How Do You Make a Magic Square?

How Do You Make a Magic Square?

One way to make a 3x3 magic square is to start with the number 1 in the middle top square. From there, add 1 each time you move to the other boxes, moving diagonally up and to the right if you can, and down if you cannot. Any move off the grid re-enters on the other side, wrapping around. A magic square is a grid in which each row, column and diagonal adds up to the same number.

This method of making a magic square works with any sequence of numbers, as long as they form an arithmetic progression, meaning the difference of any two successive numbers in the sequence is constant. For example, this sequence works because the difference between each number equals 10: 10, 20, 30, 40, 50, 60, 70, 80, 90.

Another variation on this method for larger magic squares is to start at the square above the center square, filling in as before, but moving up two squares when you hit a filled box instead of moving down one. This method works with 5x5 boxes and larger.

Both of these methods only work for odd-order magic squares, in which the number of rows and columns are the same odd number. Even-order magic squares require different methods.

The easiest way to make a magic square, even-order or odd-order, is to simply put the same number in every square.