A magic series is a set of numbers which potentially makes up a line in a magic square, adding up to its magic constant.

So in an n×n magic square using the numbers from 1 to n², a magic series is a set of n distinct numbers adding up to n(n²+1)/2. For n=2, there are just two magic series, 1+4 and 2+3, and there is no magic square. The eight magic series when n=3 all appear in rows, columns and diagonals of a 3×3 magic square.

M. Kraitchik gave the numbers of magic series up to n=7 in Mathematical Recreations in 1942 . In 2002, Henry Bottomley extended this up to n=36 and independently Walter Trump up to n=32. In 2005, Trump extended this to n=54 (over 2×10¹¹¹), while Bottomley gave an experimental approximation for the numbers of magic series:

External link

• Walter Trump's pages on magic series