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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