I assume you mean 13,20 into 13,21 but that's as far as I can help. I'm stuck there too.
When you say you're stuck there, you mean you can't get to 13,21 or you can't beat 13,21? And if you're stuck getting to it are you sure you have the room numbers right? Because 13,21 isn't accessible from 13,20. If you can clarify a bit what your problem is, I probably have a hint (if MetaMetaPuzzle doesn't beat me too it ;) )
You will definitely need two cats at some point during 13,21, but not before you get to the splitter that has both ends open. I assume then that you're stuck because you can't get your cat up past the first medusa?
You can't go into 13,21 and just start running it, that won't work. There's a little bit of setup to do back and forth between 12,21 and 13,21 relating to to exactly how room transitions behave. (although I suppose it's possible there's a way to get two cats in that I never figured out, and that's actually the "right" way to do it. It's sometimes hard to figure out what's a game mechanic and what's a bug, with how creative the puzzles are 😅)
To enter the room, you'll need to back into the room on the bottom space. Then you can use the splitter to move up one space while still facing away from the first medusa. Normally you can't step backwards - but the room transition allows it.
Beating the level takes advantage of three game mechanics:
- Action order in a turn seems to be: Move -> Reduce move counter (and kill cats if out of moves) -> trigger conveyors -> trigger splitters -> trigger medusas, with any cat on a flag after any action triggering the flag.
- Splitting doesn't change direction
- Dead cats don't get stoned
More specifically, you'll need to move the flag into a position where you can get one dead and one live cat, then revive and sacrifice the dead cat to revive the final cat.