Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced game.

As it turns out, this is by far the most difficult game of this LSAT. This is a bit surprising because at first glance, this appears to be a fairly straightforward Advanced Linear game. The rules have some twists, however, that ratchet up the difficulty.

The game scenario states that an editor will edit seven articles in succession. Each article is one of three topics (finance, nutrition, or wildlife—uh, wait, what kind of strange publication is this?). The order of the articles should be used as the base, with a row for the article name immediately on top, and then another row for the article type stacked above that, creating the following Advanced Linear setup:

PT68_Game_#4_setup_diagram 1.png

With the basic structure in place, let us examine the rules.

The first rule separates similar topics from being consecutive. Because there is only one wildlife article, this rule applies only to the finance and nutrition articles. Instead of writing out all of the individual article not-blocks, which would be time-consuming, instead represent this rule with not-blocks for each topic:

PT68_Game_#4_setup_diagram 2.png

This is a worrisome rule because it involves so many variables, and keeping track of those variables is a challenge during the game. There are also a number of possible orders available under this rule, but one variable to track is Y. Because Y is the only wildlife article, if Y is placed, then articles that are distant from Y will have to alternate between finance and nutrition. For example if Y was the seventh article, then the first through sixth articles would either be in an F-N-F-N-F-N or N-F-N-F-N-F order. More on this rule as we examine the remaining rules.

The second rule is conditional, and indicates that S is earlier than Q (S Q) only if Q is third. This can be diagrammed as:

PT68_Game_#4_setup_diagram 3.png

This rule is a also bit tricky to handle, and gets more complicated when the ensuing rules are considered. The immediate inference from this rule is that Q cannot be seventh, as that would force S to be earlier than Q (but Q would not be third, a violation), leading to the first of many Not Laws in the game:

PT68_Game_#4_setup_diagram 4.png

Note that Q and S are both nutrition articles, so if S Q and thus Q is third, S could not be second due to the first rule, and S would have to be first. Thus, the only time S can be earlier than Q is when S is first and Q is third. This situation comes into play when the contrapositive of the rule is considered. The contrapositive of this rule indicates that if Q is not third, then Q must be earlier than S:

PT68_Game_#4_setup_diagram 5.png

The implications of this contrapositive, when combined with the first rule, mean that S can never be second, because if S was second, Q could not be first (two articles of the same type cannot be consecutive; additionally, of course, Q cannot be third as that is the sufficient condition here). Thus, we can add an S Not Law on the second position:

PT68_Game_#4_setup_diagram 6.png

The relationship between Q and S is very involved, and you can see how they force each other into (or out of) different spaces. A great example is that if S is third, then Q must be first (take a look at why—Q is not third, so Q S, and with S third, from the first rule the only available space for Q is the first:

PT68_Game_#4_setup_diagram 7.png

The third rule also involves S, and establishes that S is earlier than Y:

• S Y

The immediate inferences this rule produces is that S cannot be seventh and that Y cannot be first (and if Y, the sole wildlife article cannot be first, then the first article must be finance or nutrition):

PT68_Game_#4_setup_diagram 8.png

But, since S already cannot be second, we can infer that Y cannot be second due to the third rule. Y also cannot be third, because if Y is third, then S would have to be first, and S Q, forcing a violation of the second rule which say that Q must be third. These two Y Not Laws can be added to the diagram, along with the F/N option for each:

PT68_Game_#4_setup_diagram 9.png

Note that the first and third articles will be the same topic, and the second article will be a different topic.

However, there are more inferences that can be drawn from the effects of this rule. Because S must always be earlier than Y, Q is affected. If Q is not third, then Q S. While Q cannot be seventh, consider what would occur if Q were sixth: S would be seventh, leaving no room for Y. Thus, Q cannot be sixth. Q also cannot be fifth, because if Q were fifth, S would have to be sixth and Y seventh. But Q and S are both nutrition articles, and thus that would create a violation. Let’s add those Not Laws to the diagram:

PT68_Game_#4_setup_diagram 10.png

The third rule contains a three-variable sequence:

• J G R

Without any consideration of other rules, this sequence creates six Not Laws: J cannot be sixth or seventh, R cannot be first or second, and G cannot be first or seventh. Let’s add those to the diagram:

PT68_Game_#4_setup_diagram 11.png

However, again consider the effects of the first rule: J and G are both finance articles, and so if J is first, the earliest that G could be is third (and thus the earliest that R could be is fourth). This means that G cannot be second, and R cannot be third. We’ll add those Not Laws to the diagram in a moment. In that same vein, if R is seventh and G is sixth, the earliest that J could be is fourth. Thus, J cannot be fifth.
Adding those three Not Laws to the diagram produces the following:

PT68_Game_#4_setup_diagram 12.png

There are two final Not Laws in this game, both of which are extremely hard to identify during the setup of the game. The two Not Laws are that Q cannot be fourth and S cannot be fifth. Both result from the complex interaction of S and Q, the J G R sequence, and the first rule prohibiting articles of the same topic being consecutive. We’ll add those to the final diagram, note that H is a random, and also identify the triple-options present on the second and seventh spaces (since four articles are eliminated from each position):

PT68_Game_#4_setup_diagram 13.png

[efs2111]

Hi,
Just finished up the December 2012 exam, and I had an exceptionally difficult time with the final game of section 4. I took it to be an Advanced Linear, and happily set up my main diagram accordingly, but once the questions stared rolling...ugh...I ended up doing a lot of sketching & crunching, but generally found myself overwhelmed by the possibilities (and time pressure, as I chose to tackle this game first).
Anyhow, I figure I must be missing some key inferences and limitations. I've been going over it in review, but still can't seem to find the key to maximum efficiency.
Any advice?

Thanks,
ES

[Jon Denning]

Thanks for the question! Tricky game for some people I think, primarily because you have to consider both the type and the name (letter) of each article since we have rules governing both. Here's how I set it up:

Had a base of seven spots, 1-7. Then I listed my type with each article name beside it. Finally, I showed rules and not laws. It's hard to do spacial diagrams here, so I'll just describe the not laws in a bit.

F: GHJ
N: QRS
W: Y

TT in a box with a slash (no types adjacent)

S > Q --> Q3
NOT Q3 --> Q > S > Y

S > Y

J > G > R

So that gives not laws on space 1 for G, R, and Y. Space 2 for R. Space 6 for J. And space 7 for G, J, S, and Q.

At least, those were the obvious ones. More exist, like S cannot be 2 because then either Q is 1 or 3 and S and Q are the same type (not consecutive), and Y cannot be 3 because that would put Q1 and S2 and Q and S cannot be consecutive, J cannot be 5 because that would put G6 and R7 and J and G cannot be consecutive (same type), and R cannot be 3 because that would put J1 and G2 and they can't be consecutive, etc. But truthfully I didn't worry too much about spending minute after minute at the beginning hunting for inferences like those...I simply marked the ones that were most apparent, and then trusted my understanding of the rules to help me see further inferences if answering questions required them.

For instance, a question like 20 tells you four not laws that you can add to your main diagram: the four wrong answers A, C, D, and E tell you basically what I said in the paragraph above, and it's MUCH more efficient to find those inferences via this question than to sit and attempt various combinations/hypotheticals up front.

Make sense?

[efs2111]

Thanks, Jon. Your advice is helpful, especially about seeking out the questions that can efficiently render helpful information, like question 20. I still tend to just tackle LG questions sequentially, but need to open up my approach.

I suppose my main difficulties with this game came from it's length, the number of local questions (I think around 4 or 5), and my inability to derive strong templates or secondary inferences. That especially unnerved me in question 22, since the not-law for S in 5, which requires several logical steps, had never entered my mind.
In review, though, I started to see valuable info from looking at the S<Q Q3 rule and its contrapositive, Qnot3 Q<S.
In combo with the other rules, it turns out that Q cannot be any farther back than position 3, and this inference then helped in discovering the limitations for each local question.
I'll admit that that inference took me some work to figure out, but it sort of falls out of experimenting with templates for Q after doing an initial Q in 3 diagram, as prompted by the rules.
Thanks again,
ES

[CristinaG]

Hello,

I've been having some problems trying to diagram this game correctly before moving onto the questions. I know that it is an advanced linear game with variables that cannot be placed consecutively if they are from the same group, but I was wondering if, in this particular game, it would be more useful to consider possible templates or if it was too broad to do so. If that is the case, How can I come up a series of inferences, understanding that the position of the variables depends on their placement in relation to each other?

I've also noticed this with other games like the truckload game from Game 3, Preptest 60, June 2010 and want to know what the best way to diagram this is.

Thank very much,
Cristina

[Dave Killoran]

Hi Cristina,

As I noted in our explanations to this game, "As it turns out, this is by far the most difficult game of this LSAT. This is a bit surprising because at first glance, this appears to be a fairly straightforward Advanced Linear game. The rules have some twists, however, that ratchet up the difficulty." This occurs because the first three games of this test are pretty easy, and so they needed a hard game to balance this section out.

In general, Advanced Linear games with more than 6 variables are often not the best candidates for templates because it takes so much work to make each template (the physical act of drawing each one is very time-consuming). And, in this game I would argue that Templates isn't the best approach. It's just a hard game, with some brutal rule interaction, and a few inferences that are among the toughest they've thrown out there in the past few years. Unless you catch those inferences, you simply have to plow through this game, and hopefully you would have sufficient time to do so since the first three games aren't that tough and allow most people to generate extra time for this last game.

The Mulch and Stone game you cite from the June 2010 LSAT is very different, in my opinion. That's a Basic Linear game, not an Advanced Linear game. But, in that game, the cleaning rule limitation is so powerful that it indeed results in a limited set of templates. But, that game has an almost Pattern game feel to it, whereas this December 2012 game is much more standard in terms of how it looks and feels.

So, I don't know if that helps much, but what really happened here is that you just ran into a tough game

Thanks!

[CristinaG]

Thank you for the explanation, Dave! I think you're right that it was just a very hard game and, going back to it, I noticed that a lot of my issues were it came from the lack of inferences. I'll try to just do my best on the first three if I happen to come across an equally tough one on the LSAT.

[reop6780]

I have a question in regard with the second rule, "S can be earlier than Q only if Q is third."

Since "can be earlier" not "must be earlier" is used, the rule itself does not really help, does it?

Once negated, I figured that it becomes a strong rule, "if Q is third, S cannot be earlier than Q."

Then, I got a bit confused since I am used to writing contrapositives. if the rule says A B, I write negated B negated A.

In this case, is only one rule effective? (The contrapositive of the second rule: negated Q 3 Q > S )

[Robert Carroll]

reop,

Sufficient conditions don't include necessity anyway, so "can be" is not relevant - only a necessary condition would use language like "must be." So the rule is saying:

S > Q Q3

Contrapositive is:

Q not 3 Q > S

Remember that "one at a time" creates a 1-to-1 order, with no ties. So the negation of "S before Q" is "Q before S."

The "strong rule" you have is not the contrapositive or the negation of this rule, and is a faulty inference.

The contrapositive of a conditional is another conditional, not a situation with "some." So the contrapositive of A B is not-B not-A.

The contrapositive you have at the end is correct.

Robert Carroll

[Cowboys1118]

Could someone explain to me the reasoning behind the inference that why Y cannot be in slot 2 solely because "S cannot" ? It would appear to me that S could be in 1, Y could be in 2, and Q in 3.

Thanks!