Abstract: THE writer was confronted with the problem of treating a patient who was having an average of four attacks of angioneurotic oedema a day. He was 32 years of age, and had a history of sensitivity to aspirin and penicillin ; treatment with antihistamines, and other remedies had proved ineffective, and it was considered that cortisone should not be given if it was possible to devise another form of treatment. It was thought that a food allergy was by far the most probable cause of his attacks, but apart from a protracted, elaborate, and somewhat impracticable series of trial diets, there did not seem to be any known way of isolating the offending foods. Skin testing, according to Urbach and Gottlieb (1956), is of great value in conditions such as hay fever, but is of little or no value in food allergies, or angioneurotic oedema, and it was therefore ruled out as being unlikely to be of assistance. It was thought that a solution to the problem of isolating allergens might be found if a homologous problem in some other discipline could be discovered, and for which the method of solution had been found. In order to gather data the patient was instructed to write down as accurately as possible everything that he ate, the time he took the meal, and also the times when he had an attack, and to return in a week. When this record was examined the writer felt that the data necessary for isolating the food or foods must be present, and that a suitable coding should reveal them. Refiection showed that there was a similarity between this problem and that found in certain double substitution ciphers based on the Vigenere tableaux.