Most perfect transformation

 

It takes 5 steps to transform a 4x4 square with consecutive numbers into the 3 basic panmagic 4x4 squares. Swap each time the numbers from 'yellow' and 'red' with each other.

   

                                                                                                                                    3x panmagic 4x4

1

5

9

13

 

1

5

13

9

 

1

5

13

9

 

1

8

13

12

 

1

8

13

12

 

1

8

13

12

2

6

10

14

 

2

6

14

10

 

2

6

14

10

 

2

6

14

10

 

14

10

2

6

 

15

10

3

6

3

7

11

15

 

3

7

15

11

 

4

8

16

12

 

4

5

16

9

 

4

5

16

12

 

4

5

16

9

4

8

12

16

 

4

8

16

12

 

3

7

15

11

 

3

7

15

11

 

15

11

3

7

 

14

11

2

7

                                                         
                                                         

1

3

9

11

 

1

3

11

9

 

1

3

11

9

 

1

8

11

14

 

1

8

11

14

 

1

8

11

14

2

4

10

12

 

2

4

12

10

 

2

4

12

10

 

2

4

12

10

 

12

10

2

4

 

15

10

5

4

5

7

13

15

 

5

7

15

13

 

6

8

16

14

 

6

3

16

9

 

6

3

16

9

 

6

3

16

9

6

8

14

16

 

6

8

16

14

 

5

7

15

13

 

5

7

15

13

 

15

13

5

7

 

12

13

2

7

                                                         
                                                         

1

2

9

10

 

1

2

10

9

 

1

2

10

9

 

1

8

10

15

 

1

8

10

15

 

1

8

10

15

3

4

11

12

 

3

4

12

11

 

3

4

12

11

 

3

4

12

11

 

12

11

3

4

 

14

11

5

4

5

6

13

14

 

5

6

14

13

 

7

8

16

15

 

7

2

16

9

 

7

2

16

9

 

7

2

16

9

7

8

15

16

 

7

8

16

15

 

5

6

14

13

 

5

6

14

13

 

14

13

5

6

 

12

13

3

6

 

  

Use this method to construct magic squares of order is multiple of 4 from 4x4 to infinity. See 4x48x812x1216x1620x2024x2428x2832x32

 

Download
4x4, most perfect transformation.xls
Microsoft Excel werkblad 27.5 KB