I'm completely stumped as to how to get the star in 7,20. I've got here (which gets me to 7,21's star) but I can't figure out how to get to the hallway. I feel I should somehow be able to push my way up through the splitter on the top right of the room below, but I can't make it work. Any hints?
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You can access 7,20 through either "hole" in the top wall of 7,21. The right hole gets you the star in 7,20 and the left hole helps you get to the star in 7,21.
If the timing is right (which is why MetaMetaPuzzle said you have to "waste" a move), you can push a dead cat through the splitter that would otherwise destroy it. If you've reached 12,13, the mechanic is demonstrated there.