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by L. Euler (Posted on 2012-09-08) Difficulty: 4 of 5
Is it possible to arrange 6 regiments each consisting of 6 officers of different ranks in a 6 by 6 square, so that no rank or regiment will be repeated in any row or column?


Attributed to Leonhard Euler.

L.Euler was a leading Swiss mathematician, who spent most of his adult life in St. Petersburg, Russia.
The following military ranks existed inter alia in Russia's infantry circa 1760:
polkovnik, pod-polkovnik, premier major, second major, poruchik, lieutenant.
The above lines, although redundant, were added to avoid ambiguity
and to ascertain that 6 specific , well-defined and identical sets of 6 ranks are addressed in L.E.'s problem.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution answer | Comment 2 of 7 |
(Found in various references on the web,) the answer is No.
In 1901, the French mathematician Gaston Tarry proved
the non-existence of the order six square. Later, with the use of a computer, mathematicians Parker, Bose and Shrikhande proved that the only impossible Euler squares were of order two and six.
  Posted by Dej Mar on 2012-09-08 13:13:56
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