Constructing a Magic Square

 I was first introduced to the concepts of the Magic Square in this video: A Sudoku With Only 4 Given Digits. As an aside, this Sudoku video was unbelievable to watch someone solve; I struggle enough with the basic versions of Sudoku, let alone this kind of stuff!

I remember when it was first mentioned, I thought it was such an interesting idea that almost didn't seem feasible. It felt a little unfair making this then because I had some previous knowledge of how to approach it (although I didn't completely remember how to solve it). The one thing that I remembered was important was the number 5, as when we construct the possibilities of 3 numbers added together between 1-9 to equal 15, 5 was the most common number that allowed the most possibilities, therefore it was placed in the center square. 

The easiest way to approach this was deciding what would happen with 1. If I added 1+5+9 I get 15, but I also get 1+6+8 to be 15 too. If 9 was on the diagonal, then it has to intersect with 6 or 8 on the vertical or horizontal! The problem with that is it's >=15 with only 2 values, so we know that wouldn't work. So I then wrote 1 and 9 on the horizontal and was able to solve the square going from there! It helped to write out a couple other equations that would help me logically reason through the pattern of the square. Once I was able to have 2 equations down (1 + 5 + 9 and 6 + 1 +8), the rest logically followed as there was a missing spot in the top right corner where I was able to fill in the 2...and so forth. It reminded me of a Sudoku puzzle as well, once you know the spot of a few numbers, the rest seem to flow!