LSAT Logic Games: Worlds Are Easy

Students sometimes feel lost when making worlds. They sound like this:

I’m good when it’s just two worlds, but I don’t know when it should turn into four or eight.

I end up with so many worlds, but still I leave things out.

I don’t know when to stop splitting.

I can do it for ordering, but I get lost when it’s grouping.

I freeze up—I can’t figure out where to start.

These students know more than they realize.

At its core, making worlds on LSAT logic games consists of just a few basic principles:

1. We are simplifying the game, not making it more complex.
2. We are baking rules into our worlds so that we don’t have to think about them anymore.
3. Worlds encompass all possible solutions to the game—they don’t leave anything out.
4. The point isn’t to complete every world. The point is to eliminate rules and variables so that we can play a simpler game from there.
5. There are common triggers that indicate a good place to start with worlds, but it’s not about making the perfect choice. Many roads converge on the same destination.
6. Start with one rule or one variable. Split later, if necessary. Don’t try to determine the total number of worlds up front.

You understand more about worlds than you think.

Consider a toy game where you have to put six people—P, Q, R, S, T, and U—into two groups, 1 and 2. There are three spots in each group.

P and Q are together.

If R is in group 1, so is S.

Does this seem like a good game for making worlds?

In my experience, worlds are the best way to destroy a game. I make worlds whenever possible—on 75 percent of all games, maybe more. This game looks like a good opportunity. Most games do.

If you were going to make worlds, which rule would you start with?

It doesn’t matter! Pick either the first rule or the second rule, and get to work. Then incorporate the other rule, splitting if necessary.

I’ll set it up both ways below. But now is a great time for you to get a sheet of scratch paper and do it yourself first. If you’re an intermediate or advanced student, try it both ways instead of one. Compare your results to mine.

Okay, here we go.

Worlds based on the first rule—“P and Q are together”

The first rule, P and Q are together, is a good candidate for making worlds because it’s a big block that can go in only two places. The first step looks like this:

World 1:

1: P Q _

2: _ _ _

World 2:

1: _ _ _

2: P Q _

By the way, I’m using the labels “World 1” and “World 2” for teaching purposes only. In practice, I would omit these labels.

These worlds are mutually exclusive and encompass all possible configurations of P and Q. So with this first move, the rule that “P and Q are together” drops from our consciousness. As long as we stay in one world or the other, the rule will be satisfied. If we can’t break a rule, we can stop worrying about it.

Now what about that other rule? “If R is in group 1, so is S.” Consider what happens in each of your two worlds. Is the rule still active? Has it already been triggered in one or both worlds?

In the first world, if R were in group 1, we’d be in trouble. P and Q are already there, so there wouldn’t be room for R and S both. We can’t allow the game to break itself, so the only way to satisfy this rule in the first world is to put R in group 2.

World 1:

1: P Q _

2: R _ _

In the second world, it’s a bit more complicated. But not as much as you might think. In the second world, there’s room for R to be in either group 1 or group 2. To eliminate this rule from our consciousness, we’ll split the second world based on R.

If R is in group 1, there’s plenty of room for S to be there as well. It looks like this:

World 2(a):

1: R S _

2: P Q _

If R is in group 2, it looks like this:

World 2(b):

1: _ _ _

2: P Q R

Here, the rule that “if R is in group 1, so is S” doesn’t apply because R isn’t in group 1. However, group 2 is now full in this world, so all three of the remaining players have to fill up group 1. Like this:

World 2(b):

1: S T U

2: P Q R

Our final worlds look like this:

World 1:

1: P Q _

2: R _ _

World 2(a):

1: R S _

2: P Q _

World 2(b):

1: S T U

2: P Q R

Some students feel dissatisfied at this point because they didn’t get to fill the first world or world 2(a) out completely. But that’s not the point! The point is that, in all three worlds, we no longer have any rules. All remaining players are wild cards, free to fill any available spots. In the first world, players S, T, and U can all go wherever they want as long as a spot is available. In the second world, players T and U will flip-flop between the only remaining openings. There is no point in splitting these worlds further because all we have left are wild cards—there are no more rules to eliminate.

If this were a real game, the questions would be trivial from here.

Worlds based on the second rule—“if R is in group 1, so is S”

Now consider making worlds with an entirely different first move.

The rule that “if R is in group 1, so is S” is a good trigger for making worlds because it is conditional. That is, R in group 1 “triggers” the rule and tells us where S goes. And if R is not in group 1, then the rule simply doesn’t apply. Start here:

World 1:

1: R _ _

2: _ _ _

World 2:

1: _ _ _

2: R _ _

In the first world, the rule gets triggered and S must be in group 1 along with R. In the second world, the rule doesn’t apply. So we’re here:

World 1:

1: R S _

2: _ _ _

World 2:

1: _ _ _

2: R _ _

These worlds are mutually exclusive and encompass all possible configurations of R. So with this first move, the rule that “if R is in group 1, so is S” drops from our consciousness. As long as we stay in one world or the other, the rule will be satisfied. If we can’t break a rule, we no longer have to worry about it.

Now, what about that other rule? “P and Q are together.” Consider what happens in each of your two worlds. Is the rule still active? Has it already been triggered in one or both worlds?

In the first world, there’s only one remaining group that can accommodate both P and Q—group 2. Like this:

World 1:

1: R S _

2: P Q _

In the second world, P and Q can still go in either group. So to eliminate the rule, we split:

World 2(a):

1: P Q _

2: R _ _

World 2(b):

1: _ _ _

2: R P Q

Finally, in world 2(b), since group 2 is full, everyone else has to pile into group 1. Our final board looks like this:

World 1:

1: R S _

2: P Q _

World 2(a):

1: P Q _

2: R _ _

World 2(b):

1: S T U

2: R P Q

Once again, we have not completely filled out two of our three worlds. T and U will flip-flop in the first world, while S, T, and U have flexibility in world 2(a). Once again, we’re playing a very simple game from here. We can forget about all the rules and just place the remaining wild cards in open spots. There is no point in splitting these worlds further, because all we have left are wild cards—there are no more rules to eliminate.

We got to the same destination via two different routes.

If you compare the two solutions, you’ll see that we ended up in the exact same place even though our first moves were completely different. Only the labels have changed—the possible solutions are exactly the same.

This was just a toy game. Most games have more rules. But the principles don’t change. Remember:

1)    Worlds simplify the game, not make it more complex.

2)    Bake rules into your worlds so that you don’t have to think about them anymore.

3)    Worlds encompass all possible solutions to the game—they don’t leave anything out.

4)    The point isn’t to complete every world. The point is to eliminate rules and variables so that we can play a simpler game from there.

5)    There are certain common triggers that indicate a good place to start with worlds, but it’s not about making the perfect choice. Many roads converge on the same destination.

6)    Start with one rule or one variable. Split later, if necessary. Don’t try to determine the total number of worlds ahead of time.

Like everything else on the LSAT, worlds are easier than you think.

Sometimes students struggle for weeks or months before things finally click for them on LSAT logic games. Keep grinding! Students frequently improve from the low single digits on a section of logic games all the way up to perfection—a reliable 23-for-23 every time. If you’re not there yet, that’s okay. You probably just haven’t put in the reps yet. We have over 90 full sections of games to practice. If you spread them out, you could do one new game a day for an entire year. The rewards for mastering the logic games are enormous. Your breakthrough might be right around the corner.

I’d love to hear what you think of this lesson—Email us at help@lsatdemon.com.

My goal, as always, is to show you how easy the LSAT can be.