You rematch. Mathematically, not physically! There isn't' "one more", all finite differences between infinite sets are equivalent to each other, including zero.

Ponder this if you will: how did the hotel get full in the first place? if you assume that is possible, then you can reverse the original room assignments, and reassign rooms.

The source of your confusion is that you trusted the problem is even possible to set up, without availing yourself of the power that the setup implies.

The mixing of the possible with the impossible is certainly jarring.