Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced game.

The setup for this game appears as follows:

PT61_O2010 LG Explanations-g4-setup.png

Notes:

The second and fourth rules can be combined to create a longer chain relationship: L F GK.


The majority of Not Laws on the diagram above come from the sequencing or block elements in the second, third, fourth, and fifth rules. There are two exceptions:

L’s session cannot be on the 4th: If L’s session is on the 4th, then from the second and fourth rules F must be on the 5th, G on the 6th, and K on the 7th. This configuration does not leave enough room for the H/M split block. And, because L cannot be 2nd (from the fifth rule), 4th (from this inference), 5th, 6th, or 7th (from the Not Laws generated by the sequence), we can infer that L must be 1st or 3rd.

J’s session cannot be on the 5th: If J’s session is on the 5th, a problem is created between the L F GK chain and the M/H split-block. If the GK block is earlier than J, then L-F-G-K occupies the first four days, leaving no room for the M/H split-block; if the GK block is later than J, then G-K occupies the last two days, again leaving no room for the M/H split-block. Thus, J cannot be on the 5th.

There are two triple-options present: H, L, or M must be on the 1st, and H, J, or K must be on the 7th.

There are no randoms in this game.

[camjdavis@mac.com]

On the October 2010 practice test, game #4 was by the far the most difficult and time-consuming game for me. The only way I can get the correct answers is by testing hypotheticals for pretty much all of the questions. When I took the test, there wasn't enough time for this so I ended up randomly guessing on most of this game's questions. There's gotta be a faster way to do this. After diagramming all the rules, the only inferences I made were basic not-laws and the combination of rules 2 and 4. Did I miss a structural insight/key inference that makes this game much faster?

Thanks!

[Clay Cooper]

Hi Cam,

Thanks for your post, and welcome to the forum!

This is a sequencing game, and what inferences there are to be found will depend on our accurately understanding the sequencing rules. I don't think there are any game-breaking inferences to be made here; instead, i think tracking and combining the rules we are given is probably the best we can do.

You are correct to observe that rules two and four can combine to give us:

L-F-GK

and that rule now includes four of our seven variables; keep that in mind, as it will be useful.

For instance, on 21, we are given the local rule that K precedes M. That combines with the rule given above to give us the following:

L-F-GK-M-J

and now six of our seven variables are accounted for; only H remains free. That would, on 21, solve the question for us quickly and easily.

In short, I don't think there are any shortcuts that you have missed; if you have had a hard time with this game, I would just focus on practicing correctly transcribing and applying sequencing rules in games like this one.

I hope that helps!

[Stephanie Oswalt]

We recently received the following question from a student:

Hi,

I was wondering if you could help me with the setup of this game because I was missing the global inference deductions on this game.

Thanks!
Melinda

An instructor will respond below. Thanks!

[AthenaDalton]

We recently received the following question from a student:

Hi,

I was wondering if you could help me with the setup of this game because I was missing the global inference deductions on this game.

Thanks!
Melinda

An instructor will respond below. Thanks!

Hi Melinda!

The global inferences for the setup give us two sequences to work with in this game.

By combining rule 1 (that H and J must be separated by at least two spaces) with rule 3 (J must come after M) we get a sequence of letters that looks either like this: (H _ _ J – M) or (J – M _ _ H). We don’t know how many spaces will go between J and M, if any, but this block will need to be spread out over 4 or 5 spaces on our 7-line calendar.

The next big inference comes from combining rule 2 (G must come immediately before K) with rule 4 (the L – F – K) sequence, which gives us L – F – GK. So this sequence will require at least 4 spaces to spread out on the board.

Since these two sequences take up at least 4 spaces each, they will have to overlap with each other.

The final rule is that L cannot be scheduled on day 2. Since L begins a 4-letter sequence, let’s consider where on the calendar it can fit.

The latest calendar day that L can be scheduled is day 3, to ensure that there’s enough space on the board for F-GK and either H or M to follow it. This gives us two calendar outcomes where L is in space 3, either:

__ __ L F G K __ or __ __ L F/ F/ G K

The other option is that L goes on day 1, which doesn’t give us many inferences about what the rest of the calendar looks like.

From here, we need to consider the H/M __ __ H/M sequence. Remembering that M has to precede J, let’s consider what inferences we can make the L-F-G-K sequence.

Looking again at the two sequences where L is on day 3, we can see that there is only one space available towards the end of the sequence, either day 7 or day 5:

__ __ L F G K __ or __ __ L F/ F/ G K (F can go on either day 4 or 5)

In these two sequences, if M goes after H, there’s no room for J to fit in. So we know that in these two sequences where L is in space 3, M and J will take up the first two spots and H will go in whatever space is left from the L-F-GK sequence:

M J L F G K H or M J L F/H F/H G K (either F or H can go on days 4 and 5)

So those are the two possible sequences if L goes in spot 3.

If L goes in space 1, we can’t deduce much, except for the general sequence of letters we got from the original setup: L-F-

GK and either H_ _ M or M _ _ H with M – J.

Good luck!

-Athena Dalton

[JaredBeats]

Guys,

With all due respect, your explanation to this game is a complete mess. I've read the Logic Games Bible and attempted to follow the method for Basic Linear Games outlined there, but hit a wall no matter what I did:

When I first did this game, I combined my rules, created the L-F-GK sequence, and then started making Not Laws as instructed. Bad idea! I made 18 Not Laws (which took forever), but for what? None of the questions directly tested any of these inferences, and the one question that did ask about a Not Law - where can J not be? - I didn't have an answer for. So I skipped that question and used some of the other answer choices to prove or disprove where J can or cannot be. That was frustrating, and made me question the wisdom of cranking out every possible Not Law in Basic Linear games. Seriously, how many people figure out ahead of time that J cannot be 5? And inversely, how often does the LSAT test lame ass Not Laws such as whether K can be first or whatever? I would have been better off just setting up the rules, combing them into a chain, then moving onto the questions.

So I did this game again, using Templates (an "Advanced Technique" you call it). Fine, I said to myself, the GK block can only go into one of three possible places. The thing is, the further I moved the block to the right, the less restricted the rest of the variables became. With 7 variables to contend with, and no powerful rules other than the L-F-GK sequence, the number of possible solutions seemed endless. Once again, your approach wasted my time and led nowhere.

So now I stumble on your post here, and it's so convoluted and disjointed that I have serious doubts about whether your system is universally applicable or whether you're just making it up as you go. I'm shooting for a score in the high-170's, and don't have the luxury of time to waste on the latter.

Best,

Jared

[AthenaDalton]

Hi Jared,

I'm sorry to hear that you've encountered some difficulty with this game.

As you will learn in the course of studying for the LSAT, Logic Games vary the amount of information given in the setup. Some games involve powerful inferences in the setups that give students a narrow array of templates to work with (e.g., limited solution set games, like Game #1 on the October 1994 LSAT). These types of games will involve a lot of inference-making up front, where it makes sense for students to invest a lot of time up front in the setup stage so they can speed through the answer choices. In these games, the questions will be pretty straightforward to make up for the time spent on the setup. The general rule of thumb is that if a game has seven or fewer possible solutions, it's a good idea to sketch them out in the setup stage.

Other games give students only a handful of rules or sequences that don't lock down many possibilities in the game (e.g., undefined grouping games or linear games with few rules). In these types of games, it doesn't make sense to invest a lot of time up front in sketching out every possible answer choice or not-law, since there will be too many to work through in 8 minutes and 45 seconds.

This is one of those types of games.

Here, there are two main sequences, L-F-GK and M/H _ _ M/H. A quick assessment of how these two fit together in the seven spaces will reveal that there are quite a few possibilities -- certainly more than seven. I walked through a handful of these above to show how moving one sequence left or right can impact the remaining letters.

Where the inferences in the setup are few and far between, the answer choices will often add new rules that lock down the possible sequences. For example, in this game question 20 adds a new rule -- J gets the 3rd session -- then asks about how this affects the game.

As you get more practice, you'll get a good feel for whether you're in a limited solution / template game (where you should spend time drawing up solutions) or a game with lots of possibilities, where you're best off just jumping into the questions.

Best of luck!

[JaredBeats]

Hi Athena,

Thanks for responding so quickly. Frankly, I was a bit puzzled by a few of the things you said (and, perhaps more so, by what you didn't say).

The general rule of thumb is that if a game has seven or fewer possible solutions, it's a good idea to sketch them out in the setup stage.

In the vast majority of cases, it is impossible to predict the number of Templates/Possibilities with any precision. How do you really know you'll have seven of fewer possible solutions? See, in this game I thought that the GK block being limited to only three possible locations would be sufficiently restrictive. I followed PowerScore's recommendation to focus on blocks as especially powerful elements in Linear games, which was misplaced. In the end of the day, the three GK-Templates revealed nothing of value.

On a more general note, it is a bit disingenuous to point to a few exceptionally restrictive games in the hopes of delivering a universally applicable method. I bet the vast majority of test-takers cannot predict, in the vast majority of cases, the precise number of possible solutions to any given game.

Other games give students only a handful of rules or sequences that don't lock down many possibilities in the game (e.g., undefined grouping games or linear games with few rules). In these types of games, it doesn't make sense to invest a lot of time up front in sketching out every possible answer choice or not-law, since there will be too many to work through in 8 minutes and 45 seconds.

This is one of those types of games.

You see, determining whether to go down this road is not as straightforward as you make it out to be. What makes a set of rules sufficiently restrictive? What is "sufficient" in this case anyway? I'd even argue that this game IS sufficiently restrictive, but only if you make the inference that L must be either 1 or 3. You didn't highlight this inference, an omission I found a little strange. With L in 1 or 3, we can set up two templates. Granted, one is more defined than the other, but the very process of setting them up was eye opening, didn't waste too much time, and gave me a starting point for a lot of the local setups later on.

My point is, this is not something a simple Not-Law approach would have prompted me to do. As I mentioned before, making up to 20 Not Laws was an utter waste of time (you seem to agree, because your approach doesn't even mention Not Laws). Why is this such a pronounced feature of PowerScore's approach to logic games is beyond me. It is sometimes useful, yes, but more often than not it's a complete waste of time.

Here, there are two main sequences, L-F-GK and M/H _ _ M/H. A quick assessment of how these two fit together in the seven spaces will reveal that there are quite a few possibilities -- certainly more than seven. I walked through a handful of these above to show how moving one sequence left or right can impact the remaining letters.

The M/H_ _ M/H is not a sequence. It's a rule that seeks to separate two variables by at least two spaces. Yes, this will interact with the L-F-GK sequence, but this interaction is complex and your approach doesn't help me understand it well enough. Not to mention, the M/H_ _ M/H is additionally complicated by the M-J sequence, just like the L-F-GK sequence is subject to the prohibition against placing L second. Again, merely noticing that the two "sequences" will overlap is neither groundbreaking nor terribly helpful. A far better approach would be to focus on L, which turned out to be the most critical variable in this game.

Jared

[Dave Killoran]

Hey Jared,

Thanks for the questions! You've asked several interesting, broad questions here, so I wanted to add a few thoughts that may help.

First, if it helps, this discussion thread isn't our complete and total explanation to this game. This is just us answering questions students had about the game, and our complete explanation is actually found in our Full-Length and Live Online course material. Answering questions in the Forum certainly can convey a disjointed feeling, so I understand your point. Perhaps when I have some extra time I'll come back and post a full explanation of this game here—the game is certainly difficult enough and interesting enough to warrant a broader discussion.

Second, let's talk about Not Laws in general before talking about the basic approach to this game. To me, Not Laws are a tool and while they can be very useful in many games, in other cases they aren't as useful. The same goes for just about any technique, with Templates being a perfect example—in some games they are amazingly powerful and in others they lead to destruction. Early in the LGB I place a lot of emphasis on Not Laws for a few different reasons, but two main ones are that I want everyone to get in the habit of looking for negative absolutes and that I want to make sure that identifying Not Laws is a skill that is second-nature. A parallel concept appears in LR with conditional reasoning. It's all over the LSAT, so early on we focus on it and make sure that students know it cold. We then pull back from that and place it where it should be: something you don't need to worry about unless it shows up and you need to address it. But that early emphasis makes sure that when it does show up, you are ready to handle it with ease. This is why there is a focus on Not Laws early on, but as I say later, not every game is best approached by using them (and, in fact, many games aren't, including many of those outside the Linear designation). The key, then, is to determine at which point showing Not Laws would be helpful and at which points it wouldn't. That is made more challenging because the makers of the test realize there are different solution strategies, and they intentionally move their games around the spectrum in order to make identifying the best approach more difficult.

In this game, we have that problem. There's not a single obvious strategy here that is a perfect slam-dunk that makes the game simple. There are a lot of Not Laws and so I don't love showing them all (more on this in a moment). And, although every variable appears in a rule, the rules are just open-ended enough to feel as if there are not going to be a low number of solutions. The test makers have hit the sweet spot (for them, at least) of leaving test takers in a sort of no man's land where each approach will get you moving but likely not as fast or as comfortably as you'd hope. That's not a systemic problem, that's just a higher-level difficulty problem that's built into the game, and good test making one might say. It's also why they placed this game fourth instead of first, I'd wager.

For a student shooting for the high 170s as you mention, encountering non-one-trick pony games should be nothing new. The game doesn't fit any one solution strategy perfectly because that's exactly how it was designed. Instead, what we typically do is mix approaches and let them work together to our benefit. So let's talk about that, starting with the two methods you initially used.

Let's start with Not Laws. I have immediate concerns about using Not Laws as my sole approach because as you rightly noted it's clear there are going to be way too many of them. The L - F - GK and M - J (with the connection to H) interactions suggest that I'm very quickly going to have double-digit Not Laws, and my immediate reaction is concern about the loss of time from drawing them all out. But games with double-digit Not Laws often have restricted points, and knowing those restrictions is helpful. This is why at a Not Law analysis on at least a base level is always useful: you learn about the game even if you don't show every single Not Law. What I can see here is that the endpoints of this game have limitations, and thus in my personal approach to this game I separately noted the options for a few of the spaces (triple options on 1 and 7) as well as the limitations on L (not that hard to see given the long sequence with L at the front and the specific rule about L not being 2nd). That's one of the huge features of Not Laws, seeing the remaining options that result from impossibilities, and it is one of the many reasons we always examine negatives. Ultimately though, because this game has no randoms and every variable appears in one or more rule, there are going to be restrictions on every variable. When you have that sort of situation in a game with 7 variables, I would note the most significant limitations but not show every Not Law. In this game that's a reasonable first step, doesn't require a massive amount of time, and it leaves you with base understanding of some of the key restrictions in the game.

On the Templates side, we have a similar problem. If I just dove straight into those with no prior limitation analysis, what I would see is that there are enough open-ended relationships to keep things too loose for comfort (the M and H rule is the most notable of those, but the sequential relationships also factor in). I can see that certain variables—such as the GK pair you mention—have a limited number of placements, but for me I chose to draw out the two base options that play off L. However, I'd argue that it doesn't hugely matter which you choose, and that using GK would be pretty good too. Why? Because in the process of quickly sketching out the placements of GK, I learn a lot about the game (including a lot about L's options). The key, though, is not to Identify the Possibilities (which would mean drawing out every single solution), but to instead just identify the Templates, which means sketching the general direction each placement will take. I can quickly see that as GK moves to the right that the number of solutions increases rapidly, but I wouldn't be showing them all anyway so I don't lose time there. Instead, for the template where GK are 4-5, I'd do something like this, which would be helpful:

• L (F, H/M) G K (M/H, J)
  1 2 3 4 5 6 7
  
  Sorry, the tools of this Forum don't allow me to show that quite the way I'd like, but it gets the idea across.

You actually made note of the utility of creating templates when you said that "the very process of setting them up was eye opening, didn't waste too much time, and gave me a starting point for a lot of the local setups later on." You have just described the value of identifying templates perfectly—even when we can't show everything, we often learn a lot on the way.

So what you see is a hybrid approach to this game, which is perfectly normal and appropriate. We take different skills we already have in control and combine them to get a solid approach to this where we see limitations and then chart some of the directions these limitations take. Is it perfect in the sense that it crushes the game in 3-4 minutes? No, but that's because no approach to this game can be perfect like that—it's designed not to be quite that simple. Hopefully, you were able to complete the earlier games in this section in relatively reasonable amount of time, leaving you with at least the usual amount of time for this game. If so, you can take what they give you and patiently knock out the questions using the various pieces of information you've identified and created.

Note about the questions: I totally agree with you about question #19. It's a tough inference to get using Not Laws (or really, any approach) although the template exploration makes it easier to knock out some of the incorrect answers. However, I wanted to add a point about games that are more challenging, and that is one tool you can use when the setup doesn't feel great is to use certain questions to help create hypotheticals. These hypotheticals in turn provide you with additional information about the game, and when they are created in service of a specific question, help answer that question as well. In this game, questions #18, 20, 21, and 22 either provide you with hypothetical or require you to create some along the way, and if you felt the setup wasn't providing you with sufficient information to feel comfortable, go first to the Global List questions (#18) and then to the Local Must (#22) and last to the Local Could (#20, 21). That information can then be used in this game to answer the Global Cannot (#19) and Global Could (#23) (and if they don't fully answer a question, they at least help you learn enough about the game to go a fair ways down the path of obtaining the solution). In other words, manipulate the order of what they've presented you to take advantage of the information each question produces.

I hope this helps a bit. I understand your frustration here, but the idea is to develop a set of interrelated skills that you can then call on in any arrangement. That typically starts by isolating each one and mastering each one, but at the higher ranges of difficulty—and this game is clearly on the harder side—it's more often that a combination of elements is the best approach. Thanks!

[JaredBeats]

Dave,

Thanks for your thoughtful response. Some of what you said, however, does raise important questions about the value of following a certain "method" or "approach" that, no matter how robust, can easily be circumvented by those who write the test.

Early in the LGB I place a lot of emphasis on Not Laws for a few different reasons, but two main ones are that I want everyone to get in the habit of looking for negative absolutes and that I want to make sure that identifying Not Laws is a skill that is second-nature. A parallel concept appears in LR with conditional reasoning. It's all over the LSAT, so early on we focus on it and make sure that students know it cold. We then pull back from that and place it where it should be: something you don't need to worry about unless it shows up and you need to address it.

I see your point. But, from the student's perspective, your early emphasis on Not Laws is so emphatic that any subsequent failure or refusal to conduct a detailed limitation analysis feels like a deviation from, if not a betrayal of, that method. Perhaps it worked in the mid-90's, but having done the vast majority of games since 2008 I can tell you - it's moderately helpful, at best. I don't ever use more than one of the Not Laws I make, so the cost in time tends to outweigh the benefits. I'd wager that limitation analysis is only helpful to the extent that it allows us to see what variables are "left" to occupy a limited number of spaces; very often, however, the process does not reach that far. (Triple options are rarely helpful.)

Bottom line is - learning not to worry about Not Laws, Conditional Reasoning, etc. "unless they show up" makes me question the wisdom of learning these concepts in the first place. Why? Because, technically speaking, they do show up all the time, and yet I can't recall the last time they were the key to solving the LR question or game. My accuracy in LR still hovers around 95%-100%, even though I've virtually stopped diagramming the conditional relationships I see in there. Not doing so has improved my score, strangely enough. Maybe there is a diminishing return on investment when it comes to any one particular method. There is only so much you can get out of it.

This discussion reminds me of an earlier conversation I had with my girlfriend, who is also studying to take the LSAT in June but refuses to buy into any one commercial method or system. Don't get me wrong - she's not cheap or anything. She just thinks it's counterproductive. So she's basically cranking out test after test, with some review mixed in. I'm in low-170's, and she's already got a few 180s. Case in point - she destroyed that computer virus game last year in 5 minutes, while I was still struggling to figure out if it's linear, grouping, pattern, etc. Does it matter? Nope. It doesn't. It only matters if you think it does.

Anyway, sorry if I sound jaded. My highest score is 174 and my average is barely 172... so with only a few weeks left I feel a bit frustrated. I've been reading all the blog posts on your website, and those have been helpful (well, some more than others )

Once again, thanks for your response!