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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.
As a running example, we consider a 10×10 magic square, where we have divided the square into four quarters. The quarter A contains a magic square of numbers from 1 to 25, B a magic square of numbers from 26 to 50, C a magic square of numbers from 51 to 75, and D a magic square of numbers from 76 to 100.
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 ...
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.
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2 s , where s = n 2 + 1. All pairs of integers distant n /2 along a (major) diagonal sum to s .
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 = +.
The 3×3 magic square in different orientations forming a non-normal 6×6 magic square, from an unidentified 19th century Indian manuscript. The 3×3 magic square first appears in India in Gargasamhita by Garga, who recommends its use to pacify the nine planets (navagraha). The oldest version of this text dates from 100 CE, but the passage on ...
Sallows is an expert on the theory of magic squares [1] and has invented several variations on them, including alphamagic squares [2] [3] and geomagic squares. [4] The latter invention caught the attention of mathematician Peter Cameron who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares" [5]