Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping: Defined-Fixed, Unbalanced: Underfunded, Numerical Distribution game.

The game scenario establishes that a total of six photographs appear in three different sections of a newspaper—Lifestyle, Metro, and Sports—two photographs per section. Additionally, each photograph is taken by one of three photographers—F, G, and H.

PT76_O15 LG Explanations_Game #2_setup_diagram 1.png

Since we know the exact number of photographs in each section, the game is Defined. The scenario does not establish how many photographs belong to each photographer (this information is contained in the first rule of the game, as discussed below). Nevertheless, given that the available spaces (6) outnumber the available variables (3) with which to fill them, this is an example of an Unbalanced: Underfunded Grouping game.

When you create the setup, it is critical that the correct base be selected. There are two choices: the three sections or the three photographers. Since each section contains exactly two photographs, using the sections as the base provides the highest level of numerical certainty. By contrast, we are never told exactly how many of the photographs belong to each photographer: this information is established in the first rule, and requires an analysis of the numerical distribution governing the assignment of photographs to photographers. A base of three photographers would thus be a poor choice due to this uncertainty.

Note: Always read the rules thoroughly before deciding on a setup! And, if still in doubt, take a look at the wording of the answer choices to the List question, which is invariably the first question on in the game. Here, each answer choice assigns the photographs to each section, reaffirming our decision to use the newspaper sections as the base.

The first rule states that each photographer must submit between one and three photographs. Accordingly, there are two Numerical Distributions that govern the assignment of the photographs to photographers:

• 3 - 2 - 1
  2 - 2 - 2

Note that these two distribution are Unfixed, as we don’t know how many of the photographs belong to each photographer. You should also keep in mind that this distribution is entirely independent of the requirement to allocate exactly two photographs to each section of the newspaper.

The second rule states that at least one of the photographs in Lifestyle is by a photographer who has at least one photograph in Metro. Simply put, Lifestyle and Metro must have at least one photographer in common:

PT76_O15 LG Explanations_Game #2_setup_diagram 2.png

The third rule states that the number of H photographs in Lifestyle must match the number of F photographs in Sports:

• HL= FS

Note that this number could be a total of 0, 1, or 2.

The last rule prohibits G from appearing in the Sports section:

PT76_O15 LG Explanations_Game #2_setup_diagram 3.png

A typical final diagram for the game would look like this:

PT76_O15 LG Explanations_Game #2_setup_diagram 4.png

With all the rules in place, it is not immediately clear what inferences, if any, can be drawn on the basis of them. There are two ways to proceed:

• 1. Do nothing else and move on!
  
  Some students recognized the high degree of uncertainty inherent in this setup, and realized that the rules do little to narrow it down further. So, rather than hunt and hunt for inferences or attempt to use templates, they moved quickly to the questions. And sure enough, aside from the common List question to start, every question but Question #10 is a Local question. If you moved from setup to questions relatively quickly, you should have enough time to create the requisite setups for each of these questions.
  
  2. Make Templates!
  
  Uncertainty can be distressing, particularly when it comes to Logic Games; the formation of templates (even if somewhat time-consuming) can greatly improve your confidence and help you breeze through the questions. Despite the uncertainty inherent in the numerical distribution of photographs to photographers, let’s focus on the third rule – perhaps the most difficult rule to keep track of. Guess what? You don’t have to keep track of it if you examine its implications ahead of time. According to the third rule, the number of H photographs in Lifestyle must match the number of F photographs in Sports. That number could be a total of 0, 1, or 2, giving us a perfect segue into a Templates-based approach:

PT76_O15 LG Explanations_Game #2_setup_diagram 5.png

Each of these templates is quite restricted:

In Template 1, there are no H photographs in Lifestyle, and no F photographs in Sports. The last rule prohibits G from having any photographs in Sports, leaving us with no other choice but to assign H to both photographs in Sports. And, since neither of the photographs in Lifestyle are by H, both of them must be by either F or G:

PT76_O15 LG Explanations_Game #2_setup_diagram 5b.png

In Template 2, there is exactly one H photograph in Lifestyle, and exactly one F photograph in Sports. Since G cannot have any photographs in Sports (last rule), it follows that the other photograph in Sports is by H. In Lifestyle, the other photograph must be one of F or G:

PT76_O15 LG Explanations_Game #2_setup_diagram 6.png

What do we know about Metro? That section must share at least one photographer with Lifestyle, which can be any of the three photographers. However, you should notice that the two photographs in Metro cannot both belong to F: if that were the case, then F would have the maximum number of photographs allowed (3), leaving Lifestyle and Metro with no photographer in common. Consequently, at least one of the photographs in Metro must be by someone other than F, namely, G or H:

PT76_O15 LG Explanations_Game #2_setup_diagram 7.png

In Template 3, there are exactly two H photographs in Lifestyle, and exactly two F photographs in Sports. Since each photographer must have at least one photograph, and both Lifestyle and Sports are maxed out, we can infer that G must have a photograph in Metro. In addition, Metro and Lifestyle must have at least one photographer in common (second rule), which means that the other photograph in Metro is by H:

PT76_O15 LG Explanations_Game #2_setup_diagram 8.png

[srcline@noctrl.edu]

Hello

So can someone please explain the set up for this game? This is an advanced linear game correct?

L_

M_

S_ (not G)

Also i was not understanding rules 2 and 3. For rule 3 I diagrammed this as :

Hl=Fs but I feel like I may have this backwards.

Thankyou very much.
Sarah

[Clay Cooper]

Hi Sarah,

Thanks for your question. I would categorize this as a grouping game - but I don't think it would do you any harm to think of it as an advanced linear game instead.

This is how I would diagram it:

L | M | S
_ _ | _ _ | _ _

There is a specific notation device that I like to use for rules like the second rule here (which tells us that M and L have at least one variable in common) - I draw the blank as a box and call it the magic door, and it is meant to indicate to me that what appears in one box must also appear in the other. So, I would just substitute a small box for the first blank under each of L and M (I can't figure out how to draw that in this post, so you'll have to imagine it).

I think your notation of the third rule is pretty accurate: the number of the H's that appear in L must equal the number of F's that appear in S:

HL = FS

I think that would be a great start to the setup. Does that help any?

[srcline@noctrl.edu]

Hello Clay

Okay so we have 6 total. With two spaces above L M S ( 6 photographs to 2 spaces) So numerical distribution would be 2-2-2 and 3-2-1 (1st rule states no more than 3).

So since G is not in S , S has to have F or H.

Thankyou very much for your explanations.

Sarah

[LSAT2018]

For the third rule that, the number of Hue's photographs in the Lifestyle section must be the same as the number of Fuentes' photographs in the Sports section, would this be a biconditional? So would the number of Fuentes' photographs in the Sports section affect the number of Hue's photographs?

[Jon Denning]

Yep! Any time two things are said to be the same or equal it's biconditional!

Nice catch!

[FK00144]

so the first rule is saying that each photographer has anywhere from 1-3 pictures in total right?

I don't understand the numerical distribution part. I get how you got it, but if there is 2 pictures per section how can a photographer have 3 pictures in a section? (3-2-1) I thought the three spaces/ #'s represented the sections or do they represent the photographers?

[Adam Tyson]

I see your confusion here, FK00144, and I can clear it up for you. The distributions are not about the number of pictures per section - we know that is 2-2-2 - but about the number of pictures per photographer. It's possible that one photographer has a picture in each section, for a total of 3 pictures, while another has two pictures and the third has just one. That's all 6 pictures divided unevenly between the three photographers.

[haganskl]

Thanks for the clarification here regarding the 3 templates! I got 100% correct but I didnt template. I did consider rule number 3 and determined that all 3 possibilities could exist but that determination didnt prompt me to template, which is an ability I’m trying to strengthen. This forum is invaluable!

[parytownson]

In Template 1, there are no H photographs in Lifestyle, and no F photographs in Sports. The last rule prohibits G from having any photographs in Sports, leaving us with no other choice but to assign H to both photographs in Sports. And, since neither of the photographs in Lifestyle are by H, both of them must be by either F or G:

PT76_O15 LG Explanations_Game #2_setup_diagram 5b.png

May you please explain what I have italicized in your post? Is this saying that for L, it is either FF or GG? Or are you saying the distributions could go FF, GG, FG, or GF in L?

Thank you for the clarification.