[From Thinking Mathematically, p. 67. Modified by Sam Rebelsky.]
A very heavy armchair needs to be moved. It is sufficiently heavy that it is only possible to move it by rotating it ninety degrees about one of its corners. Can it be moved so that it is exactly beside its starting position (i.e., that the left front leg is where the right front leg was and the left rear leg is where the right rear leg was) and facing the same way? If so, describe how. If not, suggest why not.