That's a great plan. "Whoever wins is fine, it's going to improve our relationship either way."
Kind of ignorant to assume rich people are ignorant about money.
If the answer of "How could you know that?" can be as simple as, "He told me," then it's not really much of a stumper.
If someone tells you the "do anything" reward you suggest is too boring, you should know she wants to use it as an excuse to do more than she's normally comfortable with.
Oh, she just admitted outright she's blushing because she's charming. Wait, that means she's actually sick. Can't have something that straightforward in a romcom.