I once used this as an opener on facebook, "Hey, I know this is really random and you don't know me but I need some advice."
Girl: "Sure :)"
Me: Well my friend has been dating this girl for a few months, and she is really good friends with her ex-boyfriend. They hang out all the time and I think she is cheating with him. My friend really likes this girl but I feel like I should break them up before he gets hurt. What should I do?"
Girl: BLAH BLAH BLAH BLAH BLAH
..and then we got to know each other etc.
It was nothing special just a way to approach her without making things awkward, a week later I shot one down her throat, if you must know.
definitely a good opener. Girls always think they know how to solve problems... so asking them for advice always makes them feel important... or I find atleast