A Question of Proof is not unlike other mysteries from the 1930s in that the setting (in this case, Sudeley preparatory school) is populated by an abundance of suspects. Algernon Wyvern-Wemyss, a most unpopular student, is found strangled. A young instructor, Michael Evans, is on the list of suspects for this heinous crime. Nigel Strangeways is asked to investigate the murder on behalf of the school, a task made more difficult as Evans and Strangeways were good friends during their school years at Oxford.
Strangeways had been having difficulty making ends meet as a poet, and had settled upon a career as a private investigator. Strangeways said it was the only career left which offered scope to good manners and scientific curiosity, and even paid, on occasion, quite handsomely. It helped somewhat that his uncle was a commissioner with Scotland Yard.
Nigel Strangeways is called in to find the murderer who has disrupted the normal chaos of Sudeley Hall, a boys preparatory school. The police suspect his friend Michael Evans, one of the teachers, who is in love with the headmaster's wife. The headmaster is stabbed while everyone is concentrating on the climax of an exciting cricket match between Parents and School. But what has happened to the murder weapon?
The faculty and student body at Sudeley are shocked but scarcely saddened when the headmaster’s obnoxious nephew, Algernon Wyvern-Wemyss, is found dead in a haystack on Sports Day. But when the young English master, Michael Evans, becomes a suspect in the case, he’s greatly relieved when his clever friend Nigel Strangeways, who is beginning to make a name for himself as a private inquiry agent, shows up to lend a hand to the local constabulary.
Strangeways immediately wins over the students and even becomes an initiate in one of their secret societies, The Black Spot, whose members provide him with some of the information he needs to solve the case. In the meantime Michael and Hero Vale, the pretty young wife of the headmaster, continue their hopeless love affair. When another murder follows, Strangeways is soon certain of the murderer’s identity, but until he can prove it, he’s reluctant to share his theory with the unimaginative but thorough Superintendent Armstrong.