In recreational mathematics, a **magic square** of order *n* is an arrangement of *n*2 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 *n*2. 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

### Other articles related to "magic square, magic squares, magic, square, squares":

**Magic Square**- Generalizations - Extra Constraints

... Certain extra restrictions can be imposed on

**magic squares**... not only the main diagonals but also the broken diagonals sum to the

**magic**constant, the result is a panmagic

**square**... If raising each number to certain powers yields another

**magic square**, the result is a bimagic, a trimagic, or, in general, a multimagic

**square**...

**Magic Square**- Related Problems -

*n*-Queens Problem

... and Tanik published a method for converting some

**magic squares**into n-queens solutions, and vice versa ...

**Magic Square**

... also brought to France from his Siamese travels a very simple method for creating n-odd

**magic squares**, known as the "Siamese method" or the "de la Loubère method", which apparently was initially ...

**Magic Square**- Types and Construction - A Method of Constructing A

**Magic Square**of Doubly Even Order

... The resulting

**square**is also known as a mystic

**square**... In the

**magic square**of order four, the numbers in the four central

**squares**and one

**square**at each corner are retained in the same place and the others are interchanged with ... A construction of a

**magic square**of order 4 Go left to right through the

**square**counting and filling in on the diagonals only ...

**Magic Square**

... An associative

**magic square**is a

**magic square**for which every pair of numbers symmetrically opposite to the center sum up to the same value ...

### Famous quotes containing the words square and/or magic:

“I would say it was the coffin of a midget

Or a *square* baby

Were there not such a din in it.”

—Sylvia Plath (1932–1963)

“Self-esteem is the real *magic* wand that can form a child’s future. A child’s self-esteem affects every area of her existence, from friends she chooses, to how well she does academically in school, to what kind of job she gets, to even the person she chooses to marry.”

—Stephanie Martson (20th century)