The problem of Euler/Tarry revisited
AbstractThe problem of Euler/Tarry concerning 36 officers can be formulated in mathematical terms: Can a latin square of order 6 have an orthogonal square, or equivalently, are there 6 pairwise disjoint transversals? This was first answered (in the negative) by Tarry (1900/01). We prove the following Theorem: If a latin square of order 6 admits a reflection, i. e. an automorphism of order two which fixes the main diagonal elementwise, then it has no orthogonal square. We list the 12 isomorphism types of latin squares of order 6 and see: they all admit such a reflection. So we get a solution of the Euler problem without the tedious task of tracing the transversals.
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1979 ◽
Vol 22
(4)
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pp. 477-481
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1988 ◽
Vol 31
(4)
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pp. 409-413
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2006 ◽
Vol 90
(519)
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pp. 425-430
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