An Intro To Basic Linear (Ordering) Games – Free LSAT Logic Games Lesson

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logicgamesbrainWhen you start out attacking LSAT logic games, basic linear games (sometimes also called ordering or sequencing games) is where you should start. Here, in a completely free, comprehensive lesson, we’ll cover some of the most effective basic techniques. The goal is to give yourself a powerful way to visualize these games so that you can do them really, really quickly without placing undue strain on the brain.

If you are starting out learning logic games or you are struggling with linear games techniques, bookmark this page now. Learn this stuff and you’ll be well on your way to mastering basic linear (ordering) games. Those of you who know linear games cold might still wish to scan through and see if there is any diagramming technique that’s unfamiliar to you.

Introduction To Basic Linear (Ordering) Games

First, a word on credentials, because who wants to listen to someone who doesn’t know what they are talking about, right? Forget being bashful– I’m pretty damn good at logic games. I’m a 173 scorer (-1 on LG, -4 RC, -1 on each LR section) and former professional LSAT tutor. So on the actual test I did get one wrong on LG. Now, I’m here to help you avoid that painful outcome. I’m just playing– a minus one on LG really isn’t that bad (You can still get a 180 with -1 LG). But, I really am here to help you get started mastering games.

If you need a goal, strive to get it so you never get more than 1 or 2 wrong on every games section. While it might seem impossible now, that kind of consistency is, believe it or not, fairly achievable on the games section. Most 170+ scorers have the games section more or less locked down. All the information is right there on page, so it’s perhaps a little less tricky than the other sections, where they lay all kinds of traps.

Also, Josh is here to help you too. He’s a 177 scorer who got none wrong on games. If you have any questions about linear games or anything else related to logic games, just ask in the comments and one of us will get back to you.

Okay, now let’s look at some basic linear games techniques. I spent a lot of my time as a tutor working independently from any prep company. These are the techniques that I consider rock solid. Adopt anything in here and you won’t go astray.

Setting Up Basic Linear (Ordering) Games – The Main Diagram

First, and this holds true for any logic game, DON’T EVEN THINK ABOUT DOING THE WHOLE THING IN YOUR HEAD. Every game that I’ve ever encountered (I’ve seen every single one) can be done faster if you setup a way to visualize the game.

First, let’s show you how to make what’s called a main diagram. You always want to do this on every problem. The main diagram is the one you get down that contains just the rules from the main prompt (also called the stimulus). It’s your way of visualizing the game as whole. With a main diagram, you’ll have an easier time picturing where things go. You’ll also have easy reference to the main rules of the game.

Linear games are just what you would think they are from the name– you are gonna to take a bunch of variables, line them up, and figure out what orders they can go in. Here is what the first part of a typical linear game prompt looks like:

A delivery van is set to deliver soda to six grocery stores—F, G, H, J, K, and L—over the course of six days. Exactly one delivery is made each day and soda can’t be delivered to any store twice.

Looking at this prompt, what we have here is two sets of variables– days and stores. With the days, you already know they go in order, 1 through 7. That’s typical of an ordering game. You are always going to know how one of the variable sets, days of the week, aisles in a store, floors of a building, etc. lines up. It’s the other set of variables that you have to place to figure out what order they’re in. Here, that’s our grocery stores.

Always, always use the group that you already know the order of as your base. Here, that’s the days. Follow that rule, and this is what your base will look like:

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The other variables, F, G, H, J, K, and L are going to be going in to these slots that you’ve made. Pretty simple huh? Don’t keep referring back to the prompt to see what your variables are. Write them out big to the left of of your main diagram like this:

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Now you can easily see the variables that you’ll be plugging into this base. Here it was an easy decision to just write F, G, H, etc., but what if the variable are named something more complicated? Say instead we are delivering to six towns: Francestown, Goffstown, Hampton Falls, Jaffrey, Keene, and Londonderry (all towns I used to play against in soccer). You would still do it exactly the same way. Don’t complicate things by writing “HF” for Hampton falls. Why? It’s not necessary, from here on out, you are just thinking about where “H” goes, not Hampton falls. Think abstractly.

Logic games are all about abstraction. What does that mean? It means that half the time by the end of the game I don’t even remember what kind of variables I’m working with are anymore. Were they towns? Grocery stores? Alien invasions? It really doesn’t matter. You are just putting some game pieces (the free variables up on the left) into some spaces (the numbered slots that make up your base). Once you strip away the irrelevant particulars, all of these games are exactly the same. The sooner you start looking past the distracting details and start looking at these games as just minor variations on the same game, the sooner these games are going to get really, really easy.

Now that we’ve got the base and the variables all written out, it’s time to add the rules.

Adding The Rules

Now, the rules are where things get complicated. Every LSAT prep company has their own ideas about how to write out rules. I’m only going to be talking about the good ways of doing it. You can choose the style you like, just remember, you want to be consistent: once you’ve decided which way to represent a rule is best for you, stay consistent when using it.

Let’s look at the most basic types of rules by adding them to the prompt we started with earlier. This is what a complete LSAT ordering game prompt might look like:

Example LSAT LG Linear Game Prompt:

A delivery van is set to deliver soda to six grocery stores—F, G, H, J, K, and L—over the course of six days. Exactly one delivery is made each day and soda can’t be delivered to any store twice.

The delivery G comes after the delivery to H.
The delivery to L comes after the delivery to J.
J’s delivery comes exactly 3 days after the delivery to F.
Delivery to H is either on the first or third day.

The rule “The delivery to G comes after the delivery to H” is a good example of the most basic type of rule you encounter in in ordering games, rules about whether an variable comes before or after another variable. G is going to go later in our diagram than H. You need a powerful way to represent that visually so you don’t forget. Don’t just rewrite the rule. Get it in diagram form! There are two really common ways to express this:

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The first method, using the ‘greater than sign’ was the way I did it when I took the test, though I’m beginning to think I prefer the dash method.  Which one of these techniques you prefer might influence which company’s books or class instruction you choose for your LSAT prep, so keep that in mind as you see them in action. It doesn’t matter here, but when the rules get really complicated it might make a difference to you which one you use. Scroll down to ‘Combining Rules’ section of this post to see what I mean.

Now, let’s look at the next two rules. The second rule is simple. That’s just another rule that you are going to write with the > sign or the dash sign:

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Mini-Lesson: Block Rules

What about this next rule? J’s delivery comes exactly 3 days after the delivery to F. That looks a little harder to represent visually. However. There is a great way to do it. check this out:

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Write that and it shows you in a straight forward visual way F is always two spaces in front of J. You know how we said these variables are like games pieces that we place? Well, I like to think of this kind of block that way too. It’s a big game piece, a chunk that is going to have to go in there somewhere an push the other pieces around. That’s why we draw a box around it, so you know that it is a fixed entity. Think to yourself “I’m going to always have to drop this big block into my base somewhere.” Or think, “I’m a big crane and I’m going to stack this giant box here somewhere.” Or maybe, “I’m making a big lego chain. This is like one of the bigger lego pieces.” I don’t really care what you think, just visualize these big chunks getting in the way of the other variables some way so that it’s memorable to you.

Also, when I work with something like this in my head, I always refer to it by the variables it contains, so I would call this the “F J block.” Always be aware of what these blocks are doing. When you get stuck in a game, it’s often because you have forgotten to take account of a rule. If you haven’t accounted for it, ask yourself “what is that F J block up to?”

There are a lot of similar rules that can be written using this block approach. They are different types of pieces that you’ll be fitting into you base. Let’s look at some rules  in this family:

Rule 1: X goes immediately after Y

Rule 2: X is always either immediately before or immediately after Y

Rule 3: There is exactly one spot between X and Y

Let’s take a look at how some of these should look when you diagram them on paper:

Our example Rule 1 is pretty straight forward. It’s gonna look like this:

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I’m always happy when I get one of those rules. They are pretty easy to work with and remember. Just drop that XY chunk in somewhere and you are good to go.

Rule 2, X is always either immediately before or immediately after Y, is a little tougher. Now they can flip around. How do you represent that? There are a few good ways I know to choose from.

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Apologies if I looks like I’m trying to teach you about sex chromosomes. I’m not. The first choice is to put a circle around it. The circle implies that X and Y could flip around. For me, that’s the preferred strategy. The circle easily helps me remember that these guys are reversible. However, some people might prefer the XY block with the little arrows indicating that they can switch. The arrow is a pretty powerful reminder. If you are really worried about forgetting that these are reversible try this:

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That shows you that there are two spots next to each other that are both taken by X and Y, but you don’t know which one is where. I like this rule representation because it is fairly screw up proof. You aren’t as likely to forget by the end of the game that these two can flip. The other reason it’s good is that it is similar to how we represent other rules. It’s also easy to drop right into the base. Let’s take a look at Rule 3. “There is exactly one spot between X and Y”. You would typically represent that like this:

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That shows that there is a space in between these two, and you don’t know for sure if X is first or Y is first. You can do this with one, two, even three spaces if you need to (though I can’t recall seeing a rule that called for more than two spaces in between).

Alright, that cover some common block rules. Let’s get back to looking at our larger example. We have another kind of rule there that we haven’t seen yet.

Mini-Lesson: Rules That Go Straight In Your Main Diagram.

The last rule from our main example is: Delivery to H is either on the first or third day. Now you might be thinking, how the heck do I write that rule out? Well, you don’t. At least not on the side. This is part of why you have a big pretty diagram– Some rules are best drawn straight in to your main diagram.

Lets take a look how this H rule looks in my main diagram.

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The arrows show you that H is going in one of these two spots each and every time. Rules that go in your diagram like this can be hard to remember because they are so damn specific. A couple problems into the game I’m usually thinking, “now where did H have to be again?” That is exactly why we put a GIANT UGLY ARROW in the middle of our main diagram! I want you to be completely unable to avoid staring this rule in the face anytime you look at your main diagram.

Writing rules straight into your main diagram is a common LG strategy, and trust me, it’s gold. On other game types it can require a little creativity, but with basic linear games it’s generally pretty straight forward. Obviously, if you know exactly which spot a variable is going in, write it straight into your main diagram.

The other very common rule type where you’ll want to use the write-in technique is with rules about where things can’t go. Let’s say we had the additional rule “J is not 5th.” The best way to deal with that is again to get it right in your main diagram:

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Just write J under spot 5 and cross that bad boy out. Now you know that for the rest of this game, it can’t go there. A word of caution. These are easy rules to forget. When you attack these games you’ll be making a lot of little mini-diagrams right next to the question you are answering to try and work through the various scenarios. Here’s some very good advice: with tricky to remember rules like the H rule and the J rule written into this diagram, it’s often a good idea to quickly redraw them each time you start a new mini-diagram next to the specific question you are answering. It doesn’t really take any time, and it will save you from mistakes. Even if you don’t do it all the way through the game, it can really help you fix the rule in your mind if you do at least a few times.

Let’s look at one more in diagram rule that’s useful for a situation I am seeing more and more on modern tests. Forget all the other rules for a moment. Let’s say that you have a new rule “G can’t be any earlier than day 4.”

That’s a tricky rule to diagram. One common suggestion is to do it kind of like we handled the J rule above. That would look like this:

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However, I’m not the biggest fan of doing that way. Often the bottom starts getting cluttered up. When a variable can only go in two or three consecutive spots, I recommend using a bracket above the base to show where it can go. Let’s take a look at that:

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Compare that with the H rule where it’s only going in one of two spots. The bracket instead tells you that it can go anywhere inside there. To me, that’s a better reminder of where that G is going to be than using the cross-outs below. Consider using this technique instead too if it seems more natural to you.

Combining The Rules For Linear Games

Now we get the tricky part. You always want to combine rules if you can do it neatly. Combined, they are easier to work with mentally. Think of as reducing the number on pieces you have to play with. Let’s take a look at this using our main example and you’ll see what I mean.

Here are the rules we had to start with:

The delivery G comes after the delivery to H.
The delivery to L comes after the delivery to J.
J’s delivery comes exactly 3 days after the delivery to F.
Delivery to H is either on the first or third day.

That’s going to result in 3 rules written out on the side:

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Now take a look at that. Is there a way to make it simpler? Two of these rules overlap. It’s better if you just jam them together, like so:

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Et voila! Genius, no? Combined rules are happy rules. It’s way easier to just deal with this one big chunk rather than juggling the two other rules. Now we’ve got the same nice big F J block and we easily remember that L lands somewhere after it. This provides a good opportunity to pause and take a look at the whole diagram altogether. Again, forget about those two rules I added. We’re just looking at the ones from this main prompt:

A delivery van is set to deliver soda to six grocery stores—F, G, H, J, K, and L—over the course of six days. Exactly one delivery is made each day and soda can’t be delivered to any store twice.
The delivery G comes after the delivery to H.
The delivery to L comes after the delivery to J.
J’s delivery comes exactly 3 days after the delivery to F.
Delivery to H is either on the first or third day.

And here’s your diagram:

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Apologies for my less than artistic drawings, but there you have it. The F J block with L is going to be very easy to work with. If only rules were always so easy to combine. Let’s take a look at a more advanced combination. Funnily enough, the toughest rules to combine are often the most basic ordering rules, but it’s still worth doing. Consider this set of rules:

T comes before W and X

Z comes before X

I’m going to show you two ways to do that and you can decide which one you like better. Using the “>” technique, these rules are going to look like this:

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This shows you that T is before W and X, but the dotted line tells you that you don’t know whether W or X comes first. They float relative to each other. Then we have another arrow to remind us that no matter what X has to come before X. Note that X can still be in front of or behind T. I like this approach– the dotted line helps me remember the inherent flexibility of the order. Now here’s the other way:

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This might strike some as more intuitive. You just draw dashes between any letters that have a relationship to each other. Just remember, no dash, then no rule. W and X for example can still be in either order relative to each other.

When you are selecting a prep company to learn from this is a key difference in strategies. Look through their free materials and you can figure out which technique they go with. Our three favorites are Powerscore, Blueprint, and 7sage. Powerscore uses something like the first approach, whereas Blueprint and 7 sage use the dash method.

Double Options

There is one last major linear/ordering game technique that we haven’t covered yet. A really common situation that comes up in logic games is that you realize that there aren’t many variables left that can go in a spot. When you narrow it down to just two, you always want to express it in your diagram:

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This, for example, would tell me that only X and Y can go in the 2 spot. As you can see, that’s really what we were doing when we had those double options blocks…

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… except here we know that this isn’t moving around. Always try to get these double options in place when you can. They make it really easy to figure out the order from there.

How To Move On From Here

Believe or not, just the techniques you learned here should be enough to tackle almost any basic linear game. We’ll have a post on more advanced aspects of making inferences and mini-diagramming (building example scenarios next to each question) very soon. We’ll also add some free explanation examples from real logic games so you can see this stuff in action. Check back on this very post because we’ll add these links at the bottom.

If you saw something in here that you prefer to whatever strategy you were using, feel free to adopt it. Just remember to stay consistent with how you diagram a given rule type. Some prep companies try to convince you that you should stick with all of their strategies, however, there just isn’t any reason not to choose your preference among equally effective strategies. Everything I’ve shown you in here is a proven technique that will help you memorize the rules effectively and attack the game quickly.

Keep checking back for more free LSAT lessons on topics ranging from the most basic techniques to advanced strategies. If you are worried you are going to miss any free LSAT lessons, SIGN UP on the sidebar to receive LSAT advice sent to your email. We don’t bombard you. It’s just the good stuff. Also, follow us on twitter @onlawschool

As always, Josh and I are here to answer your questions. If you need help picking a strategy or anything else related to logic games, just ask in the comments! We’ll get back to you quickly. Good luck with your prep and work hard!

 

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6 Comments

  1. This page was helpful in showing me better ways to write my rules. However, I have a specific question on a specific practice question I am working on. I am just going to post it in the hopes that you can help me! Please help!

    [EDITED OUT]

    I apologize for the lengthiness of this question, but your help is greatly appreciated!

    • Hi Maureen,

      Sorry, I edited the question out because we can’t have other LSAC’s material on the site. They’ll come after us! However, I can answer the question if I talk about it in the abstract:

      It’s an advanced linear game. You want to have a base of 1, 2, 3, 4
      then have a row where you put in the stops, and another where you put in who gets off. If you don’t follow, me, reread the LGB chapter on advanced linear games and that should make sense.

      The hard part that your dealing with is probably the last rule. Basically, that rule says:

      if J gets off at F or later, then G gets off at S or later.

      I know it’s hard to see that that is what that rule is saying. Don’t worry. The game you are looking at was notoriously hard. A lot of people struggled with that rule.

      The question asks us what happens is we know that G got off before S. That means that J had to get off before F as well (that’s the contrapositive of the final rule).

      Now ask yourself what other rule applies to J. V gets off before J. That means, if J gets off before F, then V had to get off before F as well. That’s your answer. D

      Though it’s a little hard to follow the chain, the key is to just calmly make the inferences that you can make and check at each stage if they answer the question. Whenever your stuck its good to see if you forgot to account for another rule. Here, that led us to the V > J rule that helped answer the question.

      • Thank you so much for your help. I do have a problem with contrapositives and it can ruin 3-4 questions for me on a game. Do you have any tips as to when contrapositives apply? Can they only be true when the rule says “if, then; otherwise”? They cannot be true if the rule says ” if, then”, is that correct?

        • Read this: http://lawschooli.com/conditional-reasoning-for-the-lsat/ You need to get that stuff down. Make sure you understand that a contrapositive is just expressing a valid inference that you can make from a conditional statement. For example, take the statement: If A then B. The contrapositive is: If not B then not A. That’s just the same as saying: If A then B. Not B, therefore, Not A. Read that lesson, you’ll be on your way to getting it.

  2. How do you notate the following rules efficiently?
    1. If A is not in, then either B or C, but not both, are in.
    2. If it is not the case that both B and C are in, then both D and E are in.

    • Hey Brent,

      For 1. Don’t obsess over it. Just anything that will help you remember.

      I would do A —-> B or C (not both)

      For rules like 2., I split that into two different main diagrams. Think of it as two different worlds.

      World 1: Not B and C —–> D and E

      World 2: Not D and E —–> B and C

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