### Method of Strachey

Take a 5x5 magic square and construct the second, third and fourth 5x5 magic square by adding (5 x 5 =) 25, (2 x 25 = ) 50 respectively (3 x 25 = ) 75 to all numbers of the first 5x5 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the third square in the top right corner and put the fourth square in the bottom left corner.

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

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap numbers, as follows. We split the 5x5 square in the top left corner and the 5x5 square in the bottom left corner in 'quarters' (marked by the blue numbers). The (yellow marked) ‘quarters’ top left and (red marked) 'quarters' bottom left of the 5x5 square in the top left corner must be swapped with the ‘quarters’ top left and bottom left of the 5x5 square in the bottom left corner. Also the (green marked) blue numbers on the border between the two 'quarters’  from the second cell up to the crossing point must be swapped. Finally the (orange marked) numbers of the top half of the last column(s) must be swapped with the numbers of the bottom half of the last column(s). Because the numbers of the first two columns must be swapped, the numbers of the last (2 – 1 = ) 1 column(s) must be swapped. See below the result.

10x10 magic square

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

ór

1x number from grid with 4x 5x5 magic square

 1 7 13 19 25 1 7 13 19 25 14 20 21 2 8 14 20 21 2 8 22 3 9 15 16 22 3 9 15 16 10 11 17 23 4 10 11 17 23 4 18 24 5 6 12 18 24 5 6 12 1 7 13 19 25 1 7 13 19 25 14 20 21 2 8 14 20 21 2 8 22 3 9 15 16 22 3 9 15 16 10 11 17 23 4 10 11 17 23 4 18 24 5 6 12 18 24 5 6 12

+25x number from grid with numbers 0, 1, 2 and 3

 0 0 0 3 3 2 2 2 2 1 0 3 3 0 0 2 2 2 2 1 0 3 3 0 0 2 2 2 2 1 0 3 3 0 0 2 2 2 2 1 0 0 0 3 3 2 2 2 2 1 3 3 3 0 0 1 1 1 1 2 3 0 0 3 3 1 1 1 1 2 3 0 0 3 3 1 1 1 1 2 3 0 0 3 3 1 1 1 1 2 3 3 3 0 0 1 1 1 1 2

= 10x10 magic square

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

Use the method of Strachey to construct magic squares of order is double odd. See 6x610x1014x1418x1822x2226x26 en 30x30

10x10, Method of Strachey.xls