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#40228
Setup and Rule Diagram Explanation

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

The game scenario establishes that each of five buildings were owned by one of three families—the Trents, the Williamses, and the Yandells, and that each family owned at least one of the buildings:
PT73_Game_#3_setup_diagram 1.png
Since exactly five buildings are being assigned to the three families, but it is yet unknown how many buildings were owned by each family, the game is Defined-Moving. In addition, since each of the buildings was owned by exactly one family, the game Balanced.

When you create the setup, it is critical that the correct base be selected. There are two choices: the five buildings or the three families. Since each building was owned by exactly one family, it may be tempting to use the buildings as the base in order to reduce the level of uncertainty inherent in each group. Notice, however, the numerical restriction placed by the first rule: the Williamses owned more of the buildings than the Yandells owned. (Always read the rules thoroughly before deciding on a setup!) A base of five buildings would be a poor choice for the purpose of tracking that uncertainty.
  • Note: When in doubt, take a look at the wording of the answer choices to the List question, which is invariably the first question in the game. Here, each answer choice assigns the five buildings to the three families, reaffirming our decision to use the families as the base.
The first rule states that the Williamses owned more of the buildings than the Yandells. This is an excellent reminder to examine the Numerical Distributions that govern the assignment of the buildings to each family. Since W > Y, there are only two possible distributions, each of which is Fixed:
PT73_Game_#3_setup_diagram 2.png
(A 3-2-0 distribution whereby the Williamses owned three of the buildings and Yandells owned two is impossible, because each family needs to have owned at least one building, and a 3-2-0 distribution leaves Trents with no buildings to own).

Since these distributions create two separate scenarios in the game, it makes sense to create basic diagrams for each option. Each diagram will likely provide a considerable amount of information, which is why a Template-based approach will probably be sufficient. Indeed, Numerical Distributions—especially Fixed distributions—often lead to setting up the game with Templates:
PT73_Game_#3_setup_diagram 3.png
In both Fixed distributions the Yandells clearly owned only one building, which is an important deduction to make early on.

The second rule states that neither I nor M belonged to the owner of F. In other words, neither I nor M can be in the same group as F:
PT73_Game_#3_setup_diagram 4.png
While the vertical Not-Blocks are visually appealing, you can also use conditional language to represent the relationship between F, M and I:
PT73_Game_#3_setup_diagram 5.png
The last rule states that either the Trents owned S, or the Yandells owned I, or both. Since at least one of these two options must occur, we need to represent this rule conditionally: if the Trents did not own S, then the Yandells must have owned I. And vice versa: if the Yandells did not own I, then the Trents must have owned S:
PT73_Game_#3_setup_diagram 6.png
(Note that if the Trents did own S, then the rule would be immediately satisfied without any necessary implications involving the Yandells. Likewise, the rule would be satisfied if the Yandells owned I, without any restrictions involving the Trents.)

Let’s examine more closely the meaning of each of the two sufficient conditions above: if the Trents did not own S, then the only families that could have owned S are the Williamses and the Yandells. Likewise, if the Yandells did not own I, then the only families that could have owned I are the Trents and the Williamses. Thus, we can rewrite the rule using positive sufficient conditions instead of negatives ones, which would greatly facilitate its application:
PT73_Game_#3_setup_diagram 7.png
You should notice that if the Yandells owned S, then—judging from the first conditional rule above—they would also have to own I. However, our Numerical Distribution analysis clearly shows that the Yandells must have owned exactly one building. Therefore, the Yandells could not have owned S, and the rule can be simplified even further:
PT73_Game_#3_setup_diagram 8.png
Finally, the last rule has a particularly limiting effect on the 1-3-1 distribution. For the same reason the Yandells cannot have owned S in either distribution, the Trents cannot have owned I in the 1-3-1 distribution. If they did, then neither the Trents could have owned S, nor the Yandells could have owned I, in direct violation of the last rule.

The final diagram for the game should look like this:
PT73_Game_#3_setup_diagram 9.png
Observant test-takers will now notice that each of the two distributions outlined above is severely restricted by the conditional rules governing the ownership of the different buildings. For instance, if the Trents or the Williamses owned I, we immediately know who owned S—the Trents did. This leaves us with only three buildings, two of which (F and M) cannot have been owned by the same family. The most efficient way to proceed, therefore, would be to examine the assignment of I to each of the three families separately, effectively creating five Templates (remember—the Trents cannot have owned I in the 1-3-1 distribution):
PT73_Game_#3_setup_diagram 10.png
Next, examine the implication of the second rule (neither I nor M can be in the same group as F) to each remaining template:
PT73_Game_#3_setup_diagram 11.png
These templates reveal important inferences that would have been virtually impossible to make otherwise. For instance, in a 1-3-1 distribution, the Williamses must own G—a random variable whose limited placement in that distribution would have been difficult to predict. In the same distribution, the Yandells must own either F or I—another key inference. The game epitomizes the central proposition that is inherent in a Templates approach: you will spend a bit more time in the setup, but this time will be regained in the lightning-fast execution of the questions. It also highlights the close link between Numerical Distribution and Templates. Granted, not all distribution-driven games can be solved with Templates, and not all Template-driven games contain Numerical distributions. Nevertheless, there is a significant association between the two.
 gwlsathelp
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#78728
Hello, I am very interested in the way you began organizing your enumerated diagrams because mine came out as an unlabeled mess. How did you decide that one diagram was to be in #1 and only two diagrams for #2 and #3?
 Paul Marsh
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#78793
Hi gwlsathelp! First off, it's OK if you didn't draw out all five diagrams above. Drawing out the five diagrams is an example of a Limited Solution Set Game. Spotting Limited Solutions can be tricky. If you false positive a Limited Solutions Game (as in, you think you've found one but you really haven't), it can be a huge waste of time to draw everything out. Limited Solutions (and how to identify them) are discussed at length in Lesson 9 of the PowerScore LSAT Course Book; I'd highly recommend giving it a look. In addition, this blog post contains some very helpful tips on them:

https://blog.powerscore.com/lsat/bid-31 ... set-games/

The general trick to recognizing a Limited Solutions Set Game is to notice when the placement of one variable has an outsized impact on the rest of the layout of the Game. Here, depending on where we put the variable "inn", the rest of the game starts to fall in place as a result. For that reason, it's helpful to draw out each of the possibilities of where "inn" can go. Those 3 possibilities quickly lead us to the five diagrams sketched above. If you do draw those five diagrams, you can breeze through the questions for this Game fairly quickly.

But again, it's not necessarily a dealbreaker if you don't notice this is a Limited Solutions game (and therefore don't draw out all five of those Limited Solutions diagrams). Take a look at the diagram drawn in the post above, right above where it says, "Observant test-takers will now notice...". If your final diagram just looks like that, you'll be just fine. Identifying Limited Solutions games can be a helpful tool, but it's certainly possible to get all the questions for this game without using it.

Hope that helps!
 gwlsathelp
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#78838
Thank you, I will review chapter 9 and the link you sent me!
 damarisfonseca50@gmail.com
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#90062
Hi,

I am curious as to why the diagram cannot be:
T=1
W=3
Y=2

I understood the rule as W owns more buildings than Y. Therefore, if W owns 3 buildings, Y can own 2 buildings and the rule would still be followed
 damarisfonseca50@gmail.com
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#90064
damarisfonseca50@gmail.com wrote: Mon Aug 30, 2021 5:13 pm Hi,

I am curious as to why the diagram cannot be:
T=1
W=3
Y=2

I understood the rule as W owns more buildings than Y. Therefore, if W owns 3 buildings, Y can own 2 buildings and the rule would still be followed
**Apologies,
I have realized that this would be the 3-2-0 error, as you explained
 g_lawyered
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#93679
Hi P.S.,
As I throughly read the game set up explanation, I didn't make inference that is stated for rule 3. For rule 2, i simply wrote it out as: Ts or Yi or both. I want to make sure that I'm understanding this part of the explanation correctly:
The last rule states that either the Trents owned S, or the Yandells owned I, or both. Since at least one of these two options must occur, we need to represent this rule conditionally: if the Trents did not own S, then the Yandells must have owned I. And vice versa: if the Yandells did not own I, then the Trents must have owned S:
PT73_Game_#3_setup_diagram 6.png
(Note that if the Trents did own S, then the rule would be immediately satisfied without any necessary implications involving the Yandells. Likewise, the rule would be satisfied if the Yandells owned I, without any restrictions involving the Trents.)

The meaning of each of the two sufficient conditions above: if the Trents did not own S, then the only families that could have owned S are the Williamses and the Yandells. Likewise, if the Yandells did not own I, then the only families that could have owned I are the Trents and the Williamses. Thus, we can rewrite the rule using positive sufficient conditions instead of negatives ones, which would greatly facilitate its application:
PT73_Game_#3_setup_diagram 7.png
You should notice that if the Yandells owned S, then—judging from the first conditional rule above—they would also have to own I. However, our Numerical Distribution analysis clearly shows that the Yandells must have owned exactly one building. Therefore, the Yandells could not have owned S, and the rule can be simplified even further:
PT73_Game_#3_setup_diagram 8.png
Finally, the last rule has a particularly limiting effect on the 1-3-1 distribution. For the same reason the Yandells cannot have owned S in either distribution, the Trents cannot have owned I in the 1-3-1 distribution. If they did, then neither the Trents could have owned S, nor the Yandells could have owned I, in direct violation of the last rule.
Question #1: Rule 3 has 3 statements in it, in which AT LEAST 1 must occur, correct? Which is why the explanation has conditional reasoning of AT LEAST 1 of Ts or Yi happening (as sufficient condition) and then Ts and Yi both happening. Is that what rule 3 means?

Question #2: We can make templates based of this rule, and infer that we CAN'T have both Ts and Yi in the 1-3-1- template because that would break rule 2.
If we had Ts and Yi in 1-3-1 it would look it: (this breaks Rule 2 that F can't be with M)
T: s
W: f, g, m
Y: i

BUT Ts and Yi together can ONLY happen in the 2-2-1 diagram as:
T: s, f/m
W: m/f, g
Y: i

Did I understand the templates correctly? Because while I did ID the Numerical Distribution, I missed the implication of Rule 3 & the templates it leads to BIG time. Can someone please clarify this? :-? :0

Thanks in advance!
 Adam Tyson
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#93849
It looks like you did understand the templates correctly, so good work there.

A statement that "either this or that must occur" can be represented conditionally as "if this does not happen, then that must happen." The possibility of both things occurring should always be considered, unless the rule explicitly states that they cannot both occur ("but not both") or some other inference, like a numeric distribution, makes that impossible. Add that to your conditional toolkit and you can expect to see it pop up again, both in games and in LR.
 g_lawyered
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#94725
Thank you for that explanation Adam!
 frk215
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#94887
Hey folks! Thank's breaking down the templates! So because there were limited options and spaces (which I recognize is a sign that the templates approach may be correct), I just plugged and chugged through the questions with the rules clearly in hand. Because it was so easy to fill in variables I was able to knock them out pretty quickly— until I hit 18. At that point, I skipped it in favor of completing the section in time. It seems like the templates are most needed for #18 because that question requires a complete list of possibilities, which as we know is pretty much impossible with templates.

So, here's my question. Let's say I've got game 3 and 4 of this section left with about 15 minutes left on the clock. Was it right for me to chug through the questions without templates (esp given that there are only 5q) or should I have done templates? Would the amount of time poured into templates and that one additional q won over be enough to justify the approach?

(PS, i ended up being able to finish the last game as well with all q right except for #23 when i ran out of time) Thanks!

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