Michael Kleber's latest brilliant analysis of Christian's new multiplicative magic square -- in terms of bit planes -- is quite reminiscent of (what I think it) Conway & Coxeter's analysis of additive magic squares as it appears in (some of) the most recent edition(s) of W.W. Rouse Ball's "Mathematical Recreations and Essays" (updated by Coxeter). Let N := the set of nonnegative integers. Then {additive magic squares of elements of N^k for some k} is in 1-1 correspondence with {multiplicative magic squares} -- just letting the components of v in N^k correspond to prime exponents. I was wondering if there could be a multiplicative magic square that was somehow not a consequence of additive ones . . . but now I see that's impossible. --Dan