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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 ...
Bordered magic square when it is a magic square and it remains magic when the rows and columns on the outer edge are removed. They are also called concentric bordered magic squares if removing a border of a square successively gives another smaller bordered magic square. Bordered magic square do not exist for order 4.
Conway's LUX method for magic squares is an algorithm by John Horton Conway for creating magic squares of order 4n+2, where n is a natural number. Method
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.
Apart from the trivial case of the first order square, most-perfect magic squares are all of order 4n. 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 ...
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 = +.
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. [1] A traditional magic square is a square array of numbers (almost always positive integers ) whose sum taken in any row, any column, or in either diagonal is the same target number .
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]