How Does Cutting a Torus with a Mobius Strip Alter Its Geometry?

[addedline8]

whats

 

[lavinia]

Consider the torus, a doughnut-shaped solid that is perfectly circular at each perpendicular cross section, and a Möbius strip, which has a single 180-degree twist and a uniform curvature throughout its length. Suppose a torus is sliced three times by a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions?
Note: Each of the Möbius strips is entirely confined to the interior of the torus.

I don't see the picture. Explain again.

 

[addedline8]

Sorry about that. Here is the attached picture. Thanks for responding.

 

[Jamma]

Are your knife cuts allowed to go over each other?

[Actually, looking at your note, they must be able to- if the strips are all in the interior of the torus then if they weren't you could never separate any pieces].

Are your Mobius strips a set size? (I don't quite understand what you mean by your note on the curvature- do you mean that you just twist the interval around the circle at a constant speed around the Mobius strip to make it, so that they are "uniform" in some sense?)