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The number zero for n = 6 is an example of a more general phenomenon: associative magic squares do not exist for values of n that are singly even (equal to 2 modulo 4). [3] Every associative magic square of even order forms a singular matrix, but associative magic squares of odd order can be singular or nonsingular. [4]
[71] [72] For an even square, there are n/2 pairs of rows or columns that can be interchanged; thus 2 n/2 × 2 n/2 = 2 n equivalent magic squares by combining such interchanges can be obtained. For odd square, there are (n - 1)/2 pairs of rows or columns that can be interchanged; and 2 n-1 equivalent magic squares obtained by combining such ...
In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic squares. For n = 36, there are about 2.7 × 10 44 essentially different most-perfect magic squares.
The Siamese method, or De la Loubère method, is a simple method to construct any size of n-odd magic squares (i.e. number squares in which the sums of all rows, columns and diagonals are identical). The method was brought to France in 1688 by the French mathematician and diplomat Simon de la Loubère , [ 1 ] as he was returning from his 1687 ...
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order n – that is, a magic square which contains the numbers 1, 2, ..., n 2 – the magic constant is = +.
Start by creating a (2n+1)-by-(2n+1) square array consisting of n+1 rows of Ls, 1 row of Us, and; n-1 rows of Xs, and then exchange the U in the middle with the L above it. Each letter represents a 2x2 block of numbers in the finished square.
I was combing the internet trying to find a method to make an arbitrary 3x3 magic square -- not a normalized one. Meaning the sum doesn't have to be 15. I remember in grade school there was a simple method they taught to do it, but I couldn't remember it. I worked out the trick, or a method. In a 3x3 magic square the center is always 1/3 of the ...
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