Belgian detective Hercule Poirot notices something unprecedented: His supremely efficient secretary, Miss Lemon, has made three typing errors in a single letter. The cause is her sister, Mrs. Hubbard, who serves as warden of a student hostel at 26 Hickory Road in London, owned by a temperamental Greek woman named Mrs. Nicoletis. For months, baffling thefts have plagued the hostel: items ranging from a single evening shoe, a diamond ring, and costume jewelry to a stethoscope, electric lightbulbs, and boracic powder. Two items have also been found slashed to pieces: a rucksack and a silk scarf belonging to Valerie Hobhouse, a sharp-tongued resident who works at a beauty salon. Poirot is fascinated by the incoherence of the list and agrees to investigate.
He arranges to visit the hostel, ostensibly to give a talk on detection. Over dinner he observes the residents: Celia Austin, a shy hospital dispenser; Colin McNabb, a dour Scottish postgraduate in psychiatry whom Celia clearly admires; Nigel Chapman, a sarcastic student of medieval history; Leonard Bateson, a large, red-haired medical student; and Patricia Lane, an earnest archaeology student devoted to Nigel. After dinner, Colin bluntly states that Poirot is really there to investigate the thefts. Poirot advises that the police should be called at once, producing a shocked silence.
Privately, Colin argues the thief has a psychological condition. As if on cue, Celia arrives and tearfully confesses. However, she denies certain incidents: spilling ink on the research papers of Elizabeth Johnston, a fellow resident studying law; stealing the stethoscope; or destroying the rucksack. Poirot suspects someone more intelligent coached Celia to attract Colin's attention and warns that the slashed items and ink sabotage suggest something more dangerous beneath the surface.
The next morning, Mrs. Hubbard arranges reparations. Celia writes a check using Nigel's green ink because her own pen has run dry. That evening, Colin announces their engagement. Celia makes a cryptic remark at dinner, suggesting that by tomorrow "everything will be cleared up," and urging whoever is responsible for the remaining incidents to confess.
The following morning, Celia is found dead from an apparent morphia overdose. A torn scrap of paper beside her reads: "Dear Mrs. Hubbard, I really am sorry and this is the best thing I can do." Inspector Sharpe investigates, but Mrs. Hubbard recalls that Celia filled her pen with green ink the previous morning, yet the note is in blue-black ink. It was not a suicide message at all; it was torn from the letter of apology Celia had written about reparations. Someone placed it beside her bed with an empty morphia bottle. Poirot declares this is murder.
Sharpe questions the students. Jean Tomlinson, a prim physiotherapist, reveals that Nigel recently bet Len he could obtain three different poisons without being traced. Nigel confirms he succeeded, acquiring hyoscine, digitalin, and morphine tartrate through various deceptions, and claims all three were then destroyed. Sally Finch, an American Fulbright scholar and fellow resident, reveals she saw Celia leaving the house around 10 o'clock on the night she died. Elizabeth Johnston offers the most striking testimony: Celia told her the evening before she died that she believed someone in the house had a forged passport.
Poirot realizes he never established the chronological order of the thefts. Mrs. Hubbard's reconstruction reveals that the rucksack's destruction was the very first incident, coinciding with a police visit on an unrelated matter. Poirot deduces that someone panicked, assumed police had come about smuggling, and destroyed the rucksack to eliminate evidence. He purchases a rucksack from a shop near Hickory Road and discovers a false bottom capable of concealing drugs or uncut gems. Students have been unwittingly carrying contraband across the English Channel in specially manufactured rucksacks.
Poirot confronts Valerie with another discovery: Patricia's diamond ring now contains only a zircon, a worthless substitute. Valerie admits she devised the kleptomania scheme for Celia, took Patricia's ring, replaced the diamond to cover gambling debts, and staged its theatrical return. Their conversation is cut short by devastating news: Mrs. Nicoletis has been found dead. The hostel owner had been increasingly frightened and drinking heavily; she left the hostel one evening, met someone she recognized at a pub, and was later found collapsed. She died at a police station. Poirot presents his smuggling theory to Superintendent Wilding of the Narcotics squad, identifying Mrs. Nicoletis as a figurehead but suspecting another mastermind.
Patricia confesses to Nigel that she secretly removed what she thought was morphia from his sock drawer, replacing it with bicarbonate of soda. The bottle she hid the supposed morphia in has now vanished. When she insists on writing to Nigel's estranged father, Sir Arthur Stanley, a famous research chemist, to urge reconciliation, Nigel furiously destroys her letter. Genevieve, a volatile French student, overhears through the door and spreads gossip.
Nigel reports the missing morphia to the police. While he is there, Patricia telephones, breathless, saying she knows who took the poison. She is cut off mid-sentence. Sharpe and Nigel rush back to find Patricia dead, struck on the head with a marble paperweight placed inside one of Nigel's socks. Two short red hairs are clutched between her fingers.
Mr. Akibombo, a West African student, provides critical testimony. Days before Celia's death, he took what he thought was bicarbonate from Patricia's drawer but became very ill; the powder was actually boracic acid. This reveals a chain of substitutions: Someone replaced Nigel's morphia with boracic acid, then Patricia unknowingly replaced the boracic with bicarbonate. The real morphia was taken by whoever made the first switch.
Poirot identifies the red hairs as a deliberate plant: Since Patricia was struck from behind, she could not have grasped her attacker's hair. The hairs were placed to frame Len Bateson. Police raid Valerie's beauty salon, Sabrina Fair, and discover false passports and bank accounts under multiple identities, confirming the smuggling operation.
Poirot makes the final deduction. Valerie left the house before six o'clock, verified by witnesses. The telephone call Patricia supposedly made to the police at eight minutes past six came not from Hickory Road but from a nearby call box, made by Valerie impersonating Patricia's voice. Nigel, who took the call, knew it was not Patricia because he had already killed her before leaving the house. He and Valerie conspired to create alibis for both of them.
Poirot visits Sir Arthur Stanley's solicitor, who produces a sealed letter. It reveals that Nigel killed his own mother with an overdose of the sedative medinal when she threatened to expose his check forgeries. Sir Arthur extracted a signed confession and struck a bargain: Nigel would leave and change his name, but if ever convicted of a crime, the confession would go to the authorities. This explains Nigel's desperation to prevent Patricia from contacting his father.
Valerie, caught on smuggling charges, confirms that Nigel killed all three victims: He slipped morphia into Celia's coffee, poisoned the increasingly unreliable Mrs. Nicoletis, and struck Patricia with the paperweight. She reveals her motive for cooperating with police: Mrs. Nicoletis was her mother. In the aftermath, Sally Finch and Len Bateson plan to marry, Miss Lemon returns to her impeccable efficiency, and Poirot recites the nursery rhyme to the bafflement of the literal-minded Miss Lemon.