So THEN I wanted to do something kind of crazy and see where it went. Because I'm not adventurous enough, or experienced enough, I stayed in a 4x4 and used the first 4 letters of my name [MICH]. Then I assigned those as a number value [13, 9, 3, 8] and then developed kind of a "mod" style number association where numbers could be negative and also higher than 26.
That is actually the finished square once I got everything to be SUPER magical and equal to 33. I tried to stay within 1-26 but it was basically impossible. I mean, is it actually impossible? Because the total was 33 so I need 24 combinations of addition expressions equal to 33 using only numbers 1-26, without repeating. So since I could NOT figure out how to do that (I'm sure there is a formula... I just can't figure out how to figure it out lol) I went to using negative numbers and numbers above 26. This led me to the above square... FINALLY without repeating - Well, technically I did repeat but when I tried to change it... I evened out all the rows, columns, and diagonals but then my quadrants and were not equal to 33 :( So I went with second best.
I subbed in the letter equivalents. However, you will notice that many of letters ended up repeating. So does this have something to do with the fact that I cycled them in a modular form... which I technically didn't even do correctly because I started A as 1 and not 0. At this point, you know I had to go back and try to fix it to be done the way it is supposed to and with a correct modular formation (because my growth mindset makes me). In this square, for the number portion I could NOT get it to be correct without repeating one number; same problem from the first time as well. However, with the letter portion, I was able to eliminate one of the repeated letters!
By default, the repeated number (12/M) would be a repeating letter but the only other letter that repeated was U when it was used as 20 and -6.
While these puzzles took a fair amount of time, going forward I would love to further research the patterns or formulas that go into making the squares "magic"... if there even is one. Based on my understanding of what math is though, I assume there must be a pattern. Reflecting on what was taking place during the activity was actually a lot of adding and subtracting. I roped my 7 year old into helping me with her birthday square, while she loves puzzles and math... it was a little over her head. She WAS however at least practicing adding 4 numbers up to equal a certain sum. So in that aspect, I believe there was educational value for her.