Ok, this is hard to describe, but on the antidote puzzle, look for the pieces which don't have connections sticking out all sides. If it doesn't have anything on the bottom right for instance, then you can't have a piece to the right which would have any piece to its bottom left...
x o--o
/ this won't work
* o--o
/ \ this might
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 "Titan Station"){kind=icon}
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