# hudson: Pandiagonal magic squares due to Hudson In magic: Create and Investigate Magic Squares

## Description

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

## Usage

 `1` ```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

`recurse`

## Examples

 ```1 2 3 4 5``` ```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))))) ```

### Example output

```Loading required package: abind
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11]
[1,]  112    3   15   27   39   51   63   75   87    99   100
[2,]   92  104  116    7   19   31   43   55   56    68    80
[3,]   72   84   96  108  120   11   12   24   36    48    60
[4,]   52   64   76   88   89  101  113    4   16    28    40
[5,]   32   44   45   57   69   81   93  105  117     8    20
[6,]    1   13   25   37   49   61   73   85   97   109   121
[7,]  102  114    5   17   29   41   53   65   77    78    90
[8,]   82   94  106  118    9   21   33   34   46    58    70
[9,]   62   74   86   98  110  111    2   14   26    38    50
[10,]   42   54   66   67   79   91  103  115    6    18    30
[11,]   22   23   35   47   59   71   83   95  107   119    10
[1] TRUE
[,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
[1,]   34   55   89  110  131  165   17   51   72    93   127   148     0
[2,]  154    6   27   61   82  116  137  158   23    44    65    99   120
[3,]   92  126  147   12   33   54   88  109  130   164    16    50    71
[4,]   43   77   98  119  153    5   26   60   81   115   136   157    22
[5,]  163   15   49   70   91  125  146   11   32    53    87   108   142
[6,]  114  135  156   21   42   76   97  118  152     4    38    59    80
[7,]   52   86  107  141  162   14   48   69  103   124   145    10    31
[8,]    3   37   58   79  113  134  168   20   41    75    96   117   151
[9,]  123  144    9   30   64   85  106  140  161    13    47    68   102
[10,]   74   95  129  150    2   36   57   78  112   133   167    19    40
[11,]   25   46   67  101  122  143    8   29   63    84   105   139   160
[12,]  132  166   18   39   73   94  128  149    1    35    56    90   111
[13,]   83  104  138  159   24   45   66  100  121   155     7    28    62
[1] TRUE
```

magic documentation built on Feb. 9, 2022, 1:07 a.m.