### Row- and column grids

Each magic square can be split up in two Sudoku grids. You can split up a 3x3 magic square in two 3x3 Sudoku grids, with (three times) the numbers 1 up to 3. Because it is easier to calculate with, we use the numbers 0 up to 2 instead of 1 up to 3.

The first Sudoku is the grid with the row coordinates (= row grid). The second Sudoku is the grid with the column coordinates (= column grid).

 Row\column 0 1 2 0 1 4 7 1 2 5 8 2 3 6 9

Each number consists of a row coordinate and a column coordinate:

0 + 0x3 +1 = 1

1 + 0x3 +1 = 2

2 + 0x3 +1 = 3

0 + 1x3 +1 = 4

1 + 1x3 +1 = 5

2 + 1x3 +1 = 6

0 + 2x3 +1 = 7

1 + 2x3 +1 = 8

2 + 2x3 +1 = 9

Use adequate row and column grid combinations to construct all eight 3x3 magic squares:

Row coordinate +1    +3x column coordinate   =    3x3 magic square

 1 2 0 0 2 1 2 9 4 0 1 2 2 1 0 7 5 3 2 0 1 1 0 2 6 1 8 1 0 2 0 2 1 2 7 6 2 1 0 2 1 0 9 5 1 0 2 1 1 0 2 4 3 8 0 2 1 1 2 0 4 9 2 2 1 0 0 1 2 3 5 7 1 0 2 2 0 1 8 1 6 0 2 1 1 0 2 4 3 8 2 1 0 2 1 0 9 5 1 1 0 2 0 2 1 2 7 6 2 0 1 1 2 0 6 7 2 0 1 2 0 1 2 1 5 9 1 2 0 2 0 1 8 3 4 2 0 1 1 0 2 6 1 8 0 1 2 2 1 0 7 5 3 1 2 0 0 2 1 2 9 4 1 2 0 2 0 1 8 3 4 0 1 2 0 1 2 1 5 9 2 0 1 1 2 0 6 7 2 1 0 2 2 0 1 8 1 6 2 1 0 0 1 2 3 5 7 0 2 1 1 2 0 4 9 2

N.B.1: You allways (that's for each magic square of each order) can swap the row grid with the column grid. Use the download below to try, and notify that the magic square turns by a quarter: rows turns into columns and columns turns into rows.

N.B.2: Try to use 2x the same grid as row grid and as column grid. You don't get 9 different numbers, but 3 x 3 the same numbers. If you add the numbers in each row/column/diagonal, you still get the magic sum of 15.

N.B.3: Notify that addition of the numbers in each row/column/diagonal of each row grid and column grid gives the same result (3).

On this website you find for each size (order) at least one method with a row grid and a column grid to construct the magic square. For odd orders from 5x5, see the shift method, for multiple of 4, see the basic key method and for double odd, see the method with reflecting grids.

3x3, row and column grids.xlsx