Khajuraho method

 

Use the famous Khajuraho 4x4 panmagic square to construct larger magic squares which are a multiple of 4 (= 8x8, 12x12, 16x16, 20x20, … magic square).

 

Rewrite the Khajuraho magic square as follows:

 

 

Khajuraho magic square                Basic magic square 

7

12

1

14

   

7

h-4

1

h-2

2

13

8

11

   

2

h-3

8

h-5

16

3

10

5

   

h

3

h-6

5

9

6

15

4

   

h-7

6

h-1

4

  

 

To construct an 8x8 panmagic square, you need the basic square and 3 extending magic squares:

 

 

7

h-4

1

h-2

+8

-8

+8

-8

2

h-3

8

h-5

+8

-8

+8

-8

h

3

h-6

5

-8

+8

-8

+8

h-7

6

h-1

4

-8

+8

-8

+8

+16

-16

+16

-16

+24

-24

+24

-24

+16

-16

+16

-16

+24

-24

+24

-24

-16

+16

-16

+16

-24

+24

-24

+24

-16

+16

-16

+16

-24

+24

-24

+24

  

 

The highest digit in the 8x8 square is 64. Fill in 64 for h and calculate all the digits. You get the following 8x8 panmagic square. 

 

 

 Panmagic 8x8 magic square

7

60

1

62

15

52

9

54

2

61

8

59

10

53

16

51

64

3

58

5

56

11

50

13

57

6

63

4

49

14

55

12

23

44

17

46

31

36

25

38

18

45

24

43

26

37

32

35

48

19

42

21

40

27

34

29

41

22

47

20

33

30

39

28

  

 

This magic square is almost Franklin panmagic. Only four 2x2 sub-squares in the middle two columns give not 1/2 of the magic sum (1/2 x 260 = 130). If you swap the colours you get the following most perfect (Franklin pan)magic 8x8 square:

 

 

Most perfect (Franklin pan)magic 8x8 square 

15

60

1

54

7

52

9

62

2

53

16

59

10

61

8

51

64

11

50

5

56

3

58

13

49

6

63

12

57

14

55

4

31

44

17

38

23

36

25

46

18

37

32

43

26

45

24

35

48

27

34

21

40

19

42

29

33

22

47

28

41

30

39

20

 

 

Download
8x8, Khajuraho method.xls
Microsoft Excel werkblad 80.5 KB