Magic square
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, …
refrensi: http://en.wikipedia.org/wiki/Magic_square
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