Have you explored the whole level?
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×The green door passage in 1E leads to a dead end in 1S1E. Why might that be there?
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×It's a multi-pass room. Starting from the dead end allows you to bring all the powder kegs out into the main puzzle area.
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×In other words, first you have to kill the eye (dropping the green door), then go down the passage to the dead end and come back.
The trick to manipulating the Soulless:
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×This room is all about setting up multi-pushes. If you push a Soulless east (whether by stepping or rotation) and that Soulless has a staff and the staff strikes something (either a keg or another Soulless), then that something will also move east.
This allows you to make some pushes that would be impossible for Beethro to manage alone, since he's only allowed to have a spear (not a staff) in this room. For instance, Beethro cannot push anything from (13,7) to (14,7), because the only ways to move a spear onto (13,7) are a diagonal rotation (which would push towards (14,8) but that's blocked) or a step east while facing NE (which is a stab rather than a push with a spear).
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50th Skywatcher