On Wed, 12 Nov 2003, Tom Conlin wrote:
>
> On Tue, 11 Nov 2003, Joel Neely wrote:
>
> >
> > Hi, Gregg,
> >
> > Gregg Irwin wrote:
> > >
> > > JN> The following 3-by-3 display is a simple magic square:
> > >
> > > JN> 0 8 4
> > > JN> 5 1 6
> > > JN> 7 3 2
> > >
> > > JN> because each row and each column sums to 12...
> > >
> > > No diagonals? I thought magic squares had to work on the diagonal as
> > > well? (not to be nit-picky or anything :)
> > >
> >
> > To be equally picky ;-)
> >
> > That's why I said "simple magic" square instead of "totally magic". I
> > was going to post a follow-up problem to refine the first program so
> > that it also checks diagonals.
> >
> > Also, not all sources I've looked at insist on diagonal operations. One
> > interesting way to generalize the problem is to "magic" rectangles with
> > different height and width. In that case, the definition of "diagonal"
> > becomes more interesting...
> >
> > -jn-
>
I did wake up in in the middle of the night remembering I had
only coverd a third of the cases. and it looks like I should not have
those dups in there ...
pprint b 3 ; normal
pprint flip b 3 3 ; about vertical axis
pprint reflect b 3 3 ; rotate left 90
flip b 3 3 ; back to normal
pprint reflect b 3 3 ; about backslash
b: head reverse b
pprint b 3 ; rotated 180 degrees
pprint flip b 3 3 ; about horizontal axis
pprint reflect b 3 3 ; rotate right 90
flip b 3 3 ; back to 180
pprint reflect b 3 3 ; about slash
but still have to handle the other 16 cases
> ok here is my first pass, Im sure there is cleanup to do
> have not done any benchmarking ... time for bed
>
>
> Rebol[
> title: "magic square generator"
> author: "Tom Conlin"
> date: 12-Nov-2003
> file: %itsawrap.r
> version: 0.0.2
> purpose: { Post from Joel Neely
>
> The following 3-by-3 display is a simple magic square:
>
> 0 8 4
> 5 1 6
> 7 3 2
>
> because each row and each column sums to 12. Write a function
> which uses the integers 0 thru 8 (once each!) to construct all
> possible 3-by-3 simple magic squares.
> Make it run as quickly as possible.
> }
> ]
>
>
> n: 3
> ns: n * n
>
> flip: func[b [series!] n[integer!]][ ; this one I like
> forskip b n[reverse/part b n]
> head b
> ]
>
> ; not so happy with this, I finaly brute forced it
> reflect: func [b [series!] n[integer!] /local t ][
> t: make block! n * n
> forskip b n[insert tail t pick b 1]
> repeat i n - 1[
> b: skip head b i
> forskip b n[insert tail t pick b 1]
> ]
> b: copy t
> ]
>
> pprint: func[b [series!] n[integer!]][
> loop n[print copy/part b n b: skip b n]
> b: head b print ""
> ]
>
> ;; to be general these should be made functions
> ;; but with non 0 array origin it makes messy modulo math
> ur: [8 9 7 2 3 1 5 6 4]
> dn: [4 5 6 7 8 9 1 2 3]
>
> s: t: 0
> for i 1 ns 1 [
> ms: copy [0 0 0 0 0 0 0 0 0]
> s: i
> poke ms s 1
> for j 2 ns 1[
> either equal? 0 pick ms t: pick ur s
> [poke ms s: t j]
> [poke ms s: pick dn s j]
> ]
> b: copy ms
> pprint b 3 ; normal
> pprint flip b 3 3 ; about vertical axis
> pprint reflect b 3 3 ; rotate left
> pprint flip b 3 3 ; about backslash
> b: head reverse copy ms
> pprint b 3 ; rotated 180 degrees
> pprint flip b 3 3 ; about horizontal axis
> pprint reflect b 3 3 ; rotate right
> pprint flip b 3 3 ; about slash
> print ""
> ]
> halt
>
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