stopping with the commas
this will be short, i will explain magic squares, and be done for the day, sorry
first, a mgic square is a n by n box, such as 3x3, or7x7, which are the two i will be discussing today
but i first need to explain, that in a magic square, each row, column, and diagonal, add up to the same number, in a three by three (3x3) all the rows and columns add up to fifteen.
now, the first thing you need to find in a 3x3 is the center number, so, i will make a three by three, where every blank space is represented by a zero
May 6-2009
-By Brad
0 0 0
0 0 0
0 0 0
alright, so, as you can see, this holds nine numbers, so to find the center number, we will need to pick one, which, added to two other numbers, can make the number 15 four different ways, one for vertically, one for horizontally, and two for each diagonal.
so, to find it, you line up the numbers, and see what you can do:
1,2,3,4,5,6,7,8,9
and actually, to take the guessing out of it, i will tell you, it is 5, it makes fifteen in these ways
5+9+1=15
5+8+2=15
5+7+3=15
5+4+6=15
so, now we have this
0 0 0
0 5 0
0 0 0
so, let's look at the first item on my addition list, a nine and a one with a five, now, a nine or a one can only make two possible combinations that could make fifteen, so let's take nine, for example, it can only make fifteen like this:9,5,1 9,4,2
so, now that we know it can only make two combos, we know it goes in a horizontal or vertical row, i will put it in a vertical row
0 9 0
0 5 0
0 1 0
so, now, we will make fifteen with the nine in the top row by adding our 4 and 2 combination
2 9 4
0 5 0
0 1 0
then we complete the diagonals by simply putting in numbers that make them add to fifteen
2 9 4
0 5 0
6 1 8
and the last two are easy, so i'll just fill those in too
2 9 4
7 5 3
6 1 8
and there you have it, all vetrical, horizontal, and diagonal lines add to fifteen
noow, the seven by seven, there is a trick to it, so i will put it up, see if you can see the pattern, and if you really can't, i will write it at the bottom (by the way, every column adds to 175 if you really want to try to prove me wrong)
30 39 48 1 10 19 28
38 47 7 9 18 27 29
46 6 8 17 26 35 37
5 14 16 25 34 36 45
13 15 24 33 42 44 4
21 23 32 41 43 3 12
22 31 40 49 2 11 20
alright, for those that got it, congrats, for those who didn't, look at the one, then go one space right to the bottom, there is the two, then go up one, right one, and you will get 3-7 until you hit 1 again, then it drops a space and goes to eight, and the pattern continues like that throughout, there is another way too, i will post it, but not explain it, this will take the question portion, what is the pattern?
16 46 27 1 31 12 42
35 9 39 20 43 24 5
47 28 2 32 13 36 17
10 40 21 44 25 6 29
22 3 33 14 37 18 48
41 15 45 26 7 30 11
4 34 8 38 19 49 23
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