Geodesic
Incomplete Diagonals of Latin Squares
Canadian mathematical bulletin, Tome 12 (1969) no. 2, p. 235

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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]. 
Marica, J.; Schönheim, J. Incomplete Diagonals of Latin Squares. Canadian mathematical bulletin, Tome 12 (1969) no. 2, p. 235. doi: 10.4153/CMB-1969-030-5
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     title = {Incomplete {Diagonals} of {Latin} {Squares}},
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