I don't know. It does not sound like you are asking them to [Like] your page; just post their idea on your page. Others are going to [Like], or not, their ideas. (Which, I believe, exempts the contest because they will win on merit, not by lottery)
Also, anyone "can" post. Even if they don't have a computer, they can go down to the local library, get onto the library’s computers, set up an email, set up a Facebook account and post their idea. It may be a lot of work, but it is not giving you anything of value.
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God made the world in only 7 days... but he didn't have any paperwork.