Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Basic Linear: Balanced Game.

The game should be set up as follows:

This game is perfectly Balanced, with 7 variables each filling one of 7 slots. An analysis of the variables reveals that S is a random, and this is indicated by the “*” notation. The first inference that can be made comes from the linkage of M and P. Since P must be delivered first or seventh, and exactly one package is delivered between P and M, it follows that M must be delivered third or fifth. Therefore, M cannot be delivered first, second, fourth, sixth or seventh. Since the earliest M can be delivered is third, that affects the delivery of T, and it can be inferred that T cannot be delivered first, second, or third.

Two other Not Laws also bear further examination. First, S cannot be delivered third because it sets off the following chain: M would be delivered fifth and P would be delivered seventh; in turn L and O have to be delivered second and fourth, with L being delivered second; this causes a problem since there is no room for N, which must be delivered after L. Second, O cannot be delivered fifth because of the problems it causes: M would have to be delivered third and P would have to be delivered first; since O and L must be separated by one package, L would have to be delivered seventh, and that is impossible since L must be delivered ahead of N.

Additionally, since the MP split-block is reduced to exactly two spacing options, one approach to setting up the game involves drawing out the two options, which are labeled #1 and #2 below:

In option #1, we can link rules and apply the M T rule, which yields the inference that T must be sixth when P is seventh and M is fifth. At this point, it should be apparent that you will have to keep an eye on L, N, and O since they are linked together. In general, the variables L, M, and P are the most powerful since each appears in two separate rules.

[ffk]

In general, I find that the basic setups from the stated rules for problems is pretty straight forward... However, many times I'll turn the page on a problem and find inferred rules in the book's setups that weren't obvious (at least not to me).

I think that the basic setup for Game#2 on pg. 97, and it's corresponding setup on pg. 98 are a perfect example:

My setup looks identical to the book minus the "Not Laws" for S and O. Reading through the explanation on pg. 98 regarding why S and O earn those "Not Laws" makes perfect sense. My issue is more along the lines of:

1) To me, the S and O Not Laws are not 'natural' conclusions from the rules listed in the game. -- They seem to be more requiring of a little after-the-fact hunt-and-peck analysis; which seems time consuming and not necessarily a fruitful approach - as it would be hit or miss based on the particular game. Or conversely, requiring some intuitive nudge, to know when to hunt-and-peck, that I have yet to develop?! In cases such as this, the book explains why the laws are valid, but never seems to explain how to I should have known to look for them in the first place.

For example, S wasn't even mentioned in the rules. The explanation on pg. 98 explains why S cannot be put in the 3rd slot - and I get the explanation. However, it never draws a line (that I can see anyhow) pointing to how we should have reached the thought of trying to stuff S in slot 3 based merely on the initial rules provided - especially at the "basic setup" point.

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2) I feel like I see the surface of problems clearly, but seem to fall short on seeing, what at times seem to be magical, inferences -- even though I understand why the resulting inferences are valid after the fact.

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Again, part of my personal assumption is that the "basic setup" is based on the stated rules, and *obvious* inferences.

As it stands, my only idea for how to address this, is to overload myself with problems until I manage to develop some magic intuition.

Any pointers?

[Nikki Siclunov]

Linking the rules in a game should not be a slow, time-consuming process, but a quick, "scanning" process. This often requires focusing on the "power variables" first, i.e. the variables that are subject to conditions that will force other variables to fall into place. For example, the dominant linkage in Game#2 on pg. 97-98 is between the three rules concerning the same three variables: P, M, and T. Any combination of rules about the same set of variables should produce a powerful linkage that you can exploit to your advantage.

Since P must be either 1st or 7th, and you must have a M/P_P/M block, that combination yields two "avenues" in which you can solve the game:

1. P _ M _ _ _ _

or

2. _ _ _ _ M T P

To see the Not Laws more clearly, diagram them for each template, focusing on the other two rules that you need to apply: the L/O _ O/L rule, and the L>N rule. Both deal with L, which will become the new "power" variable.

Once you create all the Not Laws for each template, examine any overlap between them in order to deduce inferences that must be true about the game as a whole. You can then map out the Not Laws onto your main diagram. It becomes easier to see that S cannot be third, for instance: it cannot be 3rd in the first template, and it cannot be third in the second template because of the L/O _ O/L rule combined with the L > N rule.

Internal Not-Laws are more difficult to spot, but they are the inferences that really help you speed up.

Hope this helps!

[S_Hernandez52]

Setting up the game in this game seemed to me a bit difficult especially the split dual blocks. Hoping I can get some more help to get these types of questions and get all the inferences (not laws) correctly. Thank you

[Dave Killoran]

Hey S,

Thanks for the question! There's a lot going on in this game, so it would help if you could tell us if there was a specific Not Law that troubled you (and remember, Not Laws can always be tested by reverse engineering the setup—put the variable in question in the spot and see what happens. Very quickly things should break down, and that will reveal why it does not work!).

In this game, though, the PM block is fairly easy to handle since, from the first rule, we know that P is 1st or 7th. Thus, M must be 3rd or 5th. That is so helpful because the PM block is limited to just two positions, and thus P and M are eliminated from a host of spaces thereby!

The LO block is minimally affected by the PM block. Obviously, where PM is will affect what LO can do, but in a big picture sense, the PM block by itself doesn't stop LO being placed anywhere. Instead, it's the LO block in combination with the second rule — "The messenger delivers N at some time after delivering L" — that causes some limitations (namely that L can't be seventh).

So, how to figure those things out? As you can see, the first step is always linkage: P is common to the first and last rules, so we examine how they interact; L is common to the second and fourth rules, so again consider their interaction; M is common to the third and last rules so same thing again, and so on.

Please let me know if that helps. Thanks!

[S_Hernandez52]

This definitely helped getting the Not Law's for M and P. My question though now is how do you get the not Law's for S and T in the first 3 spaces? What is the thought process of using the random variable? I hope this makes sense.

[Dave Killoran]

Great, glad that helped so far

Both the S and T Not Laws are discussed on page 166, but let me make some additional notes here about the process in general, as well as one way to use these setups.

First, the T Not Laws are ones you should look at very carefully, because the expectation from the test makers is that students will be able to find those during the initial setup. This is where deconstructing what you see in these setups is so critical—if something doesn't make sense with a Not Law, put the variable in that place and see what happens! That "a-ha" moment often helps really fix the idea and process in your mind. So, with these T Not Laws, start first with what you know about T. From the third rule, T is delivered after M (M T). Well, that rule contains M, so what do you know about M? That it is linked to P via the last rule. And what do we know about P? That according to the first rule it is first or seventh. So, we have a long chain of connections, but since P must be first or seventh, the earliest M could appear is third, and thus from the third rule the earliest T could appear is fourth. Thus, T cannot be first, second, or third. That chain of connections and the resulting inferences is really classic LSAT, and is a perfect example of what and how they think, and thus what and how they expect you to think.

The S Not Law is also discussed on page 166, but it is far more difficult to determine than the T Not Laws, and is one that you wouldn't be expected to see during the setup of the game. As you can see from the discussion, it results from another chain of interactions of variables, but the thinking here is that even though S is a random, it still occupies space. Because of that, it can affect variables that have only two choices—such as M and P. when you think about it from that perspective, this is easier to see than perhaps it appears initially. But, go back and carefully examine what happens when S is third—that chain reaction is the kind of interaction that occurs often on the test, and in this case it was triggered by a variable taking up space in combination with a variable that was already limited to just two spaces. You can teach yourself to look at things this way (and it's the point of the Bibles in the first place), so take time to check these out and internalize the thought process behind all these inferences. It's the kind of thing you will see again.

Thanks!

[S_Hernandez52]

Thank you so much for the help!!

[alberto]

Its Alberto and this question is for Mr. Jon Denning Please respectfully.
Its a silly and obvious, I ask anyway?
When a questionn says: In game #2 September 1998 questions 8-12, the proverbial, messager will deliver exactly 7 packages...etc.,and
when the rule states: The messager delivers N at sometime after delivering L., it is not immediacy,however its sometime after written like this: L_N ? Furthermore, with the space open between the L and the N to place O or S variables in accordance to what the rules stated.I hope I am correct and its a silly, asinine question but, there I asked. Its like saying something transpired earlier/or later not immediately?

Thank you if you can clear this up.
Alberto, appreciate.

[Dave Killoran]

Hi Alberto,

It's just saying at some time later, which could be immediately after, two spaces after, or more! The uncertainty there is what makes it a tougher rule to cope with (and makes it a sequencing rule, not a block). so, you are right, it is written as: L — N, as shown above.

I hope that helps. Thanks!