In recreational mathematics, a magic square is an arrangement of numbers (usually integers) in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n". A magic square that contains the integers from 1 to n2 is called a normal magic square. (The term "magic square" is also sometimes used to refer to any of various types of word squares.)
More information, including examples of magic squares and links to other magic/number shapes, on the Wikipedia page .