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#41628
Setup and Rule Diagram Explanation

This is an Advanced Linear: Balanced, Identify the Templates game.

The game scenario establishes that each of three teachers will give one of six consecutive presentations, on six different subjects.
PT65_D11 LG Explanations_game_#2_setup_diagram 1.png
PT65_D11 LG Explanations_game_#2_setup_diagram 1.png (8.17 KiB) Viewed 1877 times
Because we are told which subject each teacher will present on, the two variable sets are not independent of each other. Given the “stacked” nature of our setup, we can use vertical blocks to represent the connection between the teachers and the subjects they present on:
PT65_D11 LG Explanations_game_#2_setup_diagram 2.png
PT65_D11 LG Explanations_game_#2_setup_diagram 2.png (3.79 KiB) Viewed 1877 times
With the basic structure in place, let us now turn to the rules.

The first rule establishes that K cannot give two presentations in a row:
PT65_D11 LG Explanations_game_#2_setup_diagram 3.png
PT65_D11 LG Explanations_game_#2_setup_diagram 3.png (1.86 KiB) Viewed 1877 times
Since we know which presentations are delivered by K, we can also represent this rule with three rotating Not-blocks:
PT65_D11 LG Explanations_game_#2_setup_diagram 4.png
PT65_D11 LG Explanations_game_#2_setup_diagram 4.png (6.15 KiB) Viewed 1877 times
The implications of this rule will be examined in greater detail later in our setup.

The second rule establishes the following relationship between S and O:

..... ..... ..... ..... ..... ..... ..... S :longline: O

This rule creates an S Not Law, and an O Not Law:

PT65_D11 LG Explanations_game_#2_setup_diagram 5.png
PT65_D11 LG Explanations_game_#2_setup_diagram 5.png (4.9 KiB) Viewed 1877 times
The last rule establishes a similar relationship, this time between T and W:

..... ..... ..... ..... ..... ..... ..... T :longline: W

This rule adds two more Not Laws to our diagram:

PT65_D11 LG Explanations_game_#2_setup_diagram 6.png
PT65_D11 LG Explanations_game_#2_setup_diagram 6.png (5.58 KiB) Viewed 1877 times
We can also add another Not Law under the Teacher row. Since W is the only subject that L can teach, then if W cannot be 1st, L cannot be 1st either. That leaves only two possibilities for the Teacher of the first subject:

PT65_D11 LG Explanations_game_#2_setup_diagram 7.png
PT65_D11 LG Explanations_game_#2_setup_diagram 7.png (6.41 KiB) Viewed 1877 times
With all three rules clearly diagrammed, it is critical to focus on the most restrictive rule in the game, which is the first rule. This is because K must present on three of the six subjects, and so the rule will affect at least half of the variables we are working with. Since K cannot give two presentations in a row, we must ensure that no two of these three variables are adjacent. The Separation Principle™ applies, requiring K to present in one of the following four ways:

..... ..... ..... ..... ..... ..... ..... 1 - 3 - 5
..... ..... ..... ..... ..... ..... ..... 1 - 3 - 6
..... ..... ..... ..... ..... ..... ..... 1 - 4 - 6
..... ..... ..... ..... ..... ..... ..... 2 - 4 - 6

You should notice that in three of these scenarios, K delivers the sixth presentation, which cannot be S or T. Therefore, if K delivers the sixth presentation, that presentation must be P:
PT65_D11 LG Explanations_game_#2_setup_diagram 8.png
PT65_D11 LG Explanations_game_#2_setup_diagram 8.png (2.16 KiB) Viewed 1877 times
Thus, we arrive at the final setup for this game:
PT65_D11 LG Explanations_game_#2_setup_diagram 9.png
PT65_D11 LG Explanations_game_#2_setup_diagram 9.png (8.56 KiB) Viewed 1877 times
PT65_D11 LG Explanations_game_#2_setup_diagram 10.png
PT65_D11 LG Explanations_game_#2_setup_diagram 10.png (8.37 KiB) Viewed 1877 times
PT65_D11 LG Explanations_game_#2_setup_diagram 11.png
PT65_D11 LG Explanations_game_#2_setup_diagram 11.png (15.25 KiB) Viewed 1877 times
Due to the incredibly restrictive effect of the Separation Principle™ produced by the last rule, it is worth creating four templates to represent the ways in which K gives the three presentations. our task is also facilitated by the fact that two of K’s presentations—S and T—are each subject to a sequencing rule involving O and W, respectively.
PT65_D11 LG Explanations_game_#2_setup_diagram 12a.png
PT65_D11 LG Explanations_game_#2_setup_diagram 12a.png (14.74 KiB) Viewed 1877 times
PT65_D11 LG Explanations_game_#2_setup_diagram 12b.png
PT65_D11 LG Explanations_game_#2_setup_diagram 12b.png (14.67 KiB) Viewed 1877 times
Given the second and third rules (S :longline: O and T :longline: W, respectively), we can also infer that the fifth presentation in Template 3 must be either O or W. The same is true about the third and fifth presentations in Template 4, forcing N to be the first presentation in that template:
PT65_D11 LG Explanations_game_#2_setup_diagram 13.png
PT65_D11 LG Explanations_game_#2_setup_diagram 13.png (8.04 KiB) Viewed 1877 times
PT65_D11 LG Explanations_game_#2_setup_diagram 14.png
PT65_D11 LG Explanations_game_#2_setup_diagram 14.png (8.55 KiB) Viewed 1877 times
With these four templates in place, attacking the questions will be relatively straightforward.
 vini777
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#7291
[Game text removed due to LSAC copyright restrictions. Refer to second game from the December 2011 LSAT for the exact game wording.]

Hi Guys,

I am stuck on this above mentioned game.
Can somebody help me to draw a diagram?

My Diagram Looks like this but I think it is not correct.

J, K, L
n,o,p,s,t,w
[Jno]; [Kpst]; [Lw]
[s>o]; [t>w] K>J and L
K can not give two presentations in a row.
 Adam Tyson
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#7293
Hey there vini! Which game is this exactly?

I think your setup looks good, as far as I can tell, with two exceptions. The first one would be that you of course need to set up the base of the 6 numbered spaces, and include in that base the 4 not laws that your rules generate for you (O and W can't be first, S and T can't be last). Second, you have added an inference that I don't think is warranted - K > J & L. Isn't it possible that one of J's presentations, N, could go before any of K's? Couldn't L's presentation, W, go before both P and S? Try this solution and see if it works:

NSOTWP

or how about:

NTWSOP

Of course, it could be that one of K's variables goes first, for example:

PNSOTW

or

TNSOWP

I think there are several more solutions here - I haven't worked through the whole game yet, but I don't think this one calls for diagramming all the solutions or even doing templates. Were there any more rules to the game?

Hope that helps!

Adam
 vini777
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#7295
Hi Adam,

Thank you very much for our promt reply.
This is 12/03/2011 Test; Section: 3; Q: 6-11.
Please find attached.
P.S I am not able to upload attachment for some reason. I can email it to you if you woud like

[Moderator note: LSAT contented is copyrighted by LSAC, and cannot be posted to this forum. Giving the LSAT date and game number is sufficient, and I've added it to the thread title for easy reference. Thanks!]

Thanks again,

Vini
 Adam Tyson
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#7319
Okay, I have done this one before, now that I look at it more closely. After setting up my base of the six slots, and adding in my not laws, the first thing I noticed was that the rule about K's presentations is going to trigger a Separation Principle - that is, we have to stagger P, S and T with other variables between them. Since there are three of those and only six slots, that's going to create a lot of restrictions. I decided to play with those and ask myself what has to happen if certain variables go first or last.

For example, what happens if N goes first? Now PST have to fill the 2-4-6 spots, and since neither S nor T can go last, that forces P to last position. I now have an inference, N1 -> P6, which leads to 2 solutions: NSOTWP or NTWSOP. I began to wonder if I should do templates with this game, but I'm not there yet.

What about if P goes first? Then neither S nor T can go second, so they have to go in slots 3 and 5, in either order. Again, I get two solutions: PNSOTW and PNTWSO. Great! I now have another inference, P1 ->N2, and two more solutions.

When I look at putting either S or T first, though, things get a bit looser. With S first, for example, T could go 3rd, 4th or 5th, and vice versa. At this point I decided to stop with the templates, solutions and inferences and just dive into the game. (There do turn out to be a couple more valuable inferences, based on the Separation Principle, and you'll hit them as you work through the questions, so getting them up front would be good, but may not be essential).

They key here is going to be 1) avoiding that unwarranted inference about K > J & L, since N can go first and W can go before some of P, S & T, and 2) build the base and make a few inferences based on the rules that we do have.

Give it a go and see how you do.

Adam
 vini777
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#7324
Adam,

Thank you very much!!!
I solved it!!!

Thanks again:)
 mgardella
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#61996
What makes it obvious that this is advanced linear? When I went through the game for the first time (timed) I treated the game as a basic linear, while keeping track of the teacher assignments.
Since the teachers are always assigned to the same classes, doesn't this seem a little unnecessary? Or am I putting myself at a disadvantage by not using the top row?
 Adam Tyson
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#62015
A major disadvantage, mgardella! There are rules specifically about the classes and their sequence, and you cannot capture those solely with diagrams about the teachers. Stenciling before origami doesn't mean that K is always before J, right?
 Mariam
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#76520
I also did not do an advanced linear set up the first time I attempted this game (timed). It took me so long and I got a couple of questions wrong. I went back and re-did it with an advanced linear setup but I didn't see the templates. It still took me a while and I wasn't sure of some answers. what are the indicators in this game that make templates helpful? also, where is the separation principle (mentioned in the description above) in the course materials?

Thanks!
 Jeremy Press
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#76622
Hi Mariam,

That "Separation Principle" is the number one source of a templating approach to this game! There are three things to consider: there are only 6 slots available in the teacher line of the diagram, and 3 of those slots have to be filled by K's. That's already pretty restrictive, although without another rule it would be too time-consuming to pursue templates. But (and this is where the templates approach springs into play!) there is another rule governing the K's: they can't be next to one another. With three of them to place, only 6 slots, and a heavy restriction like this that they can't be consecutive, we're going to get very limited in our possibilities for placing the K's. So write out all available options and take it from there.

The Separation Principle is discussed in the Additional Reading in the Lesson 4 Supplemental Homework in the student center.

Have a great Monday!

Jeremy

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