Brainquarters were the living areas for the Kangs of Paradise Towers. Each faction had a brainquarter. In their competitive games, one objective was to break into another's brainquarters.
The Seventh Doctor fell down a hole into the Red Kangs' brainquarters while fleeing from some cleaners. The fall knocked him unconscious and when he woke, he warned Bin Liner about the cleaners. Fearful they were nearby, she went to check the area. The brainquarters was equipped with a telephone which the Doctor attempted to use. He found it out of service but it was on the side of a Fizzade vending machine which he used, much to the Kangs' amazement. They then all began drinking Fizzade and sat down to watch an information video on Kroagnon — the architect of Paradise Towers.
When the caretakers began breaking down the door, an alarm sounded, alerting the Red Kangs of the attack. Bin Liner used the base's periscope to view the threat and the Doctor allowed himself to be captured to allow the Kangs time to escape. After his rescue, he returned with the Kangs to the brainquarters and began plotting against Kroagnon. The Blue Kangs broke in and claimed to have won the game, but the Doctor convinced them to work together against Kroagnon.
Sometime later, when they had formulated their plan, the Kangs began setting traps in their brainquarters in anticipation of Kroagnon's arrival. These never came into effect. Kroagnon was killed when Pex took himself, a stick of explosive and the architect down a lift shaft. (TV: Paradise Towers)