The Red-Headed League by Arthur Conan Doyle, 1891
The magic trick:
Incredibly creative mystery setup
This is, in my opinion, the ultimate Sherlock story – at least this side of Baskerville Hall. It has every element that make these stories classic.
The best magic trick? The intrigue of the setup. It has to be one of the most original and creative in the mystery history. The toughest part about writing detective fiction is that you have to be even smarter than the detective. After all, you’re the one setting up the problem for the detective to solve. This one is one heck of a problem. And that’s quite a trick on Doyle’s part.
The selection:
I took the paper from him and read as follows:
“TO THE RED-HEADED LEAGUE: On account of the bequest of the late Ezekiah Hopkins, of Lebanon, Pa., U. S. A., there is now another vacancy open which entitles a member of the League to a salary of four pounds a week for purely nominal services. All red-headed men who are sound in body and mind and above the age of twenty-one years are eligible. Apply in person on Monday, at eleven o’clock, to Duncan Ross, at the offices of the League, 7 Pope’s Court, Fleet Street.”
“What on earth does this mean?” I ejaculated, after I had twice read over the extraordinary announcement.
Holmes chuckled and wriggled in his chair, as was his habit when in high spirits. “It is a little off the beaten track, isn’t it?” said he. “And now, Mr. Wilson, off you go at scratch, and tell us all about yourself, your household, and the effect which this advertisement had upon your fortunes. You will first make a note, doctor, of the paper and the date.”
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Short Story Magic Tricks 
I’m wondering what you think of the Holmes/Moriarity-related episodes of Star Trek: The Next Generation. Have you seen them?
I not familiar with those. Good?
Yes, pretty good. There was one in the second season where Commander Data becomes interested in Holmes and “plays” on the holodeck where his crewmates ‘accidentally’ created an omnipotent Moriarity. The Moriarity character makes another appearance in a later season episode. The later one is a favorite of mine. (Nerd Alert!) 🙂