Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Balanced-Defined, Moving, Identify the Templates game.

A brief glance at this game reveals that there are only five variables being distributed into three groups, with just four rules controlling the placement of the variables. This type of scenario suggests that the game should be on the easier side, and indeed this game is favorable for most test takers.

The first sentence of the game scenario establishes that five performers—T, W, X, Y, and Z—sign with three different agencies—F, P, and S. This can be diagrammed as:

PT53-Dec2007_LGE-G1_srd1.png

The second sentence establishes that each performer signs with only one agency, creating a Balanced scenario. With each agency also signing at least one performer, the minimum requirement of performers-to-agencies is 1-1-1, leaving two performers unassigned. This creates two unfixed numerical distributions: 3-1-1 and 2-2-1.

With the basics of the grouping arrangement established, we can turn to analyzing the rules.

Rule #1. This rule establishes that X is assigned to agency F.

PT53-Dec2007_LGE-G1_srd2.png

Because performers can only sign with one agency, this rule eliminates X from further placement consideration, and it also allows F to meet the minimum requirements of signing at least one performer.

Rule #2. If X and Y do not sign with the same agency, then Y cannot sign with agency F because X is already assigned to F per the first rule. This rule is best diagrammed as a not-block and a Y Not Law:

PT53-Dec2007_LGE-G1_srd3.png

Rule #3. This rule establishes that Z and Y are a vertical block, and when this rule is combined with the first and second rules, we can infer that Z does not sign with F. This inference is best drawn as a Z Not Law:

PT53-Dec2007_LGE-G1_srd4.png

With the ZY block eliminated from signing with F, the only two options for ZY are P or S. This strongly suggests making two templates—one with ZY signing with P, and one with ZY signing with S. However, we will hold off on taking that approach until after evaluating the final rule.

Rule #4. This rule introduces a conditional relationship that is best represented as:

PT53-Dec2007_LGE-G1_srd5.png

Note that this rule does not form a constant TW block because as long as T is not signed with S, T and W do not have to sign with the same agency (this is an important insight, and one that is tested in the questions). Nonetheless, this rule allows for the further inference that when T signs with S, then Z and Y must sign with P (because when T signs with S then W signs with S, and adding the ZY block to S would leave four performers signed with S, one with F, and no performers for P, a violation of the numerical conditions imposed in the game scenario). Thus, if T signs with S, Z and Y must sign with P.

With this final rule considered, the most productive step is to explore the two templates created by the ZY block.

Note that this rule does not form a constant TW block because as long as T is not signed with S, T and W do not have to sign with the same agency (this is an important insight, and one that is tested in the questions). Nonetheless, this rule allows for the further inference that when T signs with S, then Z and Y must sign with P (because when T signs with S then W signs with S, and adding the ZY block to S would leave four performers signed with S, one with F, and no performers for P, a violation of the numerical conditions imposed in the game scenario). Thus, if T signs with S, Z and Y must sign with P.

Template #1: Z and Y sign with P

When Z and Y sign with P, only T and W remain unsigned. As one of the two must sign with S in order to meet the numerical minimums established in the game scenario, we can infer that W must sign with S. This occurs because if T signs with S, then from the fourth rule W must also sign with S. And, if T does not sign with S, then W is the only remaining performer, and thus must sign with S. Thus, each performer except for T is placed, and T can sign with any of the three agencies:

PT53-Dec2007_LGE-G1_srd6.png

This template has several numerical configurations, and both the 3-1-1 and 2-2-1 distributions are possible. The 3-1-1 can only occur if P is the “3” (because P already has Z and Y), leading to a fixed 1-3-1 distribution. The unfixed 2-2-1 can match any configuration as long as P is one of the “2s,” leading to either a 2-2-1 or 1-2-2 fixed distribution.

Template #2: Z and Y sign with S

When Z and Y sign with S, T cannot sign with S because then there would be no available performer to sign with P (the last rule would force W to sign with S if T signs with S). So, T must sign with F or P.

W can sign with any of the agencies, unless T signs with F, in which case W must sign with P in order to meet the minimum numerical requirements.

PT53-Dec2007_LGE-G1_srd7.png

This template also has several numerical configurations, and both the 3-1-1 and 2-2-1 distributions are possible. The 3-1-1 can only occur if S is the “3” (because S already has Z and Y), leading to a fixed 1-1-3 distribution (and W would be the third performer signed with S). The unfixed 2-2-1 can match any configuration as long as S is one of the “2s,” leading to either a 1-2-2 or 2-1-2 fixed distribution.

Combining the numerical information in both templates, only the following fixed configurations are possible:

PT53-Dec2007_LGE-G1_srd8.png

With just the two templates in hand, you should feel in control of the game as you attack the questions. If you take the further step and consider the numerical implications created by each template (as you always should), you will find this game easy.

[SherryZ]

Dec 2007 LSAT, Sec 2 LG:

Hi there, thank you for your generous help!

I would like to know what kinda set up is the most efficient way to solve this question. I listed out different kinds of templates and possibilities, but it took me much time

Also, could you tell me how to solve the Q3 quickly? It is a global question. It try each answer choice would be time-consuming.

Thank you so much for your help!

---Sherry

[Dave Killoran]

Hi Sherry,

When you make templates or possibilities, the problem is that often it does take longer. But then you gain back that time while doing the questions. The way we approach this game is to make templates, so that is the most efficient approach. It sounds like it might have made you a bit nervous to spend that extra time, however. That's part of the bargain you make when you choose that approach.

In question #3, one of the benefits of the two templates is that it makes Global questions much easier, and we simply scan those two templates to eliminate incorrect answer choices. This is, again, one of the benefits of spending that extra time in the setup. Time-consuming questions like this one suddenly become less time-consuming because you know so much more about the game.

Thanks!

[knightcap]

you mention two templates. I came up with 4 or 5 templates. Can you post your two templates? Thanks!

[Eric Ockert]

Hi there!

It's a bit difficult to draw the diagrams themselves on this Forum. But the two templates essentially revolve around the placement of the YZ block. Since X is always with the Fame Agency, and Y cannot be with X, then Y must be with either the Premier Agency or the Star Agency along with Z. So the two templates would be:

#1

X: Fame Agency
Y: Premier Agency
Z: Premier Agency

W: Star Agency (at least one person has to go to Star. Either W or T, and if T goes there W is automatically there. So W is always on the Star Agency.
T: Random, can be placed on any of the three agencies.

#2

X: Fame Agency
Y: Star Agency
Z: Star Agency

T: Fame or Premier Agency (T cannot be on the Star Agency here, because it would force W to be there too, which would leave no one for the Premier agency.)
W: Random, can be placed on any of the three agencies.

Hope that helps!

[kvb]

Hi,

Besides the fact that Y and Z can't go on Fame Agency, are there any other global inferences in this game?

[Jennifer Janowsky]

Hi!

There are a few more inferences that can be made if you look further.

As we saw, there are 2 major templates in this case:

F P S
X Z _
. . Y

and

F P S
X _ Z
. . . . Y

This illustrates all of the rules, except that Ts---->Ws. On the first diagram, W and T need to be placed. T can go into any: if T is placed in F or P, S is blank and W must fill S. Additionally, if T is placed in S, then Ts---->Ws. Therefore, W must be in S in the first template:

F P S
X Z W
. . Y

In the second template, T cannot go into S because Ts---->Ws, leaving P empty. T could, however, go in either F or P. Either W or T must occupy P, as it cannot be empty:

F P S
X W/T Z
. Y

Those are some additional Global inferences.

Hope that helps!

[kvb]

Thank you.

[okjoannawow]

Hi,

I had a question concerning the ST WT rule. When the necessary (ST I think) is failed, that means the sufficient fails, right? Which means that W cannot be placed with in S. I've seen in some explanations of this game W is free to float between any of the talent agencies, including S without T. I'm confused about that rule.

Thank you!

[Jay Donnell]

Hi okjoannawow!

I want to hop in and help clear up this question, as I know how frustrating this feeling can be!

Rule 4 in the game states that: "If Traugott signs with Star Agency, West also signs with Star Agency."


I personally would have built my game diagram like the following, which then allows me to draw the rules exactly
as they fit into the game:

F: ___

P: ___

S: ___

(We only know that at least one person is guaranteed into each agency, so the one dash per agency is all I will use to begin the diagram)

With this master diagram, I would draw out rule four as such:

S: T --> S: W cp: (~S: W --> ~S: T)

This means that IF Traugott signs with Star Agency, then West must also. But, if Traugott does not sign with Star, then the rule essentially evaporates and allows West to sign anywhere they please.

Also, West signing with Star agency is no guarantee in itself that Traugott must as well, as we can never use a necessary condition as if it has any power to guarantee deductions running backward across the one-way conditional arrow.

I think perhaps your initial misunderstanding of the rule itself was more of an issue than a broader conditional concern, but I hope this provided some help either way!