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.
- 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:
- 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:
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:
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!