Given any two potatoes (let's keep them regular, though), is it always possible to draw a pair of closed congruent curves, one on each?

Question

andriod09 · Answer

Yes and no. Yes because some of the potatoes will be smooth, flat, things like that, and then others, could be bumpy, or a part of the potato could be bent (the way its grown)

zugzwang · Answer

ehhh... not quite...  
Besides, the question was is it *always* possible, so it must be either a yes or no, and since you said "sometimes", well, that's not always, so your answer is no.

zugzwang · Answer

Oh well... imagine the potatoes could just go right through each other... they would intersect at a closed curve...  so yeah, it is always possible to draw the pair of congruent curves..