I've found a simple closed form for the number of cuts required. I believe that
it extends easily to the n-dimensional problem, as well.
Chris Long, Mathematics Department, Rutgers University
Mozart needs food. Beethoven now has extra fight power. Bach is about to die.
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I'd have to say I doubt that most of the solutions submitted are actually correct. There are subtle cases if the number of layers that may be cut at once is large relative to the area of the fabric. If the area is sufficiently large relative to k, there's a simple formula that I've proven is correct.