Basic key method (ultra magic)

 

See below the key to construct an ultra magic 8x8 square. Notify that the second grid is a reflection of the first grid.

 

 

 1x digit                               +     8x [digit -/- 1]                   =    Ultra magic 8x8 square

1

7

4

6

6

4

7

1

   

1

8

1

8

1

8

1

8

   

1

63

4

62

6

60

7

57

8

2

5

3

3

5

2

8

   

7

2

7

2

7

2

7

2

   

56

10

53

11

51

13

50

16

1

7

4

6

6

4

7

1

   

4

5

4

5

4

5

4

5

   

25

39

28

38

30

36

31

33

8

2

5

3

3

5

2

8

   

6

3

6

3

6

3

6

3

   

48

18

45

19

43

21

42

24

1

7

4

6

6

4

7

1

   

6

3

6

3

6

3

6

3

   

41

23

44

22

46

20

47

17

8

2

5

3

3

5

2

8

   

4

5

4

5

4

5

4

5

   

32

34

29

35

27

37

26

40

1

7

4

6

6

4

7

1

   

7

2

7

2

7

2

7

2

   

49

15

52

14

54

12

55

9

8

2

5

3

3

5

2

8

   

1

8

1

8

1

8

1

8

   

8

58

5

59

3

61

2

64

 

 

This 8x8 magic square is panmagic, 2x2 compact, symmetric and each 1/2 row/column gives 1/2 of the magic sum.

 

You can use this key to construct magic squares which are a multiple of 4 from 8x8 to infinite (= 8x8, 12x12, 16x16, ... magic square).

 

 

Download
8x8, Basic key method (symmetric).xls
Microsoft Excel werkblad 45.0 KB