Magic Squares with Magic "Subsquares"

Hello All,

I was reading in my text about how one can have a magic square within a magic square. It says that we can form a magic square M that appears in such form:

M = $\displaystyle \begin{pmatrix}

a & a & a & b & b & b & c & c & c\\

a & a & a & b & b & b & c & c & c\\

a & a & a & b & b & b & c & c & c\\

d & d & d & e & e & e & f & f & f\\

d & d & d & e & e & e & f & f & f\\

d & d & d & e & e & e & f & f & f\\

g & g & g & h & h & h & i & i & i\\

g & g & g & h & h & h & i & i & i\\

g & g & g & h & h & h & i & i & i

\end{pmatrix}$

where M itself is a magic square, but M can be broken into ninths and each ninth is also a magic square.

As an example, $\displaystyle \begin{pmatrix}

a & a & a\\

a & a & a\\

a & a & a

\end{pmatrix}$ is a magic square as well which exists inside of M.

Can anyone think of an example where this is the case (in 9x9) ?

This question I can answer

Starting off with:

8 1 6

3 5 7

4 9 2

where each row, column and diagonal sums to 15. Now replace the number 1 by the magic square we just started with, replace the number 2 by 2 times the 3 x 3 magic square we just started with, replace the number 3 by 3 times the 3 x 3 magic square we just started with all the way up to replacing the number 9 by 9 times the 3 x 3 magic square we started with. This completes the solution of your problem (I'm curious - which math class are you taking that gave you this problem?)

To mention there's another type of magic square (nested magic square) where peeling off each border leaves you with another magic square.