Problem

Imagine three shapes or make them out of three paper strips. The first shape is a band, the second one is a Mobius strip, and the third shape is a double-twisted Mobius strip. Here is how to make these shapes out of paper strips. Tape (or glue, or staple) two ends of the first strip to make a band. Twist one end of the second strip and then glue both ends together. This shape is called Mobius strip after its inventor. Note that Mobius strip has only one side and one edge. Look at the image above. Twist one end of the third strip twice and then glue both ends together. This double-twisted strip is also called Mobius strip, but this one has two sides.

Now imagine what happens when you cut these shapes lengthwise. First, guess what you get when cutting each band in half lengthwise. Second, imagine what happens when you cut Mobius strips lengthwise in thirds. Alternatively, you can draw a line along every band and then cut it by the line. After that, you can draw two lines and cut the bands into thirds.

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