It is just before Christmas when a young lady called Monica Deane calls at the Blunt's agency. She and her impoverished, invalid, widowed mother inherited a house from a well-off sister of her father's some time back. They also expected to inherit some money to go with the house but to their surprise there was little forthcoming. They didn't want to sell the house as it provided plenty of room for them compared to their small flat and they had plans to open it to paying guests to supplement their income. All went well for a time until they started to have strange occurrences with pictures falling off walls and crockery being smashed when no one was in the room – a poltergeist, which scared all their guests and their income away. A Dr. O'Neill from a Society for Physical Research has visited them and has offered to buy the house from them to continue his investigations. Monica however is certain that he is also younger man in disguise who previously made them an offer for the house. The only other resident in the house now is Crockett, an elderly maid of Monica's aunt who has a younger nephew of whom she is very proud.
Tommy and Tuppence travel to the "Red House" and begin their investigations, harbouring suspicions that the old lady has hidden money in the building which would account for the remainder of her fortune being missing. Tommy makes a visit to the local bank and manages to the find out from the manager that the aunt did indeed withdraw all of her money some time before she died. Under the guise of potential buyers, they explore the house and Monica gives them various papers of her aunt's. Before they can investigate these further, they hear a crash and find a jug and basin broken in a room overhead. They quickly interview Crockett and notice that she is out of breath. Mentioning to her that they intend to buy the house, Monica receives a message soon afterwards from "Dr. O'Neill" that his own offer has increased – it is obvious that the old maid is the one creating "disturbances" and that the "Doctor" is her nephew trying to get the house in order that he can investigate himself the location of the missing fortune.
Tommy and Tuppence look over the papers and realise that one of them contains a puzzle anagram. They work it out and the solution is "potatoes". Another of the papers, on the theme of recipes, refers to the trick of burying new potatoes in a tin to keep them fresh for the winter and they realise that this is their lead. They question the gardener to see if the old lady ever used this technique and find out that she did. They dig in the spot and find several tins of potatoes and, in one of the tins, a bag containing two hundred pounds in gold sovereigns, twenty thousand pounds in banknotes and a string of expensive pearls. Monica Deane and her mother will have their fortune and she and the Beresfords will be each able to celebrate a happy Christmas.