Rory gives Professor Layton and Luke a couple of puzzles during the game whenever they are in Folsense. The first puzzle you will get from Rory is "Plaza Puzzle". The second puzzle that Rory gives them is the puzzle "Disappearing Act 3".
Rory's the youth you may have seen standing outside Folsense staition all day long. Though he seems like a slacker, he's just a guy who's been waiting outside the station for his girlfriend to return for a very long time.