unique characters of Jabez Wilson and his assistant, and the dramatic ending involving a huge fortune in gold. This explains why the story is so often assigned in high school English classes. There are several especially interesting scenes, including the one in which it looks as if all the red-headed men in London are responding to the newspaper ad to fill a vacancy in the fictitious Red-Headed League. The story combines adventure and ratiocination, as is the case with most of the Sherlock Holmes stories.