Conway's LUX method for magic squares

Conway's LUX method for generating magic squares is an algorithm for generating magic squares of order 4n 2, where n is a positive natural number, named after the English mathematician John Horton Conway.

As a beginning ( initialization) you create a square matrix of dimension (2n 1) x (2n 1). The first n 1 rows are completely filled with Ls, then a line described fully with Us and then the remaining n-1 rows of X. ( Hence the name LUX method).

Example for n = 2

L L L L L L L L L L L L L L L U U U U U X X X X X Now you exchange the middle U with the L above.

So:

L L L L L L L L L L U L L L L U U U U L X X X X X With Siam method to generate a magic square with order 2n 1, which comes to rest on the letter.

You start with the letter at the top in the middle.

So:

L = 19 L = 25 L = 1 L = 7 L = 13 L = 24 L = 5 L = 6 L = 12 L = 18 L = 4 L = 10 U = 11 L = 17 L = 23 U = 9 V = 15 L = 16 U = 22 U = 3 X = 14 X = 20 X = 21 X = 2 X = 8 Now simply fill the order after four numbers in the letter, according to the procedures of the corresponding letter.

L =

4 1   2 3 U =

1 4   2 3 X =

1 4   3 2 It is envisioned to draw the letters with a pen.

Example:

[ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6] [ 7 ] [ 8 ] [ 9 ] [ 10]   [ 1 ] 68 65 96 93 4 1 32 29 60 57   [2, ] 66 67 94 95 2 3 30 31 58 59   [3, ] 92 89 20 17 28 25 56 53 64 61   [4, ] 90 91 18 19 26 27 54 55 62 63   [5, ] 16 13 24 21 49 52 80 77 88 85   [ 6 ] 14 15 22 23 50 51 78 79 86 87   [ 7 ] 37 40 45 48 76 73 81 84 9 12   [ 8 ] 38 39 46 47 74 75 82 83 10 11   [ 9 ] 41 44 69 72 97 100 5 8 33 36 [ 10 ] 43 42 71 70 99 98 7 6 35 34 see also

Magic Cube, Magic Klangquadrat, palindrome, Sudoku, completely perfect magic square