Many years ago, math professor Grant McCallister published a paper mathematically analyzing the structure of murder mystery fiction. He even selfpublished a collection of short stories illustrating several of the mathematically interesting permutations before suddenly abandoning his wife to live alone on a remote island. Now, a young editor arrives with the supposed intention of reading those old stories with him so that they can finally be professionally published, but she seems to have an ulterior motive.
That framing story undergoes several surprising twists and unexpected turns, but the key ideas that McCallister has created a mathematical framework for studying the whodunnit and that the theory is demonstrated by the stories we hear as they are read aloud on the island remain fixed.
The mathematical theory itself, while not terribly deep, is sensible and at least somewhat interesting. Pavesi, who has a PhD in mathematics, describes it well and so I will simply quote
(quoted from The Eighth Detective)
"The circles represent the four ingredients that we've already discussed: a set of characters called the suspects, another called the victims, the detectives, and the killers. To this we add four requirements. The number of suspects must be two or more, otherwise there is no mystery, and the number of killers and victims must be at least one each otherwise there is no murder. We express those mathematically by talking about the cardinality, or size, of the sets: The cardinality of S is at least two, and the cardinalities of K and V are both at least one."
"Yes," she said. "That's straightforward."
"Then the final requirement is the most important: The killers must be drawn from the set of suspects. K must be a subset of S."
To illustrate this last point, he rubbed out the circle labeled K and drew it again, smaller, inside the circle labeled S. "That is how we show subsets in a Venn diagram."

Within that framework, there are still many possibilities. Which of those sets have a nontrivial intersection or are subsets of which others? What are their cardinalities? Those are the different possibilities that the seven short stories embedded in the novel are meant to realize.
So, this work of mathematical fiction shares with The Geometry of Narrative the conceit that it presents a mathematical tool for analyzing fiction. In fact, we can apply the concept of "Narrative Distance" from that other work to this one. Because the short stories in The Eighth Detective are works of fiction being read by the fictional characters in this novel, they are at a greater distance from us. That makes them harder to get emotionally invested in. This is even more true because we learn that each of those stories contains intentional inconsistencies that have been left for the careful reader to find. That might be enjoyable for some who enjoy such puzzles, but it certainly makes it harder to suspend disbelief. I think that may be partly why this book has received some negative reviews mixed in among its glowingly positive ones. It does end up feeling a bit more like an exercise  a worked example  than a piece of literature. But, that isn't necessarily a bad thing.
