After saving Agate City from Team Meteor, you gain access to a house next to the Pokemon center. Sarena will ask you use the Meteor ID card to a location where it can be used. Head to the alley leading to the Meteor base in the North Obsidia Ward near the Spyce restaurant. Once you use the ID. the doors will open leading you to a magic square puzzle. THIS HAS MULTIPLE solutions.the code will appear as white colors from left to right.
Rewards for completing the puzzle initially: TM 24 Thunderbolt, Gardevoirite, Darkinium-Z.
Rewards for when you go to Sarena again with the code: Manectite and Department store sticker (this should be the sticker leading to the 11th floor by this point in the game)
After completing the application quest for the Aqua Gang or the Magma Gang, you will find a person related to one of the leaders in one of the buildings. They will trade you the Pokemon you didn’t get from the application quest. If you pick the Aqua Gang, they will trade you an Oshawott for a Ledian. If you pick the Magma Gang, they will trade you a Litten for a Stantler.
The Pokedex Quest
In the building south-west of the city, you will meet a lady named Bee who wants to see the Pokemon you have caught in your Pokedex. She will give various rewards for how many Pokemon you have caught: