Fun games for Facebook fandom fan pages?

[Sara]

I started a Percy Jackson fan page a little under a month ago, and it now has almost 700 likes. The fans like playing games, so I sometimes do a blind elimination game, email game, chain photo spam game, etc.
I need some more ideas for games though. Any fun ones that you have heard of or played before? What are the rules for the games?
What would be a fun way to have admin games? Games for the admins. Like maybe a hunger games sort of thing where only one admin wins... But this is a PJO fan page. An admin game where the fans vote on the winner? Or the fans run the contest?
I need ideas!
Thank you.