Quality research material

• Stargate SG-1 S2E17 "Holiday"
• Futurama S6E10 "The Prisoner of Benda"

In both of these episodes, the characters are faced with a similar dilemma: a device is able to switch the minds/bodies of any two individuals, but it has the limitation of not being able to switch back any pair that had previously used the device together. As Sam says, the solution to get everybody back to normal in both episodes is to "play a little musical chairs".

While this meme implies that the Futurama episode came first, note that this Stargate episode aired in 1999 and this Futurama episode aired in 2010. But despite airing later, the Futurama episode is more famous due to the fact that the writers had actually published a mathematical proof regarding switching bodies without repeat switches. Notably, the characters in Stargate had essentially followed this proof without even knowing it. The big difference between the episodes (and really what prompted the need to come up with a proof in order to solve the problem in Futurama) is the fact that in Stargate, only four individuals were swapped (two pairs who had each swapped once), but in Futurama, there were seven individuals who had swapped amongst each other multiple times. With nearly twice as many initial swaps and all the interswapping between individuals who have swapped before, it was significantly more complicated to figure out how to swap everybody back in Futurama.

A full scientific paper on the subject: MIND SWITCHES IN FUTURAMA AND
STARGATE https://mathweb.ucsd.edu/~revans/starrev8.pdf