Consider a book having one page and front and back covers, all joined along a common spine. Is it possible to cut a Moebius strip out of such a one-page book? (Of course, you can use only a scissors and the given book -- no additional tape.)
More precisely: Take three sheets of paper and attach them along one of their edges to a common spine. Thus they form a book with a cover and one page. Can you cut a Moebius strip out of this topological object?