Statistical Papers

, Volume 50, Issue 4, pp 917–941 | Cite as

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

  • George P. H. StyanEmail author
  • Christian Boyer
  • Ka Lok Chu


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 Abbé François-Guillaume Poignard (Chez Guillaume Fricx, Imprimeur & libraire ruë Bergestract, à l’enseigne des quatre Evangelistes, Bruxelles [4] 79 pp. (p. 71 folded), 1704) and József Dénes (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.


Bachet’s square Bibliography Bi-square Raj Chandra Bose József Dénes Diagonal Latin squares of order 6 Leonhard Euler Euler squares Eulerian squares Euler’s conjecture Sir Ronald Aylmer Fisher Graeco-Roman squares History Simon de La Loubère Knut Vik design Knight’s move design Knight’s tour Magic squares MOLS Mutually orthogonal Latin squares Jacques Ozanam Ozanam–Grandin solution to the Magic Card Puzzle Edward Tilden Parker Parker’s Graeco-Latin square of order 10 Georges Perec Abbé François-Guillaume Poignard Sharadchandra Shankar Shrikhande Thirty-six officers problem Topical philately Weißwurst Äquator 

Mathematics Subject Classification (2000)

01A45 01A50 05A99 05B15 62K05 62K10 62K15 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • George P. H. Styan
    • 1
    Email author
  • Christian Boyer
    • 2
  • Ka Lok Chu
    • 3
  1. 1.Department of Mathematics and StatisticsMcGill UniversityMontréalCanada
  2. 2.Enghien-les-BainsFrance
  3. 3.Department of MathematicsDawson CollegeWestmountCanada

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