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36 Officer Problem


How can a delegation of six regiments, each of which sends a colonel, a lieutenant-colonel, a major, a captain, a lieutenant, and a sub-lieutenant be arranged in a regular 6×6 array such that no row or column duplicates a rank or a regiment? The answer is that no such arrangement is possible.


See also

Euler's Graeco-Roman Squares Conjecture, Latin Square, Trigonometry Angles--Pi/3, Trigonometry Angles--Pi/6

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References

Bose, R. C.; Shrikhande, S. S.; and Parker, E. T. "Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture." Canad. J. Math. 12, 189, 1960.Bruck, R. H. and Ryser, H. J. "The Nonexistence of Certain Finite Projective Planes." Canad. J. Math. 1, 88-93, 1949.Parker, E. T. "Orthogonal Latin Squares." Not. Amer. Math. Soc. 6, 276, 1959.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, p. 31, 1999.Tarry, G. "Le problème de 36 officiers." Compte Rendu de l'Assoc. Français Avanc. Sci. Naturel 1, 122-123, 1900.Tarry, G. "Le problème de 36 officiers." Compte Rendu de l'Assoc. Français Avanc. Sci. Naturel 2, 170-203, 1901.

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36 Officer Problem

Cite this as:

Weisstein, Eric W. "36 Officer Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/36OfficerProblem.html

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