Solution: Möbius Mysteries

In order to understand what is happening with the two strips of paper, it is important to examine how they are taped together. Before the two strips are twisted and taped together, they are placed one on top of the other. Each strip in the beginning configuration has a left and right end. (It might help to label these ends beforehand: TL, TR, BL, & BR..) When the strips are given a half twist and their ends joined, the right end of the top strip ends up being taped to the left end of the bottom strip. Likewise, the left end of the top strip ends up being taped to the right end of the bottom strip. In this way the finished product appears to be two separate Möbius loops nested within each other when in actuality they form one large loop with two half twists. This means that when the pencil is inserted between the two pieces of paper, it must travel twice around the loop to return to its original orientation.

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