Having answered all the questions in Game 1 of the June 2007 LSAT, a couple final notes: 1) There's no scratch paper allowed on the LSAT, so you must write on your test pages in order to solve the games. Here's what my test page for Game 1 looked like when I got done with it:
2) I call the approach I took here "Making Worlds," for lack of a better term. This is extremely powerful when applied at the right time, and Game 1 was perfect for such an attack. But when applied at the wrong time, or in the wrong way, this approach can be a colossal waste of time. So before I make Worlds, I look for two criteria: First, I want a limited number of Worlds--preferably just two of them. Second, I want to be able to fill out some stuff, with certainty, in at least one and preferably all Worlds.
Here, in Game #2, I had a perfect opportunity to make only two Worlds which were mutually exclusive (there was no overlap between the two) and encompassed all possibilities (there were no missing ways to complete the product code--any acceptable code had to fit into one of the two Worlds). And in both of my two Worlds, I knew exactly what the first and second digits were--with further soft inferences about the possibilities for the third and fifth spots. So it was a green light to make two Worlds, and I ended up crushing this game.
3) I think this is a terrific game to study. It's a very common task--putting things in order--and the question types are very manageable/learnable. If games are bothering you, THIS is the game to try to master. Before you can tackle tougher games, you certainly need to understand relatively simple games like this one.
See my class schedule for more opportunities to learn about Logic Games--including my Logic Games Boot Camps. And check out my book Cheating the LSAT on either CreateSpace.com or Amazon.com for a dissection of an entire recent test, including the Games.