Consecutive magic squares are magic squares that contain all numbers from
1 to $$n^2$$, where n is the order of the magic square. So, if $$n^2$$ was 49 (n=7), all integers 1 through 49 would have to
be in the magic square. Consecutive magic squares are more perfect than
non consecutive magic squares, as they are harder to create. Most
types of magic squares
are consecutive, as the goal of any magic square is to be as perfect as
possible. Non-consecutive magic squares are the opposite of consecutive
magic squares. These magic squares do not need to use all numbers 1
through $$n^2$$, they can use any values they like. However, even when being
non consecutive, these types of magic squares want to be as close as
possible to a consecutive magic square. Therefore, often only a few
integers from 1 through $$n^2$$ will be missing inside a non-consecutive magic
square. An example is an
order 4n+2 pandiagonal magic square.
