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So what if I woulda just take this, so let me just take this right over here, and copy and paste that. And I can do it for each of these, for each of these now. And you’ll see the pattern still holds, we went from one, two, three, four, five, six, seven, eight, nine, and now we got to 10 followed by a zero. The mathematical study of magic squares typically deals with its construction, classification, and enumeration.Now how can I complete this going all the way to 99 pretty fast?
In regard to magic sum, the problem of magic squares only requires the sum of each row, column and diagonal to be equal, it does not require the sum to be a particular value.
Thus, although magic squares may contain negative integers, they are just variations by adding or multiplying a negative number to every positive integer in the original square..
Except for n ≤ 5, the enumeration of higher order magic squares is still an open challenge.
The enumeration of most-perfect magic squares of any order was only accomplished in the late 20th century.
Beside this, depending on further properties, magic squares are also classified as associative magic squares, pandiagonal magic squares, most-perfect magic squares, and so on.
More challengingly, attempts have also been made to classify all the magic squares of a given order as transformations of a smaller set of squares.
So let me just start, so I’m gonna start at zero, one, two, three, four, five, six, seven. Well it’s a 12, which is a one followed by a two, and then 13, 14, 15, 16, 17, 18, and 19. This next row of numbers as I went from 10 to 19 looked just like the first ones, so the 2nd number is the same in yellow, but then I added a purple one to the front of it. So just doing that I think you already see the pattern.
eight, and nine, and instead of, of course we know the next number is 10, which I could write down but instead of doing that I’m just going to copy and paste all of this. And one way to think about it is, each of these numbers, the purple one that I added, that represents 10. So let’s take another row , my original row, and what do I get to after 19? So 20, two zero and then 21, 22, 23, 24, 25, 26, 27, 28, 29. The number on the right we keep going from zero, one, two, three, four, five, six, seven, eight, nine, and then the number on the left, if we’re between 10 and 19, you’ll always have a one.
Voiceover: The goal of this video is to essentially write down all the numbers in order from zero to a 100.
But I’m going to do it in an interesting way, a way that maybe will allow us to see some patterns in the numbers themselves. So the first number 30 is 30 plus zero, 30 plus one, 30 plus two, 30 plus three which is 33, 34, 35, 36, 37, 38, 39.