For the first time in this work, two new concepts in construction of magic square are considered:

  1. Using small blocks of magic or bordered magic rectangles. It is not always possible to write bordered magic rectangles for the non-sequential entries. In this case, the simple magic rectangles are considered.
  2. Using algebraic formula (a+b)2.

The whole work contains magic squares of even orders starting from order 8. This part is only for order 16. For orders 8, 10, 12 and 14 see the links below:

  1. Inder J. Taneja, Different Styles of Magic Squares of Orders 8, 10 and 12 Using Bordered Magic Rectangles and the Formula (a+b)2Zenodo, September 18, 2022, pp. 1-30, https://doi.org/10.5281/zenodo.7090737.
  2. Inder J. Taneja, Different Styles of Magic Squares of Order 14 Using Bordered Magic Rectangles and the Formula (a+b)2Zenodo, September 18, 2022, pp. 1-45, https://doi.org/10.5281/zenodo.7090764.
  3. Inder J. Taneja, Different Styles of Magic Squares of Order 16 Using Bordered Magic Rectangles and the Formula (a+b)2Zenodo, September 18, 2022, pp. 1-85, https://doi.org/10.5281/zenodo.7090770.

Below are 153 Examples of Magic Squares of order 16. These are written in four parts:

  • Part 1: Magic Squares of Order 16: Traditional and Bordered Magic Rectangles.
  • Part 2: Magic Squares of Order 16: (A+B)2-Type: A=10, B=6.
  • Part 3: Magic Squares of Order 16: (A+B)2-Type: A=12, B=4, where A as Two Blocks of Magic Rectangles of Order 4×6.
  • Part 4: Magic Squares of Order 16: (A+B)2-Type: A=12, B=4, where A as Magic Rectangles of Order 4×12 or Magic Squares of Oder 4.

Part 1: Magic Squares of Order 16: Traditional and Bordered Magic Rectangles

Part 2: Magic Squares of Order 16: (A+B)2-Type: A=10, B=6

Part 3: Magic Squares of Order 16: (A+B)2-Type: A=12, B=4, where A as Two Blocks of Bordered Magic Rectangles of Order 4×6

Part 4: Magic Squares of Order 16: (A+B)2-Type: A=12, B=4, where A as Magic Rectangles of Order 4×12 or Magic Squares of Order 4