At the one I went to (Jacksonville, November 2009), they did three cycles of contestants each in two days. I asked if I could go through the line and fill out another form if I didn't get called onstage in the first hour, and was told that I could. I finally got called onstage in the third hour.
If I remember correctly, the onstage Speed-Up game is five at a time, not three at a time.
Don't fret too much about trying to solve the puzzle. However, don't forget the basic things — most common letters and letter patterns, category, etc. Some of the puzzles have a local theme, so be prepared for something like NEYLAND STADIUM.
Another thing that helps is if you have something fun or unique about yourself. I played air guitar at my audition after I mentioned that I'm a musician. I'm told they like musicians, dancers, singers, etc. One thing to avoid is saying "I'm a big fan".
If you make it onstage, go home and wait for a letter from Sony. This is an invitation to a second round of auditions (usually held in a hotel meeting room or the like) that you have to pass before getting on.
Good luck, have fun and I hope you get on!