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#41655
Setup and Rule Diagram Explanation

This is a Basic Linear: Unbalanced, Underfunded, Identify the Templates game.

The game scenario establishes that five television programs must be shown over the course of three hours, beginning at 1 PM. At first glance, this appears to be an Unbalanced, Overloaded game, as the number of variables (5) exceeds the number of hourly slots (3). However, notice that four of the programs are half-hour long—R, S, T, and W—and one is an hour-long—G. So, we are probably better off using “half-hour” slots as our base, so that we have a total of six slots for the five programs.

Technically, then, the game is Unbalanced, Underfunded. To make it Balanced, we need to represent the hour-long program (G) using a GG Block, because that program must take up two adjacent “half-hour” time slots in our base:
PT65_D11 LG Explanations_game_#4_setup_diagram 1.png
Remember, however, that the GG Block counts as one program, not two! So, if the GG block occupied the first two spaces, for instance, then the program beginning at 2:00 would be the second program shown, not the third. This is an important “kink” that you must keep in mind as you attack the questions. Some students hoped to avoid this complexity by using the order in which the programs are shown as the base, regardless of the hourly slots:
PT65_D11 LG Explanations_game_#4_setup_diagram 2.png
While initially attractive in its simplicity, such a setup is a terrible idea. For one thing, it does not allow us to represent the first or the second rules internally, making it exceptionally difficult to keep track of whether each slot in our setup refers to the hour or the half-hour. This would depend on where G is relative to the rest of the variables: if G is the first program shown, then the second slot would be referring to 2:00, because G is an hour-long program. But if any of the other programs were shown first, then the second slot would be referring to 1:30, because they are all half-hour long. Confusing? You bet! This is a mess we would rather avoid at all costs. This is why it is critical to examine the rules before settling on a particular setup: the setup must allow you to represent the rules clearly and accurately, so as to avoid unnecessary confusion down the road.

With our original structure in place, let us now turn to the rules.

The first rule establishes that G must start on the hour rather than the half hour:
PT65_D11 LG Explanations_game_#4_setup_diagram 3.png
Representing this rule can be challenging. Many students mistakenly decided to create G Not-Laws at the 1:30, 2:30, and 3:30 time slots. Although G cannot start on the half hour, it will clearly run into the “half hour” slot following its starting time, because G lasts a full hour. So, we cannot create any Not-Laws to reflect the application of this rule, unless we use G1 G2 subscripts, which only adds complexity to an already complicated setup. Indeed, the only way to competently represent what must be true is to create three Templates based on the three possible placements of the GG Block:
PT65_D11 LG Explanations_game_#4_setup_diagram 4.png
What may strike you as unusual is our decision to undertake a Templates-based approach early on, without fully evaluating if the game is sufficiently restricted. Admittedly, the decision was partially prompted by our realization that there is no other way to clearly represent the first rule. Furthermore, even if the remaining rules are not sufficiently restrictive (though they are), the rule generates only three templates.

The second rule tells us that T starts on the half hour rather than the hour. Since T is a half-hour long program, this rule generates three T Not Laws:
PT65_D11 LG Explanations_game_#4_setup_diagram 5.png
The second rule also generates Split-Dual options for T in each of our three templates, because each template contains only two possible time slots that can accommodate T:
PT65_D11 LG Explanations_game_#4_setup_diagram 6.png
The third rule establishes the following sequence:

..... ..... ..... ..... ..... ..... ..... ..... R :longline: S

This sequence generates two Not Laws, an R Not Law, and an S Not Law:
PT65_D11 LG Explanations_game_#4_setup_diagram 7.png
The fourth rule establishes the following conditional block:
PT65_D11 LG Explanations_game_#4_setup_diagram 8.png
Examine the meaning of this rule carefully. The rule does not generate a simple WT Block, because if W is not shown earlier than T, then the rule is not activated and a WT Block does not need to be formed. The block is only necessary if W is shown earlier than T! So, for instance, if W were shown at 1:00, then W would be shown earlier than all other programs, including T, triggering the Block formation. Likewise, if T were shown at 3:30, then all other programs would be shown earlier than T, including W, requiring W to be shown immediately before T, at 3:00.
PT65_D11 LG Explanations_game_#4_setup_diagram 9.png
Now let’s examine this rule in the context of our templates. Each template allows T to be placed in one of two possible positions. Observant test-takers will notice that exactly one of these two positions, in each template, triggers the sufficient condition in the last rule! If T is shown at 3:30—as may be the case in Templates 1 and 2—then W would need to be shown earlier than T, triggering the WT Block. In Template 3, if T were shown at 2:30, then W would again be shown earlier than T, and immediately before it.

It should be apparent by now that the precise location of T within each template can affect the placement of W. This, in turn, would restrict the placement of the remaining two variables, R and S, which—as we know—are bound by a sequencing rule. The optimal way to proceed, therefore, is to split each Template into two, based on the scheduled showing of T:
PT65_D11 LG Explanations_game_#4_setup_diagram 10.png
PT65_D11 LG Explanations_game_#4_setup_diagram 11.png
PT65_D11 LG Explanations_game_#4_setup_diagram 11b.png
As mentioned earlier, W would be shown earlier than T by default in Templates 1B, 2B, and 3B. Consequently, W must be shown immediately before T in all three of these templates. The remaining variables—R and S—must be sequenced in accordance with the third rule. Templates 1B, 2B, and 3B are therefore completely determined:
PT65_D11 LG Explanations_game_#4_setup_diagram 12.png
Interestingly, the last rule virtually no effect on the placement of W in Templates 1A, 2A, and 3A. This is because if W is shown earlier than T in any of these templates, W would have to be shown immediately before T, regardless of the last rule. Alternatively, if W is shown after T, then the last rule does not apply and W can be shown anywhere after T. Either way, we can completely disregard the last rule when analyzing any of these three templates. The only rule we need to consider is the R S sequence, which generates two Dual-options in each template:
PT65_D11 LG Explanations_game_#4_setup_diagram 13.png
With these six templates in place, we arrive at the final setup for this game:
PT65_D11 LG Explanations_game_#4_setup_diagram 14.png
PT65_D11 LG Explanations_game_#4_setup_diagram 15.png
PT65_D11 LG Explanations_game_#4_setup_diagram 16.png
This game epitomizes the central proposition that is inherent in a Templates approach: you will spend more time in the setup, but this time will be regained in the lightning-fast execution of the questions. Here, the approach is advantageous for several reasons: First, each template is severely restricted, which obviates the need to create local diagrams for any of the local questions. Second, the first rule would be difficult to represent without the use of templates, making such an approach virtually essential to the avoidance of misinterpretation. Third, the templates already take into account the implications of the conditional rule, so you no longer run the risk of misapplying it as you attack the questions. Finally, consider the fact that this game contains seven questions, rather than, say, five. The higher the number of questions, the more benefit you can expect to derive from your initial investment of time.
 lusk2006
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#22253
I am working back through my Dec. 2011 test and re-working it. I need help with the setup on these two questions. I managed to get quite a few of the questions right on Game 4 (TV Programs), but not because I set it up well. Please help!
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 Dave Killoran
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#22254
Hey Lusk,

The first thing to understand is that this Linear setup should be based on the half-hour slots. Then, the one hour show should be shown as a GG block. That GG block rule is key because it has only three possible placements:

GG in 1 and 1:30
GG in 2 and 2:30
GG in 3 and 3:30

The limitations of the forum graphics prevent me from showing every detailed step, but when you consider the placement of the various shows (the T limitation) and the restrictions (the W > T rule and the R > S rule) and add them to the GG block, there are really only about six powerful templates built on top of the 3 GG placements (2 templates for each GG placement--and tracking T is key for those templates). Those limitations make this game a lot easier than it looks at first (but it is still a tough game!).

Let me know if that gets you started on this game. Thanks!
 lusk2006
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#22256
Thank you, Dave!
 crharke42
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#4985
I was wondering if someone could help me with the setup and inferences for the 4th Logic Game on the December 2011 LSAT.

Thanks!!
 crharke42
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#4988
Well initially I was rushed through this game because I didn't have a lot of time left. But I did 5 spaces for the 5 programs. As I look at it again I realize that was probably not the best choice because one of the programs is an hour long and the others are not.


Then I took the first rule and put Not-Laws for G underneath the second and fourth spaces. For the second rule I put Not-Laws for T underneath 1,3 and 5 so implying that T had to be either in the 2 or 4 spot.

The third rule I had

R > S so i had a Not Law for S under the first space and a Not Law for R under the 5th space
For the fourth rule I had

W>T -----> WT

I got numbers 19, 20 and 21 wrong on this problem
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 Dave Killoran
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#5003
crharke42 wrote:Well initially I was rushed through this game because I didn't have a lot of time left. But I did 5 spaces for the 5 programs. As I look at it again I realize that was probably not the best choice because one of the programs is an hour long and the others are not.
Thanks for that info--it is really helpful. A lot of people were tricked by this setup because the five programs so easily suggested five slots. But, as you noted, the differing lengths of the programs throw a wrench into the proceedings. So, how to remedy that?

Because there are three hours worth of programming, the best solution is to create a base setup with six slots, one for each half-hour, like so:


..... ..... ..... 1 ..... 1:30 ..... 2 ..... 2:30 ..... 3 ..... 3:30


Then, G, the hour-long program, becomes a GG block, signifying that it takes up two consecutive slots. You can number them as G1 and G2, which then allows you to create G1 Not Laws at 1:30, 2:30, and 3:30.

The remainder of the variables appear as singles, noting that each takes up a half-hour.

Note that, with the GG block restricted to starting at 1, 2, or 3, there are a limited number of solutions that can occur, and one great approach to this game is to show the six basic templates that result from placing GG in those three spots.

The rest of your rules look pretty strong, so please take a shot at this game again, and let me know how it goes. If something is still troubling you, we'll then look at that in-depth.

Please let me know if that helps. Thanks!
 karlaurrea
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#6792
I was confused as to what type of diagram I should star with, and also interpreting two rules that perhaps I misunderstood or that I simply did not place them correctly in my diagram.

I set it up as linear showing: 1pm 1:30pm 2pm 2:30pm 3pm
but then I found myself only getting so far because the rules that Generations starts on the hours, would mean for me based on the diagram 1, 2, or 3pm but then the rule about Terry starting 1/2hr would put him in the half hours; but what confused me is, well if G takes a whole hour long- using this diagram I would have to show G G R S T and because I only have 5 spaces I would be missing a variable.

I then thought about it in terms of 1hr, 1/2hr, 1/2hr, 1/2hr. 1/2hr; but I was still questioning how to place the variables....

Especially for Ques 17- It was difficult for me to choose between A and B because to me, all of them met the rules, and I am sure it had to do with the placement of G and I just don't see it.

Any help with the initial setup, or key insight you can give me would be great... I am sure that after knowing that, and why question 17 the correct answer is B, will definitely help me with all the other questions

Thanks!!!
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 Dave Killoran
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#6822
Hi Karla,

You were on the right track, but you made a small error in showing the time slots that then caused you some confusion. Let's take a look at that, and then I think you'll be ok going forward.

First, you had exactly the right idea in using half-hour increments for the base. And second, you were spot-on with doubling G to show the hour-long nature of that program. The place where you ran into problems was that the block of time is 3 hours long, but your diagram only shows 2.5 hours. What you needed to add was a final slot for 3:30:


..... ..... ..... 1 ..... 1:30 ..... 2 ..... 2:30 ..... 3 ..... 3:30

That base, when combined with the variables GG, R, S, T, and W then accounts for all the programs with the correct number of spaces for them.

Please let me know if that helps. Thanks!

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