Tommy takes Tuppence to lunch at an ABC shop where he decides to mimic the tastes and habits of “The Old Man in the Corner” with Tuppence playing the part of Polly Burton. To test his abilities as this detective he has brought along a cutting from a newspaper on the recent case of what is known as the Sunningdale Mystery.
The facts are that two men, Captain Anthony Sessle and Mr. Hollaby, business partners and both members of Sunningdale Golf Club, played a full round of golf on the course on a Wednesday and decided to play a few more holes before it went dark. As they approached the tee on the seventh hole, Hollaby saw Sessle talking to a mysterious woman in a brown coat. These two went off talking down a side path and after a moment Sessle reappeared. Something had upset him for his game fell apart and two holes later Sessle gave up and walked off alone, ostensibly to his bungalow home. The existence of the woman in brown, Sessle's temporary departure with her and his subsequent poor game were all witnessed by two other members who were on the previous hole and awaiting their turn.
The next morning, Sessle was found dead on the seventh tee, stabbed with a hatpin through the heart. The police found forensic evidence on the man which led them to trace a young girl called Doris Evans. She was arrested and told a story of meeting Sessle at a cinema. He invited her to his bungalow on a day when, as she subsequently found out, his wife and servants would be away. On the day in question, the man met her as he arrived home from the golf course. He behaved strangely and then, suggesting a stroll, he took her to the golf course. On the aforementioned seventh tee he suddenly became deranged and produced a revolver, wildly suggesting a suicide pact. Doris escaped his grasp and ran off. One further fact which has come to light is that Sessle and Hollaby's assurance business is in liquidation and the funds embezzled.
Over their table, Tuppence counters that Doris would not have murdered the man as very few women nowadays use hatpins and that suggests that a man, not conversant with present fashions, committed the crime and tried to frame a woman. Tommy soon remembers that near to the seventh hole on the course is a small hut and the two talk about the possibility that the woman in brown could have been a man in disguise. This leads them to wonder who it could have been and, linked to a theory of Tuppence's that the embezzler of the company was not Sessle but Hollaby and his son, they speculate if the woman was Hollaby Junior, who is also connected with the assurance firm. They reconstruct the crime: Hollaby's son lures Sessle away in full view of the other two players on the course. He stabs him with a hatpin and hides the body in a hut, changing clothes with the dead man. The two witnesses on the course see at a distance the deterioration in his game and "Sessle" then goes to his bungalow where he meets Doris Evans as arranged and goes through a series of actions which lead to the innocent girl being arrested.
The Beresfords wonder how to convince the police of the plausibility of their theory but they have failed to spot Inspector Marriot at the next table. He has overheard the conversation and, already suspicious of the Hollaby's, promises to set enquiries in motion.