This is a typically intelligent and offbeat mystery by Julian Symons. I am adding this note to point out that the situation that starts the book in motion, and the structure of the opening chapters, is lifted directly from the beginning of Anthony Trollope's The Prime Minister. (Though the plot goes off in a completely different direction from there.) This is not possibly coincidental as Symons was a Trollope scholar and wrote the introductions to an edition of some Trollope novels (though not that one apparently).