If you ate the vegetables you can still get into the room by finding hidden notes in the city that give you the number combo to open the door via talking to the book, I could never find the 3rd vegetable and I just ended up opening the door without the passwords.
If your lazy then...
What fun is it without trying to find it?
[spoiler]Are you sure?
[spoiler]Fine.
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This is of course the shielded door to the forbidden archives in the prancing seahorse we are talking about, because the key to Laniel's room is dropped from...