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In case people hadn't realised, the square we're looking at is actually pandiagonal, so that all of the diagonals -- not just the two main ones -- have the magic property. Just pretend they wrap around the edges of the square.

thanks, gweilo. Took me some minutes to work out what you were getting at. What I see is that any three-figure diagonal works by adding the opposite corner to it ...

and two-figure diagonals add up with their opposite two-figures. Very clever - I wonder if it can work with other numbers? Is it a well-known phenomenon?

aha - https://cosmosmagazine.com/mathematics/how-solve-magic-square/

and the four corners!

Well, I've finally worked out the way to calculate the magic number, but at least one digit must be wrong. But I still haven't worked out how to parse 17D, although I know what it must be (and this is the problem with the magic number I think). Also, 22A seems pretty impenetrable. Is the Tolkien reference just three letters backwards, and does it start with a girl's name (not to say too much!)? Thanks.

OK. Got 22A. Sorry.

If something is very difficullt it could be described as a ???

promote is a reversal indicator for "teacher"

defn as for 11a

Thanks, Ixion. It hasn't clicked, but it might after a little thought. Either way, I am sure I can go with my original idea. Thanks again.

Pendragon, teacher isn’t miss but ???

That took much longer than it should have because apparently I can’t count through the alphabet!