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It's 1895 and Holmes and Watson are at an unnamed English university. It's unnamed because this case is mildly scandalous, and Watson doesn't want to get anyone in trouble.
However, you have a 50/50 chance of guessing correctly since Watson describes the university as a famous one with lots of gothic architecture. So it's probably either Oxford or Cambridge.
Anyway, Holmes is there doing research or something, and a man named Hilton Soames comes up and begs for help.
Holmes wants him to go away but Hilton is insistent.
Holmes finally says OK and Hilton tells his story.
He's a Greek professor and is about to administer a big exam tomorrow for a scholarship prize. The test involves translated a long Greek passage.
Soames had the text in his office, and he had to step out for a bit.
His butler, Bannister (one of the best butler names ever) accidentally left the key in the office door.
When Soames returned he found papers scattered around the room and fears that someone copied the test and plans to cheat tomorrow.
Bannister flipped out and had to sit down. Soames left him freaking out and went to find some help.
Holmes is interested, and he grills Soames for more details.
Soames describes some clues left at the scene.
He also says an Indian student, named Daulat Ras, came to visit him earlier, but that the exam was rolled up at the time. So, Ras couldn't have seen anything.
Holmes goes to investigate the scene and does his super detective routine, finding all sorts of tiny clues.
He finds pencil shavings, a small triangle of black putty on the floor, and a scratch on a table.
He decides that the likeliest suspects are the three students who live in dorms above Hilton's office.
Soames describes the three students.
Gilchrist is a superstar athlete and excellent student; Daulat Ras is a quiet and hard-working student; and Mile McLaren is smart, but is a slacker.
Bannister has recovered from his shock, and Holmes goes to question him.
He's not very helpful: he just corroborates Soames's own story and says he can't think of who would try to cheat.
They go outside for a bit and notice Daulat Ras pacing in his room.
Holmes and Watson then pose as tourists. They visit each of the three students' rooms to check out the gothic architecture, giving Holmes time to use his detective mojo on them.
These dorm rooms suck if they're on some sort of historical tour route and people can just barge in whenever.
Gilchrist is friendly, Daulat Ras just wants them to leave, and McLaren won't let them come in because he's frantically studying.
Holmes then says thanks for the tour, peace out.
Soames says what the heck, fool, solve the case.
Holmes says he will and then leaves.
That night Holmes asks Watson whom he suspects, and Watson goes for the two obvious students. McLaren or Daulat.
The next day Holmes goes out early and then comes back announcing that he's solved it.
They go to see Soames, who is having a panic attack.
Holmes tells him that the exam can proceed as planned since the cheater won't be taking it. That sounds ominous.
He confronts Bannister, but Bannister won't squeal.
Then Holmes has Gilchrist come in. He breaks down and confesses.
Holmes explains that Gilchrist runs track and came back from practice with his cleats.
He saw the exam, jumped in the window, and yielded to temptation and copied it. But he was interrupted so he hid in Soames's bedroom.
Gilchrist's cleats caused the scratch on the table and the black putty that Holmes found was mud from the shoes. Gilchrist also owned a pencil that left the shavings at the scene.
Also he dropped his gloves. Bannister saw them and covered them up by sitting on them in a chair, faking a panic attack until Soames left.
Turns out Bannister used to work for Gilchrist's father and knew Gilchrist as a child.
He covered for the young man.
Gilchrist apologizes to Soames. The student says that he's dropping out of school and is taking a commission with the police force in South Africa.
FYI: In this era a lot of young men took jobs out in the empire, especially if they didn't have lots of education or much money back in England. Taking a job in the empire was a good way to start a career and save up some money for later on in life.
Holmes tells Gilchrist good luck in the future, and the cheating crisis is over.