This work brings magic squares of orders 3 to 10 in terms of single letter “a”, where a can take any value from 1 to 9. The magic squares of orders 8 and 9 are written in two ways, i.e, one as normal magic squares and another as bimagic squares. In case of order 10, we have written it in three different ways. One as normal way, the second as block of order 8, divided again in four blocks of order 4. The third is with inner block of order 8 as bimagic square.

As we wrote above, this work brings magic squares with single letter “a”, where a can take any value from 1 to 9. The work can be downloaded at the following link:

Below are examples of the magic squares done in this work:

Magic Square of Order 3

Magic Square of Order 4

Magic Square of Order 5

Magic Square of Order 6

Magic Square of Order 7

Magic Squares of Order 8

Magic Squares of Order 9

Magic Square of Order 10

Observations:

The last two magic squares of order 10 are known as block-bordered magic squares. For more details see the link below:

  1. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – I, Zenodo, August 18, 2020, pp. 1- 81, http://doi.org/10.5281/zenodo.3990291
  2. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – II, Zenodo, August 18, 2020, pp. 1-90, http://doi.org/10.5281/zenodo.3990293
  3. Inder J. Taneja, Block-Bordered Magic Squares of Prime and Double Prime Numbers – III, Zenodo, September 01, 2020, pp.1-93 http://doi.org/10.5281/zenodo.4011213

Before we write examples of magic squares, below is an idea of single letter representations of numbers:

More details on above work see the link below:

Inder J. Taneja, Single Letter Representations of Natural Numbers, https://inderjtaneja.com/2017/08/19/single-letter-representations-of-natural-numbers/

One thought on “Creative Magic Squares: Single Letter Representations

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