So I'll start obvious: You need to get the queen to go out the top of her corridor, which means that you need to get below her while she's in the main corridor.
However,
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×the only place to do that
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×(SW corner)
will push her back into the side corridor, so you need a way to get her out, and then
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×block off that side entrance
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×the button that is protected by a trapdoor will close the door into that corridor
So, if the queen is in the side corridor, you need to be able to:
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open the side corridor
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×N Central Orb
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drive the queen E and then S
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and then be able to get back around to the trapdoor-orb, and the SE corner of the board.
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×use the trapdoor path since the direct route at the N end of the board will be blocked off
Here's a step-by-step:
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From the start, go straight north, hit the N Central orb and get the queen into the side coridor, then close the door (hit N Central Orb while standing on North yellow door)
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Hit the West-most orb to open the trap-door orb.
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You should be able to walk all the way back around to the N-central orb. Hitting NCO will open the queen's corridor, and close off the passage to the NE orb.
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Walk over to the W to move the queen out of her corridor, then move quickly back to the E so that the queen doesn't get trapped in the East corridors.
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Now that the queen is at the S end of the long corridor, use the trapdoor route at the N end of the room to get around to the trap-door orb which will close the W corridor.
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Continue to the SE corner to drive the queen north and out of the long corridor.
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