June 2007 LSAT, Game 1 Setup

Logic Games are troubling for nearly every LSAT student I've ever met--on the first day of class. But Games are also, by far, the most teachable section of the test. On Logical Reasoning and Reading Comprehension, improvements tend to happen slowly, incrementally... like a long uphill march. On Logic Games, improvements tend to happen all of a sudden, in jumps and spurts... like launching off a trampoline. I've seen a zillion students walk into my classroom getting their asses kicked by Games. And I've seen a zillion students walk out of my classroom scoring perfectly on the Games. (It's by far the most commonly fucked-up section. And it is also, by an even wider margin, the most common section where perfect scores are achieved.) This is the most fun section of the test, and it's also, in large part, where I make my money.

Games are easy to teach in class, but I've been skeptical about trying to teach them in writing. Luckily, Game 1 of the June 2007 LSAT  is fairly straightforward, so if explaining logic games in the blog format is ever going to be possible, it's got to be possible on this game. I promise I'll give it my best. You're probably going to want to print yourself a copy of the test, if you haven't already. And take 5-10 minutes attempting Game 1 (questions 1-5) on your own before reading these explanations. That's the best way to learn. When you've done that, come back.

The game simply asks us to put five things in order: the numbers 0, 1, 2, 3, and 4. There are five digits, and they can go in any order, subject to a few rules. Here we go.

--Each digit goes exactly once. --The second digit is twice the first. --The third digit is less than the fifth.

If you've prepared at all for the LSAT, you've been told repeatedly that the key to Logic Games is "making inferences." This is true, of course, but it's unhelpful without an explanation of what "making inferences actually means. Drumroll, please.

The Super-Secret Magical Definition of "Making Inferences":  

...

Uhm. Well. Yeah. All this means is "combine the rules together and see what you've learned."

Sorry to disappoint you, but this shit is simply not rocket science. The LSAC knows that the reason most people end up taking the LSAT is that they basically sucked at their science and math classes in high school and college. Most of the inferences you're going to make on the LSAT's logic games are very simple combinations of two, or maybe three, rules. If you blink, it looks like magic. But if you pay close attention, you'll realize that each baby step is basically obvious. All you have to do is simply look at each rule in the context of every other rule, and see if the two (or three) rules in combination teach you anything else that's new. Here, let me show you:

There's a rule that says the second digit has to be exactly twice the first. And there's a rule that says that each digit (0, 1, 2, 3, and 4) are each used exactly once.

Okay, so:

If the first digit is 1, then the second digit has to be 2:

  1     2    __  __  __

And if the first digit is 2, then I guess the second digit has to be 4:

  2     4    __  __  __

And if the first digit is 3, then the second digit has to be 6. But there IS no 6. So the first digit can't be 3. Likewise, the first digit can't be 4, because there is no 8. And the first digit can't be 0 either, because two times 0 is 0, and we can only use 0 once.

So really, there are only two ways to do this game. (The two ways I've drawn out, above.) And that, my friends, is the magic of making inferences. Easier than you thought? I hope so.

And we don't want to stop there. We need to reconsider what we've just learned (there are only two ways to do the first two digits) with the REST of what we know about the game. (The other rules.) This is like playing solitaire. In solitaire, every time you make a move, no matter how small, you get to go back through the entire deck to see if anything has changed. In Logic Games, every time we make an inference, we need to consider that inference in light of all the other stuff we know about the game, to see if we learn anything ELSE that's new.

Here, I'm thinking about the rule that says the third digit has to be less than the fifth. Let's consider the world that looks like this:

  1     2    __  __  __

What can go third and what can go fifth? Well, I'm thinking that 4 could never go third there (because that's the highest number) and 0 could never go last (since that's the lowest number). So it's this:

  1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

Likewise, let's consider the world that looked like this:

  2      4    __  __  __

I'm pretty sure in that world, the third spot can't be 3 (since that's the highest remaining number) and the last spot can't be 0 (since that's the lowest number). So it's this:

  2      4     0/1  __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

I'm left with two templates for solving this game:

World 1:

  1      2     0/3   __   3/4  (where the third spot and the fifth spot can EACH be 3, but they can't SIMULTANEOUSLY be 3).

World 2:

  2      4     0/1    __   1/3  (where the third spot and the fifth spot can EACH be 1, but they can't SIMULTANEOUSLY be 1).

And that's about enough for today. Tomorrow, I'll start answering the questions for this game. But believe it or not, we've already done all the heavy lifting. From here, the questions will be easy. We're in position to crush this game. And that's your first, most important, lesson on the Logic Games: Do as much work as you can BEFORE you even look at the questions. I bet we've already answered some of the questions, before we've even seen them. This should be fun.