**Background:**

In recreational mathematics, a magic square is an arrangement of integers in a square grid, where the numbers in each row and in each column, as well as the numbers in the forward and backward main diagonals, all add up to the same number. Using standard math notation,

*n*equals for the number of rows (and columns) it has. Thus, a magic square always contains

*n^2*numbers, and its size (the number of rows and columns it has) is described as being "of order

*n*".

**Your Task:**

There are many different ways to construct magic squares of all

*n*x

*n*(that is, except for

*n*=2). Create some of your own magic squares, and try to look for underlying patterns. Are there finitely many magic squares for each

*n*? Are there patterns in the "sums" of magic squares? (Sums being the constant value obtained when adding all terms of each individual column, row and diagonal). Can we learn any neat findings about combinatorics & other fields of math in the process?

Also research the history of magic squares, as numerous interesting insights in their study date back to Ancient Chinese mathematicians around 650 BCE, and Arab mathematicians around the 7th Century CE.

**Links:**

http://en.wikipedia.org/wiki/Magic_square

http://mathworld.wolfram.com/MagicSquare.html

http://www.jcu.edu/math/vignettes/magicsquares.htm