Fwd: 6-variable solve



I saw a puzzle posted recently
(http://www.boingboing.net/popscipuzzles1960.jpg), and wanted to try
to use maxima to solve it.

I boiled it down to: there are 2 sets of 3 integers each (a, b, c, and
d, e, f) where each set has a product of 225, and the sums of the sets
are equal.

I tried:

declare(a, INTEGER)$ declare(b, INTEGER)$ declare(c, INTEGER)$
declare(d, INTEGER)$ declare(e, INTEGER)$ declare(f, INTEGER)$
assume(a>0,b>0,c>0,d>0,e>0,f>0)$ solve([a*b*c=225, d*e*f=225,
a+b+c=d+e+f], [a,b,c,d,e,f]);

but I get:

ALGSYS cannot solve - system too complicated.
 -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);

I went ahead and worked it out by hand, but now I really want to help
maxima figure it out too.

Any suggestions?

Thanks,
Ben