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The Secret Chamber

Begin by inserting your left hand into a hole and your right hand into the hole immediately to its right, and flip the switches into the "up" position. Pull both hands out at the same time. If no secret chamber shows up, you know that there's at least one switch in the down position. Insert your hands into any two holes that are on opposite sides of the column and flip both switches up. If no chamber opens up, you now know EXACTLY one switch is in the down position (because you've flipped two adjacent and two opposites up, at most one switch could be still down, and the lack of a secret chamber means that it is down). Next, reach into any two opposite holes again. If you find a switch down, flip it up and your're done. But if both switches are up, flip one down. You'll see why in a moment. Now there are two switches up, and two switches down. Not only that, but both pairs are adjacent to each other, not opposite. After the column stops spinning, reach into two adjacent holes and flip both switches-- whether they're up or down. This will either open a secret chamber (if they were both the same) or leave the switches in a state where an up is opposite an up, and a down is opposite a down. The next step is obvious- inverting any two opposite switches guarantees that all four switches are in the same state, and there's the secret chamber.
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