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.

(In reply to difficulty level by Charlie)

Charlie,

Amusing, but a bit harsh, I think. I don't believe there was anything wrong with posing this as a problem, even if it does turn out to have a bit of depth. Certainly it could have been D5, but in a massive 37 comments, no-one suggested that.

Collectively, Perplexites have a considerable amount of math talent. It's not beyond the realms of possibility that someone could have come up with a new way of looking at this problem.

And given the history of the problem, it's impossible to suggest that it's not 'interesting' - I wouldn't want anyone to be discouraged from posting 'classic problems, just because they've been solved before on the Internet!

Posted by broll on 2012-09-09 00:28:20