Thirty-six officers problem

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The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782.[1][2]

The problem asks if it is possible to arrange 6 regiments consisting of 6 officers each of different ranks in a 6 × 6 square so that no rank or regiment will be repeated in any row or column. Such an arrangement would form a Graeco-Latin square. Euler correctly conjectured there was no solution to this problem, and Gaston Tarry proved this in 1901;[3] but the problem has led to important work in combinatorics.[4]

It is possible to solve the equivalent problem for all other sizes of square other than a 2 by 2 squares.

[edit] References

  1. ^ Euler, L., Recherches sur une nouvelle espece de quarres magiques (1782).
  2. ^ P. A. MacMahon (1902). "Magic Squares and Other Problems on a Chess Board". Proceedings of the Royal Institution of Great Britain XVII: 50–63. 
  3. ^ G. Terry (1900–1901). "Le Probléme de 36 Officiers". Comptes Rendu de l' Association Française pour l' Avancement de Science Naturel 1: 122–123 & 2170–2203. 
  4. ^ Dougherty, Steven. "36 Officer Problem." Steven Dougherty's Euler Page. 4 Aug 2006.

[edit] External links