The room Alex entered on the 13th floor was one where a massive formation diagram hovered in the air. There was a simple description of the formation to the side, and the challenge was to figure out what was wrong with either the design or the description.
Alex got lucky with not many there having any knowledge about formations, so he managed to answer the 2nd one correctly and moved up a floor.
On the 14th floor, he waited for his turn and entered a room where the challenge was dueled between two people randomly chosen by the room. To Alex's surprise, half of the 20 people that entered this room were allowed to go up.
Depending on the lottery, some of them could move up without having to break a sweat. Unfortunately for Alex, he wasn't so lucky.
His opponent was a 2-meter-tall woman with a Saint Core cultivation base. Unlike many others before him, he couldn't just swing an arm and be done with the fight.