The magic constant of a magic square, an n-by-n matrix, is defined such that the sum of any row, column or main diagonal yields the same result, denoted M_{2}(n). If the numbers in the magic square are 1, 2,..., n², then

.

Paul Muljadi discovered and proved the Magic constant of n-Queens Problem is also the Magic constant of a Magic Square of order n > 3.

The first few magic constants are 15, 34, 65, 111, 175, 260, 369, 505

In mathematics, a magic square (å¹»æ–¹) of order n is an arrangement of nÂ² numbers in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

The earliest magic square of order four was found in an inscription in Khajuraho, India, dating from the eleventh or twelfth century; it is also a panmagic square where, in addition to the rows, columns and main diagonals, the broken diagonals also have the same sum.

Odd and doubly even magic squares are easy to generate; the construction of singly even magic squares is more difficult but several methods exist, including the LUX method for magic squares (due to John Conway) and the Strachey method for magic squares.

Share your thoughts, questions and commentary here

Want to know more? Search encyclopedia, statistics and forums:

Press Releases |
Feeds |
Contact
The Wikipedia article included on this page is licensed under the
GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms, 1022, m