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Something like going up to them and saying that they are a person that got most of my interest in the room, so I want to find out if their personality fits me. I think it shows confidence, gives girl a sign that you are interested while at the same time showing you do not care for looks and challenges them to earn you through what they are.
I think the bold statements contradict eachother, unless you have a valid reason to think the girl's interesting (if you heard her speak or saw her do something). Otherwise you'd still be walking up to her because of her looks.
Also, a fitting personality is such a broad concept that with any girl reasons can be found why your personalities don't fit. I think it's better to narrow it down to a specific attribute which you find interesting, and you can be direct about that.