Some comments on Latin squares and on Graeco-Latin squares, illustrated with postage stamps and old playing cards

Abstract

We present some comments on Latin squares and on Graeco-Latin squares, with special emphasis on their use in statistics and in a historical context. We also comment on the Knut Vik square, the knight’s move design and the knight’s tour, as well as the Magic Card Puzzle. We consider the well-known 36 officers problem studied by Euler (Verhandelingen uitgegeven door het zeeuwsch Genootschap der Wetenschappen te Vlissingen, vol. 9 (Middleburg 1782), pp. 85–239, 1779/1782), and give two examples of diagonal Latin squares of order 6 due, respectively, to Abbe Francois-Guillaume Poignard (Chez Guillaume Fricx, Imprimeur & libraire rue Bergestract, a l’enseigne des quatre Evangelistes, Bruxelles [4] 79 pp. (p. 71 folded), 1704) and Jozsef Denes (J Lond Math Soc Ser 2, 6(4):679–689, 1970). We illustrate our comments with images of postage stamps and old playing cards. An extensive annotated bibliography ends the paper.