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Other 4N+0 Magic Square Sizes:
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A 8x8 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (260)

A Magic Square is a square of numbers in which every row, every column, and both diagonals add up to the same number. This number is often called the magic sum. The 8 by 8 magic square shown below has a magic sum equal to 260.

Though magic squares can be made with non-consecutive and non-regular sequences, they are usually seen made up of consecutive numbers, possibly because it is harder to be consecutive.

The method described below can be used to create all 4N+0 (multiple-of-four) magic squares. This is just one method for creating magic squares, there are many other methods, and many-many-many magic squares to be found.

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How to Create a 8x8 Magic Square
with a Magic Sum of 260

The method described on this page can be used to create 4x4, 8x8, 12x12, 16x16 and larger 4N+0 magic squares

Steps:

  1. Draw a 8x8 blank grid and color in the two main diagonals.
  2. Also, color in the two main diagonals of each 4x4 box within this 8x8 square.
  3. Starting in the top left corner, moving left to right through the rows, count the squares, 1, 2, 3, 4, but only write down the numbers you say when you get to one of the colored in squares. If you do this properly, you will write 1 in the top left corner and write 64 in the bottom right corner.
  4. Next, do the same thing, starting in the bottom right corner, moving right-to-left upward through the rows, again count from 1 to 64, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 8x8 blank grid and
shade in the two main diagonals

You don't necessarily have to shade in the squares. You could simply draw a light line that passes through these squares. You only need to be able to tell the difference between squares that are on these 4x4 diagonals and those that are not.
                        
        
        
        
        
        
        
        

Step Two: Shade in all the 4x4 diagonals

If you are making a square larger than 4x4, the entire square can be visualized as a collection of 4x4 squares. Shade in the main diagonals of each 4x4 square within the big square.

If you do this correctly, by the time you are done, you will have shaded in exactly half the squares in your overall grid. If you had simply drawn diagonal lines through those squares, you would see a series of X's.

                        
        
        
        
        
        
        
        

Step Three: Count the squares
(writing only on the shaded squares)

This is fairly straightforward. Starting in the top left corner, and moving left-to-right through each row, count the squares, but only write down the numbers in the shaded squares, but remember to count all the blank squares. In the first four spaces, you would write down 1, count 2 and 3, and write down 4. Continue until you have written down the last number (64).
1  45  8
 1011  1415 
 1819  2223 
25  2829  32
33  3637  40
 4243  4647 
 5051  5455 
57  6061  64

Step Four: Count the squares again, counting backward,
writing into the blank squares

This time, you can either
  • Start counting backward, starting with 64 (which you would not write down) and count downward, writing down the number whenever you come to a blank square. The last two numbers you write down would be 3 and 2 just before you get to the 64 which you wrote down in Step Three.
  • Or, if you prefer counting upward, start with 1 in the bottom right corner and move right-to-left through each row until you get to the top left corner. Working this way, you will skip 1 (because 64 is already written in that square), write down 2 and 3, then skip 4, etc.
163624559588
5610115352141549
4818194544222341
2539382829353432
3331303637272640
2442432120464717
165051131254559
577660613264
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A 8-by-8 Magic Square

(Magic Sum = 260)

163624559588
5610115352141549
4818194544222341
2539382829353432
3331303637272640
2442432120464717
165051131254559
577660613264
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