The Doctor takes Adric and a young air hostess named Tegan Jovanka, who has come aboard the TARDIS by accident, to the planet Logopolis, home of a race of mathematicians whose help he hopes to enlist in reconfiguring the outer shell of the TARDIS. The mysterious, wraith-like Watcher brings Nyssa from Traken to join them and warns of impending danger - something that is borne out as the Master arrives and kills a number of the Logopolitans.

The inhabitants of the planet Skonnos have been promised by an alien Nimon that he will restore their empire to greatness if they in return provide young sacrifices and radioactive hymetusite crystals, both of which they are obtaining from the nearby planet Aneth.

Joe Rotella creates a pop-up card inspired by Dr. Who and metallic colors. Gay Isber makes unique bangles with colored gemstones. Tori Weyers is back to "collect colors."