Abstract
Bartering problems in arithmetic books appear on the surface to be merely an exercise in the rule of three. However there is a type of problem that contains a surprise for modern readers. This article traces some of the appearances of barter problems in arithmetic textbooks over a period of more than 400 years, and from Italy to England, and examines the methods by which they were solved. It is based on a talk given in Oxford in December 2006 and is part of an ongoing study on this subject. The author would be grateful to learn of further examples in any culture.
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