Squares of Subtraction (21)

Office Applications and Entertainment, Magic Squares of Subtraction
	Index	About the Author

List of Attachments

Squares of Subtraction (4 x 4)

Attachment 4.1	Miscellaneous Magic Squares of Subtraction Res4 = 4, 6 and 8, Pair Sum = 17
Attachment 4.2	Magic Squares of Subtraction, Res4 = 4, 6 and 8 Main - and Broken Diagonals sum to s4 = 34
Exhibit 4	Enumeration Magic Squares of Subtraction

Squares of Subtraction (5 x 5)

Attachment 5.1	Associated Magic Squares of Subtraction Res5 = 13, Pair Sum = 26
Attachment 5.5	Associated Magic Squares of Subtraction Res5 = 13, Square - and Diamond Inlays, s3 = 39
Attachment 5.4	Associated Magic Squares of Subtraction Res5 = 13, Main - and Broken Diagonals sum to s5 = 65
Attachment 5.2	Simple Magic Squares of Subtraction Miscellaneous Residuum Values
Attachment 5.3	Crosswise Symmetric Magic Squares of Subtraction Res5 = 13, Pair Sum = 26
Exhibit 5	Enumeration Magic Squares of Subtraction

Squares of Subtraction (6 x 6)

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

Squares of Subtraction (7 x 7)

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

Squares of Subtraction (8 x 8)

Attachment 8.1	Associated Bimagic Squares s1 = 260, s2 = 11180, Res8 = 32
Attachment 8.2	Pan Macic and Complete Bimagic Squares s1 = 260, s2 = 11180, Res8 = 32
Attachment 8.3	Magic Squares of Subtraction, s8 = 260 Miscellaneous Residuum Values
Attachment 8.4	Pan Macic Squares, s8 = 260, Res8 = 16 Composed of Pan magic Sub Squares, s4 = 130
Attachment 8.5	Pan Macic Squares, s8 = 260, Res8 = 16 Pan Magic Square Inlays, s4 = 130
Attachment 8.6	Ultra Macic Squares, s8 = 260, Res8 = 16 Non Overlapping Sub Squares (2 x 2)
Attachment 8.7	Simple Magic Squares of Subtraction (8 x 8), Medjig Solutions, s8 = 260, Res8 = 32
Attachment 8.8	Associated Magic Squares of Subtraction (8 x 8), Medjig Solutions, s8 = 260, Res8 = 32
Attachment 8.9	Pan Magic and Complete Squares of Subtraction (8 x 8), Medjig Solutions, s8 = 260, Res8 = 32

Squares of Subtraction (9 x 9)

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

Squares of Subtraction (10 x 10)

Exhibit 10	Construction of Semi Magic Squares s10 = 505, Res10 = 49
Attachment 10.3	Magic Squares of Subtraction, s10 = 505 Miscellaneous Residuum Values

Squares of Subtraction (11 x 11)

Exhibit 11

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

Squares of Subtraction (12 x 12)

Attachment 12.2

Magic Squares of Subtraction, s12 = 870
Miscellaneous Residuum Values

Composed Squares of Subtraction

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