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Magic squares

Magic Squares

Magic numbers was first recorded by Chinese in 2200BC and known to Arab mathematicians, when they conquered India and learnt about Indian mathematics, astronomy and other aspects of combinatorial mathematics. Magic squares is the arrangement of the distinct numbers (each number used once) in a square array, in which the sum of the Row, Column and all diagonals have the same number known as Magic constant. Magic square that contains the number from 1 to n2 is called as normal magic numbers.

Number of rows and column in the magic squares is always equal and represented by 'n'.

The constant that is the sum of every row, column and diagonal is called as Magic constant. It can be determined with the formula

M = n(n2 + 1) / 2

Consider normal magic square of the order 3 x 3. For 3 x 3 grid, fill numbers 1, 2, 3...9 in the square array, such that the sum of the number in the row, column and diagonal should be 15. For example, if n = 3, 4, 5.... then the magic consonants are 15, 34 , 65 respectively.

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