I don't want to spoil how many cats there are, but if your cat counter has too many cats, the ending the won't trigger. There is one cat that doesn't disappear once found, so talking to it again after leaving the room and coming back will make it impossible to finish the game. (Conversely, you can win the game using only this cat by talking to it once for all the cats there are.)
Cute game, and solid graphical aesthetic. I like the push B button UI and the tiny (rather than 8x8) font that's used in some places.