As far as that goes, the problem doesn't say anything about straight cuts. Even if you're restricted to two dimensions, and say a cut cannot cross itself, the first cut will yield two pieces, and the second can cross the first one any number of times.
So, I say the number of cuts is:
2^n - 1, 0 ≤ n ≤ 1
∞, n > 1
(n ∈ Z)

Posted by DJ on 2003-10-28 22:26:29