Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

The initial scenario establishes that six buildings will be inspected over three days, one each morning and one each afternoon. This creates an Advanced Linear setup:

PT28-Jun 1999 LGE-G3_srd1.png

As always, you can place the morning row on the top or bottom of your diagram—the decision is entirely up to your personal preference.

The first rule establishes that no hotels are inspected on Wednesday, creating G, J, and L Not Laws on each Wednesday time period:

PT28-Jun 1999 LGE-G3_srd2.png

The first rule, which states that hotels are not inspected on Wednesday, leads to an interesting set of inferences. First, the three hotels—G, J, and L—must be inspected on Monday and Tuesday, and thus only S, V, and Z are available for inspection on Wednesday. Therefore, exactly two of S, V, and Z are inspected on Wednesday, and G, J, L and the remainder of S, V, and Z are inspected on Monday and Tuesday:

PT28-Jun 1999 LGE-G3_srd3.png

The second rule establishes a sequence, namely that G > J. As with all Advanced Linear games, this does not preclude the variables from being inspected on the same day; G must only be inspected at an earlier time than J. This leads to two Not Laws, one for J on Monday morning, and one for G on Tuesday afternoon (because neither G nor J can be inspected on Wednesday):

PT28-Jun 1999 LGE-G3_srd4.png

Because G, J, and L must be inspected on Monday and Tuesday, further inferences can be drawn about the relationship of G and J. Because G must be inspected at some time before J, G cannot be inspected on Tuesday afternoon, and if G is inspected on Tuesday morning, then J must be inspected on Tuesday afternoon. Conversely, if J is inspected on Monday afternoon, G must be inspected on Monday morning. These relationships are tested repeatedly in the game.

The third rule establishes a vertical, rotating not-block:

PT28-Jun 1999 LGE-G3_srd5.png

The fourth and final rule establishes that if Z is inspected in the morning, then L is inspected in the morning:

PT28-Jun 1999 LGE-G3_srd6.png

Because every building must be inspected in the morning or afternoon, this game contains a two-value system. When a two-value system is present, always consider the contrapositive of any conditional rule. In this case, when L is not inspected in the morning, it must be inspected in the afternoon, and when Z is not inspected in the morning, it must be inspected in the afternoon, resulting in the following translated contrapositive:

PT28-Jun 1999 LGE-G3_srd7.png

Note that Z and L are not always in the same time slot: L can be inspected in the morning while Z can be inspected in the afternoon.

Adding in that V is a random, we arrive at the final diagram for the game:

PT28-Jun 1999 LGE-G3_srd8.png

[srcline@noctrl.edu]

Hello

So the setup here is giving me problems, as usual.

I set this game up as:
attached.

Dont the MTW have an inherent sense of order as well as the morning and afternoon that why I chose them as my base.


Thankyou
Sarah

[David Boyle]

Hello

So the setup here is giving me problems, as usual.

I set this game up as:
attached.

Dont the MTW have an inherent sense of order as well as the morning and afternoon that why I chose them as my base.

Thankyou
Sarah

Hello,

Yes, both sets have an inherent sense of order. Most people would rotate that diagram 90 degrees so that the days are on the bottom, and morning and afternoon are stacks rising vertically above the days. In the vast majority of games, when days of the week appear, they are the base of the game, and times (AM/PM) are layered on top of the days of the week. However, the game can be set up in either fashion, and functionally the two presentations would be identical!

David

[cboles]

I believe I set the game up right but had trouble moving through the questions based on the rules presented. I wasn't able to place any of the hotels or restaurants in any spots based off the inferences I made so it was very difficult. Here is the diagram I built:

M ___ ___ ___
A ___ ___ ___
M T W

The only limitations I made were that J could not be in the morning on Monday and none of the hotels could be inspected on Wednesday.


Can someone tell me what I am missing?

[Jonathan Evans]

Hi, Cboles,

You're not missing much. You might hurdle the uncertainty on W to note that the two spaces on Wed will be filled with a combination of two of SR, VR, and ZR.

You will note that GH cannot be Tue PM.

Note also that all three H will be on Mon and Tue and exactly one R will be on Mon and Tue. Note the relationship between ZR and LH.

Because this is a reasonably open-ended game, there is a lot of "hurdling the uncertainty" involved. You have a general idea what happens where without definite assignments.

You must proceed by making sure rules are not violated, specifically the GS rule, the ZL conditional, and the GJ rule.

[LSAT2018]

Other than the inferences in the previous post and this additional conditional rule, I did not find any other.

If Zeno is inspected in the morning, Lido is also inspected in the morning:
Zeno (Morning) → Lido (Morning)
Lido (Afternoon) → Zeno (Afternoon)

Would that be right?

[Adam Tyson]

Correct! One other that was not mentioned in Jonathan's post was that J cannot be Monday morning, for the same reason that G cannot be Tuesday afternoon - G is before J and neither of them can be Wednesday. You could, perhaps, take that one step further, like so:

If J is on Monday, then Monday has G in the morning and J in the afternoon.

If G is on Tuesday, it's Tuesday morning and J is Tuesday afternoon.

I don't think those need to be incorporated into the main diagram, but you will surely make those inferences as needed as you go through the questions. Question 16, for example, which allows you to quickly eliminate answers C and D (because J has to be in the middle of the list).

[gwlsathelp]

For those of whom want a horizontal diagram: