Magic Square

Create a magic square.

magic(n)

Arguments

n

numeric scalar specifying dimensions for the result; n must be a scalar greater than or equal to 3.

Details

A magic square is a square matrix where all row and column sums and also the diagonal sums all have the same value.

This value or the characteristic sum for a magic square of order \(n\) is \(sum(1:n^2)/n\).

Value

Returns an n-by-n matrix constructed from the integers 1 through N^2 with equal row and column sums.

Note

A magic square, scaled by its magic sum, is doubly stochastic.

Author

P. Roebuck roebuck@mdanderson.org for the first R version in the package `matlab'. The version here is more R-like.

Examples

magic(3)
#>      [,1] [,2] [,3]
#> [1,]    8    1    6
#> [2,]    3    5    7
#> [3,]    4    9    2