I have studied your list a bit further and found quite a number of omissions and duplicates
as well. In the end I decided to write a small computer program myself in order to find the complete list, and I have just succeeded doing so. As expected the conclusion was, that there are indeed all in all 880 unique solutions or 880 x 8 solutions if you count all rotations and reflexions. I made the program in such a way, that you can choose either and step through all the solutions displayed one by one.

Most of the solutions are not particularly interesting though. For instance I find those, where both the 2 x 2 subsquares at the corners and the subsquare at the center add up to the same sum as the rows, columns and two diagonals particularly pleasing. There are quite a number of those, around 350 unique ones I believe.

I have set of 100 integers organized in 10*10 table. Only the sums of two rows are different by +1 and -1 compared to the sum required for the magic square. Can you help me in checking if we can get with these numbers a magic square table?

Thanks

I have just studied your list further and can confirm, that your list is far from comprehensive and indeed also contain quite a number of duplications (i.e. solutions that can be derived through reflexion and/or rotation of other solutions on the list). I you are interested, I might myself have a look on your code :-)

Also, as several commenters have pointed out, it seems that my list is not comprehensive. I haven’t taken the time yet to look back at my old code and determine why this is so, but at some point, I certainly should do so.

Thanks to all of you for your comments, and especially to Søren for continuing to work on this puzzle. Even though I haven’t done any work on this myself in a long time, it’s still quite fun to think about. :)

By the way, I have found, that on your otherwise quite impresive complete list of 4×4 magic square solutions there are in fact repetitions (assuming of course, that magic squares, that can be derived from other magic squares by mirroring and rotation are only counted first time, they occur). At least I have found, that solution

#388: is in fact identical to solution #120:

14 1 8 11 7 6 10 11
15 4 5 10 12 9 5 8
3 16 9 6 13 16 4 1
2 13 12 7 2 3 15 14

1 14 13 4
12 6 7 9
8 10 11 5
13 3 2 16

Thanks,
Jhansi.

By perfect 4×4 magic squares I mean squeres where not only do both of the diagonals add up to 34, but so do the numbers in each of the small 2×2 squares at each of the corners, the central 2×2 square, and the sums of the 2 numbers in the middle of the top and the bottom row as well as the sums of the 2 numbers in the middle of the leftmost and rightmost columns.

By the way, I am thinking of writing a small book displaying all of these solution (not dwelving into theories and methods though because it is meant primarily for enjoyment. Do you think, that might have any interest?