You can't follow the instructions from the blue dragon secretary lady, she's trying to get you lost in the library. I kind of just guessed randomly in each room. If you end up back in the room with the book on the bottom left table and nothing on the bottom right table, you're back at the beginning. Otherwise, keep track of which door you go through and when.
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Well, kind of. The rooms don't change. If you follow the same path each time and just change which door you go through in the furthest room you make it before being sent back to the beginning, you'll eventually make it through. It's not that many rooms and it's not that many doors, so it won't take ages.