Panmagic squares of order 8

Produces each of a wide class of order 8 panmagic squares

Usage

panmagic.8(chosen = 1:6, vals = 2^(0:5))

Arguments

chosen

Which of the magic carpets are used in combination

vals

The values combined to produce the magic square. Choosing 0:5 gives a normal magic square.

References

https://www.grogono.com/magic/index.php

Author

Robin K. S. Hankin

Note

Not all choices for chosen give normal magic squares. There seems to be no clear pattern. See website in references for details.

See also

panmagic.4

Examples

is.panmagic(panmagic.8(chosen=2:7))
#> [1] TRUE
is.normal(panmagic.8(chosen=2:7))
#> [1] FALSE
is.normal(panmagic.8(chosen=c(1,2,3,6,7,8)))
#> [1] FALSE

#to see the twelve basis magic carpets, set argument 'chosen' to each
#integer from 1 to 12 in turn, with vals=1:

panmagic.8(chosen=1,vals=1)-1
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,]    1    1    0    0    1    1    0    0
#> [2,]    0    0    1    1    0    0    1    1
#> [3,]    1    1    0    0    1    1    0    0
#> [4,]    0    0    1    1    0    0    1    1
#> [5,]    0    0    1    1    0    0    1    1
#> [6,]    1    1    0    0    1    1    0    0
#> [7,]    0    0    1    1    0    0    1    1
#> [8,]    1    1    0    0    1    1    0    0
image(panmagic.8(chosen=12,vals=1))