Shift method (2)

 

Put in the first row of the first grid the digits 0 up to 8. Construct the second and the third row of the first grid by shifting the first row each time 3 places to the left.

 

 

                                  First grid, first three rows

           

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

     

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

     

0

1

2

3

4

5

6

7

8

0

1

2

3

4

5

6

7

8

           

 

 

The first three rows of the first grid consists of three 3x3 sub-squares. Construct row 4 up to 6 by swapping the sequence of the three columns in the three 3x3 sub-squares into 2-3-1 (instead of 1-2-3). Construct row 7 up to 9 by swapping the sequence of the three columns in the three 3x3 sub-squares into 3-1-2 (instead of 1-2-3).

 

 

 First grid

0

1

2

3

4

5

6

7

8

3

4

5

6

7

8

0

1

2

6

7

8

0

1

2

3

4

5

1

2

0

4

5

3

7

8

6

4

5

3

7

8

6

1

2

0

7

8

6

1

2

0

4

5

3

2

0

1

5

3

4

8

6

7

5

3

4

8

6

7

2

0

1

8

6

7

2

0

1

5

3

4

 

 

The second grid is a reflection (rotated by a quarter) of the first grid. Take 1x digit from first grid +1 and add 9x digit from the same cell of the second grid.

 

 

 1x digit +1                                 9x digit                                        panmagic 9x9 square

0 1 2 3 4 5 6 7 8     8 5 2 7 4 1 6 3 0     73 47 21 67 41 15 61 35 9
3 4 5 6 7 8 0 1 2     6 3 0 8 5 2 7 4 1     58 32 6 79 53 27 64 38 12
6 7 8 0 1 2 3 4 5     7 4 1 6 3 0 8 5 2     70 44 18 55 29 3 76 50 24
1 2 0 4 5 3 7 8 6     2 8 5 1 7 4 0 6 3     20 75 46 14 69 40 8 63 34
4 5 3 7 8 6 1 2 0     0 6 3 2 8 5 1 7 4     5 60 31 26 81 52 11 66 37
7 8 6 1 2 0 4 5 3     1 7 4 0 6 3 2 8 5     17 72 43 2 57 28 23 78 49
2 0 1 5 3 4 8 6 7     5 2 8 4 1 7 3 0 6     48 19 74 42 13 68 36 7 62
5 3 4 8 6 7 2 0 1     3 0 6 5 2 8 4 1 7     33 4 59 54 25 80 39 10 65
8 6 7 2 0 1 5 3 4     4 1 7 3 0 6 5 2 8     45 16 71 30 1 56 51 22 77

 

 

This 9x9 magic square is panmagic and 3x3 compact (but not symmetric).


You can use this method to construct magic squares of order is odd square (= 9, 25, 47, 81, ...).


This method gives not many possibilities (try it yourself).

 

 

Download
9x9, Shiftmethod 2.xls
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