Rich announces: << Congratulations to Christian Boyer and Walter Trump, who have found a magic cube of size 5!

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That's really cool! (I hadn't even knownrealized this question was unsolved.) I can't help wondering about whether there is such a thing as a "magic torus" T with maximum magicity. Meaning: Viewing T as the group (Z_k)^n, consider all "affine lines" of the form L = { v + j*w | v,w are in T, and 0 <= j < k } such that card(L) = k. QUESTION: For which (k,n) does there exist an assignment of 1,2,...,k^n to the points of (Z_k)^n such that *every* affine line has the same sum? Or less generally, what is known about this question? --Dan