The idea of nested magic squares is well known in the literature, generally known by bordered magic squares. In this work, nested magic squares are studied in such a way that the magic sums are equal to the order of the magic square. The study include integer values. In some cases decimal entries with positive and negative entries are also used. The magic sums of sub-magic squares lead us to a general formula. The work is for the bordered magic squares of orders 3 to 25.
Bordered Magic Square of Order 20 with magic sum 20×20
For a day 20 of each month of 2020
The work can be download at the following link:
- Inder J. Taneja, Bordered Magic Squares With Order Square Magic Sums, Zenodo, January 20, 2020, pp. 1-26, http://doi.org/10.5281/zenodo.3613690
Below are examples considered in the work:
Numbers Magic 
How do you like this magic square?
Brief description of the magic square:
– All rows, horizontally, vertically and diagonally, give the sum of 4 million 999 thousand 995 (4999995).
– The table has 9 equal sections, with 9 numbers in each ..
– In all sections, all rows horizontally and columns vertically have a sum of 1666665.
– In table does not even have two numbers with the same digits.
– All numbers are six-digit, non-zero, multi-digit.
This is one square from the series «Uarza Magic Tables» (or «магические таблицы уарза»).
Таблица № 6 – сторона 3 в магическом квадрате / 4999995
864297 678912 123456 297531 912345 456789 531864 345678 789123
= 4999995
372615 726159 567891 615948 159483 891234 948372 483726 234567
= 4999995
429753 261594 975318 753186 594837 318642 186429 837261 642975
= 4999995
123457 864295 678913 456781 297538 912346 789124 531862 345679
= 4999995
567892 372619 726154 891235 615943 159487 234568 948376 483721
= 4999995
975316 429751 261598 318649 753184 594832 642973 186427 837265
= 4999995
678914 123458 864293 912347 456782 297536 345671 789125 531869
= 4999995
726158 567893 372614 159482 891236 615947 483725 234569 948371
= 4999995
261593 975314 429758 594836 318647 753182 837269 642971 186425
= 4999995
4999995 4999995 4999995 4999995 4999995 4999995 4999995 4999995 4999995 \ 4999995
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