Sudoku method 1

 

How to use a (4x4) Sudoku to construct a (4x4 pan)magic square?

A sudoku mostly consists of 9 rows and 9 columns. In each row and in each column (and in each 3x3 section) you find all the digits from 1 up to 9. Take a 4x4 Sudoku and construct a 4x4 (pan)magic square in 4 steps.

 

(1st) Fill in the digits 0 up to 3 instead of 1 up to 4. Take care that you find all the digits from 0 up to 3 in each row, column and diagonal.

 

(2nd) Construct the second grid by rotating the first grid a quarter to the right.

 

(3rd) Take 4x digit from first grid and add 1x digit from the same cell of the second grid.

 

(4th) Add 1 to each cell.

 

 

  4x digit               +    1x digit                =   +1                              magic square  

0

1

2

3

 

2

1

3

0

 

2

5

11

12

 

3

6

12

13

3

2

1

0

 

3

0

2

1

 

15

8

6

1

 

16

9

7

2

1

0

3

2

 

0

3

1

2

 

4

3

13

10

 

5

4

14

11

2

3

0

1

 

1

2

0

3

 

9

14

0

7

 

10

15

1

8

 

 

This magic square happens to be panmagic!

 

 

Most perfect (Franklin pan)magic 8x8 square

It is also possible to use the Sudoku grids of a panmagic 4x4 square to construct a most perfect (Franklin pan)magic 8x8 square.  Construct three 8x8 grids.

 

● The first 8x8 grid is 2x2 the first 4x4 Sudoku grid.

 

● Split the second 4x4 Sudoku grid to construct the second 8x8 grid:

 

 

  Split the second 4x4 Sudoku grid:                 Complete the grids by filling in crosswise: 

 

1

3

   

2

   

0

   

0

1

3

2

 

2

3

1

0

3

   

1

   

0

2

     

3

2

0

1

 

1

0

2

3

0

   

2

   

3

1

     

0

1

3

2

 

2

3

1

0

 

2

0

   

1

   

3

   

3

2

0

1

 

1

0

2

3

 

 

Combine the two 4x4 Sudoku grids and copy the two grids to complete the 8x8 grid.

 

● The third (fixed) 8x8 grid is the same as the second grid of basis pattern method 1.

 

 

Take 4x digit from 1st grid    +    1x digit from 2nd grid          +    16x digit from 3rd grid

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

   

0

3

0

3

0

3

0

3

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

   

0

3

0

3

0

3

0

3

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

   

3

0

3

0

3

0

3

0

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

   

3

0

3

0

3

0

3

0

0

1

2

3

0

1

2

3

   

0

1

3

2

2

3

1

0

   

1

2

1

2

1

2

1

2

3

2

1

0

3

2

1

0

   

3

2

0

1

1

0

2

3

   

1

2

1

2

1

2

1

2

1

0

3

2

1

0

3

2

   

0

1

3

2

2

3

1

0

   

2

1

2

1

2

1

2

1

2

3

0

1

2

3

0

1

   

3

2

0

1

1

0

2

3

   

2

1

2

1

2

1

2

1

  

 

  +1                                                      Most perfect (Franklin pan)magic 8x8 square 

0

53

11

62

2

55

9

60

   

1

54

12

63

3

56

10

61

15

58

4

49

13

56

6

51

   

16

59

5

50

14

57

7

52

52

1

63

10

54

3

61

8

   

53

2

64

11

55

4

62

9

59

14

48

5

57

12

50

7

   

60

15

49

6

58

13

51

8

16

37

27

46

18

39

25

44

   

17

38

28

47

19

40

26

45

31

42

20

33

29

40

22

35

   

32

43

21

34

30

41

23

36

36

17

47

26

38

19

45

24

   

37

18

48

27

39

20

46

25

43

30

32

21

41

28

34

23

   

44

31

33

22

42

29

35

24

 

 

Download
8x8, Sudoku method (1).xls
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