Back to: LSAT Logic Games

Now, remember how I said that an LSAT logic game is just a game, with a playing board and some rules about where you can put the pieces. That’s 100% true. The only thing is, you have to learn how to draw it all yourself before you can even play—the board, the pieces, and a visual representation of the rules about where the pieces can go. Don’t worry; the games are purposefully designed to be drawn out. It will be tricky some of the time, but it’s always possible, and it’s always worth doing.

Let’s go through the game we looked at earlier and diagram it all out. You don’t have to learn these diagramming techniques yet, but it will help you see how this works when it’s all flowing together.

All of the rule diagramming techniques you see here will be covered in detail later in the course. For now, prepare to feel a little overwhelmed. That’s okay. This game is a bit more complicated than the ones we will start out with when we begin the core games lessons.

Here is the prompt again:

A transport ship line is scheduling seven week-long voyages for the ship Freedom. Each voyage will occur in exactly one of the first seven weeks of the season: weeks 1 through 7. Each voyage will be to exactly one of four destinations: Guadeloupe, Jamaica, Martinique, or Trinidad. Each destination will be scheduled for at least one of the weeks. The following conditions apply to Freedom’s schedule:

Jamaica will not be its destination in week 4.

Trinidad will be its destination in week 7.

Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages.

Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica. No destination will be scheduled for consecutive weeks.

This is the just scenario and the rules (no questions).

Always, always, always when you are trying to figure out what’s going on, you want to be looking at the scenario part (the part before the more specific rules) first. That’s where you learn about your game pieces and the game board.

The Pieces

First, let’s talk about the “game pieces.” This is an ordering game, and the fundamental task in this game is to figure out the order these voyages can go in. These seven voyages are the moving parts, the game pieces that will go on your board in various orders.

We know there are going to be seven of them, and they’ll be ordered from one to seven according to the rules. To make seven, some will of these will have to show up more than once.

Rather than writing the full words out (e.g., “Guadeloupe”), it’s always best to just abbreviate with letters to save time and space. So “Guadeloupe” as “G,” “Jamaica” as “J,” and so on.

We have Martinique, Jamaica, Guadeloupe & Trinidad, so “M” “J” “G” & “T.” These are your game pieces. You may also hear them referred to as variables. It’s always a good idea to list them out.

You’ll draw your diagram in the blank space at the bottom of an LSAT game (if taking the paper-and-pencil test) or on scrap paper provided (for Digital LSAT). We’ll talk in more detail about where exactly you draw all this stuff later on. Unfortunately, the traditional paper-and-pencil LSAT doesn’t allow you to use scrap paper, so you have to be efficient with the space they give you. We’ll fill in this diagram more completely as we move through the scenario and rule. Start with a list of your game pieces up in the top left:

Note that we have only four game pieces so far. If you read the scenario carefully, you’ll notice that although there are only four destinations, there are a total of seven voyages. Therefore, some of these destinations will be visited on multiple voyages.

The set of seven letters we need is an example of a variable set that can change: First, the order can be switched around. Second, we don’t always have the same mix of game pieces—for example; maybe we learn later that Martinique is visited twice, Jamaica twice, Guadeloupe twice, and Trinidad once. In no particular order, this how our games pieces would look.

M M J J G G T

Whereas in another possible schedule, we could visit Martinique twice, Jamaica and Guadeloupe once, and Trinidad three times. That would look like this (again, not in any correct order):

M M J G T T T

We don’t know yet how this is all going to play out, so if I were listing my game pieces, I would just stick with the list of four, and write it like this:

It’s good practice to do what I did and add a reminder that we need to use each of these letters at least once.

Now that we have an idea what our game pieces will look like let’s take a look at the board.

The Board

Now, what about the board? Where are these spots I’ve been talking about where you will put these game pieces?

For the board (also often called “the base”), you use another set of variables: the weeks. Week 1 through week 7.

This is an example of a variable set that can’t change at all. In this game, no matter what else happens, you will have seven weeks. Better still, they are always fixed: they have an inherent natural order, and you will work with them fixed in that order, which goes cleanly from 1 to 7.

Here, we’ve added the base to our game board:

The voyages, your “game pieces,” will fill these seven spots that make up your board. Each spot can have only one piece in it, and all of them need to be filled. You will plug the pieces into this board to make an acceptable order. But to make sure you were doing it right, you would have to keep looking back and forth to the rules and re-reading them. To make it way easier, you have to start working with the more specific rules…

Diagramming The Rules – The Main Setup

Now we’ve got our game pieces, and our board all plotted out. You are going to want to keep a nice clean game board right in the middle of your blank space. Here’s what mine looks like right now:

This will form what we call your “main setup” or “main diagram.” It’s where you diagram all the information from the scenario and rules.

It’s time to start adding in all the information contained in the rules. The first rule tells us that:

Jamaica will not be [the ship’s] destination in week 4.

Rather than just writing that off to the side and trying to remember it, there is a much better way. With diagramming rules, the idea is that you always want to do it in a way that creates a powerful visual reminder of the rule. Here’s how we do it for this rule:

Now, anytime you peek back at your main diagram, you get a visual cue that J cannot ever go in the 4th spot. You’ll find that writing it like this also makes it much easier to remember. It should be pretty clear to you that this strategy beats repeating to yourself four times “J shall not go in 4.” Drawing it out hijacks your memory and does a much better job helping you see what the rule means for how your pieces will go on the board. Let’s keep working with this strategy.

For our next rule, we have:

Trinidad will be its destination in week 7.

This is the easiest and best kind of rule. You simply slap a T game piece in the 7th spot. Now that T is there for any possible order you can make. The possibilities for the game get a lot more limited with that T stuck there. Here’s how our main setup looks now:

Next, we have the rule:

Freedom will make exactly two voyages to Martinique, and at least one voyage to Guadeloupe will occur in some week between those two voyages.

Now things are getting a little bit harder. This one should not be drawn right in the main diagram. Instead, put it off to the side, below your list of game pieces, like this:

This visually captures the fact that you need to see a chain in there with M, at least one G, then another M. I use the abbreviation “AL1” for “at least one,” as it’s quite common to see rules that call for at least one or at least two of something. I’d also do a little modification to your list of game pieces, now that you have more information on them. Put a bracket around two M’s, and now you know you have exactly two “M” pieces.

Next rule:

Guadeloupe will be its destination in the week preceding any voyage it makes to Jamaica.

This is an example of a conditional rule, meaning it’s a rule that only applies if certain things happen. In this game, anytime you see a J, you need to see a G in front of it. Anytime a J happens to be in the order, that G in front is absolutely required. Here’s how we diagram that:

This newly diagrammed rule tells us that anytime we see a J, we better see a G in front of it, or we’ve made an error. Conditional rules can be tricky at first. We’ll help by drilling you like crazy on them in later lessons.

Finally, we reach our last rule.

No destination will be scheduled for consecutive weeks.

This really starts to limit the orders. No two Gs can be next to each other, no two Js, etc. I diagram this rule like this:

…where the XX box stands for any two variables of the same kind (e.g., GG or TT or JJ or MM). The slash across the XX box means that we can’t see the same letter twice in a row.

This is a bunch of separate rules combined. If it seems easier at first, it would be totally okay to write them all out separately. Ultimately, the best way to diagram a rule is usually the way that will help you understand it best.

Here’s how our main diagram looks now, with all the rules either written in the diagram or off to the side (nothing new is added here):

With this all drawn, it’s going to be about 100 times easier to play around with how the variables get ordered. At this point, you might want to get a first look at how this all works for solving the actual questions.

Watch this video for a complete walkthrough of this game and its accompanying questions. Again, there is no need to pay super close attention and memorize the diagramming techniques yet. The idea is just to see what the process of solving a game looks like.

June ’07 Game 3 Walkthrough

That’s it! As far as basic ordering games go, it does not get more complicated than this game. Armed with a similar diagram, you can crush any basic ordering game you face.

When it’s all flowing together like this, games look pretty easy. Here’s the good thing: almost every single game in the history of the LSAT works just like this one. There is a set of variables, and you will be placing them on a board according to the rules. Fundamentally, you are always doing the same couple of tasks.

Right now, I want to uncover for you the fundamental nature of all games. Keep this in your head, and you will always know what you should be doing when you solve games.