Office Applications and Entertainment, Magic Squares  
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B (3 x 3)
b1
b2
b3
b4
b5
b6
b7
b8
b9
Medjig Square A (3 x 3)
a1
a2
a3
a4
a5
a6
a7
a8
a9
a10
a11
a12
a13
a14
a15
a16
a17
a18
a19
a20
a21
a22
a23
a24
a25
a26
a27
a28
a29
a30
a31
a32
a33
a34
a35
a36
Magic Square C (6 x 6)
b1+9*a1
b1+9*a2
b2+9*a3
b2+9*a4
b3+9*a5
b3+9*a6
b1+9*a7
b1+9*a8
b2+9*a9
b2+9*a10
b3+9*a11
b3+9*a12
b4+9*a13
b4+9*a14
b5+9*a15
b5+9*a16
b6+9*a17
b6+9*a18
b4+9*a19
b4+9*a20
b5+9*a21
b5+9*a22
b6+9*a23
b6+9*a24
b7+9*a25
b7+9*a26
b8+9*a27
b8+9*a28
b9+9*a29
b9+9*a30
b7+9*a31
b7+9*a32
b8+9*a33
b8+9*a34
b9+9*a35
b9+9*a36
The rows, columns and main diagonals of Square C sum to 2 times the corresponding sum of Magic Square B plus 9 times the corresponding sum of Medjig square A which results in s1 = 2 * 15 + 9 * 9 = 111.
Similarly, for any larger integer n, a magic square C of order 2n can be constructed from any n x n medjigsquare
Medjig Squares are described by the same set of linear equations as shown in section 6.2 for Magic Squares, however with magic sum 9 and following additional equations:
a( 1) + a( 2) + a( 7) + a( 8) = 6
which can be reduced, by means of row and column manipulations, to the minimum number of linear equations:
a(31) = 9  a(32)  a(33)  a(34)  a(35)  a(36)
The linear equations shown above are ready to be solved, for the magic constant 9.
6.6.3 Symmetrical Main Diagonals
With the option 'Symmetrical Main Diagonals' enabled, routine MgcSqr6d counted 125184 Medjig Squares within 5,5 minutes, of which the first 120 are shown in Attachment 6.8.3.
A few (120 ea) of the resulting Magic Squares with Symmetrical Main Diagonals, based on the first 3^{th} order Magic Square listed in routine
MgcSqr6d, are shown in Attachment 6.8.4.
6.6.4 Almost Associated (16 pairs)
With the option 'Almost Associated' enabled, routine MgcSqr6d counted 7296
Almost Associated Medjig Squares within 52 seconds, of which the first 120 are shown in Attachment 6.8.5.
A few (120 ea) of the resulting Almost Associated Magic Squares, based on the first 3^{th} order Magic Square listed in routine
MgcSqr6d, are shown in Attachment 6.8.6.
The linear equations shown in section 6.6.2 above can be applied in an Excel spreadsheet
(Ref. CnstrSngl6d).

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