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 > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
