In recreational
mathematics, a magic square of order n is an arrangement of n² numbers,
usually distinct integers, in a square, such that the n numbers in all
rows, all columns, and both diagonals sum to the same constant. A normal
magic square contains the integers from 1 to n². The term "magic
square" is also sometimes used to refer to any of various types of word
square.
Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3.
Normal magic squares exist for all orders n ≥ 1 except n = 2, although the case n = 1 is trivial—it consists of a single cell containing the number 1. The smallest nontrivial case, shown below, is of order 3.
The
constant sum in every row, column and diagonal is called the magic
constant or magic sum, M. The magic constant of a normal magic square
depends only on n and has the value
For normal magic squares of order n = 3, 4, 5, …, the magic constants are:
15, 34, 65, 111, 175, 260, …
Source : http://en.wikipedia.org/wiki/Magic_square
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