A better way would be having slightly more tricky questions, say, 15 of them, and the first person to PM you the complete list of correct answers wins. If you do this once a day at the same time, for example, it cuts down on luck for who refreshes, and who can type the fastest. In addition, it cuts down on what appears like spam and provokes more discussion. Add in the fact that the same person is winning every question and it goes to show this fact, really. It's simply unfair.
Just a thought. It's what I did with the gamrChat and it went quite well.