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I want to do a contest on Facebook, and the qualifier will need the contestant to Like the page before he can participate. As it stands, I am unable to do that, because even those who haven't liked a fan page can comment on activities going on in the page.
How can I achieve this?
This is called Like-gating and is explicitly not allowed in any way, no workarounds.
See Platform Policy for more info https://developers.facebook.com/policy
