Tuesday, June 28, 2016

Go Shawty... It's My Birthday... In A Super Magical Square (6)

Well it's not my birthday today... so I'll celebrate a couple weeks late.  I was totally in love with and fascinated by these magic squares, especially by using your birth date.  I love Sudoku puzzles and this reminded me of that, but using more math!  I know, here I go again... but Jo B says that puzzles are a perfect way to engage your mind in mathematical thinking.  I started by using my own birthday and honestly, that one was pretty easy.  Like many others who have explained their thinking, I started by doing the diagonal first (obviously after the first row) and once I got that to add up to 120 then I worked down from there.  However, I quickly realized my other diagonal was not adding up to 120 and was much lower.  So I had to do some rearranging.  Since I had two low numbers in the first two columns as the top square, and one much higher number in the last column, I was able to use a nice range of numbers to get to my sum (120).  After I got the whole square set with each column, row, and diagonal adding up to 120... I decided to add a little extra challenge and make it a SUPER magic square.  So I focused on making the 4 corners add up to 120, then the first, second, third, and fourth quadrants to also add up to 120.  Lastly, I calculated the middle square to see if it would add up to 120 and it already did!

 So I decided to try more birthdays... because I'm a puzzle addict.  So I started to work on Emma's, one of my littles, and since she was born 4-2-20-11... I didn't have a huge number range to work with and I didn't have a very big sum to work with either (37).  The amount of combinations I could use to total 37 without repeating was very tricky.  So I gave up for a little while and did my boyfriend's birthday instead.  Even though he was born in January, eliminating early my ability to use the number 1, the rest of his numbers gave me a good range: 25, 19, 80.  I tackled his the same way I did mine by starting with the diagonals but for his, since I had already worked with quadrants for my square, I decided to try those first.  I think this actually made it easier... because once I got all the quadrants and middle squared away... with very minor adjustments the rows and columns were already in place.

Now for my crazy little Emmeline, I had to get creative.  So like Nick did, I also used a negative number.  I felt like this was probably an "illegal" move also... but it was the only way I could get it t work.  Especially since she already had 2 and 4 in her birthdate, I was limited about which small numbers I could use to adjust the sums.

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.

1 comment:

  1. Nice exposition of your thinking. I especially like how you got to more questions about it. And I super like bringing in family members.

    C's: 5/5