Sorry to say this but this is against facebook rules.
"Competitions can’t use a Facebook mechanic
This really does restrict you further, but the guidelines state that you can’t use a native Facebook action to facilitate entry to a competition. I.e. you can’t ask someone to like a page, upload a photo/video, comment on a post, promote a post to friends. If you want to run a competition that involves one of these, such as entering a photo, then this has to be administered through a third party application."
So a "like-competition" isn't allowed.