Editing Magic square (section)

===For bordered magic squares===
* A bordered magic square remains a bordered magic square after permuting the border cells in the rows or columns, together with their corresponding complementary terms, keeping the corner cells fixed. Since the cells in each row and column of every concentric border can be permuted independently, when the order ''n'' ≥ 5 is odd, there are <math>((n-2)!  (n-4)!  \dots \cdot 3!)^2</math> equivalent bordered squares. When ''n'' ≥ 6 is even, there are <math>((n-2)! (n-4)! \dots \cdot 4!)^2</math> equivalent bordered squares. In the example below, a square of order 5 is given whose border row has been permuted and (3!)<sup>2</sup> = 36 such equivalent squares can be obtained.
{{col-begin|width=auto;margin:0.5em auto}}
{{col-break|valign=bottom}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:10em;height:10em;table-layout:fixed;"
|-
| 1 || '''23''' || '''16''' || 4 || 21
|-
| 15 || style="background-color: silver;"|14 || style="background-color: silver;"|7 || style="background-color: silver;"|18 || 11
|-
| 24 || style="background-color: silver;"|17 || style="background-color: silver;"|13 || style="background-color: silver;"|9 || 2 
|-
| 20 || style="background-color: silver;"|8 || style="background-color: silver;"|19 || style="background-color: silver;"|12 || 6
|-
| 5 || '''3''' || '''10''' || 22 || 25
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:10em;height:10em;table-layout:fixed;"
|-
| 1 || 16 || 23 || 4 || 21
|-
| 15 || style="background-color: silver;"|14 || style="background-color: silver;"|7 || style="background-color: silver;"|18 || 11
|-
| 24 || style="background-color: silver;"|17 || style="background-color: silver;"|13 || style="background-color: silver;"|9 || 2 
|-
| 20 || style="background-color: silver;"|8 || style="background-color: silver;"|19 || style="background-color: silver;"|12 || 6
|-
| 5 || 10 || 3 || 22 || 25
|}
{{col-end}}
* A bordered magic square remains a bordered magic square after each of its concentric borders are independently rotated or reflected with respect to the central core magic square. If there are ''b'' borders, then this transform will yield 8<sup>''b''</sup> equivalent squares. In the example below of the 5×5 magic square, the border has been rotated 90 degrees anti-clockwise.
{{col-begin|width=auto;margin:0.5em auto}}
{{col-break|valign=bottom}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:10em;height:10em;table-layout:fixed;"
|-
| 1 || 23 || 16 || 4 || 21
|-
| 15 || style="background-color: silver;"|14 || style="background-color: silver;"|7 || style="background-color: silver;"|18 || 11
|-
| 24 || style="background-color: silver;"|17 || style="background-color: silver;"|13 || style="background-color: silver;"|9 || 2 
|-
| 20 || style="background-color: silver;"|8 || style="background-color: silver;"|19 || style="background-color: silver;"|12 || 6
|-
| 5 || 3 || 10 || 22 || 25
|}
{{col-break|valign=bottom|gap=1em}}
{| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;width:10em;height:10em;table-layout:fixed;"
|-
| 21 || 11 || 2 || 6 || 25
|-
| 4 || style="background-color: silver;"|14 || style="background-color: silver;"|7 || style="background-color: silver;"|18 || 22
|-
| 16 || style="background-color: silver;"|17 || style="background-color: silver;"|13 || style="background-color: silver;"|9 || 10 
|-
| 23 || style="background-color: silver;"|8 || style="background-color: silver;"|19 || style="background-color: silver;"|12 || 3
|-
| 1 || 15 || 24 || 20 || 5
|}
{{col-end}}