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A 24x24 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (6924)

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 24 by 24 magic square shown below has a magic sum equal to 6924.

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 24x24 Magic Square
with a Magic Sum of 6924

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 24x24 blank grid and color in the two main diagonals.
  2. Also, color in the two main diagonals of each 4x4 box within this 24x24 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 576 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 576, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 24x24 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 (576).

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

This time, you can either
  • Start counting backward, starting with 576 (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 576 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 576 is already written in that square), write down 2 and 3, then skip 4, etc.
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A 24-by-24 Magic Square

(Magic Sum = 6924)

1575574455715708956756612135635621617559558202155555424
552262754954830315455443435541540383953753642435335324647529
528505152552454555215205859517516626351351266675095087071505
735035027677499498808149549484854914908889487486929348348296
97479478100101475474104105471470108109467466112113463462116117459458120
456122123453452126127449448130131445444134135441440138139437436142143433
432146147429428150151425424154155421420158159417416162163413412166167409
169407406172173403402176177399398180181395394184185391390188189387386192
193383382196197379378200201375374204205371370208209367366212213363362216
360218219357356222223353352226227349348230231345344234235341340238239337
336242243333332246247329328250251325324254255321320258259317316262263313
265311310268269307306272273303302276277299298280281295294284285291290288
289287286292293283282296297279278300301275274304305271270308309267266312
264314315261260318319257256322323253252326327249248330331245244334335241
240338339237236342343233232346347229228350351225224354355221220358359217
361215214364365211210368369207206372373203202376377199198380381195194384
385191190388389187186392393183182396397179178400401175174404405171170408
168410411165164414415161160418419157156422423153152426427149148430431145
144434435141140438439137136442443133132446447129128450451125124454455121
4571191184604611151144644651111104684691071064724731031024764779998480
481959448448591904884898786492493838249649779785005017574504
725065076968510511656451451561605185195756522523535252652749
485305314544534535414053853937365425433332546547292855055125
55323225565571918560561151456456511105685697657257332576
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