Recently, author worked with cornered magic squares of order 6. Later this work is extended up to order 24 (paper1, paper2, paper3). This work is for odd order magics squares. It for the orders 31. In this work we have covered two types of magic squares. One centered magic squares. These are traditionally previous known magic squares. The second one is double digits bordered magic squares. Some examples of embedded type magic squares are also given. For previou work on odd orders from 3 to 29 refer author's website. Further studies are for the orders 33, 35, etc.

The pdf file of complete work is available at author's site: https://numbers-magic.com/?p=9493