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Panmagic (or extra magic) 6x6 squares do not exist. The structure of 6x6 squares is irregular. To
produce pure 6x6 squares, you need to puzzle. The funniest method is the medjig method of Willem
Barink (source: Wikipedia, Dutch language version). The fastest method, is the method of Strachey.
The most simple method is Paul Michelet's trick.
Medjig method
Take as 1st square a pure magic 3x3 square, but ‘blow it up’ by presenting the digits 2x2. Produce a
2nd square existing of 9 (2x2) medjig tiles.
Note that an 2x2 medjig tile consists of all the digits 0, 1, 2 en 3, but not always in the same sequence;
you must choose the tiles, taking care that the sum of the digits of each row/column/diagonal is (6 x
1,5 =) 9. Take (1x) a digit from the 1st square and add 9x a digit from the same cell of the 2nd square.
1x digit + 9x digit = pure magic 6x6 square
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You can use this method to produce 'double odd' (= 6x6, 10x10, 14x14, 18x18, …) as well as 'double even'
(= 8x8, 12x12, 16x16, 20x20, ....) magic squares. For example to produce a 10x10 square use as 1st square
a pure (pan)magic 5x5 square, use a 2nd square existing of 25 (2x2) medjig tiles, taking care that the sum
of the digits of each row/column/diagonal is (10 x 1,5 =) 15 and add 15x a digit from the 2nd square.
N.B.: If you don't like to puzzle, use the Medjig method without puzzling (= LUX method);
see page '14x14 magic square'.
Method of Strachey
Instead of the mejig method you can use the method of Strachey. Make a 2x2 carpet of a
magic 3x3 square and add 9x the digit from a fixed pattern.
1x digit + 9x digit = magic 6x6 square
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To use the method of Strachey to produce bigger ‘double odd’ magic squares (= 10x10, 14x14,
18x18, …) it is a disadvantage that you need to swap more and more digits to get a correct magic
square. See the improved method of Strachey to produce a 10x10 magic square (you need to swap
less digits).
N.B.: It is possible to produce a 18x18 magic square with an extra magic feature, because 1/3 row/
column/diagonal gives 1/3 of the magic sum!!!
Paul Michelet's trick
With Paul Michelet's trick you can make a 6x6 magic square as follows:
Fill in 2x2 Luo shu add 9x digit swap the marked digits Paul's 6x6 magic square
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N.B.: This trick was probably known almost thousand years ago. Look at Yang Hui's 6x6 magic square.
http://www.gap-system.org/~history/Biographies/Yang_Hui.html
Notify that there is an other alternative method of construction: Bordered squares (4x4 inside 6x6).
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