The puzzle in the tower require the player to move two stones to a spotlight. However, the player can only move one of the stones, with the other stone mirroring its movement. Use the obstacles to manipulate the other stones movement. The tower is completed after solving 6 of the puzzle rooms.
If the player completes the puzzles in the tower and go through the exits, they will end up outside the tower (this is however the fake exit) head down the desert to enter the Chosen Room that rewards the player a Normalium-Z, TM Will-O-Wisp, and a Honedge. Approach the Honedge by the top to obtain it. Also, in the fake exit, the player has a chance to encounter a Phione using a super rod in the ponds.
When you first enter the tower, use rock smash on the mirrors (like in Serra’s gym) until you find one you can enter. This will let you access the tower basement which has various pokemon. Its dark so use Flash for better navigation. At the end of the basement, you can find a Mimikyu and a Poison Memory.
According to Taka, the Mirage Tower was created by the Arceus-believing ancestors of Reborn City and was made to serve as a training ground to fight Giratina, whom was reponsible for many distortions in the city.
Climbing the top of the tower was then used as a tradition to serve as a reminder of their victory, with Honedge sitted atop representing the weapon used to defeat Giratina.