Hmm, could there possible be a trick to this question? Like, if you worded it correctly in your first post, I'm going along with the logic of so:
In 1v1 you can't hit EVERY Pokemon because you're only versing one opponent. Thus in order for this riddle to be possible the opponent you're facing must be EVERY Pokemon, so either:
1. You're facing a Pokemon that can Transform into any Pokemon (Ditto or Mew).
2. If you were to combine ALL the types together, you'll get a Pokemon who's only weak to Rock-type (and the move Freeze-Dry).
As for why they limit you to 3 moves, it's meant to throw you off (or to assure there wasn't any other possible answer).
Now I could just be overthinking this, but to me this sounds like there's a curve ball coming because whoever came up with this question must have an answer and if there's a legitimate answer they would have to have spent a long time figuring it out and making sure no other Pokemon can stop it (because just one Pokemon that stops it means that the riddle is faulty).