Mind Switcher Mind Switcher
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- Oh no! Is it possible to get everyone back to normal using four or more bodies?

- I'm not sure. I'm afraid we need to use... MATH.

"Futurama" - Season 6 Episode 10 - "The Prisoner of Benda"

Sophia's drones are simple robots which do dangerous work. Just in case one breaks, Sophia has a backup machine for these drones. This machine can copy a robots mind and has a secret and undocumented function. The backup machine can also operate as a mind switcher for robots.

Sophia forgot to turn off the machine and left the drones in the...

We have a log from the machine, of which drones minds were swapped. There is however one slight problem - no pair of bodies can swap minds more than once. However, with two additional bodies we can return the switching chaos back to a normal state of things. Nikola and Sophia have offered to help us ("nikola" and "sophia").

You are given an array with with information about the recent swaps. Each entry is a set with two names of robots (bodies). You can operate with bodies which were written in the journal and with two additional bodies - "nikola" and "sophia". Find the sequence of the swaps required to return all minds to their original bodies. The result should be represented as a list/tuple of sets with two names in each.

A journal as a tuple of sets. Each set contains two strings.

The sequence of actions as a list/tuple of sets. Each set contains two strings.

mind_switcher(({"scout", "super"},)) == ({"super", "nikola"}, {"sophia", "scout"},
                                         {"nikola", "scout"}, {"sophia", "super"},
                                         {"nikola", "sophia"})

    

The theorem from this mission is based on group theory. And group theory has application in cryptography, physics and chemistry.


0 < len(journal) ≤ 55
is correct.

Cohen, David (2010). Futurama volume 5 DVD episode 10 "The Prisoner of Benda" (DVD). 20th Century Fox.

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