Incomplete Diagonals of Latin Squares

Abstract

The following question has been asked by J. Dénes [2]: If n - 1 elements of the diagonal of an n × n array are prescribed, is it possible to complete the array to form an n × n latin square?" It is known that if n diagonal elements are given such a completion is not always possible.That the answer to Dénes' question is yes follows directly from a theorem of M. Hall Jr. [1].