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The 3x3 magic square is square, because it has as many rows (from left to right = horizontal) as columns
(from top to bottom = vertical).
The 3x3 magic square consists of 3 rows which multiplied by 3 columns is 9 cells.
The 3x3 magic square must contain 9 different digits. A pure magic 3x3 square contains the digits 1, 2, 3, 4,
5, 6, 7, 8 and 9.
The magic square is magic, because the sum of the digits of each row, each column and both diagonals al-
ways give the same result. The sum can be calculated as follows, the (odd) size of the square multiplied by
the middle digit: 3 x 5 = 15.
What is the secret behind the 3x3 magic square?
The secret behind the 3x3 magic square is easy to explane. If you must take 3 (different) digits out of the digits
1 up to 9, which total each time to 15, than there are the following possibilities:
1+5+9
1+6+8
2+4+9
2+5+8
2+6+7
3+4+8
3+5+7
4+5+6.
There are 8 possibilities.
The minimum features of the 3x3 square are 3 row features plus 3 column features plus 2 diagonal features total
to 8 features. Because there are 8 possibilities and 8 features, there is only one solution of the 3x3 magic square.
If we count the appearance of the 1, 2, 3, 4, 5, 6, 7, 8 and 9 in the 8 possibilities, than we get the following result:
1 = 2x
2 = 3x
3 = 2x
4 = 3x
5 = 4x
6 = 3x
7 = 2x
8 = 3x
9 = 2x
The middle cell takes part of the middle row, the middle column and both diagonals, that is 4 features. That is why
you must always put the 5 in the middle cell. The corners take part of one row, one column and one diagonal, that
is 3 features. That is why you must put the 2, 4, 6 and 8 (= even digits) always in the corners. Fill the digits 1, 3, 7
and 9 in the empty cells (in the middle of the sides). Because you put the 5 in the middle, the sum of the other two
cells of a diagonal must be (15 - 5 = ) 10. To get the total of 10 with the even digits in the corners there are only
two possibilities: 2+8 or 4+6. That is why you must put 2 and 8 or 4 and 6 in the same diagonal.
Like I have already told, there is only one solution of the 3x3 magic square, that is excluding rotation and/or mirror-
ring (see explanation on page ‘panmagic 4x4). Including rotation and/or mirroring there are (1 x 8 = ) 8 solutions of
the 3x3 square
How to produce a 3x3 magic square?
A ‘trick’ to produce the 3x3 square is the diagonal method of (the Dutch) professor van der Blij:
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