Office Applications and Entertainment, Magic Squares of Subtraction

Attachment 4.1

Attachment 4.2

Exhibit 4

Miscellaneous Magic Squares of Subtraction
Res4 = 4, 6 and 8, Pair Sum = 17
Magic Squares of Subtraction, Res4 = 4, 6 and 8
Main - and Broken Diagonals sum to s4 = 34
Enumeration Magic Squares of Subtraction

Attachment 5.1

Attachment 5.5

Attachment 5.4

Attachment 5.2

Attachment 5.3

Exhibit 5

Associated Magic Squares of Subtraction
Res5 = 13, Pair Sum = 26
Associated Magic Squares of Subtraction
Res5 = 13, Square - and Diamond Inlays, s3 = 39
Associated Magic Squares of Subtraction
Res5 = 13, Main - and Broken Diagonals sum to s5 = 65
Simple Magic Squares of Subtraction
Miscellaneous Residuum Values
Crosswise Symmetric Magic Squares of Subtraction
Res5 = 13, Pair Sum = 26
Enumeration Magic Squares of Subtraction

Attachment 6.1

Almost Associated Magic Squares
s6 = 111, Res6 = 15

Attachment 6.2

Almost Crosswise Symmetric Magic Squares
s6 = 111, Res6 = 15

Attachment 6.3

Simple Magic Squares of Subtraction
Miscellaneous Residuum Values

Attachment 6.4

Partly Crosswise Symmetric (6 x 6)
s6 = 111, Res6 = 15

Attachment 7.1

Associated Magic Squares
s7 = 175, Res7 = 25

Attachment 7.2

Associated Magic Squares, s7 = 175, Res7 = 25
Square Inlays, s3 = 75, s4 = 100

Attachment 7.3a

Associated Magic Squares, s7 = 175, Res7 = 25
Diamond Inlays, s3 = 75, s4 = 100

Attachment 7.3b

Associated Lozenge Squares, s7 = 175, Res7 = 25
One Diamond Inlay, s4 = 100

Attachment 7.4

Associated Magic Squares, s7 = 175, Res7 = 25
Overlapping Sub Squares, s4 = 100

Attachment 8.1

Attachment 8.2

Associated Bimagic Squares
s1 = 260, s2 = 11180, Res8 = 32
Pan Macic and Complete Bimagic Squares
s1 = 260, s2 = 11180, Res8 = 32

Attachment 8.3

Attachment 8.4

Attachment 8.5

Attachment 8.6

Attachment 8.7

Attachment 8.8

Attachment 8.9

Magic Squares of Subtraction, s8 = 260
Miscellaneous Residuum Values
Pan Macic Squares, s8 = 260, Res8 = 16
Composed of Pan magic Sub Squares, s4 = 130
Pan Macic Squares, s8 = 260, Res8 = 16
Pan Magic Square Inlays, s4 = 130
Ultra Macic Squares, s8 = 260, Res8 = 16
Non Overlapping Sub Squares (2 x 2)
Simple Magic Squares of Subtraction (8 x 8),
Medjig Solutions, s8 = 260, Res8 = 32
Associated Magic Squares of Subtraction (8 x 8),
Medjig Solutions, s8 = 260, Res8 = 32
Pan Magic and Complete Squares of Subtraction (8 x 8),
Medjig Solutions, s8 = 260, Res8 = 32

Attachment 9.2

Associated Magic Squares, s9 = 369, Res9 = 41
Square Inlays, s4 = 164, s5 = 205

Attachment 9.3

Associated Lozenge Squares, s9 = 369, Res9 = 41
Diamond Inlays, s4 = 164, s5 = 205

Attachment 9.4

Associated Magic Squares, s9 = 369, Res9 = 41
Overlapping Sub Squares, s5 = 205

Exhibit 10

Construction of Semi Magic Squares
s10 = 505, Res10 = 49

Attachment 10.3

Magic Squares of Subtraction, s10 = 505
Miscellaneous Residuum Values

Exhibit 11

Construction of Semi Magic Squares
s11 = 671, Res11 = 61

Attachment 12.2

Magic Squares of Subtraction, s12 = 870
Miscellaneous Residuum Values

Attachment 12.1

Construction of Magic Squares of Subtraction (12 x 12)
Associated, Res12 = 24, Pair Sum = 145

Attachment 16.1

Construction of Magic Squares of Subtraction (16 x 16)
Associated, Res16 = 32, Pair Sum = 257

Attachment 16.2

Construction of Magic Squares of Subtraction (16 x 16)
Res16 = 32, Main - and Broken Diagonals sum to s16 = 2056

Attachment 64.1

Associated Bimagic Squares (64 x 64)
Res64 = 256, s1 = 131104, s2 = 358045024

Attachment 64.2

Pan Macic Bimagic Squares (64 x 64)
Res64 = 256, s1 = 131104, s2 = 358045024