One of my favorite cartoons is Futurama. I happen to think the animation is fantastic. There is an episode where the professor builds a machine that allows to people to switch bodies. After the first switch he discovers there is a problem with his design. The problem is that once 2 people switch with another's body, you can't switch back. So he figures he would just use a third body as a temporary holding container but quickly realizes that two people will be left in the wrong bodies. The problem gets further complicated by several people switching bodies for various reasons. The professor is dumbfounded, so he enlists the help of aliens who happen to be math wizs (the Harlem Globe Trotters). One of the Globe Trotters quickly develops an algorithm to switch everyone back in the right bodies. I say two people will always be left out no matter how many people are involved. Is is true or not? If not true, what is the minimum number of people needed to make the switch?