No such thing as a small change  
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tilly,
Yes, this is exactly what I was guessing at. There are also constraints as to what x, y and z can be within the confines of this puzzle. I didn't have a chance last night to work on this though because the following entered my mind as I was leaving work
I haven't convinced myself that you don't need to iterate over other series of equations. Still thinking on it though. Update: In fact, I think I can show that your statement "By rotating and reflecting we can make the largest corner be x+y" is not in fact true  consider the following square: You have X+Y and X+Z both in a corner so you need to make a relationship between them to determine which is the largest value. Also, I noticed that I showed it is possible to have X+Y+Z in a corner and am now convinced that multiple series of equations must be iterated (though you can reuse the values for X, Y and Z). Cheers  L~R In reply to Re^4: magic squares
by Limbic~Region

