Most perfect transformation

 

It takes 5 steps to transform a 4x4 square with consecutive digits into the 3 basic panmagic 4x4 squares. Swap each time the digits 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

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1

8

11

14

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4

10

12

 

2

4

12

10

 

2

4

12

10

 

2

4

12

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10

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15

10

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4

5

7

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7

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13

 

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8

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7

                                                         
                                                         

1

2

9

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10

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2

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8

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1

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1

8

10

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4

11

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4

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4

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14

11

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16

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16

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16

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5

6

14

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12

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3

6

 

  

You can use the most perfect transformation to construct most perfect magic squares which are a multiple of 4 (= 4x4, 8x8, 12x12, 16x16, ... magic square).

 

 

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