Futurama Theorem/Historical Note

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Historical Note on Futurama Theorem

This theorem was developed and proved by American comedian Kenneth Keeler for an episode of the television show Futurama titled The Prisoner of Benda [1].

In the episode, there exists a device which can switch any two peoples minds.

However, it is discovered that no two bodies can be switched more than once.

The question is asked:

Once a switch has happened, can all the minds be returned to their proper bodies?

In the episode, it is claimed that no matter how permuted a group becomes, all minds can be returned to their proper bodies with at most two additional individuals.