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A 28x28 Magic Square

Scroll down to see a magic square
in which all rows, columns, and both diagonals
add up to the same magic sum (10990)

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 28 by 28 magic square shown below has a magic sum equal to 10990.

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 28x28 Magic Square
with a Magic Sum of 10990

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 28x28 blank grid and color in the two main diagonals.
  2. Also, color in the two main diagonals of each 4x4 box within this 28x28 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 784 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 784, but this time, only write down the numbers in the non-shaded squares.

Step One: Draw a 28x28 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 (784).

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

This time, you can either
  • Start counting backward, starting with 784 (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 784 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 784 is already written in that square), write down 2 and 3, then skip 4, etc.
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A 28-by-28 Magic Square

(Magic Sum = 10990)

17837824577977889775774121377177016177677662021763762242575975828
7563031753752343574974838397457444243741740464773773650517337325455729
7285859725724626372172066677177167071713712747570970878797057048283701
85699698888969569492936916909697687686100101683682104105679678108109675674112
113671670116117667666120121663662124125659658128129655654132133651650136137647646140
644142143641640146147637636150151633632154155629628158159625624162163621620166167617
616170171613612174175609608178179605604182183601600186187597596190191593592194195589
197587586200201583582204205579578208209575574212213571570216217567566220221563562224
225559558228229555554232233551550236237547546240241543542244245539538248249535534252
532254255529528258259525524262263521520266267517516270271513512274275509508278279505
504282283501500286287497496290291493492294295489488298299485484302303481480306307477
309475474312313471470316317467466320321463462324325459458328329455454332333451450336
337447446340341443442344345439438348349435434352353431430356357427426360361423422364
420366367417416370371413412374375409408378379405404382383401400386387397396390391393
392394395389388398399385384402403381380406407377376410411373372414415369368418419365
421363362424425359358428429355354432433351350436437347346440441343342444445339338448
449335334452453331330456457327326460461323322464465319318468469315314472473311310476
308478479305304482483301300486487297296490491293292494495289288498499285284502503281
280506507277276510511273272514515269268518519265264522523261260526527257256530531253
533251250536537247246540541243242544545239238548549235234552553231230556557227226560
561223222564565219218568569215214572573211210576577207206580581203202584585199198588
196590591193192594595189188598599185184602603181180606607177176610611173172614615169
168618619165164622623161160626627157156630631153152634635149148638639145144642643141
645139138648649135134652653131130656657127126660661123122664665119118668669115114672
6731111106766771071066806811031026846859998688689959469269391906966978786700
8470270381807067077776710711737271471569687187196564722723616072672757
5673073153527347354948738739454474274341407467473736750751333275475529
757272676076123227647651918768769151477277311107767777678078132784
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