A Magic Square of order n is an arrangement of the numbers from 1 to n^2 (n-squared) in an n by n matrix. The sum of any row, any column, or any main diagonal must be the same. The smallest non-trivial case is of order 3. The same idea can be extended to other shapes such as stars, cubes, circles, and so on. These are called Magic objects. Magic Square Recreations Math Science.

In recreational mathematics, a magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number, called the " magic constant . (wikipedia)

- Wikipedia: In recreational mathematics, a magic square is a square grid filled with distinct numbers such that the numbers in each row, and in each column, as well as the numbers in the main and secondary diagonals, all add up to the same value, called the magic constant. A magic square having n rows is said to be of order n. Thus, a magic square of order n always contains n2 numbers, usually integers. A magic square that contains the integers from 1 to n2 is called a normal magic square.
- Arithmetic sequence - In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
- Combinatorial design - Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.
- Freudenthal magic square - In mathematics, the Freudenthal magic square is a construction relating several Lie algebras. It is named after Hans Freudenthal and Jacques Tits, who developed the idea independently.
- John R. Hendricks - John Robert Hendricks was a mathematician specializing in magic squares and hypercubes. He has published many articles in the Journal of Recreational Mathematics as well as other Journals.
- Hexagonal tortoise problem - The hexagonal tortoise problem, a.k.a. jisuguimundo, jisugwimundo was invented by Korean aristocrat and mathematician Seok-jeong Choi, who lived from 1646 to 1715.
- Latin square - In combinatorics and in experimental design, a Latin square is an n n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column. An example of a 3x3 Latin square is...
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