Build a Facebook app - An interactive puzzle

We want a simple game, where we can ask people to fix a scrambled puzzle, once it is fixed it gives a message. We want to drive this on the Facebook and also embed it into our website. We want people to be able to invite five of their friends to play the game, who are not our fan on the page. We want also to be able to see a leader-board base on how fast people complete the puzzle. And every person can enter only once.