Inlaid magic squares are magic squares inside of another magic square. For
example, an order 8 magic square might have 4 order 4 magic squares inside
of it. These magic squares inside of other magic squares can also be
different types of magic squares. For instance,
semimagic,
magic and
pandiagonal squares. They can also have borders, through which order 13 magic squares can
have an order 9 magic square inside it that also has 9 order 3 magic
squares inside of it. They do not even have to have squares inside of
them; they can also have other shapes such as diamonds. In the case of
inlaid diamonds, the sides of the diamonds (diagonals in the square) sum
to a magic constant. For example the order 7 inlaid magic square on the
right has a magic constant of 175, however the column, row and diagonals
of the order 4 magic diamond have a magic constant of 100 and those of the
order 3 inlaid diamond 75.
