Office Applications and Entertaiment, Magic Squares Attachment 5.5.3 About the Author

Magic Squares, 5 x 5, Magic Constant 65

Tranformation based on Permutation lines 1, 2, and 4, 5
:

Base
 8 2 21 20 14 16 15 9 3 22 4 23 17 11 10 12 6 5 24 18 25 19 13 7 1
Sw12
 15 16 9 22 3 2 8 21 14 20 23 4 17 10 11 19 25 13 1 7 6 12 5 18 24

Tranformations based on Permutations lines n and (6 - n):

Base
 8 2 21 20 14 16 15 9 3 22 4 23 17 11 10 12 6 5 24 18 25 19 13 7 1
Tr1
 1 19 13 7 25 22 15 9 3 16 10 23 17 11 4 18 6 5 24 12 14 2 21 20 8
Tr2 = Rot(Tr1)
 8 20 21 2 14 12 24 5 6 18 4 11 17 23 10 16 3 9 15 22 25 7 13 19 1
Tr12 = Rot(Base)
 1 7 13 19 25 18 24 5 6 12 10 11 17 23 4 22 3 9 15 16 14 20 21 2 8

Transformations based on Combined Permutations:

Sw12(Base)
 15 16 9 22 3 2 8 21 14 20 23 4 17 10 11 19 25 13 1 7 6 12 5 18 24
Sw12(Tr1)
 15 22 9 16 3 19 1 13 25 7 23 10 17 4 11 2 14 21 8 20 6 18 5 12 24
Sw12(Tr2) = Rot(Sw12(Tr1))
 24 12 5 18 6 20 8 21 14 2 11 4 17 10 23 7 25 13 1 19 3 16 9 22 15
Sw12(Tr12) = Rot(Sw12(Base))
 24 18 5 12 6 7 1 13 25 19 11 10 17 4 23 20 14 21 8 2 3 22 9 16 15

Resulting Unique Transformations:

Base
 8 2 21 20 14 16 15 9 3 22 4 23 17 11 10 12 6 5 24 18 25 19 13 7 1
Tr1
 1 19 13 7 25 22 15 9 3 16 10 23 17 11 4 18 6 5 24 12 14 2 21 20 8
Sw12(Base)
 15 16 9 22 3 2 8 21 14 20 23 4 17 10 11 19 25 13 1 7 6 12 5 18 24
Sw12(Tr1)
 15 22 9 16 3 19 1 13 25 7 23 10 17 4 11 2 14 21 8 20 6 18 5 12 24