Introduction to Logic Games
A logic game is a puzzle that tests your ability to make logical inferences. Each LSAT analytical reasoning section is made up of four logic games. Some games are harder than others, and there are numerous different types of logic games that you could encounter of the LSAT. However, all LSAT logic games have the same three main components: the scenario, the rules, and the questions.
Logic game scenarios lay the groundwork of the puzzle you are going to solve. The scenario also tells you what variables you will work with in the game. A scenario might look something like this:
Ann, Bethany, Charlie, Ellen, Gertrude, and Juan occupy 6 spots in a line to purchase tickets for a musical. Each person occupies a spot in line, and no person occupies more than one spot. There are only six spots in the line.
You now know what your logic game variables are (Ann, Bethany, Charlie, Ellen, Gertrude, and Juan) and that the variables are arranged in a line. Variables are also called “game pieces.” In the game scenario above, you will likely be asked to determine which game pieces could be in various spots in line. But in order to do that, you will need some rules to follow.
In logic games, the rules are your friends. The rules make it possible for you to answer the questions below, and the more rules you have to work with, the more inferences you can typically make in advance (more on this later). The rules look something like this:
The following conditions apply: Charlie is standing in front of Gertrude. Charlie is not first in line. Gertrude stands directly behind Juan. Ellen is not last in line.
From the rules, you can draw inferences. Logic games inferences are hidden rules that must be true. You are never directly told an inference; you must find inferences by thinking logically. For instance, from the rules given above you can determine the following:
1. Charlie is standing in front of Gertrude. (First rule)
2. Gertrude stands directly behind Juan. (Third rule)
3. Charlie must be standing in front of both Juan and Gertrude. (Inference)
The first two statements are rules. The third is an inference that you can know by thinking about the first two rules. If Charlie is somewhere before Gertrude in line (C – G) and Gertrude is directly behind Juan (JG), then Charlie must be standing in front of Juan (C – JG). Inferences like this one are useful when you approach the logic games questions.
A logic game question might look something like this:
If Charlie is fourth in line, then which of the following must be false? A. Juan is fifth in line. B. Ellen is first in line. C. Bethany is second in line. D. Gertrude is third in line. E. Gertrude is behind Ellen.
The question requires you to not only look at the rules but to make an inference from the rules. In this case, the inference is the one we just saw above: “Charlie must be standing in front of both Juan and Gertrude.” So if Charlie is fourth in line (out of only 6 spots), the fifth and sixth spots must be taken up by Juan and Gertrude respectively. Answer D then must be false, and is therefore the correct answer.
When working through a logic game, you always begin with the scenario. You then move to the rules, where you make inferences. Finally, you answer the questions.
Types of Logic Games
There are four primary types of logic games featured on the LSAT: sequencing games, grouping games, odd games, and hybrid games. Sequencing games, grouping games, and hybrid games make up the overwhelming majority of logic games. But odd games have been popping up on the test more frequently in the past few years than they used too, which makes them important to talk about as well.
In sequencing games, you are required to determine the potential locations of variables lined up in a sequence. This could be a simple as some people standing in a straight line. The rules of sequencing games usually focus on where the variables are allowed to be in the sequence. For example, you might learn in the rules that Harold must be first in line or that Yolanda must be somewhere in front of Steve.
In grouping games, you are asked to sort variables in two or more groups. For example, you might have to sort nine marching band members into brass, woodwind, and percussion sections. Sometimes these logic games only deal with a single group but you must determine which variables are in the group and which variables are not in the group. The rules in these games often rely heavily on conditional reasoning. For example, you might learn that if Glenda is in the brass section then Trent is in the woodwind section.
Odd games rely on logic other than simple sequencing or grouping. The most common are circles games (which require you to sequence variables in a circle) and pattern games (a name often given to logic games that involve some kind of repeating pattern or configuration of variables). But some games seem to defy any helpful category other than being odd.
Hybrid games are combinations the other game types—usually sequencing and grouping. For example, a logic game might require to determine the order in which seven job candidates interviewed as well as which job candidates were hired.
Logic Game Question Types
At the end of each LSAT logic game is a set of 5-7 questions. These questions test your ability to make inferences from the rules. The questions can be broken down into four common categories: “must be true” questions, “could be true” questions, “cannot be true” questions, and rule substitution questions.
Could Be True
“Could be true” questions require you to determine what is possible. For instance, you might see a question like this on the LSAT:
Which of the following could be an accurate schedule for Mary’s meeting?
Notice the word “could” in the question. The answer choices for a question like this will include four schedules that are not possible (given the rules of that particular logic game) and one schedule that is possible.
Let’s look at another example:
Assuming that Mary must discuss the layoffs before discussing the new recycling policy, which of the following could be true about Mary’s meeting schedule?
Again, this question asks about what is possible. But this time there’s a twist: you are given a new rule to work with. You are told here to assume one more rule for this question. The answer choices will include four impossible answers (assuming the new rule) and one answer that is possible with the new rule. But remember that question-specific rules (like this one) cannot be used on other questions. The assumption given in this question only applies to this question.
Must Be True
“Must be true” questions ask you to identify necessary conditions. In other words, the questions require you to pick the answer that cannot be false. It is not enough here for an answer to be possible under that particular games’s rules; it must be impossible for the answer to false. Simply put, the answer must be true.
Let’s look at an example:
Which of the following must be true about the movies shown on Stanley’s television?
The answers will include 4 answers that are not necessarily true (but perhaps could be!) and one answer that absolutely must be true according to the rules of that particular game. A good way to eliminate answer choices in these questions is to show that the answers could be false. If you can imagine a scenario (while strictly following the rules) in which an answer choice is false, then it is not the answer you are looking for.
“Must be true” questions can also have question-specific rules. For instance:
If Stanley’s television shows Casablanca at 3:00, what must be true about the other movies shown?
You will be given four answers here that could potentially be false (assuming this new rule) and one answer that must be true with this new rule thrown in the mix. You, of course, need to find the answer that must be true.
Cannot Be True
“Cannot be true” questions require you to identify an answer that is not possible under that particular game’s rules; in other words, you need too find the answer that contradicts the rules of the game.
Let’s look at example:
Which of the following cannot be true about the Chattanooga bus routes?
In “cannot be true” questions, you will be give four answers that could be true and one that cannot. To eliminate an answer, you need think of a scenario (within the boundaries of the rules) in which that answer could be true. If an answer is possible, it’s wrong.
“Cannot be true” questions can also feature question-specific rules. For instance:
If the downtown bus leaves the hub at 4:00, what cannot be true about the Chattanooga bus routes?
Just like the other question-specific rules, the new rule applies to this question alone.
Rule substitution questions are a bit strange. These questions require you to replace one of the original rules given to you with a new rule. For example:
Which one of the following, if substituted for the condition that Barney stands before Charles in line, would have the same effect on the ordering of the water fountain line?
You will then be given a list of five potential rules to choose from. You must determine which of the rules is logically equivalent to the original rule. In other words, which rule would give you the exact same logic game?
These questions are tricky, and many student struggle with them. They can be conquered though. The best approach is to use the process of elimination. Work through the answer choices and find answers that allow for game possibilities that the original logic game would not allow. For example, the original logic game might forbid Cathy from standing first in line. So if an answer choice allows Cathy to stand first in line, you know that answer is wrong. Try to find answer choices that contradict the logic game. If you can eliminate four answers, then the remaining answer must be true.
There is a variant of the rule substitution question type that actually gives you a new rule to use. For instance:
If you ignore the condition that Barney stands before Charles in line and instead assume that Charles stands before Victoria, then which of the following must be true?
In this variant, you are told to eliminate an old rule and follow a new rule instead. In order to solve this question, you will need to ignore not only the old rule but every inference you made based on that rule. You will also need to make new inferences based on the new rule.
Just like the question-specific rules, rule substitutions do not carry to other questions. The rule applies to that particular question only.
How to Approach the LSAT Logic Games
Each logic game is different, but your general approach to each game should be the same. Work through each of the following steps calmly and methodically.
Get a Sense of the Game
The first step with any logic game is to read the scenario and skim the rules. As you do this, you should be attempting to answer the following questions:
- What kind logic game is this?
- What are my variables?
- How should I diagram the game?
We’ve covered the various logic game types, and you’ll become even more familiar with them later. Soon, you’ll find it easy to recognize a logic game type after reading through the scenario. But for now, make a habit of reading through the scenario carefully. As you do, identify your variables. Usually they will appear in a list (Gabriel, Henry, Jeremy, Katherine, Laura, and Nancy are on a business trip…).
Write Down the Variables
If possible, use one letter for each variable. And try not to use the same letter twice. Write each variable down in small but legible handwriting at the bottom of the page. The bottom of the page is where your entire logic game set-up will be drawn.
Draw a Basic Diagram
The next step is to draw the basics of your diagram. What kind of diagram you draw will depend on the logic game type. You’ll learn how to draw each game board in the following lessons.
Write Your Rules in Logical Notation
Go through each rule one-by-one, and write each one down in logical notation. This step may seem silly to you now, but soon you will be able to read logical notation much faster than you will be able to read a rule written in English words. Plus writing the rules in logical notation makes it harder for the LSAT to trick you with weird wording.
You should also illustrate the rules on the game board itself whenever possible. Illustrating the rules serves two purposes:
- It helps you understand the impact that rule has on the game.
- It makes it easier for you to see the rule later when answering questions.
Again, you’ll learn all about how to complete these steps in later lessons.
Make Inferences as You Write the Rules
As you read through the rules and write them down, make inferences. You makes inferences by either considering how rules can be combined or by considering how the game creates limitations. If your inference is valid, then it matters just as much as the rules given to you by the game. So make as many inferences as you can. Every inference you draw makes the game easier.
Circle the Wildcard Variables
After you go through each rule and inference, look for variables that have no rules attached to them. These are your wildcards. (also called floaters). Circle them; quickly identifying your wildcards will be useful later.
If Necessary, Quickly Rewrite your Rules or Redraw Your Diagram
You need to be able to reference your rules and main diagram quickly. So if you made a mess while writing your rules, inferences, or diagram, then it is time quickly (but neatly!) redraw your set-up. The key here is easy readability; nothing can be confusing.
Tackle the Questions
At this point, it’s time to go through the questions. That hard work is done now. If you draw your set-up correctly, then most of the questions will be a breeze.
Here’s an important tip to keep in mind: Once you tackle the questions, never touch your main set-up. Students are frequently tempted to write on the main set-up in order to solve individual questions, but this is a bad strategy. For each question, draw a small diagram next to the question. Use that small diagram to work on the question. This will give you two big advantages:
- Drawing new diagrams is actually faster than erasing old work.
- Drawing new diagrams allows you to keep your old work, which can be useful later.
Because of benefit number two, never erase your work unless you make an error. This will make more sense later, but for now just remember that you do not erase your diagrams unless you make a mistake.