Magic square

In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary 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.)

Normal magic squares of all sizes except 2 × 2 (that is, where n = 2) can be constructed. The 1 × 1 magic square, with only one cell containing the number 1, is trivial. The smallest (and unique up to rotation and reflection) nontrivial case, 3 × 3, is shown below.