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In recreational mathematics, a magic square of order n is an arrangement of n² numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n². The term "magic square" is also sometimes used to refer to any of various types of word square.

Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3. The constant sum in every row, column and diagonal is called the magic sum or magic constant, M. The magic constant of a normal magic square depends only on n and has the value

M(n) = \frac{n^3+n}{2}

The middle number can be found by

= \frac{n^2+1}{2}
where n is the order of the square. For normal magic squares of order n = 3, 4, 5, …, the magic constants are:
15, 34, 65, 111, 175, 260, …
(sequence A006003 in OEIS)

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