Concentric magic square (start)

 

 

The smallest concentric magic square of even order is a 6x6 magic square consisting of a 4x4 magic square with a border around it. In a concentric magic square of odd order you find allways the middle number in the middle cell of the square. It is not possible to create a 4x4 magic square with the middle four numbers in the middle 2x2 cells. Closest to that is a symmetric 4x4 magic square, for example the Dürer magic square (see famous magic squares). 

 

 

16

3

2

13

5

10

11

8

9

6

7

12

4

15

14

1

 

 

Add 10 to all numbers of the 4x4 magic square and construct a 6x6 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 concentric magic square. Add 14 to all numbers of the 4x4 in 6x6 magic square and construct a 8x8 border with the lowest and the highest numbers. So you get a 4x4 in 6x6 in 8x8 concentric magic square. You can put borders around it to infinite.

 

Remove the border of a 4x4 in 6x6 in 8x8 in 10x10 concentric magic square and you get an (impure) 8x8 magic square. Remove the border and you get a 6x6 magic square. Remove the border and you get a 4x4 magic square.

 

 

See how the concentric magic square on this website is growing bigger and bigger: 

3x34x45x56x67x78x89x910x1011x1112x1213x1314x1415x1516x1617x1718x1819x1920x2021x2122x2223x2324x2425x2526x2627x2728x2829x29,  30x3031x31 and 32x32