There are several strategies you can employ to get a date with a girl who is quiet and won't talk to you. 

1) Find out some of her interests. You might be able to locate some of her hobbies and interests on Facebook, LinkedIn, Instragram, and other social media sites.

2) Talk to any mutual acquaintances who know her and might be able to give you more information on her hobbies, likes, and dislikes.

Once you're aware of some of her interests you can approach her and strike up a conversation about things you know that interest her. For example, if you find out she is a fan a band that you also enjoy you might ask her about her favorite album and if the conversation goes well you could invite her to attend a concert with you and some other friends. 

However, you should also be careful not to force yourself on someone who doesn't want to talk to you. There are circumstances where people suffer from social anxiety so in those situations you may want to reach out in a less intrusive way such as on social media to introduce yourself. It's also important to be respectful and kind whether they agree to form a friendship or not.
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