The Strachey method for magic squares is an

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

for generating magic squares of

singly even In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. The former names are traditional ones, derived from ancient Gree ...

order 4''k'' + 2. An example of magic square of order 6 constructed with the Strachey method: Strachey's method of construction of singly even magic square of order ''n'' = 4''k'' + 2. 1. Divide the grid into 4 quarters each having ''n''²/4 cells and name them crosswise thus 2. Using the

Siamese method 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 ...

(De la Loubère method) complete the individual magic squares of odd order 2''k'' + 1 in subsquares A, B, C, D, first filling up the sub-square A with the numbers 1 to ''n''²/4, then the sub-square B with the numbers ''n''²/4 + 1 to 2''n''²/4,then the sub-square C with the numbers 2''n''²/4 + 1 to 3''n''²/4, then the sub-square D with the numbers 3''n''²/4 + 1 to ''n''². 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. 3. Exchange the leftmost k columns in sub-square A with the corresponding columns of sub-square D. 4. Exchange the rightmost k - 1 columns in sub-square C with the corresponding columns of sub-square B. 5. Exchange the middle cell of the leftmost column of sub-square A with the corresponding cell of sub-square D. Exchange the central cell in sub-square A with the corresponding cell of sub-square D. The result is a magic square of order ''n''=4''k'' + 2.W W Rouse Ball Mathematical Recreations and Essays, (1911)

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