Magic Square Made Easy
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Magic Square Made Easy

This is a neat trick that I have learned in high school. It was taught by a very smart and charming lady and I have not forgotten it ever since. In fact, this method of creating a magic square has long been published by a French diplomat in 1693 (source Wikipedia). I find it interesting that a seemingly complex magic square could easily be constructed using a few simple rules. Read on to find out more.

This method of creating a magic square would only be applicable for odd numbered columns and rows. You could make a 3x3 magic square, 5x5, 7x7, and so on - as long as it is an odd numbered grid.

Let us first study on how to make a 3x3 magic square. To easily create a magic square, we always start by putting the number 1 in the top middle portion of the grid as shown below:

 

The next step in constructing the magic square is to put the next number diagonally upward to the right. This is the motion in which the numbers would be put in the grid. 2 is the next number and should be placed diagonally upward to the right of number 1. However, there is no grid in the upper right corner of the number 1. The solution to this is to put the number 2 in the next column to the right at the lowest grid that has no number written on it.

Next is the number 3. Again, we should move diagonally upward to the right. However, there are no more grids to the right of number 2. The solution is to put the number 3 to the left most square on the column right above the number 2 as shown in the figure below.

After placing the number 3 in the left side, we now move on to number 4.  Again we must put the number 4 on the upper right grid of the number 3 but the grid is already filled by the number 1. If this is the case, we should put the number 4 below the number preceding it (number 3).

The number 5 should be placed diagonally upward to the right of number for and number 6 should be placed diagonally upward to the right of number 5.

Number 7 should be placed diagonally upward to the right of number 6 but there are no more grids to the right of 6. To remedy this, the number 7 should be placed below number 6.

The number 8 should be placed diagonally upward to the right of number 7 but since there is no grid to the right of number 7, the number 8 should be placed to the top left most portion of the magic square.

The last number is 9 and should be placed diagonally upward to the right of number 8. However, there is only one grid left thus number 9 should be placed in the last grid to complete the magic square.

The sum of the numbers, horizontally, vertically and diagonally all amount to 15. To really get the hang of it, let us try a to make a magic square in a 5x5 grid:

Still place the number 1 in the top middle portion of the grid then just continue filling the grid by moving diagonally right and up. If there is no grid to move up and right, move down (number 2). If there is no grid to move down to, move to the far left grid (number 4) then continue moving up an right again.

The sum of the numbers, vertically, horizontally and diagonally amounts to 65. The smallest magic square that could be constructed using this method is a 3x3 magic square. And you can make larger magic squares to your heart’s content as long as it is odd numbered. Have fun.

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