A crime that should be simple enough to solve is complicated by a love-motivated cover-up and turns into an enjoyable battle of probabilities and logic.
The Devotion of Suspect X
At the beginning of The Devotion of Suspect X, Yasuko has made a nice home for herself and her daughter, until her ex-husband Togashi enters their Tokyo apartment making death threats. Yasuko promptly strangles him.
This dramatic start presents a crime that most police detectives would easily solve, except that Yasuko's next-door neighbour is Ishigami, who is willing to orchestrate a cover-up (he has a crush on Yasuko, as the book's title suggests).
There are two factors the reader should simply accept in order to enjoy this crime fiction. First, there's no such thing as a plea of self-defence; Yasuko must follow Ishigami's instructions exactly if she's to avoid murder charges.
Second, Ishigami's former university colleague Yukawa happens to be helping the police with their investigation. His presence is the unpredictable variable in an otherwise regulation formula.
Beneath the pleasantries of old acquaintances reuniting, Ishigami and Yukawa lock horns in a battle of probabilities, assumptions and logic that's thrilling even if you're no good at maths.