This may sound impossible though it most definitely is not. There are a few criteria that your account must meet in order for this system to work.
1. You must be female and have a beautiful profile picture.
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2. Your account must have some activity on it showing that you are a real person
If your facebook account meets the 2 points above then you are ready to use this method of getting friends on facebook without sending friends requests.
First of all you want to get a few friends requests in order to get your account out there to the people. Join a few add me groups and post your facebook url in the groups when your join request is accepted.
This will get you a few hundred friends requests. As the requests start to come in you will need to scan through the people who add you and look at the amount of friends they have. Only accept requests from people with over 1000 friends. The reason for this is simple. Your account will appear as someone that their friends may know. So that means the more friends your friends have the more friends you get.
It is also a good idea to turn on the follow option so that anyone can follow you. What this means is that people how send you friends requests that you do not accept will automatically become your followers.