The Futurama Mind-Switching Explained!S

Here's the progression of each mind through the various bodies in "The Prisoner of Benda":

The Professor —> Amy —> Bender —> Bubblegum Tate —> The Professor
Amy —> The Professor —> Leela —> Hermes —> Sweet Clyde —> Amy
Bender —> Amy —> Wash Bucket —> The Emperor —> Bubblegum Tate —> Bender
Leela —> The Professor —> Sweet Clyde —> Leela
Fry —> Dr. Zoidberg —> Bubblegum Tate —> Fry
Dr. Zoidberg —> Fry —> Sweet Clyde —> Dr. Zoidberg
The Emperor —> Wash Bucket —> Bubblegum Tate —> The Emperor
Wash Bucket —> Amy —> Sweet Clyde —> Wash Bucket
Hermes —> Leela —> Sweet Clyde —> Hermes
Sweet Clyde —> Fry —> Bubblegum Tate —> Wash Bucket —> Sweet Clyde
Bubblegum Tate —> Dr. Zoidberg —> Sweet Clyde —> The Professor —> Bubblegum Tate