A personal relic

kw: artifacts, family history

I was ten when I learned that there are more than one kind of Magic Square. This one I constructed in 1958 has a reduced magic number of 16. The magic number for an order-4 square is normally 34. The standard magic number M_s is found from order N thus:

M_s = ½N(N² + 1)

This produces the series 1, 5, 15, 34, 65… A magic square with M <>s has a reduced magic number, and one with M > M_s has an augmented magic number. Only if M ≥ M_s can all the cells contain a unique number, and then only where N > 2. The only other requirement is that M ≥ N, though where M = N the result is trivial.

Of course I didn't know all that fifty years ago. I just knew that magic squares added up to a constant, both rows, columns and diagonals. When I showed this to a teacher, she was kind enough to thank me and ask if I knew how to make one with every number different. At age ten, I couldn't, but I found an answer in the encyclopedia.