Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Balanced, Defined Grouping game.

While this is not a terribly difficult game, it initially presents an organizational challenge. For each student, we have two attributes to keep track of—a speech topic and a major—which is why a decision must be made as to which variable set to use as the grouping base. The reason why we face this problem is inherent in the very nature of Grouping games: unlike Linear games, where linearity dictates the choice of base, Grouping games often present no obvious base set. Below we examine the pros/cons of each possible base:

Speech topics

• Using the speech topics as the base (F and L) creates a dual-value system, which is good news. And, thanks to the first rule of the game, we would know the exact size of each group (two students speak on friendship, and three speak on liberty). Unfortunately, we need to know not only who delivers each speech, but also what his or her major is. The relationship between these two variable sets would be difficult to represent using the speech topics as the base.

Student majors

• If we used the three student majors as the base (G, H, and J), the exact size of each group is given in the game scenario as 2-2-1, and need not be inferred from the rules. Unfortunately, as with the approach outlined above, for each group there would be two sets of variables to keep track of—the student’s name as well as the topic of his or her speech. This would be quite cumbersome, and the probability of mixing up the variable sets is quite high.

Student names

• We can also use the five student names as the base (M, N, O, P, R), which is promising for a number of reasons. Although this would generate the largest number of uniquely defined groups (5), each group would have only two attributes—a speech topic and a major. And, since each student delivers exactly one speech and has exactly one major, we can easily keep track of that information by creating a stacked set-up where each stack keeps track of a different attribute. Using the student names as the base would also let us create vertical blocks to represent the relationship between speech topics and majors, minimizing the uncertainty inherent in either of the first two approaches.

So, while each approach would allow you to complete the game, the simplest and most efficient way to set up this game would be to use the student names as the base.

Topics: F, L
Majors: G G H H J5

oct12_game_1_diagram_1.png

(It does not matter how you arrange the two stacks: either the Topic or the Major can be the top stack, and either one can be the bottom stack. What matters is that you keep the two variable sets separated).

With this basic structure in place, let us now turn to the rules.

The first rule indicates that exactly two students speak on friendship. Since there are a total of five students delivering speeches, and each speech is on exactly one of two topics (friendship or liberty), it follows that exactly three students speak on liberty:

• Topics: F F L L L5

To avoid having to remember which variable belongs to which stack, list the two variable sets to the right of their respective stacks, as shown below:

oct12_game_1_diagram_2.png

The second rule can be represented with two vertical blocks:

oct12_game_1_diagram_3.png

Additionally, because exactly two of the students speak on friendship (first rule), we can infer that the remaining three majors—G, H, and J—all speak on liberty:

oct12_game_1_diagram_4.png

The third and the fourth rules should be represented internally, directly on the diagram:

oct12_game_1_diagram_5.png

You should immediately notice an inference resulting from the third rule. Since no journalism major speaks on friendship, M cannot be a journalism major. This creates a J Not Law, leaving a G/H dual-option for M’s major, which must be added to the diagram:

oct12_game_1_diagram_6.png

The fifth rule adds two G Not Laws to the diagram, each resulting an H/J dual-option for P’s and R’s majors:

oct12_game_1_diagram_7.png

The last rule tells us that N is one of the two geology majors (with either M or O as the other geology major):

oct12_game_1_diagram_8.png

The final diagram for the game should look like this:

oct12_game_1_diagram_9.png

The first two rules proved crucial in establishing the relationship between speech topics and majors (the five blocks). These blocks, along with the rules that place some variables and create Not Laws for others, make the game quite manageable. 

[Brittney]

I had trouble with this grouping game. I wasn't sure how to really set this game up, so it threw me off. I listed the five people along the bottom. I know P and R can't be a geology major. I know N is a geology major and gives a friendship speech. M is a history major and gives a friendship speech. I know R gives a liberty speech. O would have to be geology because P and R can't and there are two. P and R are history or journalism. Is that everything?

[Jacques Lamothe]

Hey Brittney,

I think that there is a better way to set up the game. I recommend setting it up as a type of grouping game with Friendship and Liberty on the bottom. From clue 1, we know that exactly two people will be in the F group, which tells us that 3 will be in the L group. We can also determine which majors will be speaking in each group. Group F will have 1 geology major and 1 history major. That means we know group L will have 1 geology, 1 history, and 1 journalism major.

These are the types of clues you want to look for when deciding what variable should be the base when you encounter complex games. If you can determine things like exactly how many variables will be in a group and what kinds of majors will be in each group, that immediately give you some powerful inferences that you can use on the game.

However, I am not seeing how to reach some of the inferences that you mention. How did you get that N must give a friendship speech? Even though N is a geology major and there is a geology major that gives a friendship speech, that does not necessitate that N gives the speech. It's possible that missed something, so can you explain your reasoning? Thanks!

I hope this helps!

Jacques

[scoronado]

I'm having some trouble setting up this game. What should my base be?? Agh help!!

October LSAT 2012
Section 4
Question 1:

***The content of this question has been removed due to LSAC licensing restrictions***

[Nikki Siclunov]

Hi scoronado,

Thanks for your question about Game 1 from the October 2012 LSAT. While this is not a terribly difficult game, you are correct in that it initially presents an organizational challenge. For each student, we have two attributes to keep track of—a speech topic and a major—which is why a decision must be made as to which variable set to use as the grouping base. The reason why we face this problem is inherent in the very nature of Grouping games: unlike Linear games, where linearity dictates the choice of base, Grouping games often present no obvious base set. Below we examine the pros/cons of each possible base:

Speech topics

Using the speech topics as the base (F and L) creates a dual-value system, which is good news. And, thanks to the first rule of the game, we would know the exact size of each group (two students speak on friendship, and three speak on liberty). Unfortunately, we need to know not only who delivers each speech, but also what his or her major is. The relationship between these two variable sets would be difficult to represent using the speech topics as the base.

Student majors

If we used the three student majors as the base (G, H, and J), the exact size of each group is given in the game scenario as 2-2-1, and need not be inferred from the rules. Unfortunately, as with the approach outlined above, for each group there would be two sets of variables to keep track of—the student’s name as well as the topic of his or her speech. This would be quite cumbersome, and the probability of mixing up the variable sets is quite high.

Student names

We can also use the five student names as the base (M, N, O, P, R), which is promising for a number of reasons. Although this would generate the largest number of uniquely defined groups (5), each group would have only two attributes—a speech topic and a major. And, since each student delivers exactly one speech and has exactly one major, we can easily keep track of that information by creating a stacked set-up where each stack keeps track of a different attribute. Using the student names as the base would also let us create vertical blocks to represent the relationship between speech topics and majors, minimizing the uncertainty inherent in either of the first two approaches.

So, while each approach would allow you to complete the game, the simplest and most efficient way to set up this game would be to use the student names as the base.

Try it out and let me know if you encounter any problems. There is a fair amount of deductive work you need to do before attacking the questions, but once you make the right inferences this game is a cakewalk

Thanks!

[scoronado]

Thanks Nikki. I appreciate your time and help. I finally figured it out and got all the answers correct but it took me much more time than I have.

[oktos92]

Hello,

I agree that this is a very easy question. I literally solved it so easily after seeing how powerscore suggested we arrange it. However, when I first saw this question, like the previous students who posted, nailing down what will be my base was the issue. Please in a somewhat tricky question like this, is there any tip you can give that can help me determine instantly (at least on time) what might be the easiest way to set up the base?

Thanks

[Nikki Siclunov]

Hi oktos92,

The question you just asked is precisely what I sought to address by considering all three of the variable sets as the base, and then selecting the students as the base. I hope my reasoning is pretty clear, but if not - please don't hesitate to ask for clarification.

Thanks!

[angelsfan0055]

Would it be appropriate to do a templates approach for this game?
When I did it in my practice test I did not — though I did do a similar setup to what's in the explanation — but did not fare well.

When I reviewed, once I did the templates approach, the game was significantly easier.

Essentially what I did is I made one template for Manolo with History and another with Manolo in Geography. Through inferences, in Diagram 1: it becomes clear that Manolo has to go with History, N with Geography and O with Geography, Peng with Journalism and Rana with History.

Diagram 2 is a little more nuanced, but Manolo is wth Geography, N with Geography, Owen has options, P has options and Rana is History or Journalism.

Does this make sense at all? I've included a diagram too.

[Adam Tyson]

This game can be done with templates, although they aren't absolutely necessary. If I were to do templates on it, I would do them based on the distribution of F and L, since once I place a second F somewhere I will absolutely know that the other open spaces are Ls. That gives you three templates rather than two .

As to your diagram, it looks like you may have missed a few things. First, remember that there are exactly two Gs and two Hs and just one J. When M is an H, O MUST be the second G, because P and R cannot be. That means that one of P and R is an H and the other is a J. Which of those two Gs gets an F and which gets an L is up in the air.

In your second diagram you have three Gs, which is incorrect. If M is a G, then O, P, and R are all H or J - one J and two Hs, with no way to tell which is which. But you can at that point infer that N is an L! Be sure when doing your templates that you apply all the rules to each template, filling in everything that must be true. Pay attention to numbers, and to conditional rules, and to blocks, and sequences, etc.