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MAGIC SQUARES AND LATIN SQUARES
ABSTRACT
The n × n array defined by a magic matrix is called a magic square. When the entries are consecutive
positive integers, then it is said to be classic ( natural or normal)magic square. In this paper, we study
nxn magic matrices in which all the numbers in the rows and columns and in the 2 main diagonals
add up to the same magic constant (sum), S. Magic squares have been known for 4000 years. Magic
squares are usually presented as a mathematical recreation. Especially, 4x4 standard magic squares
and their properties are investigated. These squares have a sequence of integers 1 thru 16, arranged
such that the sum across each row, sum down each column, and the sum across each diagonal equals
the same magic constant, S=34. This paper describes the construction of magic squares from an or-
thogonal pair of diagonal latin squares. The pandiagonal 4x4 magic square sum to the magic constant
along every broken diagonal is given, We define a “philatelic magic square” as a square arrangement
of images of postage stamps so that the associated nominal values form a magic square. Furthermore,
Latin square design models are illustrated visually by special stamps.
Keywords: Latin square, , Magic constant, Magic square, Semi-magic square.

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