Well, if you want specific hints on this puzzle:
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×On the way in, go to the right first and take the first crack on your left
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× you'll go down, around the corner and up at the first crack on your right. From there, it should be pretty clear where to go but...
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×enter the queen room from the right side.
Getting out I thought was a bit easier to see, but I think went out of the bottom of the room
As for general ways to solve these puzzles, I start by trying to guess the solution, and if that doesn't work, I find a systematic way to examine all my possibilities.
Also, wherever possible, step diagonally (since you don't have to clear all the trapdoors and you don't want to have your way blocked because you took an unnecessary step somewhere early).
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