BlueSpark wrote:I don't think so, although my reasoning was meant to apply only to the sudokus that are "magic" according to the original poster's definition (where the diagonals' content doesn't matter). 2/5/8 contains exactly one of the numbers 4, 5, and 6 and so would be included in the list of "usable" triplets. All bets are off with respect to my reasoning when applied to perfect magic sudokus!

What I could only say is your reasoning was just based on 1 of the 2 possible dimensions. From the start you've made the more obvious observation that for a 3x3 magic square (diagonals not considered) each row & column must contain 1 of {4,5,6}. What you failed to observe was each row & column must also contain 1 of {2,5,8} (check carefully if you don't believe me!!). In fact, each row & column must contain 1 from each of the 6 sets: {1,2,3},{4,5,6},{7,8,9},{1,4,7},{2,5,8},{3,6,9}. Just that {4,5,6} & {2,5,8} happen to sum to 15. So after you consider both dimensions only 6 sets could be remained!