メビウスの殺人 (mebius no satsujin, Moebius Murder, 1990) is the only book I've read by ABIKO Takemaru (我孫子 武丸, born 1962). It's a bit unfortunate that it's actually the third and last in a series.
HAYAMI Kyouzou (速水恭三) is a Tokyo policeman, his younger brother Shinji (慎二) runs a café, helped by their younger sister Ichio (一郎). The names are unusual: I imagine that there's some joke in them that I'd understand if I'd read the first book. Kyouzou is a little bit a figure of fun, serious, but intellectually lazy, tending to take the easiest explanation for any oddity he comes across in an investigation. Unlike Kyouzou, Shinji and Ichio are both fans of detective fiction and relate their discussions of the case to the patterns found in classic mysteries. Ichio wants things to be interesting and tends to favour fantastic explanations. Shinji too treats deductions as a game, but one he takes seriously.
The case here is a serial murder case; and Abiko is already playing with us in the very partial list of characters at the start of the book, which includes the name of the killer SHIINA Toshio (椎名俊夫). We follow Toshio in alternate sections; and it becomes clear that he is not alone. He seems to be playing some kind of game with an unknown figure that he met online, whom he only knows by the name Cat o' Nine Tails. What we don't understand is what the plan behind it all is. What links the various apparently unconnected victims? What do the pair of numbers that Toshio leaves by his victims mean?
Readers familiar with classic mystery will by now have guessed that this is a novel referencing Ellery Queen, particularly, but not exclusively, Cat of Many Tails (1949). As in that book, we have a hunt for a missing link and a depiction of a city reacting to a serial killer. The latter is a lot weaker here than my memory of what Ellery Queen did, partly because Abiko works a lot more with humour. The jokes are not always especially funny and they tend to undermine any tension in the story. The most interesting depiction is of online life in 1990, surprisingly modern in some respects, curiously different in others.
The heart of the story is an interesting game of wits between murderer and investigators. Parts of the puzzle are very satisfactory. As to the solution at the end, I liked it in one sense. I had considered the identity of the Toshio's online friend (given the small cast, there are not that many red herrings, and it would have been irritating if it had turned out to be one of them); but the motivation of this character, which I hadn't considered, made a good story, I thought. On the other hand, this last part is at best hinted, not fully clued.