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, consisting 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, ... (sequence A006003 in OEIS).
Read more about Magic Square: History, Types and Construction, Related Problems
Famous quotes containing the words magic and/or square:
“To play safe, I prefer to accept only one type of power: the power of art over trash, the triumph of magic over the brute.”
—Vladimir Nabokov (1899–1977)
“If the physicians had not their cassocks and their mules, if the doctors had not their square caps and their robes four times too wide, they would never had duped the world, which cannot resist so original an appearance.”
—Blaise Pascal (1623–1662)