The normal logical sequence is probably that after the protagonist, graduate student Martin, lodged at the female teacher's house, the female teacher's daughter fell in love with him and killed the female teacher (that is, the dead old woman) because of his unintentional words of "pursuing freedom". When Arthur, a professor of mathematics, learned of this incident, he wanted to help the murderer cover it up and immediately rushed to the crime scene. But at this moment, Martin also arrived. It is impossible for the professor to destroy the evidence, but to set it up in other ways, as if the murderer had left a mathematical clue and would continue to commit crimes. With Martin involved in the case, the professor only needs to continue to sort out clues, stir up all cases that were not directly related to each other into a major case, and hang all the clues on a mathematical serial killer. Only in the end, the real criminal died, and everyone thought the case was solved. Only then did the professor tell Martin the truth.

In short, it is a game created by the professor to cover up the original teenage criminals, deceiving the police and fooling the audience a little.

I don't know. Have I made myself clear?

Have a nice summer