This type of magic square is a close family to the
panmagic square.
Associative magic squares are also known as associated, regular, symmetric
and regmagic squares. Some order of magic squares can be
both associative and panmagic and some can only be one of the two. An associative
magic square occurs when two numbers, symmetrically opposite of one another
(square 1 and 25 for example) sum up to $$n^2 + 1$$. So n is in this case 5
(magic square to the order of 5), therefore 1 + 25 must equal to $$5^2$$ + 1 =
26. A 5x5 magic square has 48 different associative magic square
combinations. The smallest associative magic square is the
Lo Shu (3x3)
magic square.
