Hercule Poirot receives a strange letter for assistance from an elderly woman, Miss Amelia Barrowby, who lives at Rosebank in Charman's Green. She is extremely vague in defining exactly what the problem is but states several times that discretion is paramount and that family is involved. The letter intrigues Poirot who has Miss Lemon draft a reply saying that he is at the lady's service.
Five days later Miss Lemon spots an announcement in the "personal column" of The Morning Post about the death of Miss Barrowby. Poirot sends a letter to Rosebank saying that he will call on Miss Barrowby but this is to provoke a response from the next of kin and he duly receives a reply from Mary Delafontaine, the lady's niece, saying that his services are no longer required. Nevertheless, he goes to the house and admires the well-maintained garden with its spring flowers and edging of shells. Let into the house by a maid, the first person he meets is a young Russian girl called Katrina Reiger who speaks cryptically of the money that by rights is hers. She is interrupted by Mary Delafontaine and her husband who dismisses Katrina and they meet Poirot. They seem shocked to find that he is a detective.
Poirot interviews the local police inspector who tells him that they now know that Miss Barrowby died from a dose of strychnine but the problem is that the victim and her two family members all ate the same meal. The Delafontaines are suspected as they will inherit a large sum of money, which they very much need, but it was Katrina who gave her employer her medicinal powders and it is possible the strychnine was in those. However, Katrina does not appear to have benefitted in any way from Miss Barrowby's death, and would, in fact, have been out of a job.
The next day, however, brings the news that Miss Barrowby left most of her money to Katrina, thereby providing a motive and she has duly been detained. A packet of strychnine powders is then found under Katrina's mattress which seems to clinch the matter. Poirot though is not convinced and arranges matters in a methodical order in his own mind. It is then he remembers the garden. He sends out Miss Lemon to make particular enquiries and then interviews Katrina who confirms that she ate separately to the family, as she always did, but had the same food as them.
Having met Miss Lemon and ascertained the results of her enquiries, he calls at Rosebank and sees Mary Delafontaine. At the front door, he points the unfinished row of shells – the only unsymmetrical item there – and points out they are oyster shells. Miss Lemon has found the fishmonger who sold the oysters to the Delafontaines. They gave Miss Barrowby the poison in the oysters, thus disguising the taste and then planted the shells in the garden as they didn't want Katrina or the maid to know that an extra item had been included in the family meal. Mrs Delafontaine confesses that she and her husband have been taking money from her aunt for many years and couldn't let the money go to Katrina.