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March 30, 2022

Diagramming Logic Games

The key to mastering LSAT Logic Games is learning how to make a good diagram. Your diagram is your Rosetta Stone as you work through a game and its questions. A good setup gets the rules out of your head and built into solutions on the page.

So, how do you make a good logic game diagram?

Things to Consider When Setting Up Your Diagram

Understand the Rules

No matter how complicated a logic game feels when you first read it, all the information you need to solve it is right there on the page. However, if you misread or misinterpret any of its rules, you will not be able to solve it correctly.

You may need to re-read certain rules multiple times—that’s okay. Do the work upfront to save time and effort later.

Link Rules Together Where Possible

The rules don’t immediately give away all the correct answers, but when you link them together, they reveal a breadcrumb trail of deductions.

If one rule says, “Helen must present before Barbara,” and another says, “Helen cannot be the first person to present,” these two rules are linked by the variable “Helen.” Once you spot this link, you can deduce that Barbara can’t be the first person to present, even though it isn’t explicitly stated in the rules.

Once you have your diagram, and before jumping into the questions, look for any variables that are unrestricted by the rules. LSAT Demon teachers call these free variables “floaters” or “wildcards.”

Bake the Rules Into Your Diagram

Let’s say you’re trying to figure out the order in which Helen, Barbara, and three other people are presenting. Given the rules that (1) Helen must go before Barbara and (2) Helen can’t go first, you know that neither Helen nor Barbara can be in spot #1. You also know that Barbara can’t go in spot #2 and that Helen can’t go in spot #5 because Barbara has to follow Helen. 

Creating a diagram means you don’t have to hold all these rules in your head. You can incorporate or “bake” them into your diagram. Here, “x” next to a variable means that variable cannot go in that spot:

        __    __    __    __    __
          1       2       3       4       5
        xH    xB                       xH

As you get comfortable with Logic Games, you’ll develop your own notation style.

Should You Make Worlds?

Short answer: Yes, in almost all cases.

Making worlds” refers to diagramming a comprehensive set of solutions for the variables in a game, following all the game’s rules. Worlds must be mutually exclusive, and together, they must encompass all possible solutions to the game. That’s not to say that you should try to write out every possible scenario—it’s often easier and more efficient to represent multiple solutions in one world. The purpose of making worlds is to eliminate rules by incorporating them into your diagram.

You will need to base your worlds on at least one rule or variable in each game. You may base worlds on one variable whose placement is restricted by multiple rules, for example, or you may base worlds on a particular rule that affects multiple variables.

Each possible slot a variable can fill is a possible “world” for that variable.

Placing your “base variable” limits the possible arrangements of the other variables. By eliminating options, you may even be able to place other variables into their exact positions. To reduce the flexibility of a world, you may decide to “split” it by incorporating another variable’s movement or another rule.

Common Setups for Different Types of Logic Games

There is no one correct diagram for any game. There may be many ways to arrive at the same solution. But there are a few key elements you should incorporate into your diagram for each type of LSAT logic game.

How to Diagram Ordering Games

Ordering games involve determining the sequence in which a number of variables can be placed. A simple ordering diagram includes a lineup of spots in which to place these variables. 

Let’s say you’re asked to put five people, Alex, Bailey, Candace, Deanna, and Esteban, in order from tallest (#1) to shortest (#5). Your lineup should have five spots, numbered 1 through 5:

        __    __    __    __    __
          1       2       3      4       5

As you gather information about these people’s relative heights, you’ll place their initials into the spots. 

If a rule tells you that “Deanna is taller than Esteban,” for example, then you know that Deanna must be placed somewhere to Esteban’s left, which can be represented like this:

        D … E

Connect rules to make deductions about where different variables can and cannot go.

How to Diagram Grouping Games

Grouping games involve placing a number of variables into groups, or categories.

To diagram a grouping game, organize the variables into a table or chart. Let’s say you’re sorting six people into two teams of three. Your diagram may look like this:

        Team Barcelona         Team Milan
                  ____                          ____
                  ____                          ____
                  ____                          ____

You won’t always be told explicitly how many variables are in each group. If, for example, the size of each group is undetermined, but there must be at least one variable in each group, you’ll need a more flexible diagram:

        Team Barcelona         Team Milan
                  ____                          ____

If you know the exact size of only one of the groups (say there’s a rule that “Team Barcelona has exactly three players”), you might draw a period or a double underline to remind you that there can be no more variables added there:

        Team Barcelona         Team Milan

You’ll develop your own conventions as you practice more Logic Games, watch explanation videos, and learn what works best for you. 

How to Diagram Hybrid Games

Hybrid games involve both operations discussed above: placing variables into groups and determining their sequence. To diagram a hybrid game, you’ll need to incorporate both grouping and ordering elements into your setup. 

This might look like a chart containing two or more groups that each have ordered lineups for their variables:

                      Group A                                       Group B
        __    __    __    __    __           __    __    __    __    __ 
          1       2       3      4       5              1       2       3       4       5

Or it might look like a lineup of slots, each of which specifies group membership:

Variable:    ____    ____    ____    ____    ____    ____
Group:          A/B       A/B        A/B       A/B       A/B       A/B

Neither approach is inherently better than the other. Choose a diagram that allows you to organize the game’s variables in a way that makes sense to you. 

How to Diagram Miscellaneous Games

Miscellaneous games are the rare “oddball” games that involve neither ordering nor grouping. There is no common formula to solve these games because they are, by nature, dissimilar to other types and do not belong to any discrete category.

One way to approach a miscellaneous game is to visualize the game in your head and try to reproduce that visual on paper as a diagram. As you move through the game, adapt your approach as the components of your diagram prove to be more or less helpful.

Miscellaneous games are often simpler than they initially appear. One such game from a previous LSAT asks students to figure out how many of seven light switches must be turned on based on the board’s circuit load. It sounds complicated at first, until you realize that there are only five viable worlds and you can draw out each solution almost completely, before even looking at the questions. To practice this game and hundreds more, create an LSAT Demon account and get to work.

Start Practicing Logic Games Today

Remember: Time spent practicing logic games is much more valuable than time spent reading about game types! Get started today on solving hundreds of LSAT logic games, watching thousands of video explanations, and attending daily Logic Games classes with the LSAT professionals at LSAT Demon.