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I've discovered a glitch in Lumiose City gym.
Disappointing because I'm 60 hours in.
When you answer all the questions you get an option to go to the 4th floor, well I went to the 1st floor, left the city and saved my game.
Upon returning to the gym, I can only go back to the first floor, I have no way of getting to Clement on the 4th floor.