Three bodies are found. Beside each lies a copy of the ABC Railway Guide. The police are baffled. But the killer has made one mistake. He has challenged Hercule Poirot to unmask him.
Poirot falls asleep on a short aeroplane flight from Paris to London, and one of the other passengers, Madame Giselle, is killed by a poison dart while he sleeps. Poirot finds out that she was a money-lender, which may provide a motive for the killing.
Mabelle Sainsbury-Seale meets her old friend Alistair Blunt coming out of Dr Morley's dental surgery. And soon afterwards, Dr Morley (Poirot's dentist) is found dead. Japp thinks it was suicide, but Poirot disagrees.