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Hercule Poirot, the famous Belgian detective, learns that British Intelligence has assigned one of their men, Hastings, to follow him while he is in London visiting his tailor. Poirot seems to attract crime, and while in London, an aquaclown, Albert Aachen, is found murdered in a swimming pool. Killed by a poisoned dart, Aachen's body is found by police next to a copy of the A. B. C. guide to London. While Poirot and Hastings enjoy a Turkish bath, Amanda Beatrice Cross enters in a frenzy and declares that she is a compulsive murderer; then she vanishes, leaving behind a handbag bearing the initials A. B. C. and a bowling alley score card. Poirot's investigation leads him to Betty Barnard, a bowling instructress who is murdered shortly afterwards, again by a poisoned dart. Since the first two victims had the initials A. A. and B. B., Poirot deduces that the next victim will be C. C., and further inquiries convince him that the killer will strike Sir Carmichael Clarke. Inspector Japp believes the case is solved when Amanda Cross is cornered on a high crane and jumps into the Thames. Poirot, however, continues to investigate and finally proves that Amanda did not perish in her plunge. A schizophrenic, she committed the murders because of her obsession with the alphabet.