The LSAT sequencing games require you to arrange variables. In order to demonstrate how to notate and diagram these games, let’s take a look at a basic sequencing logic game.  A PDF version of the logic game can be found here. Work through the logic game yourself as you read this post. Writing on paper will help you retain the information.

Sequencing Logic Game

As you read through the scenario, you should be attempting to identify which game type you are dealing with. Obviously, you knew in advance this time that you were dealing with a sequencing game. But you also could have identified the game type just by looking for clues in the scenario. The words “stand in line” are a big hint that you will probably be arranging the order of the variables. The words “the spots are numbered 1-7 from front to back” are also a big hint. And if you still weren’t sure of the game type, a quick glance at the rules would give you definitive evidence that you are dealing with a sequencing game.

From the scenario, we learn that the this sequencing game contains seven spots numbered 1-7. To make this easier to visualize, you should make a diagram like so: Each position in the diagram represents a corresponding position in the game.

We should also list our variables: We’ll use our variables on the diagram. Think of the variables as game pieces, and think of the diagram as a game board. And as with all games, we need to know the rules.

We will write each rule down in a easy-to-read form of logical notation. If possible, we will also create a visual representation of the rule on our diagram.

RULE 1

Gertrude must stand before Linda.

In logical notation, we use a dash to represent sequence. In this rule, G is before L in line. Therefore, in logical notation, this rule reads: So what does this rule tell us? It states that G must come before L in line. To be clear, we don’t know anything about how far apart these two variables are; G could be directly before L or six spaces before L. We only know that G is somewhere before L.

We can make two inferences from this rule. First, we know that G is not last in line. After all, how can G be last in line if it comes before L? Second, we know that L is not first in line.

RULE 2

Katherine must not stand 2nd in line.

We will write this rule as: The “2” represents position 2 on the diagram, and the tilde (~) represents a negation. You can also put a slash through the variable to represent negation if you prefer.

This rule is self-explanatory. Katherine cannot be in the 2nd spot in line.

We will also represent this rule visually on our diagram. RULE 3

Nancy stands third in line.

We will write this rule like so: We will also represent this rule visually on our diagram. RULE 4

Henry must stand after Gertrude.

This is a similar rule to the first. We will represent it with a dash: Notice though that both this rule and rule 1 involve the variable G. This should alert you that the rules might be related. Thus you should attempt to combine the rules. When we combine this rule with rule 1, we get: So G must come before both L and H in line. We now know that the earliest G can be in line is fifth. We also know that neither L nor H can be first in line.

RULE 5

Mary stands either fourth or sixth in line.

We will represent this rule like so: M must be in either spot 4 or 6. So if M is not in the fourth spot, then it must be in the sixth. And if M is not in the sixth spot, then it must be in the fourth spot.

We will also represent this rule visually on our diagram. FINAL SET-UP

We now need to look for any floaters. Floaters are variables without rules. In this game, the only floater is J. So we’ll circle J to represent its special floater status.

With this in mind, our final set-up for this game looks like this: Now, we’re ready to tackle the questions.

QUESTION 1

From front to back, in which of the following orders could the students be standing?

You will see a lot of questions like this with sequencing games. The best approach here is to go through your rules one by one (the ones you numbered on your set-up) and eliminate each answer that violates the rule.

A. Gertrude, Katherine, Nancy, Mary, Linda, John, Henry

B. John, Gertrude, Nancy, Katherine, Linda, Mary, Henry

C. Linda, John, Nancy, Gertrude, Henry, Mary, Katherine

D. Katherine, Gertrude, Nancy, Linda, Mary, John, Henry

E. Gertrude, John, Katherine, Nancy, Henry, Mary, Linda

QUESTION 2

If Gertrude is fourth in line, which of the following must be true?

This is a “must be true” question.

Note that this question gives you a hypothetical situation that only applies to this question. For hypothetical questions like these, it is best to draw a small diagram next to the question. So if G is fourth, then we know that M must be sixth according to rule 4. And we know that L and H must come after G according to rule 1, which means that only 2 spots remain for these two variables! Because of rule 2, only one spot now remains for K: Which means that we only have one spot left for J as well: Now that we've made inferences, let's take a look at the answer choices.

A. Linda is fifth in line.

Linda could be fifth in line, but Linda could also be seventh in line.

B. John is first in line.

John cannot be first in line; he must be second.

C. Linda is seventh in line.

Linda could be seventh in line, but Linda could also be fifth in line.

D. Katherine is seventh in line.

Katherine must be first in line, not seventh.

E. John is second in line.

QUESTION 3

If John is 6th in line, which of the following cannot be true?

This is a “cannot be true” question.

First, we need to draw a small game board with this question’s hypothetical rule represented. We now look at the rules. Have any rules been triggered? Rule number 4 mentions position 6, which should alert you. And indeed, it has been triggered. With J in the sixth position, we now must put M in the 4th position. None of the other rules are directly triggered, so we now move to the answer choices. Try each one out until you find an impossible answer.

A. Gertrude is 5th in line.

Answer A is the correct answer. G cannot be fifth because there isn’t room for L and H to come after (as required by rule 1).

B. Linda is ffith in line.

Answer B is possible and therefore incorrect.

C. Katherine is first in line.

Answer C is possible and therefore incorrect.

D. Gertrude is second in line.

Answer D is possible and  therefore incorrect.

E. Henry is second in line.

Answer E is possible and therefore incorrect.

QUESTION 4

If Gertrude is 5th in line, which of the following could be true?

This is a “could be true” question.

Let’s make a small diagram. This scenario triggers rule 1, because H and L are now forced into the sixth and seventh positions. Since position 6 is now taken by either L or H, we’ve triggered rule 4. M must now be placed in the fourth position. These leaves only the first and second positions open, and rule 2 states that K cannot be in the second position. Therefore, K must be in position 1. This leaves only position 2 for J. Now, we just eliminate any answers that contradict our small diagram.

A. Henry is second in line.

Incorrect. Henry must be either sixth or seventh.

B. Linda is sixth in line.

This is the correct answer. Linda could be either sixth or seventh in line.

C. Mary is sixth in line.

Incorrect. Mary must be fourth in line.

D. John is first in line.

Incorrect. John must be second in line.

E. Katherine is fourth in line.

Incorrect. Katherine must be first in line.

QUESTION 5

Assuming that Linda and Henry stand directly next to each other in line, which of the following cannot be true?

This is a “cannot be true” question.

This question proposes a new rule that we cannot directly represent on our game board. Instead, we’ll translate the rule into logical notation. This is done by putting the variables next to each other with a “switch” sign above to represent that we don’t know the order of the variables. This can be combined with rule 1: Now all you need to do is try each answer out and see if the new rule will work with the answer.

A. Gertrude is second in line.

This is possible and therefore incorrect.

B. Henry is fourth in line.

This is possible and therefore incorrect.

C. John is second in line.

This is possible and therefore incorrect.

D. Katherine is seventh in line.

This is possible and therefore incorrect.

E. John is fourth in line.

Answer E is the correct answer. Putting J in the fourth position leaves no room for both L and H to stand next to each other. You might think that positions 1 and 2 are available, but G must come first. Putting J fourth makes the new rule impossible, which makes Answer E the correct answer.

The Basics of an LSAT Sequencing Logic Game