"We've got far too much of everything."
But as for the mystery! Tuppence says the above of the story at one point and I'm afraid it's true. Dame Agatha must have realized. There's a gang that's been pulling off spectacular heists for years--the Irish Mail, etc.--that Tommy hears about in his professional aspect; there's some maniac who's killing children around Sutton Chancellor; and there's another serial killer doing in elderly women in nursing homes. Because this is Agatha Christie and not, say, Ed McBain or J. J. Marric (John Creasey) I suspected that all these cases would tie together and they do, but it is just a little too much of everything...
Oh, well, it was still amusing, and I would definitely read another Tommy and Tuppence story. In fact I picked up N or M? at the same charity sale as this one and as it's earlier I should probably have read it first, especially as this one refers to it (I think) on several occasions.
Just The Facts Challenge, Silver Era
Who: Professional is the Main Sleuth.
Tommy and Tuppence run a detective agency, though frankly there's not much sign of it in this one.