A Palindromic Magic Square for the Year 2019

2019 palinhdromic magic square.png

The above 4 × 4 magic square only has the digits 2, 0. 1, and 9 (from the year 2019) and as a bonus, the four digits in its upper-left section form “2019”. It has a magic sum of 132. This means the sums of the magic square’s columns, rows, and diagonals are all equal to 132. It is also a semi-pandiagonal magic square since it contains some of the features of a pandiagonal magic square, namely:

  • Partial Panmagic Square — The 2-2 broken diagonals (on both sides) of this magic square have a magic sum of 132 as well. For this to be a panmagic square, the 3-1 broken diagonals should also be equal to the magic sum, but unfortunately, this magic square does not have that property. From here on, note that the sum of the cells with identical background colors is equivalent to the magic sum, which in our case is 132.

2019 semi-panmagic square

  • Complete Magic Square — For an order-4 magic square to be considered “complete”, any 2 × 2 arrays, but not including the inner 2 × 2 arrays, must be equal to the magic sum (132). The four corners of any 3 × 3 arrays should also be equal to the magic sum. Finally, the sum of the four corners of the magic square should be equal to the magic sum. This magic square satisfies all the requirements:

2019 complete magic square

  • Partial Most-Perfect Magic Square — The prerequisites of being a most-perfect magic square are not easy. For a 4 × 4 magic square, to be a most-perfect magic square, the sum of any of its 2 × 2 arrays and 2-2 broken horizontals and broken verticals must be equal to the magic sum (132). However, this magic square only fulfilled the requirements partially:

2019 partial most perfect magic square.png

Nonetheless, the most remarkable feature of this magic square is that it’s palindromic. This means that you can reverse all the digits of this magic square and you would still get a valid magic square with the same magic sum of 132:

18 12 28 16 06 27

What’s more, the abovementioned features are also applicable to the palindromic version of this magic square!

It took me quite a while to create this magic square, but I think the result that I got is worth it even though it was not a true pandiagonal magic square. The palindromic nature of this magic square was a pleasant bonus.

Happy New Year!

Posted by

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

19 thoughts on “A Palindromic Magic Square for the Year 2019

  1. Reblogged this on e-Quips and commented:
    Although math is a language, it has never been one I am fluent in. This ‘magic’ square is never something I could come up with and it is interesting.


  2. Reblogged this on Explorations of Inventories and commented:
    Explorations of Inventories is a 12 Step blog, so why this reblog? Because the premise of the blog is an expansion of select mathematical ideas into metaphors that serve as tools for solving personal problems. Magic squares could be used that way, dissolving a situation into the pieces of a square with intentional gaps. Fill in the gaps creatively, and a previously unseen solution may emerge.

    Liked by 3 people

    1. Thanks.

      Other people use computers though I personally do them manually as it’s more fun. However, the advantage of using a computer is that you can easily create higher order magic squares and magic squares with more impressive properties.

      Liked by 4 people

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