Before going down to Stoke Moran, Holmes tells Watson briefly what he suspects, including the following:
"...Miss Helen Stoner heard a metallic clang, which might have been caused by one of those metal bars that secured the shutters falling back into its place."
"The Adventure of the Speckled Band" is an example of what is called a "locked-room murder mystery." The prototype for such stories was probably Edgar Allan Poe's "The Murders in the Rue Morgue." The essential part of the mystery is "How could the victim be murdered when he (or she) was inside a apparently impenetrable room with locked doors and shutters?" Holmes makes it clear that this is the main problem when he tells his friend Watson:
“Yet if the lady is correct in saying that the flooring and walls are sound, and that the door, window, and chimney are impassable, then her sister must have been undoubtedly alone when she met her mysterious end.”
When the two men take the short train ride to Leatherhead and the cab out to Stoke Moran, the detective is especially interested in examining the shutters from the outside.
Holmes, after a careful examination through the open window, endeavoured in every way to force the shutter open, but without success. There was no slit through which a knife could be passed to raise the bar. Then with his lens he tested the hinges, but they were of solid iron, built firmly into the massive masonry. “Hum!” said he, scratching his chin in some perplexity, “my theory certainly presents some difficulties. No one could pass these shutters if they were bolted."
After inspecting the shutters, Holmes examines the room in which Helen Stoner is currently sleeping, which had been Julia Stoner's bedroom at the time of her death. Holmes next examines Dr. Roylott's adjoining bedroom. He sees a number of things in both rooms that lead him to form an entirely different theory. Most suggestive are the ventilator between the two rooms, the dummy bell-rope in Helen's room, the fact that her bed is bolted to the floor, and the steel safe and saucer of milk in Dr. Roylott's room. Holmes realizes that the words "the speckled band" have nothing to do with a band of gypsies, as he had originally assumed. At the end of the story, Holmes explains to his friend Watson:
"The idea of a snake instantly occurred to me, and when I coupled it with my knowledge that the doctor was furnished with a supply of creatures from India, I felt that I was probably on the right track."
The fact that the bedroom shutters were impregnable made Holmes think that the ventilator was the only entry into the locked bedroom and that only a snake could crawl through such a tiny opening. The steel safe in Dr. Roylott's bedroom, along with the saucer of milk and the leash with a loop at its end, all led Holmes to believe that Helen's stepfather had used a poisonous snake to kill Julia and was now trying to do the same thing to kill Helen. So Holmes solves two mysteries at the same time and saves his client from certain death.
Dr. Roylott has to be portrayed as a violent man who is only half-sane and who is strongly motivated to keep the money that would go to his step-daughters if they married. His is also a doctor who has spent a great deal of time in India and who collects exotic animals.