In an episode of the cartoon, a machine lets characters swap bodies, but they can’t switch back with the same person. At the very end, you swap out xwith i + 1 and y with 1: (1, x) (2, x) (3, x) ... (i, x) × (i + 1, y) (i + 2, y) ... (n, y) × (i + 1, x) × (1, y). Expressing their false composition abstractly by (2, 1), we get the following set with Clyde (x) and Tate (y): (2, 1, x, y). Thus, according to Keeler’s approach, the following permutations are necessary: (1, x), (2, y), (2, x) and (1, y). Performing them one after the other, the set changes as follows: (2, x, 1, y), (y, x, 1, 2), (y, 2, 1, x), (1, 2, y, x).