Symmetric transformation

 

Marios Mamzeris shows us that you can transform a odd square with sequencial numbers into a symmetric magic square in two steps (https://www.youtube.com/watch?v=JPEB8aT7XiU):

 

 

Step 1, horizontal swap

 

   < 1 2 3 4 5     2 3 4 5 1
   < 6 7 8 9 10     8 9 10 6 7
  11 12 13 14 15     11 12 13 14 15
  16 17 18 19 20  >   19 20 16 17 18
  21 22 23 24 25  >   25 21 22 23 24

 

 

Step 2, vertical swap

 

  ^ ^                    
  2 3 4 5 1     8 12 4 17 24
  8 9 10 6 7     11 20 10 23 1
  11 12 13 14 15     19 21 13 5 7
  19 20 16 17 18     25 3 16 6 15
  25 21 22 23 24     2 9 22 14 18
        v v              

 

Download
5x5, symmetric transformation.xlsx
Microsoft Excel werkblad 9.5 KB