# How to construct a 3x3 magic square

In this section we will be constructing the basic magic square with the dimension 3x3 starting value 1 and common difference 1. If you do not know what a magic square is please refer to the Magic Squares: Introduction section. It is also important to note that this method works with all magic squares that have an odddimension. i.e. 5x5 7x7 9x9.......

1. ) First we will begin with an empty 3x3 array.

2.) Next we place the starting value 1 in the middle of the top row.

3.) Now we move right one space and up one space,

but as we can see highlighted in yellow this places the 2

outside the bounds of the 3x3 square.When this happens we

simply bring the 2 down to the bottom square of the column it is positioned over.

4.) In this step we start with the 2 and once again we go right

one space and up one space. And once again this leaves us

out side the bounds of the 3x3 square so we place the 3 at the

beginning of the row it is outside of.

5.) Here we start with the 3 and once again move right

one space and up one space, but this time it puts us in an

occupied space. when that happens we simply place the 4

underneath the 3.

6.) In this step we start with the 4 and again move right one

space and up one space. This space is within the bounds of the

square and unoccupied so we can simply leave the 5 here.

7. ) Here we start with the 5 and go one space right and one

space up and as we can see we can once again simply just

place the 6 in this unoccupied space

8.) This time when we move right one space and up one

space. we are not only outside the bounds of the square

but we are also on a diagonal In case this happens we

place the 7 underneath the 6.

9.) Here we start with the 7 and move right one space

and up one space. Here we are again out side the bounds

of the square so we simply take the 8 and place it at the

beginning of the row it is beside.

10.) now in the final step we only have one space left where we could go ahead and place the 9 there how ever I am still going to illustrate that the pattern still applies when there is only one space. so we start with the 8 move right one space and up one space. and again we are out side the bounds of the square, so we will move the 9 to the bottom of the column it is over.

Next in the series we will be looking deeper into the math behind these squares.

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