June 2007 LSAT, Game 2 Setup

Game 2 of the June 2007 LSAT is a bit different, and a bit more complicated, than Game 1. In that game, all we had to do was put five digits in order. Here, we have to select which things are going to be chosen AND put them in order. It's not an impossible game, but it's definitely a step up in complexity. In Game 1, the digits 0-4 were each used exactly once. Here, the films G, H, and L are all going to be shown at least once during a three-day festival, and no more than once on any given day. In other words, every film must be shown 1, 2, or 3 times, and can never be shown twice on any one day. Furthermore, we have to show at least one film every day. All of these rules are hidden in the introductory paragraph of the game. Make sure you don't ignore them.

My basic setup will look like this:

Thursday:

Friday:

Saturday:

I'll fill in the films as horizontal lists, from earliest to latest, for each day. I'm doing it this way simply because it seems the most natural to me. If I were creating a film festival calendar in real life, it might look something like this. So that's how I'll do it on the LSAT as well. Your calendar might look different, and that's perfectly fine. I'm improvising a solution that makes sense to me. That's always the first step.

The rules:

Rule 1)  This is a two-part rule:  First, Harvest has to be shown on Thursday.  Second, Harvest has to be the last film shown on Thursday. I can put that into my calendar like this:

Thursday:                                                             H |

Friday:

Saturday:

Here, I'm using the | to denote that nothing else can come after the H on Thursday. (Because H has to be last on Thursday). I'm sure there are other ways of doing this, but this will work for me.

Rule 2)  This is a three-part rule:  First, G or L has to be shown on Friday. Second, G and L can't both be shown on Friday. Third, G or L has to be the last film shown on Friday. I'll add that to my diagram, like this:

Thursday:                                                             H   |

Friday:                                                             G/L     | (not both G&L)

Saturday:

Is it perfect? I don't know, maybe not. But it's rarely going to be perfect. The games are highly improvisational, and I think it's a huge mistake to think that you can simply memorize all the different "types" of games and then force every game you encounter on the test into one of your templates. If you do that, you're going to be trying to jam square pegs into round holes. Far better, in my view, to learn a set of skills and then practice improvising solutions using those skills. We're adding tools to your toolbelt, so that you can cobble together a solution to whatever you might face on test day.

Rule 3)  Another three-part rule, just like Rule 2. First, either G or H must be shown on Saturday. Second, G and H can't both be shown on Saturday. Third, G or H must be the last film shown on Saturday. I'll add that to my diagram, like this:

Thursday:                                                            H   |

Friday:                                                             G/L    | (not both G&L)

Saturday:                                                         G/H   | (not both G&H)

Okay. Let's take a step back and think about where we're at. My thoughts, in the order they come to me:

  • H has already been used, (on Thursday) so we don't have to use it again (although we certainly can). G and L still both need to be used at least once.
  • There will be no problem making sure we have at least one film every day, since the rules gave us a film for Thursday and a choice for the last film for both Friday and Saturday. We're never going to have to worry about accidentally putting zero films on any day.
  • The only day on which L can be the final film is Friday.
  • H can be last on both Thursday and Saturday.
  • G can be last on Friday and Saturday.
  • Any film can be first on any day, although if H is first on Thursday, it's also the only film shown on Thursday.  Similarly, if G or L is first on Friday, it's also the only film shown on Friday. Similarly, if G or H is first on Saturday, it's also the only film shown on Saturday.
  • Every film can be shown on every day.
  • Every film can be shown on all three days consecutively.
  • But it's not possible to show BOTH G and L on all three days simultaneously, or BOTH G and H on all three days simultaneously, because of Rules 2 and 3.

Okay. What I'm doing here is just considering the landscape of the game, and all the rules that apply to the game, in the context of one another. I was hoping that some big inferences were going to appear, but they're really not happening. That's fine. As it turns out, there's a lot of flexibility in this game. I've practiced enough on the games to know that you can't always make big inferences. This seems to be that type of game, soI'm just going to have to go on to the questions and see what happens.

A note about "worlds":  On Game 1, I ended up realizing that there were only two basic templates that would account for all possible outcomes for the game. The code had to start either 1-2 or 2-4, and by penciling out those two options I was able to come up with two highly constrained templates that allowed me to quickly answer the questions. I call this "Making Worlds."

It's an extremely powerful technique when correctly applied at the right time. But on this game, I see no such opportunity to make worlds. When I'm making worlds, I look first for variables or spots that have very limited possibilities. For example, in Game 2, because of Rule 2, we know that either G or L has to go last on Friday. So it's true that we could make World 1 where G goes last on Friday, and World 2 Where L goes last on Friday. In World 1, L wouldn't be able to go at all, and in World 2, G wouldn't be able to go at all. The problem is that, beyond what I've just stated, we would know nothing more about the game. We'd be left with two Worlds that were essentially empty, which would be of no use to us at all. (Alternatively, we could make our Worlds using Rule 3's requirement that either G or H goes last on Saturday... we'd end up with a similarly unsatisfying result.)

So if I'm going to make Worlds, I'm looking for:

1) Very limited options (preferably just 2 options). 2) The ability to fill out a lot of additional stuff in at least one World (preferably both Worlds).

In this Game, requirement 1 is met but requirement 2 is not. So I won't make Worlds here--I suspect it would be a waste of time.