You know those situations where you walk on to a train and you're the only person in the carriage, except for one, really hot girl. Well... maybe not! But this happened to me so I needed to come up with an opener for this situation, here's what I have; it should be pretty transferable to other situations too...

Walk up to where the girl is sitting and say "Hey, excuse me..." (she will probably have headphones in) "I know that the social etiquette of a train carriage dictates that I should pick an empty row and sit on my own, but since this is only going to be a short journey, I thought I would break the rules, come over, sit next to you and have a conversation."

From that point you've set a really nice frame where you can just start talking about whatever the fuck you want as it will just be regarded as a kooky way of starting up a conversation. Or if she does have the headphones how about, "what are you listening to?"

Any feedback?

Not field-tested yet but I will do when I get the opportunity.

Synergy.

I think there's a danger of her reaction being "what do you want, a medal?"

I think better to say "I hope you don't mind me sitting here but this was the only available seat"

Haha, surely she would have to be pretty cold to say that!

Haha I like yours though, I would struggle to hold back a laugh during the delivery!

Synergy.