hudson: Pandiagonal magic squares due to Hudson

In magic: Create and Investigate Magic Squares

Pandiagonal magic squares due to Hudson

Description

Returns a regular pandiagonal magic square of order 6m+/-1 using a method developed by Hudson.

Usage

hudson(n = NULL, a = NULL, b = NULL)

Arguments

n	Order of the square, n=6m+/-1. If NULL, use the length of a
a	The first line of Hudson's A matrix. If NULL, use Hudson's value of c(n-1,0:(n-2))
b	The first line of Hudson's B matrix. If NULL, use Hudson's value of c(2:(n-1),n,1). Using default values for a and b gives an associative square

Details

Returns one member of a set of regular magic squares of order n=6m+/-1. The set is of size (n!)^2.

Note that n is not checked for being in the form 6n+1/6n-1. If it is not the correct form, the square is magic but not necessarily normal.

Author(s)

Robin K. S. Hankin

References

C. B. Hudson, On pandiagonal squares of order 6t +/- 1, Mathematics Magazine, March 1972, pp94-96

See Also

recurse

Examples

hudson(n=11)
magicplot(hudson(n=11))
is.associative(hudson(n=13))
hudson(a=(2*1:13)%%13 ,  b=(8*1:13)%%13)
all(replicate(10,is.magic(hudson(a=sample(13),b=sample(13)))))

magic documentation built on Nov. 16, 2022, 9:06 a.m.