Never seen before.
By boarded magic squares we understand that if we remove the external border still, we are left with magic squares of lower orders with sequential entries. Single digits bordered magic squares are well-known. This work brings ver different types of bordered magic squares but are of corner-type, known by cornered magic squares. Instead of removing the whole border, here we remove only last row and column. By doing so, we still left with lower order cornered magic squares. This work is up to order 81. We start with order 5.
Lower order cornered magic suares (up to order 23) can be calculated using software by Harry While: Downloads (budshaw.ca).
During past days author did few works in this direction. These are as follows:
- Inder J. Taneja, Cornered Magic Squares of Order 6, Zenodo, May 23, 2023, pp. 1-23, https://doi.org/10.5281/zenodo.7960679.
Site Link: Cornered Magic Squares of Order 6.
- Inder J. Taneja, Cornered Magic Squares of Orders 5 to 13, Zenodo, June 03, 2023, pp. 1-71, https://doi.org/10.5281/zenodo.8000467.
1. Cornered Magic Squares of Orders 5 to 10.
2. Cornered Magic Squares of Orders 11 to 13.
- Inder J. Taneja, Cornered Magic Squares of Orders 14 to 24, Zenodo, June 03, 2023, pp. 1-39, https://doi.org/10.5281/zenodo.8000471.
Site Link: Cornered Magic Squares of Orders 14 to 24.
Corned Magic Squares: Orders 5 to 30
Below are examples of cornered magic squares of orders 5 to 30. The total work is up to order 81. Most of the work is done manually. For the complete work see the excel file attached at the end.
For more examples see the excel files below:
Excel files for Download
File 1: Cornered Magic Squares: Orders 5 to 81.