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.
Start by creating a (2n+1)-by-(2n+1) square array consisting of
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.
Now replace each letter by four consecutive numbers, starting with 1, 2, 3, 4 in the centre square of the top row, and moving from block to block in the manner of the Siamese method: move up and right, wrapping around the edges, and move down whenever you are obstructed. Fill each 2x2 block according to the order prescribed by the letter:
Let n = 2, so that the array is 5x5 and the final square is 10x10.
L | L | L | L | L |
L | L | L | L | L |
L | L | U | L | L |
U | U | L | U | U |
X | X | X | X | X |
Start with the L in the middle of the top row, move to the 4th X in the bottom row, then to the U at the end of the 4th row, then the L at the beginning of the 3rd row, etc.
68 | 65 | 96 | 93 | 4 | 1 | 32 | 29 | 60 | 57 |
66 | 67 | 94 | 95 | 2 | 3 | 30 | 31 | 58 | 59 |
92 | 89 | 20 | 17 | 28 | 25 | 56 | 53 | 64 | 61 |
90 | 91 | 18 | 19 | 26 | 27 | 54 | 55 | 62 | 63 |
16 | 13 | 24 | 21 | 49 | 52 | 80 | 77 | 88 | 85 |
14 | 15 | 22 | 23 | 50 | 51 | 78 | 79 | 86 | 87 |
37 | 40 | 45 | 48 | 76 | 73 | 81 | 84 | 9 | 12 |
38 | 39 | 46 | 47 | 74 | 75 | 82 | 83 | 10 | 11 |
41 | 44 | 69 | 72 | 97 | 100 | 5 | 8 | 33 | 36 |
43 | 42 | 71 | 70 | 99 | 98 | 7 | 6 | 35 | 34 |