In this book the unsolved problem is posed by the murder of an unpopular school master, a bully who torments selected students and colleagues, and who has affairs with married women. He is a man with a lot of enemies, but nonetheless his world is defined by the school community and the local village, so that the number of potential suspects is restricted to the school pupils, the rival masters, the three women the victim was romantically involved with, his fiance's father and a local farmer. Various people hold particular grudges and various people have witnessed incriminating scenes, all of which act in concert to both reveal and obscure the true solution. It's all fairly typical stuff. But the interesting fact revealed by reading a series of these crime novels is that even within this fairly constrained format, each author has a distinguishing voice. A different way of doing the same thing. So far, Gladys Mitchell's approach has been my least favourite.
Ms Mitchell has a sleuth named Mrs Lestrange Bradley, and she solves her crimes using witchcraft and Freudian psychoanalysis. She is unbearably smug and supercilious, without even the slightest doubt in the effectiveness of her grab bag of psychoanalytical tools. She divines everything in advance: what each witness will say, where each clue will be revealed, and how the crime has been committed. No deductive reasoning required, and hence no challenge to the reader.