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Magic cubes of order 2n+1

magiccube.2np1.Rd

Creates odd-order magic cubes

Usage

magiccube.2np1(m)

Arguments

m

n=2m+1

References

website

Author

Robin K. S. Hankin

See also

magic

Examples


#try with m=3, n=2*3+1=7:

m <-7                     
n <- 2*m+1


apply(magiccube.2np1(m),c(1,2),sum)
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12]
#>  [1,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [2,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [3,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [4,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [5,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [6,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [7,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [8,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [9,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [10,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [11,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [12,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [13,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [14,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [15,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>       [,13] [,14] [,15]
#>  [1,] 25320 25320 25320
#>  [2,] 25320 25320 25320
#>  [3,] 25320 25320 25320
#>  [4,] 25320 25320 25320
#>  [5,] 25320 25320 25320
#>  [6,] 25320 25320 25320
#>  [7,] 25320 25320 25320
#>  [8,] 25320 25320 25320
#>  [9,] 25320 25320 25320
#> [10,] 25320 25320 25320
#> [11,] 25320 25320 25320
#> [12,] 25320 25320 25320
#> [13,] 25320 25320 25320
#> [14,] 25320 25320 25320
#> [15,] 25320 25320 25320
apply(magiccube.2np1(m),c(1,3),sum)
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12]
#>  [1,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [2,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [3,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [4,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [5,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [6,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [7,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [8,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [9,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [10,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [11,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [12,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [13,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [14,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [15,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>       [,13] [,14] [,15]
#>  [1,] 25320 25320 25320
#>  [2,] 25320 25320 25320
#>  [3,] 25320 25320 25320
#>  [4,] 25320 25320 25320
#>  [5,] 25320 25320 25320
#>  [6,] 25320 25320 25320
#>  [7,] 25320 25320 25320
#>  [8,] 25320 25320 25320
#>  [9,] 25320 25320 25320
#> [10,] 25320 25320 25320
#> [11,] 25320 25320 25320
#> [12,] 25320 25320 25320
#> [13,] 25320 25320 25320
#> [14,] 25320 25320 25320
#> [15,] 25320 25320 25320
apply(magiccube.2np1(m),c(2,3),sum)
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10] [,11] [,12]
#>  [1,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [2,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [3,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [4,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [5,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [6,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [7,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [8,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>  [9,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [10,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [11,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [12,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [13,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [14,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#> [15,] 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320 25320
#>       [,13] [,14] [,15]
#>  [1,] 25320 25320 25320
#>  [2,] 25320 25320 25320
#>  [3,] 25320 25320 25320
#>  [4,] 25320 25320 25320
#>  [5,] 25320 25320 25320
#>  [6,] 25320 25320 25320
#>  [7,] 25320 25320 25320
#>  [8,] 25320 25320 25320
#>  [9,] 25320 25320 25320
#> [10,] 25320 25320 25320
#> [11,] 25320 25320 25320
#> [12,] 25320 25320 25320
#> [13,] 25320 25320 25320
#> [14,] 25320 25320 25320
#> [15,] 25320 25320 25320

#major diagonal checks out:
sum(magiccube.2np1(m)[matrix(1:n,n,3)])
#> [1] 25320

#now other diagonals:
b <- c(-1,1)
f <- function(dir,v){if(dir>0){return(v)}else{return(rev(v))}}
g <- function(jj){sum(magiccube.2np1(m)[sapply(jj,f,v=1:n)])}
apply(expand.grid(b,b,b),1,g)  #each diagonal twice, once per direction.
#> [1] 25320 25320 25320 25320 25320 25320 25320 25320