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You are given two potatoes. You want to make a finite loop of wire so that you can put it on either of them at some location at your choice, so that there are no gaps between the potato and the wire. You can't deform the loop after you have created it.

Is it possible to make such a loop for any two potatoes?

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Yes, such a loop of wire can be made for any two potatoes:

Just consider the potatoes as abstract geometric objects in three-dimensional space. Take these two objects, push them towards each other, let them collide, keep pushing, keep pushing, and make their surfaces intersect. The intersection of the surfaces will contain a closed curve. Now design your loop of wire to match this closed curve.

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