Theoretical Statistics and Mathematics Unit, ISI Delhi

A matrix approach to construct magic rectangles of even order

by J. P. De Los Reyes, Ashish Das and Chand K. Midha

Magic rectangles are well-known for its very interesting and entertaining combinatorics. In a magic rectangle, the numbers 1 to $mn$ are arranged in an array of $m$ rows and $n$ columns so that each row adds to the same total $M$ and each column to the same total $N$. In the present paper we provide a new systematic method for constructing any even by even magic rectangle. The method proposed is extremely simple as it allows one to arrive at the magic rectangles by simply carrying out some matrix operations. It is also seen that the magic rectangles of lower orders are embedded in a magic rectangle of higher order.

isid/ms/2007/07 [fulltext]

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