MAGIC SQUARE

 Sumanth R
3rd Sem B.Sc(EMCs)-NCMS

Magic square: a square array of numbers, usually positive integers is called a magic square. if the sums of the numbers in each row, each column, and both main diagonals are the same. The order of the magic square is the number of integers along one side (n), and the constant sum is called the magic constant. If the array includes just the positive integers {\displaystyle 1,2,...,n^{2}}, the magic square is said to be normal.

A square divided into an equal number n of columns and rows with the resulting cells containing the first n² natural numbers whose sum in each column, each row, and the two main diagonals is the same [being equal, as can be shown, to (½) n(n² + 1)]. It has been proved that a magic square can be constructed for any n beginning with n = 3. as shown in figure 1 magic squares for n = 3 and n = 4. There exist magic squares that satisfy a number of additional conditions, as for example, a magic square with 64 cells (see Figure 2), which can be divided into four smaller squares each containing 16 cells such that the sum of the numbers of any row, any column, or the main diagonals is the same (130). Magic squares were used as talismans in India and some other countries. The construction of magic squares is a classical example of mathematical games and puzzles.