Sudoku method (3)

 

How to construct a most perfect (Franklin pan)magic 1024x1024 square in 9 steps by using only one 4x4 Sudoku

 

 

4x4 Sudoku

2

1

3

0

1

2

0

3

0

3

1

2

3

0

2

1

 

 

Step 1

Use the 4x4 Sudoku and a shifted version of the 4x4 Sudoku on a 2x2 carpet to construct a 4x4 panmagic square.

 

 

4x4 Sudoku shifted on 2x2 carpet 

2

1

3

0

2

1

3

0

1

2

0

3

1

2

0

3

0

3

1

2

0

3

1

2

3

0

2

1

3

0

2

1

2

1

3

0

2

1

3

0

1

2

0

3

1

2

0

3

0

3

1

2

0

3

1

2

3

0

2

1

3

0

2

1

 

 

4x number            +   1x number          +1                          = 4x4 panmagic square

2

1

3

0

 

2

0

3

1

 

10

4

15

1

 

11

5

16

2

1

2

0

3

 

3

1

2

0

 

7

9

2

12

 

8

10

3

13

0

3

1

2

 

0

2

1

3

 

0

14

5

11

 

1

15

6

12

3

0

2

1

 

1

3

0

2

 

13

3

8

6

 

14

4

9

7

 

 

Step 2

Use a grid with 2x2 the 4x4 panmagic square and a grid with 2x2 the shifted versions of the 4x4 Sudoku to construct an 8x8 most perfect (Franklin pan)magic square.

 

Construct the grid with 2x2 the shifted versions of the 4x4 Sudoku as follows:

 

 

                     
         

+

         
                     
                     
                     
 

+

             

+

 
                     
                     
         

+

         
                     
                     

 

 

 1x number                                 +    16x number                   = 8x8 Franklin panmagic square 

11

5

16

2

11

5

16

2

   

2

1

3

0

3

0

2

1

   

43

21

64

2

59

5

48

18

8

10

3

13

8

10

3

13

   

1

2

0

3

0

3

1

2

   

24

42

3

61

8

58

19

45

1

15

6

12

1

15

6

12

   

0

3

1

2

1

2

0

3

   

1

63

22

44

17

47

6

60

14

4

9

7

14

4

9

7

   

3

0

2

1

2

1

3

0

   

62

4

41

23

46

20

57

7

11

5

16

2

11

5

16

2

   

0

3

1

2

1

2

0

3

   

11

53

32

34

27

37

16

50

8

10

3

13

8

10

3

13

   

3

0

2

1

2

1

3

0

   

56

10

35

29

40

26

51

13

1

15

6

12

1

15

6

12

   

2

1

3

0

3

0

2

1

   

33

31

54

12

49

15

38

28

14

4

9

7

14

4

9

7

   

1

2

0

3

0

3

1

2

   

30

36

9

55

14

52

25

39

 

 

Step 3

Use a grid with 2x2 the 8x8 most perfect (Franklin pan)magic square and a grid with 2x2 the shifted versions of 8x8 Sudoku grid to construct an 16x16 most perfect (Franklin pan)magic square. See step 2 to construct the Sudoku grid

 

 

 1x number

43

21

64

2

59

5

48

18

43

21

64

2

59

5

48

18

24

42

3

61

8

58

19

45

24

42

3

61

8

58

19

45

1

63

22

44

17

47

6

60

1

63

22

44

17

47

6

60

62

4

41

23

46

20

57

7

62

4

41

23

46

20

57

7

11

53

32

34

27

37

16

50

11

53

32

34

27

37

16

50

56

10

35

29

40

26

51

13

56

10

35

29

40

26

51

13

33

31

54

12

49

15

38

28

33

31

54

12

49

15

38

28

30

36

9

55

14

52

25

39

30

36

9

55

14

52

25

39

43

21

64

2

59

5

48

18

43

21

64

2

59

5

48

18

24

42

3

61

8

58

19

45

24

42

3

61

8

58

19

45

1

63

22

44

17

47

6

60

1

63

22

44

17

47

6

60

62

4

41

23

46

20

57

7

62

4

41

23

46

20

57

7

11

53

32

34

27

37

16

50

11

53

32

34

27

37

16

50

56

10

35

29

40

26

51

13

56

10

35

29

40

26

51

13

33

31

54

12

49

15

38

28

33

31

54

12

49

15

38

28

30

36

9

55

14

52

25

39

30

36

9

55

14

52

25

39

   

+

 

 64x number

2

1

3

0

3

0

2

1

3

0

2

1

2

1

3

0

1

2

0

3

0

3

1

2

0

3

1

2

1

2

0

3

0

3

1

2

1

2

0

3

1

2

0

3

0

3

1

2

3

0

2

1

2

1

3

0

2

1

3

0

3

0

2

1

0

3

1

2

1

2

0

3

1

2

0

3

0

3

1

2

3

0

2

1

2

1

3

0

2

1

3

0

3

0

2

1

2

1

3

0

3

0

2

1

3

0

2

1

2

1

3

0

1

2

0

3

0

3

1

2

0

3

1

2

1

2

0

3

0

3

1

2

1

2

0

3

1

2

0

3

0

3

1

2

3

0

2

1

2

1

3

0

2

1

3

0

3

0

2

1

2

1

3

0

3

0

2

1

3

0

2

1

2

1

3

0

1

2

0

3

0

3

1

2

0

3

1

2

1

2

0

3

2

1

3

0

3

0

2

1

3

0

2

1

2

1

3

0

1

2

0

3

0

3

1

2

0

3

1

2

1

2

0

3

0

3

1

2

1

2

0

3

1

2

0

3

0

3

1

2

3

0

2

1

2

1

3

0

2

1

3

0

3

0

2

1

  

=

  

 Most perfect 16x16 (Franklin pan)magic square

171

85

256

2

251

5

176

82

235

21

192

66

187

69

240

18

88

170

3

253

8

250

83

173

24

234

67

189

72

186

19

237

1

255

86

172

81

175

6

252

65

191

22

236

17

239

70

188

254

4

169

87

174

84

249

7

190

68

233

23

238

20

185

71

11

245

96

162

91

165

16

242

75

181

32

226

27

229

80

178

248

10

163

93

168

90

243

13

184

74

227

29

232

26