Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

This game is also discussed in our Podcast, at the 48:04 mark: LSAT Podcast Episode 37: The November 2019 LSAT Logic Games Section

This was easily the most challenging game on the November 2019 LSAT. It's a game filled with multiple variable sets, rules that address many different aspects of the game, and a number of intricate relationships.

The game begins by introducing three separate variable sets:

• Four Months: 1, 2, 3, 4
  
  Three Factory Sites: F, G, I
  
  Four Representatives: V, W, Y, Z

The four months have sense of inherent order, so you should select those as the base:

• 1 2 3 4

The next choice is whether to stack the Factory Sites or the Representatives above the months, and in this case we will choose the Factory Sites since each one has exactly four visits to fill. We can then use the representatives to fill in all twelve spaces. If you chose the Representatives, it makes less sense because each has only three visits each. With this in mind, our base diagram appears as:

• France:       ___ ___ ___ ___
  
  
  Ghana:       ___ ___ ___ ___
  
  
  India:          ___ ___ ___ ___
  1  2      3  4

With the base diagram in place, let's analyze the rules on a basic level. Afterwards, we will dive into some of the interactions that lead to inferences:

• Rule #1: This rule establishes that V's visits will be in a I G I sequence. This is an extremely limiting rule, and focusing on the implications of this rule is one of the keys to the game.
  
  
  Rule #2: This rule assigns W to G at least once.
  
  
  Rule #3: This rule pairs with Rule #2 and creates a YW block in the G row. Thus, the G row is filled in part with V (from the first rule and YW, in some order. Note the language in this rule, in that it says "immediately preceding a month," and not "any" month. This means that once you have YW as a block in that row, you don't automatically rule out using W or Y again (you'd only need one block, not two since it's a "a" month and the block satisfies that. "And" month would have changed the outcome there).
  
  
  Rule #4: This rule eliminates Y from the fourth month, which leaves just V, W, and Z available to make the three visits in the fourth month. Since each representative can only visit a single spot in a month, this means each one will appear just once in the fourth column.
  
  
  Rule #5: This is another powerful rule, and one that prohibits F and I from sharing representatives. the immediate implication is that V cannot visit France (since V already visits I from the first rule).

The question now is, "Where should you start in analyzing what can occur?" Given that Ghana appears in the first three rules, examining the G row is a logic choice.


Because of the first rule, V's visit to Ghana can only be in the second or third month. Pairing that with the YW block created in the third rule results in two basic templates for the G row:

• Ghana:       ___ _V_ _Y_ _W_
  
  Ghana:       _Y_ _W_ _V_ ___
  1  2      3  4

There are more limitations present in this row based on the consequences of other rules, but for now this is sufficient.


Next, consider the India row. Since V must appear twice, and must be sandwiched around the appearance of V in the second or third month in Ghana, there are initially only three possible configurations foe the placement of V in the India row:

• India:          ___ _V_ ___ _V_
  India:          _V_ ___ ___ _V_
  India:          _V_ ___ _V_ ___
  1  2      3  4

These configurations are NOT all possible; as we will see in the discussion of Rule #4, the bottom option above cannot occur. However, just from considering the first rule, the above initially appears to be the case.

Rule #5 also interacts with India, so let's examine that rule next. Since France and India cannot be visited by the same representative, we can immediately infer that V can never visit France.

This also means that each site must have exactly two representatives make all four site visits. This is a tricky inference, so let's explain in more detail:

• Each site cannot have just one representative visit, because there are four months, and each representative only makes three visits. So, just from the structural setup of the game each site would have to have at least two representatives visit.
  
  There also cannot be three different representatives to visit France or India because if one of those sites had three representatives visit, then the other site could not have those three representatives visit, meaning only one representative would be available, and we've already established that is impossible. Of course, if three representatives is impossible, four is also impossible.
  
  Thus, we can establish that France and India each have exactly two representatives visit the site, and due to the language in the fifth rule, those must each be two different pairs of reps.

The one rule as yet unexamined is Rule #4. With Y unavailable for the fourth month, only V, W, and Z can make visits in the fourth month. This is extremely limiting since each can only make a single visit in the month. While this information alone is useful, there's a further inference that can be drawn that is extremely tough to make during the setup. That inference is that V must visit India in the fourth month. Let's explain why:

• V's visits are already limited to India and Ghana. But, because of the sequence created in the first rule, V cannot visit Ghana in the fourth month. Thus, the only site where V can make a fourth month visit it India. And, since V must make one of the fourth month visits per rule #4, it follows that V must visit India in the fourth month, leaving W and Z as the options in the fourth month for Ghana and France.

The above inference is very tough, and isn't tested as a standalone question in the game (which is surprising!). However, it also means that in the India row, only these two options exist for the positioning of V's visits:

• India:          ___ _V_ ___ _V_
  India:          _V_ ___ ___ _V_
  1  2      3  4

Consequently, V must visit India in the fourth month

Overall, the setup to this game has a lot of moving parts, which makes this game very difficult. There are decent angles of attack here, if you start by focusing on the limitations: The Ghana row, the India row, and the options for the fourth month.

The following is close to the final setup for the game (and will be replaced later with a setup not as limited by the graphical tools of this forum):

• France:       ___ ___ ___ _Z/W_ V
  
  
  Ghana:       ___ _V_ _Y_ _W_
  Ghana:       _Y_ _W_ _V_ _W/Z_
  
  
  India:          _V/_ _/V_ ___ _V_
  1  2      3  4

This explanation is still in progress. Please post any questions below!

[robobrain]

there's a further inference that can be drawn that is extremely tough to make during the setup. That inference is that V must visit India in the fourth month.

I don't understand why this must be true. Why can't it be W in India month 4? Or even Z? Consider this arrangement:

F: Y Y Z Z
G: Z V Y W
I: V W V W

What is wrong with this arrangement?

[Dave Killoran]

there's a further inference that can be drawn that is extremely tough to make during the setup. That inference is that V must visit India in the fourth month.

I don't understand why this must be true. Why can't it be W in India month 4? Or even Z? Consider this arrangement:

F: Y Y Z Z
G: Z V Y W
I: V W V W

What is wrong with this arrangement?

You've got W visiting two separate sites in the fourth month, and the last line of the scenario indicates they make no more than one site visit per month

[robobrain]

the last line of the scenario

Oh, that's what I misread. I thought the "no more than one in a month" was just a repeat of the previous sentence where it said "exactly one representative for each site in each month". I didn't even consider that the last line meant that you can't stack vertically like that.

Tricky language.

[Dave Killoran]

Yeah, it's super easy to miss. The whole game is hard—I think it's harder than any game on the September 2019 LSAT.

[lathlee]

I labell this kind of advanced Linear LG Type as Patternish Adv Linear, that there is definitely certain pattern element(s) exists and once one recognize certain patterns how they function in LG, it makes solving it easier. But ultimately it is advanced linear game solving technique and mindset ultimately determines.

[Sie23]

Hi! I had a question regarding this structure:
1 )Ghana: ___ _V_ _Y_ _W_
2) Ghana: _Y_ _W_ _V_ _W/Z_

How can the second line here work? If W is in the 4th spot wouldn't that require Y to be in the 3rd-month due to the rule that Y must be the month preceding W in G?

If that's the case then really there is only the first template that works which would in turn force Z into the 4th spot for F.
Creating the final diagram:
France: ___ ___ ___ _Z_
Ghana: ___ _V_ _Y_ _W_
India: _V/_ .. _/V_ .... . ___ _V_
1 2 3 .. 4

Thanks for all your help! You guys are really helping me get better at the LSAT.

[Christen Hammock]

Hi Sie!

The rule says that Y must visit G in a month immediately preceding a month where W visits G—not that W in G automatically triggers a WY block every time!

Christen

[Diggity]

What’s the best way to visually represent the rule that any rep who visits France cannot also visit India?


I put down [x]Fr <—|—>In [x] where x is just a place holder for any of the representative variables but was hoping there was a stronger way to visually represent this rule.

Having trouble with number 20 where it asked which one of the following could be true...knocked out B,C,E with the V sandwich formation between Ghana and India but ultimately just guesses between A and D and not sure which rule leads to the correct answer or if it’s a matter or hoping time is on the clock to pound out hypos.

Edit. I don’t know how I knocked out B now but figured out why to knock out A.[ which is because all 3 V’s are placed and thus need to fill in in 2 slots in a India which requires at least one of 3 remaining variables which means at most 2 variables could go to france [and st least 2 must go bc of the four slots which means can’t go with B as need 2 variables to fill in the four slots at minimum for both countries...cool figured it out!] so yeah back to just needing to know if better way to present the not France and India rule!

[Jeremy Press]

Hi Diggity,

It's not so much the rule representation that is important to think through with that rule (I would've chosen a double-not arrow for representing the rule, as you've done), as it is the consequences of that rule, which are pretty huge!

The first thing that's clear is, because the rules require V in India, V can't be in France. That knocks France down to three possible representatives (W, Y, Z). But you won't be able to include all three of those in France. If you did, then V would have to fill all the spots in India (which is not possible from the rules). Further, since you can't have just one variable filling all four of a country's spots, there must be exactly two representatives visiting France: two of W, Y, and Z. Those two representatives cannot visit India, so V and the other representative (1 of W, Y, Z) will have to. Seeing that in advance is more important than coming up with a fancy diagram for the F/I rule. Just remember also that when you're building solutions within templates (as Dave did above) or within local questions (if you don't choose to template), as soon as you place a variable in F, it gets "not-lawed" out of I. As soon as you place a variable in I, it gets "not-lawed" out of F. That's the best you can do with that rule.

I hope this helps!

Jeremy