In the episode, Professor Farnsworth and Amy build a machine that allows them to switch minds so that they may each pursue their lifelong dreams.
The episode was written by Ken Keeler and directed by Stephen Sandoval and was met with acclaim from critics.
The title and the story's main subplot is a reference to the 1894 adventure novel The Prisoner of Zenda by English novelist Anthony Hope.
Likewise, Amy longs for her younger days of constantly eating and wishes to use the Professor's skinny body to gorge herself with food for a while.
Washbucket, now in Amy's body, professes her love to Scruffy, and even suggests they run away together, but he sadly turns her away, reminding her that he is still a man and she is janitorial equipment.
Back on the yacht, Nikolai's cousin and fiancee reveal to Bender that they have been having an affair, and are planning to kill him and blame the burglar.
Finally, two Globetrotters, Ethan "Bubblegum" Tate and "Sweet" Clyde Dixon, mathematically prove that everyone's minds can be restored using two additional bodies.
For any i ∈ {1 ... k} let σ be the permutation obtained as the (left to right) composition: Note that these are distinct transpositions, each of which exchanges an element of [n] with one of x,y.
The episode's title and the Robo-Hungarian emperor subplot are references to the 1894 adventure novel The Prisoner of Zenda, in which a king is replaced by a commoner, by English novelist Anthony Hope.
Handlen compared the episode favorably to the season 4 episode "The Farnsworth Parabox", writing, "Really, this is pure silly from beginning to end, using the show's internal logic to arrive in unpredictable places, and bringing to life a piece of fan fiction I doubt anyone has ever had the courage to write.
Merrill Barr of Film School Rejects also gave the episode a positive review, praising the character development of Scruffy the Janitor in particular.
With respect to the logic puzzle nature of the plot,[8] Barr stated, "I have never understood less of what was going on in a single episode of Futurama.
[9] He praised the intricate plot and writing, also comparing it to "The Farnsworth Parabox" and "Teenage Mutant Leela's Hurdles", writing, "...this sort of intertwined, Altman-esque plot offers up a level of complexity rarely offered by sitcoms, or any episodic television.
'The Prisoner of Benda' was a perfect example of how Futurama takes an extremely simple concept and executes it in a daring and unique way.
It's not as showy as 'A Clockwork Origin' or 'The Late Philip J. Fry' from an animation standpoint, but with writing this tight we could be watching stick figures at 8 frames a second and it would still be worth seeing.
The high-concept idea of switching minds/bodies was taking [sic] to extremes and delivered fantastic lines and great laughs throughout.
'The Prisoner of Benda' easily could have stretched out to a 70-minute DVD movie, but I'm just as happy to see it as 22 minutes of finely concentrated crazy.