Poirot is spending a week-end with the Angkatells, at their country house called The Hollow. The good-looking Dr John Christow is also there, with his plain wife, but he is flirting (or perhaps more) with Henrietta Savernake, a young artist. Meanwhile, Lady Angkatell is match-making between Henrietta and Edward Angkatell, to the distress of Midge, who loves Edward.
Then a game of murder turns into the real thing, when Christow is shot dead by the swimming pool. Gerda Christow is found holding the gun, but was she set up? Sir Henry Angkatell asks Poirot (how could he do anything else?) to find the killer, and it soon appears that several of the house party had motives for killing Christow, including Henrietta and Lady Angkatell... then the ballistic evidence comes in, and there is a big surprise.
Poirot will surely outwit the murderer. Or will he?