Diagonal sums are indeed the issue I overlooked.
Thanks!
#(#~ 15 = 2 {"1 +//.@|."2) (#~ 15 = 2 {"1 +//."2) mso3
8
Thanks again,
--
Raul
On Sat, Nov 7, 2020 at 6:51 AM 'Mike Day' via Chat <[email protected]> wrote:
>
> Without looking at the details, is it clear whether diagonal sums count or
> not?
> Sloane’s example has diagonals 258 & 654 which do both sum to 15, so I
> suspect they do!
>
> Cheers,
>
> Mike
>
> Sent from my iPad
>
> > On 7 Nov 2020, at 11:00, Raul Miller <[email protected]> wrote:
> >
> > A recent post involving magic squares got me thinking about the subject.
> >
> > There are 72 magic squares of order 3 (beware email induced line wrap):
> >
> > mso3=: (#~ 15 15 15 -:"1 +/"2)(#~ 15 15 15 -:"1 +/"1)3 3$"1(i.362880) A.
> > 1+i.9
> >
> > #mso3
> > 72
> >
> > Meanwhile, OEIS A006052 states that there's one magic square of order
> > 3, and that the others can be obtained through rotation and/or
> > reflection of that square. But there's 9 rotations (0 1 2 for each
> > dimension) and 4 reflections (no or yes for each dimension), which
> > only gives us 36 different squares which can be generated from a
> > single magic square.
> >
> > So it seems like it ought to be possible to find two magic squares of
> > order three which cannot be rotations or reflections of each other.
> >
> > And, indeed, if we swap the second and third row of an order 3 magic
> > square, we get a pair of squares which cannot be made equivalent
> > simply through rotations or reflections:
> >
> > 2{.mso3
> > 1 5 9
> > 6 7 2
> > 8 3 4
> >
> > 1 5 9
> > 8 3 4
> > 6 7 2
> >
> > But... before I go off and claim that an oeis entry is mistaken, I'd
> > like to make sure that I haven't overlooked something obvious about
> > that entry that I am overlooking.
> >
> > https://oeis.org/A006052
> >
> > Thoughts?
> >
> > Thanks,
> >
> > --
> > Raul
> > ----------------------------------------------------------------------
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