Logic Game Strategies: Making Worlds
The Purpose of Making Worlds
Put simply, the purpose of making worlds is to eliminate rules. Rather than having to process rules repeatedly as you work through the questions, creating worlds allows you to bake rules into your diagram and eliminate them from your thought process.
How to Make Worlds
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. Here are the rules:
P and Q are together.
If R is in group 1, so is S.
This game looks like a good opportunity for making worlds. 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.
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. Then compare your results to the setups below.
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 _
The labels “World 1” and “World 2” are for teaching purposes only. Omit these labels in practice.
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 both R and S. The only way not to violate this rule in the first world is to put R in group 2.
World 1:
1: P Q _
2: R _ _
In the second world, there’s room for R to be in either group 1 or group 2. To eliminate this rule, 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
The rule that “if R is in group 1, so is S” doesn’t apply to world 2(b) because R isn’t in group 1. (If you’re not sure what this means, click here to learn about conditional rules. But group 2 is now full in this world, so all three of the remaining players have to fill 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 out the first world or world 2(a) 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 wildcards, 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 remaining openings. There’s no point in splitting these worlds further because all we have left are wildcards. 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 “if R is in group 1, so is S” is a good starting place for making worlds because it’s conditional. That is, R in group 1 “triggers” the rule and tells us where S goes. If R is in group 2, 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 so 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 our 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 group that can accommodate both P and Q together—group 2. So that’s where they both must go:
World 1:
1: R S _
2: P Q _
In the second world, P and Q can still go together 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
In world 2(b), group 2 is full, so 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, two of our three worlds are incomplete, and that’s okay. T and U will flip-flop in the first world, while S, T, and U have flexibility in world 2(a). From here, we can forget about all the rules and just place the remaining wildcards interchangeably in open spots. There’s no point in splitting these worlds further because all we have left are wildcards—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 exactly the same place even though our first moves were completely different. Only the labels have changed—the solutions are the same.
This was just a toy game. Most games have more rules. But the principles don’t change. Remember:
- Worlds make the game simpler, not more complex.
- Bake rules into your worlds so you don’t have to think about them anymore.
- Worlds encompass all possible solutions to the game—they don’t leave anything out.
- 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.
- Certain common triggers indicate a good place to start with worlds, but many roads converge on the same destination.
- Start with one rule or one variable. Split later, if necessary. Don’t try to determine the final 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. LSAT Demon has around 100 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.
Worlds Are Not Arbitrary Scenarios - What Not to Do When Making Worlds
Making worlds isn’t about writing out every possible combination for each game. It’s about making deeper-level deductions (things that must be true) that you couldn’t initially spot when you first read through the rules. These new deductions may provide information that you can bake into your original diagram.
Sometimes students think they’re creating “worlds” by just haphazardly applying rules without exploring every possibility–in other words, without extracting the full value of the process. Consider the following rule: “If P is in group 1, Q is in group 2.” It’s great if you make a rule where P is in group 1 (and Q is in group 2), but don’t forget to also make the world where P is not in group 1, and/or the world where Q is in group 1.
The best way to figure out this sweet spot is to practice making worlds for yourself. Do this first without looking at the clock to get used to it—accuracy before speed. Ready to get started? Head over to LSAT Demon to start drilling.
FAQs About Worlds
Read on for some common questions our students ask about worlds.
Where Should You Start Making Worlds?
A great place to start making worlds is with conditional rules that set off two scenarios. For example, let’s say you’re sorting six people into two groups. A rule that says “If F is in group 1, M is in group 2” is a great place to start with worlds:
World 1 (if F is in group 1):
1: F
2: M
World 2 (if M is in group 1, or if M is not in group 2):
1: M
2: F
Keep in mind that if F is in group 2, M can go anywhere. You don’t necessarily have to explore this world—more on this below.
In particular, look out for rules that set off a “chain of events,” triggering other rules as you go along. Using the example above, let’s add a few more rules: “M and S must be in the same group; S and Z cannot be in the same group.” Although F isn’t directly mentioned in these new rules, where F goes will have a downstream impact on where S and even Z end up! We can add these new rules into our worlds from above:
World 1 (if F is in group 1):
1: F,Z
2: M,S
World 2 (if M is in group 1, or not in group 2):
1: M,S
2: F,Z
These rules are perfect for making worlds because they are all connected; F impacts M, which impacts S, which impacts Z!
Now that we have these worlds, with just a small piece of information (for example, “M is not in group 2”) we know exactly where four of the six people must go. That’s a great head start on the question.
Is it Always Best to Make Worlds?
While worlds are effective in the vast majority of Logic Games, some games just don’t call for worlds.
Let’s say you’ve got to figure out on which days a bunch of people go to the gym between Monday and Friday, and one of the rules says: “Of the days Natalie goes to the gym each week, at least two are consecutive.” There are five days in the week and no limit on how many days each person can go. This is a great example of a situation where the rule doesn’t give rise to helpful worlds. If you tried to build worlds from this rule, you’d get something like this:
1: N N _ _ _
2: _ N N _ _
3: _ _ N N _
4: _ _ _ N N
5: N _ N N _
6: _ N N _ N
7: _ _ N N N
8: _ N N N N
9: And so on. You get the point.
I cannot stress this enough: this is an utter waste of time. And none of the other rules are much better for worlds. In games like these, you’re better off taking the time you need to understand and absorb every single rule, making a solid diagram, and moving on to the questions knowing you’ve done everything you could.
Making this distinction quickly will come with practice. You’ll find that in some games, worlds seem to “emerge” from the rules. If you’re raking your brain to figure out how to set up worlds, this might not be the best strategy for that game.
When Should You Stop Making Worlds?
You’re done making worlds when you’ve achieved a deeper understanding of the downstream implications of the rules and of how the rules work together. Most games have one or two “deeper-level” deductions that aren’t immediately obvious from reading the rules. Once you’ve unlocked these insights, stop doodling and move on to the questions.
In the grouping example with F and M above, don’t worry about the two other people who aren’t mentioned in the rules. These people are “floaters,” or “wildcards,” because they can go anywhere—they are not restricted by any rules but, rather, only by where the other people end up. You don’t need to map out every possible combination for these wildcards.
This is not a hard-and-fast rule, but two to six solid worlds usually do the trick. Trying to write out every possible scenario is a waste of precious time that leaves you with more worlds than you’ll need for the questions. Take the time you need to make useful deductions, but don’t waste your time going down rabbit holes.
FAQ
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