While still inside the Infinite Hotel, the Hotel Girl and I kept playing her game. The strategy to win it was quite simple, first I complimented her at every turn.
Miwen: "I'd say the cookies of the Infinite Hotel are the best in the universe..."
Hotel Girl: "That's correct! You earn a bazillion points!"
Miwen: "The rooms are all neatly decorated, and the receptionist is beautiful too, I want to come every weekend!"
Hotel Girl: "I'll double your points if you go into detail about how much you like me!"
With the points I was getting, I could ask any question... theoretically. But there were a few that she refused to answer no matter how many points I acquired.