3x3 (not pure) in 5x5 (pure) magic square

 

Use the row and column grids of the 3x3 magic square to construct the 3x3 inlay.

 

 

 

 

 

 

 

   

 

 

 

 

 

 

1

2

0

 

   

 

0

2

1

 

 

0

1

2

 

   

 

2

1

0

 

 

2

0

1

 

   

 

1

0

2

 

 

 

 

 

 

   

 

 

 

 

 

 

 

To get the right numbers of the 3x3 inlay add 1 to all numbers.

 

 

Column grid 3x3 inlay                              Row grid 3x3 inlay

 

 

 

 

 

   

 

 

 

 

 

 

2

3

1

 

   

 

1

3

2

 

 

1

2

3

 

   

 

3

2

1

 

 

3

1

2

 

   

 

2

1

3

 

 

 

 

 

 

   

 

 

 

 

 

 

 

Construct the column grid of the 5x5 border and take care that the sum of opposite numbers in the border is allways 4 and the sum of a row or a column is allways 10. Put the numbers as follows (n.b.: Put 2x the middle number from 0 up to 4 cross in the corners):

 

 

Column grid 5x5 border

2

1

3

4

0

0

 

 

 

4

4

 

 

 

0

0

 

 

 

4

4

3

1

0

2

 

 

Construct the row grid of the 5x5 border and take care that all combinations of row coordinates and column coordinates are unique, so you get all the numbers from 1 up to 25 in the magic square.

 

 

Row grid 5x5 border 

0

4

4

0

2

1

 

 

 

3

4

 

 

 

0

3

 

 

 

1

2

0

0

4

4

 

 

Take 5x a number from the column grid, add the number of the same cell from the row grid and add 1.

 

 

5x number from column grid       +        1x number from row grid + 1       =         3x3 in 5x5 magic square

2

1

3

4

0

   

0

4

4

0

2

   

3

22

24

5

11

0

2

3

1

4

   

1

1

3

2

3

   

6

8

19

12

20

4

1

2

3

0

   

4

3

2

1

0

   

25

17

13

9

1

0

3

1

2

4

   

3

2

1

3

1

   

16

14

7

18

10

4

3

1

0

2

   

2

0

0

4

4

   

15

4

2

21

23

 

 

Use this method to construct inlaid squares of odd order from 5x5 to infinity. See 5x57x79x911x1113x1315x1517x1719x1921x2123x2325x2527x2729x29 & 31x31

 

Download
5x5, 3x3 in 5x5.xlsx
Microsoft Excel werkblad 11.0 KB