5.3 - Diagramming Conventions

As you study Logic Games, you'll run into lots of different diagramming conventions.

If you've studied with other prep companies, you'll probably be familiar with some of these. If not, don't sweat it—they're beginner-friendly and you'll use them as you progress.

In this lesson we'll cover:

• General layouts you'll use in Logic Games
• Common diagrams used to solve ordering, grouping, and hybrid games
• An example of a game that defies conventional game types
• Short-hand notations that account for flexibility

Let me start off by saying, none of the following advice is necessarily gospel. No one's going to look over your shoulder on test day and dock you for not using a standard ordering layout on an ordering game. Do what works for you. As long as your diagramming makes sense and logically accounts for the game's constraints, it's fine. These are just common conventions you'll see me and other teachers use.

That said, let's dive in.

Common Layouts

These are easiest to explain by example, so we'll go one layout at a time.

Remember, these are just methods for organizing information. Get used to making similar diagrams, but be prepared to deviate from them when it makes sense to do so.

Ordering Layouts

Imagine we had the following game:

Brandon is filing four folders—A, B, C, and D—into a filing cabinet. His neuroses require him to file the folders from first through fourth in accordance with the following constraints:
Brandon hates the letter A, so it must be the last folder filed.
B is the second folder filed

We might lay out such a game like so:

The four dashes represent the order in which I'll file the folders. The letters represent the folders themselves.

Recall from earlier, this is entirely up you—do what makes sense. For instance, if it makes more sense to you to set this game up vertically, with the dashes above and below one another, that's fine too.

Web Layouts

Sometimes, we put things in order using what are often called web diagrams.

Webs are just another way to organize information. We typically use them when we know game pieces' positions relative to one another, but not necessarily what spot they take up in a given sequence.

Let's convert Brandon's file folders game into something more conducive to a web diagram.

Brandon is filing four folders—A, B, C, and D—into a filing cabinet. He's still neurotic, so he must file them in order according to the following:
He files folder A before folder D
He files folder C before folder B, but after folder A

Here's how you might diagram such a web:

Sometimes people use dotted lines instead of dashes / hyphens in their web games. Either is fine. Do what's intuitive to you.

Grouping Layouts

Sometimes we're asked to group things together. These so-called grouping games take different shapes, usually based on the number of groups involved.

Here's an example of a typical grouping game using our folders-and-files idea from earlier:

Brandon's filing away five documents—a tax return, a healthcare policy, a vehicle registration, a utility bill, and a marriage license. Each document must be filed in one of three folders—A, B, and C—according to the following constraints.
Each document is filed and there are no copies of any document.
Each folder contains at least one but no more than two documents.
The marriage license and healthcare policy must be filed in the same folder.
The tax return is filed in Folder A.

The diagram below shows how we might lay out this grouping game horizontally (on the left) or vertically (on the right). Note that these diagrams are logically equivalent to one another, we've just pitched them 90 degrees.

There are variations on these styles, too. Some folks use conventions more akin to swim lanes than spaces to separate their groups, for example. Find what works best for you.

In-Out Grouping

Sometimes we're asked to group things into two finite groups. We call these in-out games because the rules often stipulate players either having or not having a given characteristic.

To keep things simple, we'll adjust our previous game example to incorporate two groups instead of three:

Brandon's filing away five documents—a tax return, a healthcare policy, a vehicle registration, a utility bill, and a marriage license. Each document must be filed in one of two folders—A and B—according to the following constraints.
Each document is filed and there are no copies of any document.
Each folder contains no more than three documents.
The marriage license and healthcare policy must be filed in the same folder.
The tax return is filed in Folder A.

Really, any game involving precisely two groups could be handled with the following diagramming conventions.

On the left, we have what's commonly called a T Chart. On the right, we're demonstrating the circle-slash approach.

In the example, we've baked in the rule about T being in Folder A to demonstrate how we use these diagrams. Notice in the left-hand diagram, we've assigned T to Folder A and removed T from our list of remaining game pieces. In the right-hand diagram, we've circled T, suggesting that the Folder A's items would be circled, whereas Folder B's would end up slashed.

There's no one right way to employ these diagrams. I often find myself gravitating toward circle-slash when an in-out game involves lots of conditional logic. But I use T Charts all the time, too.

Go with what works best for you in each scenario.

Hybrid Layouts

Some games ask us to assign players to groups while also keeping track of an order or sequence. We tend to call these hybrid games because they combine conventions of ordering and grouping.

Here's our files-and-folders scenario rehashed as a hybrid game:

Brandon's filing away five documents one at a time—a tax return, a healthcare policy, a vehicle registration, a utility bill, and a marriage license. Each document must be filed in one of two folders—A and B—, and in an order that satisfies the following constraints:
Each document is filed once and there are no copies of any document.
The tax return is filed third and in folder A
The marriage license must be filed earlier than the healthcare policy, but in the same folder.
The healthcare policy cannot be the last document filed.

And here's how we might lay out such a game:

Note, we baked in one of the rules again to demonstrate how we might use this diagramming convention—I placed T in the third position, signifying its folder beneath it. You can use a similar convention if a game gives you a morning (top) and afternoon (bottom) convention. Or you can use things like superscripts or subscripts. It's entirely up to you.

I've heard folks advocate that you should always order things horizontally and group things vertically so you can combine these conventions on hybrid games. I think that gets a little dogmatic. For instance, you could make the same argument for ordering things vertically and grouping them horizontally. As always, do what makes intuitive sense to you.

Random Layouts

The name says it all. There's no one right way to diagram random games. That said, the game will hint at ways you might consider organizing the information.

There are several great examples out there, but one in particular comes to mind.

It's a game about a fictitious country called Zendu with a plane flying over it. I've always loved this game, because it completely defies convention. Your job is to figure out which of a handful of radar zones the plane flies in and out of as it crosses Zendu. Most people attack it with a sort of Venn diagram-looking sketch. You're not going to lay it out with any of the diagrams above and have a very fun time answering the questions.

Zendu teaches us that we must always be prepared to improvise and get creative.

Notation

The main thing separating easier games from harder ones is how much flexibility remains as you go about building worlds and baking in constraints. On some games, you'll have baked in all the rules but won't end up with finished diagrams.

LSAT world has come up with a handful of useful conventions for accounting for different kinds of flexibility.

Handles

Handles are shorthand that accounts for two positions a game piece might occupy. I've heard other teachers refer to these as arcs or hooks, but I tend to call them handles. Refer to them however you like.

For example, we might use a handle to account for these rules...

Either A or B occupies the first position.
A must come either immediately before or immediately after B.

...like this:

Again, all this signifies is that A and B can move back and forth between the first and second spots. You could just as easily place A second and B first.

Slashes / Fractions

Let's look at the same rules from our handle example, but diagram it using a slash—one possible value on top, the other on bottom.

In this example, we're accounting for A and B's possible locations with a slash.

When we use this convention, we're either playing with the numerators (the values on top) or the denominators (the values on bottom). That is, we either read this diagram along the top—with A first and B second—or we read it along the bottom—with B first and A second.

Combining Handles and Slashes

You may be wondering why we'd have two different ways to diagram the same thing. Well, because sometimes a variable game position (like spot 1 above) might allow for both a slashed game piece to move back and forth from one position to another using a handle.

Let's tweak our fictional rules here to see what combining these tools looks like in practice:

C is either first or fifth.
If C is first, then either A or B is fifth.
If C is fifth, then either A or B is first.

We might diagram these rules as follows:

Notice we don't know where the other B/A ends up. We just know that C must go either first or fifth, and whichever spot it doesn't occupy must be occupied by either A or B.

Blocks

Some rules stipulate that certain pieces always go together or are always used sequentially in a specific order. We call these blocks.

For instance, if we had these rules...

A goes first
B goes immediately after A

...it would look something like this:

Blocks + Handles

Sometimes, blocks involve two pieces that can ultimately switch positions inside their block.

Let's adjust the rules from our previous example so that we end up with a flexible block that incorporates a handle.

A and B occupy positions 1 and 2, not necessarily in that order.

We'd get something like this:

Relative Position

Sometimes we get rules that specify pieces' positions relative to one another. We demonstrated these relationships in our web game diagram. Let's look at it once more.

When reading rules involving relative position, it's important to recognize who is constrained and how.

If A, B, C, and D were the only pieces in this game, I'd know several things already. For instance, I'd know A goes first. How? Because A has no constraints to its left. I'd also know that either B or D go last because neither has a constraint to its right. Alternatively, C can go neither first nor last because it has constraints in both directions.

But what about D and C's relationship? Can we infer anything between the two of them? Sort of. They aren't explicitly related to each other. For example, C could totally come before D (D can go last, remember?). But D could also precede C. The only thing we know for sure about D is that it comes after A.

That's all to say that the dashes / dotted lines connecting pieces together in web game are elastic, so be careful how you draw and interpret them.

Flexible / Inflexible Game Spaces

Sometimes rules affect game spaces. For instance, you might be told that Group B contains exactly one person or that it has a minimum of one member and a maximum of two.

I often handle flexible game spaces with a dotted line to represent that this game space could be used, but doesn't have to be.

Here's what this looks like:

As for fixed quantities, I typically put a box around them just like I do with blocks.

So here's what it would look like if B had exactly one item:

Negative Rules

Negative rules are game constraints that use negating language. For instance, A cannot go first. You might have heard them referred to as "no-laws".

Incorporating a negative rule into your diagram is as simple as noting where something isn't allowed to happen.

Let's use our earlier example—A cannot go first:

It's a good rule of thumb to try and turn negatives into affirmatives and to then bake those affirmatives directly into your diagrams. But this isn't always the best thing to do.

Not allowing A to go first provides a useful example. Absent other rules, that leaves four possibilities—A ending up somewhere second through fifth. Those four possibilities might not teach us that much more about the overall game. We'll cover this idea in a later lesson about when to split diagrams.

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There you have it—the most common LG diagramming conventions all in one place. See you in our next lesson, where we talk all about the key to perfecting logic games: making worlds.

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What'd you think of this lesson? Leave me some feedback in the comments to help me improve the course.