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You have three rooms to find:

8,11: double teleport from 8,16. Spawn an extra kitten using the flag at the entrance.

6,10: you get there through a wormhole in 8,15, which you access from 8,20. Create an extra kitten there and use it to reach the two lower wormholes. You'll need at least three.

15,8: MetaMetaPuzzle posted a hint below.

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.

I don't think there's any room built into the game proper that allows you to get to 4,4. My hint is that you'll have to figure out how to make it yourself.

Got it, thanks!

Now to figure out how to get to 13,13.

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?