Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Unbalanced: Underfunded game.

Because this game features the days of the week, they should be used as the base, and then a row for the morning interviews and a row for the afternoon interviews should be stacked above the base, making this an Advanced Linear game:

D96_Game_#3_setup_diagram 1.png

Note that while we use the morning interviews as the bottom row, you could just as easily use the afternoon interviews as the bottom row.

In the diagram there are 12 available interview times (2 times per day over 6 days), but there are only 10 total variables (6 nonhostile and 4 hostile). Further, because two of the nonhostile witnesses are interviewed together, there are 9 variables available for the 12 interview times. Thus, there must be three empty interview times in each solution (these will shown with three “E” variables).

While the nonhostile witnesses are given in standard variable form, the hostile witnesses are bit unusual. They are not specified as variables, but rather as a two-day block (shown above as a block around four Hs). Because interviewing the hostile witnesses takes up two full consecutive days of the week (and X is already assigned to Thursday morning), the hostile witnesses can only be interviewed on Monday and Tuesday, Tuesday and Wednesday, or Friday and Saturday. This point will be discussed in more detail later in this setup discussion.

As mentioned before, the first rule helpfully assigns X to Thursday morning. The second, third, and fourth rules are sequential in nature, and, when combined, create a large chain sequence:

D96_Game_#3_setup_diagram 2.png

This sequence generates a number of Not Laws, which are shown on the final diagram:

D96_Game_#3_setup_diagram 3.png

The last rule states that Z must be interviewed after X, which is interviewed on Thursday morning. Thus, Z must be interviewed on Thursday afternoon, any time Friday, or any time Saturday. Therefore, if the hostile witnesses are interviewed on Friday and Saturday, Z must be interviewed on Thursday afternoon. Via the contrapositive, if Z (or Y) is interviewed on Friday or Saturday, the hostile witnesses must be interviewed either on Monday and Tuesday or on Tuesday and Wednesday. Essentially, if Z is interviewed on Friday or Saturday, hostile witnesses must be interviewed Tuesday and either Monday or Wednesday. This inference is one of the keys to the game.

Because the hostile witness block has only three options, and there are severe restrictions on the nonhositile witnesses, there is a strong argument to be made that this game should be attacked by Identifying the Templates. While this approach is not necessary to successfully solve this game, it is useful, and so we will show each template below:

Template #1: Hostile witnesses on Monday-Tuesday

• In this template, the hostile witness block occupies Monday and Tuesday. Thus, from the second and third rules, U must be interviewed on Wednesday morning, and Q and R must be interviewed on Wednesday afternoon. Y Z then occupies part of Thursday, Friday, or Saturday:
  
  
  D96_Game_#3_setup_diagram 4.png
  Note that both Y and Z could be interviewed on Saturday, so no global Not Law prohibits Y from being interviewed on Saturday. However, if Y is interviewed on Saturday, it must be in the morning, and Z would be interviewed on Saturday afternoon.

Template #2: Hostile witnesses on Tuesday-Wednesday

• In this template, the hostile witness block occupies Tuesday and Wednesday. Thus, from the second and third rules, U must be interviewed on Monday morning, and Q and R must be interviewed on Monday afternoon. Y Z then occupies part of Thursday, Friday, or Saturday:
  
  D96_Game_#3_setup_diagram 5.png
  Note that both Y and Z could be interviewed on Saturday, so no global Not Law prohibits Y from being interviewed on Saturday. However, if Y is interviewed on Saturday, it must be in the morning, and Z would be interviewed on Saturday afternoon.

Template #3: Hostile witnesses on Friday-Saturday

• In this template, the hostile witness block occupies Friday and Saturday. Thus, from the last rule, Z must be interviewed on Thursday afternoon. The remainder of the sequence occupies part of Monday, Tuesday, or Wednesday:
  
  D96_Game_#3_setup_diagram 6.png

Again, showing these templates is not necessary, but when a significant factor in the game (in this case, the hostile witness block) has limited options, attacking the game with templates is always an option.

[alee]

Hi!

I have a question about the optimal setup for Game 3, on Prep Test 21, Section 1 (Dec 1996 Attorney's Interviews game). This was my setup

_ _ _ X _ _ _ am
_ _ _ _ _ _ _ pm
m t w th fr sat, qr, u, x, y ,z: 5 into 8 slots (since 4 slots are for hostile interviews)
u>qr>x>z, with y>z

Key inferences:
-2 *consecutive* days reserved for hostile: Tuesday + either Mon or Wed, *or* Fri + Sat.
-z must be the last interviewed

It seems that there is a great deal of *uncertainty* in this game, in that (at least I) wasn't able get inferences until provided with local conditions in the questions. For example, 14, 15, and 17 which provide inferences which lead to inferences about which days must be the those reserved for hostiles.

What would you suggest is the optimal setup to the game?

Thanks!

[Jon Denning]

Hey alee - thanks for the question. That's pretty much exactly how I set the game up as well (except I had am as the bottom row, pm as the top). There's not much that you can fill in, so you have to just focus on the not laws--like no Q, U, R on Thurs, Fri, or Sat--and the big sequence that you've shown below. In doing this game I realized that I wasn't going to be able to definitively place a lot of variables in my setup, so I moved quickly to the questions to allow myself plenty of time there.

Thanks and keep up the hard work!

[HYS]

I have a question regarding one of the conditions in the stimulus.

It seems like everyone is assuming the sentence "the only witnesses who will be... are Q and R" to mean as "Q and R interviewed simultaneously with each other." However, I thought the phrase "the only" precedes a sufficient condition which would mean the sentence "the only witnesses who will be... are Q and R" would be diagrammed as "interviewed simultaneously with each other Q and R." Understanding it as such would allow the case where Q and R are interviewed at different times and make the whole game a completely different one.

I have looked up how "the only" is used in LSAT (https://forum.powerscore.com/lsat/viewtopic.php?t=7614) and even after reading this post, it seems like my interpretation is right. Am I missing something from the stimulus?

[Claire Horan]

Hi HYS,

The rule states that the only witnesses who will be interviewed simultaneously are Q and R. This sentence can be rephrased in various way. For one, it could be rephrased as "Q and R are the only witness who will be interviewed simultaneously." From your everyday experience, I think you'll agree that this sentence means "Q and R will be interviewed simultaneously" AND "no other witnesses will be interviewed simultaneously." Sometimes restating a sentence in your own word is a helpful way to check its meaning. Take an example that might feel a little more natural. If I said, "You are the only friend I have who will come to the party," it would mean both that you are coming to the party and that none of my other friends are coming to the party.

If the rule stated instead that the only witnesses who may/can be interviewed simultaneously are Q and R, it would mean that no one else could be interviewed together, but there would still be a possibility that Q and R were not interviewed together. I mention this to show you that you should not isolate single words like "only" from the meaning of the sentence as a whole. Both example rules included the word "only," yet they had different meanings that would be diagrammed differently.

I hope this explanation helps! Good luck with your studies!

[olenka.ballena@macaulay.cuny.edu]

Hi,

I've gone through this thread and done the game, and I understand the game more thoroughly now but I had a question regarding the hostile witnesses and the three empty interview times that are inferenced. The question stem never says that the hostile witnesses are only interviewed once (in fact it only says that about the non hostile witnesses), so how was I supposed to assume that the three left over "slots" were empty spaces as opposed to another hostile witness being interviewed? I think when I first did the game this was clouding over my head and I was under the impression that the hostile witnesses could occur more than four times. I'm not sure if that even changes anything in regards to solving the game, but I'm still having trouble with the inference that those are empty interview slots. Any help would be appreciated, thanks!

[Adam Tyson]

how was I supposed to assume that the three left over "slots" were empty spaces as opposed to another hostile witness being interviewed?

You don't have to make that assumption, Olenka! Try the game again and imagine that you could also have hostile witnesses in other spaces. Does anything change about how you do the diagrams or answer the questions? I don't think it does. But also, don't make the assumption that they CANNOT be empty spaces, because the rules don't require that every space be filled, either. Leaving them blank is the simplest way to handle that uncertainty, right? Plug in what is know - the block of hostile witnesses, the sequential relationships, etc. - and leave the rest alone. That's the most flexible approach that requires no special assumptions on your part.